Optical semiconductor device and method for manufacturing optical semiconductor device

Abstract

To obtain an optical semiconductor device in which film thicknesses of respective coating films of an antireflection film composed of multilayer coating films can be easily determined.SOLUTION: An optical semiconductor device 500 of the present disclosure has an effective refractive index nc and includes an antireflection film 40 composed of a plurality of coating films. The plurality of coating films include: n(n≥2) coating-film pairs constituted by a first coating film made of a first material having a refractive index n1 smaller than nc1 / 2, and a second coating film made of a second material having a refractive index n2 larger than nc1 / 2; and m (1≤m≤2) single coating films. When a reference film thickness of the first coating film is d1 and a reference film thickness of the second coating film is d2, a film thickness of an i (2≤i≤n)-th coating-film pair is expressed as pid1+pid2 using a weighting coefficient pi. When a reference film thickness of a j (1≤j≤m)-th single coating film is dk(k=j+2), the reference film thickness dk is identical to either d1 or d2. The refractive index of the j-th single coating film is nk, and the refractive index nk is different from the refractive indices n1 and n2.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present disclosure relates to an optical semiconductor device and a method for manufacturing an optical semiconductor device. [Background technology]

[0002] The semiconductor optical device described in Patent Document 1 uses three materials with different refractive indices: tantalum oxide (Ta2O5), aluminum oxide (Al2O3), 、 and silicon dioxide (SiO2) as a multilayer coating film. The triple-layer anti-reflection coating is configured as a pair consisting of a coating film made of a first material, Ta2O5, with an unknown thickness x and a coating film made of a second material, Al2O3, with an unknown thickness y. The thickness d3 of the coating film made of a third material, SiO2, is set as a known value. For semiconductor optical devices using specific substrates for specific wavelength bands, such as the 900-nm-band semiconductor optical device using a GaAs substrate described in Patent Document 1, specifying the thickness of a specific coating film is effective for ensuring reliability and preventing moisture absorption. However, designing an anti-reflection film to expand the reflectance band of the anti-reflection film has been difficult.

[0003] In the quantum cascade laser described in Patent Document 2, the effective refractive index n c The desired wavelength is λ and the end face of the quantum cascade laser has a refractive index of n c 1 / 2 and the film thickness is gλ / 4 / n c 1 / 2 It has been disclosed that a single-layer antireflection coating (g=1, 3, or 5...) is replaced with two materials having different refractive indices. The inventors have been diligently searching, but have not yet succeeded in replacing the single-layer antireflection coating with a two-layer coating made of two materials having different refractive indices. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2010-219568 [Patent Document 2] Japanese Patent Application Laid-Open No. 2013-254765 [Patent Document 3] Japanese Patent Application Publication No. 2023-110494 [Non-patent literature]

[0005] [Non-Patent Document 1] Y.Matsuoka et. al., Appl.Opt., Vol.57, No.7, pp.1645-1649(2018) [Non-patent document 2] Tsukuda, Journal of the Chemical Society of Japan, No.8, pp.1106-1108(1979) Summary of the Invention [Problem to be solved by the invention]

[0006] In conventional anti-reflection film designs, when three or more materials with different refractive indices are used as the anti-reflection film, the film thicknesses of more than two materials must be set in advance, which makes it difficult to design the film thickness of each coating film.

[0007] Furthermore, when replacing an anti-reflection coating made of a single layer coating with a two-layer coating made of two materials with different refractive indices, there is a problem in that it is very difficult to set the film thickness of each material.

[0008] The present disclosure has been made to solve the above-mentioned problems, and aims to provide an optical semiconductor device with excellent element characteristics by making it possible to easily determine the film thickness of each coating film of an antireflection film consisting of a multilayer coating film, and to obtain a method for manufacturing an optical semiconductor device that can easily manufacture such an optical semiconductor device. [Means for solving the problem]

[0009] The optical semiconductor device according to the present disclosure comprises: The laser oscillation wavelength is λd and the effective refractive index is n c An optical semiconductor device comprising: an anti-reflection film formed on one end surface of the optical semiconductor device and including a plurality of coating films; The plurality of coating films are c 1 / 2 a coating film made of a first material having a refractive index n1 smaller than n c 1 / 2 and at least m (1≦m≦2) single coating films other than the coating film pairs, When the reference thickness of the coating film made of the first material is d1 and the reference thickness of the coating film made of the second material is d2, the thickness of the ith (2≦i≦n) coating film pair is given by a weighting coefficient p i Using p i d1+p i It is represented by d2, The reference thickness of the jth (1≦j≦m) single coating film is d k (k=j+2), the reference film thickness d k is the same as either the reference thickness d1 of the coating film made of the first material or the reference thickness d2 of the coating film made of the second material, and the refractive index of the j-th single coating film is n k and the refractive index n k is different from the refractive index n1 and the refractive index n2, and the film thickness is a weighting coefficient q j Using q j d k The present invention is characterized in that it is represented by the following formula:

[0010] A method for manufacturing an optical semiconductor device according to the present disclosure includes: The laser oscillation wavelength is λ d and the effective refractive index is n c A method for manufacturing an optical semiconductor device, comprising: forming an anti-reflection film made of a plurality of coating films on one end surface of the optical semiconductor device; The plurality of coating films are c 1 / 2 a coating film made of a first material having a refractive index n1 smaller than nc 1 / 2 and at least m (1≦m≦2) single coating films other than the coating film pairs, When the reference thickness of the coating film made of the first material is d1 and the reference thickness of the coating film made of the second material is d2, the thickness of the ith (2≦i≦n) coating film pair is given by a weighting coefficient p i Using p i d1+p i It is represented by d2, The reference thickness of the jth (1≦j≦m) single coating film is d k (k=j+2), the reference film thickness d k is the same as either the reference thickness d1 of the coating film made of the first material or the reference thickness d2 of the coating film made of the second material, and the refractive index of the j-th single coating film is n k and the refractive index n k is different from the refractive index n1 and the refractive index n2, and the film thickness is a weighting coefficient q j Using q j d k is expressed as The elements of the characteristic matrix of the plurality of coating films consisting of the n coating film pairs and the m single coating films are defined as m 11 , m 12 , m 21 , m 22 In this case, the real and imaginary parts of the complex reflectance r expressed by the equation (3) described later are d are both zero. [Effects of the Invention]

[0011] According to the optical semiconductor device of the present disclosure, since the thickness of each coating film made of two or more materials that constitute the antireflection film is treated as a variable, and since it is not a simple replacement for an antireflection film made of a single-layer coating film, it is possible to obtain an optical semiconductor device with a wide reflectance band and a thin antireflection film as a whole.

[0012] According to the method for manufacturing an optical semiconductor device of the present disclosure, the thickness of each coating film made of two or more materials that constitutes the antireflection film is treated as a variable, which makes it easy to design the antireflection film, thereby achieving the effect of easily manufacturing an optical semiconductor device with a wide reflectance band and a thin antireflection film as a whole. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a schematic view of a quantum cascade laser device, which is an example of an optical semiconductor device according to a first embodiment. [Figure 2] 1 is a cross-sectional view taken along the line ya-yb of a quantum cascade laser device which is an example of an optical semiconductor device according to a first embodiment. [Figure 3] 2 is a schematic diagram illustrating a band structure of a conduction band of one stage of a quantum cascade laser device that is an example of an optical semiconductor device according to the first embodiment. FIG. [Figure 4] 1 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a first embodiment. [Figure 5] 4 is a diagram showing the wavelength dependency of the reflectance of the antireflection film in the optical semiconductor device according to the first embodiment. FIG. [Figure 6] FIG. 1 is a schematic diagram illustrating the configuration of an antireflection film in an optical semiconductor device according to the first embodiment, which has a reflectance band wider than that of a single-layer coating film having a refractive index of nc 1 / 2 and a film thickness of λd / 4 / nc 1 / 2. [Figure 7] 10 is a diagram showing the wavelength dependency of reflectance when the film thickness d3 of the third material is changed relative to the film thickness d1 of the first material in the antireflection film of the optical semiconductor device according to the first embodiment. FIG. [Figure 8] FIG. 10 is a diagram showing the wavelength dependence of reflectance when the film thicknesses of the first material and the third material are changed and when the film thickness of the second material is changed in the antireflection film of the optical semiconductor device according to the first embodiment. [Figure 9] 3 is a diagram showing the complex reflectance r of the antireflection film in the optical semiconductor device according to the first embodiment on a complex plane. FIG. [Figure 10]4 is a diagram showing the wavelength dependence of the reflectance when the complex reflectance r=0, 0.0054772256, and −0.0054772256 in the antireflection film of the optical semiconductor device according to the first embodiment. FIG. [Figure 11] 4 is a diagram showing the wavelength dependence of the reflectance when the complex reflectance r=0, 0.070710678, and −0.070710678 in the antireflection film of the optical semiconductor device according to the first embodiment. FIG. [Figure 12] 10 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a second embodiment. FIG. [Figure 13] FIG. 10 is a diagram showing the wavelength dependency of the reflectance of an antireflection film in an optical semiconductor device according to the second embodiment. [Figure 14] FIG. 10 is a schematic diagram illustrating the configuration of an antireflection film having a wider reflectance band in an optical semiconductor device according to a second embodiment. [Figure 15] FIG. 10 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a third embodiment. [Figure 16] FIG. 10 is a diagram showing the wavelength dependence of the reflectance of an antireflection film in an optical semiconductor device according to the third embodiment. [Figure 17] FIG. 11 is a schematic diagram illustrating the configuration of an antireflection film having a wider reflectance band in an optical semiconductor device according to a third embodiment. [Figure 18] FIG. 10 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a fourth embodiment. [Figure 19] FIG. 10 is a diagram showing the wavelength dependency of the reflectance of an antireflection film in an optical semiconductor device according to the fourth embodiment. [Figure 20] FIG. 10 is a schematic diagram illustrating the configuration of an antireflection film of an optical semiconductor device according to a fourth embodiment, which has a reflectance band wider than that of a single-layer coating film having a refractive index of nc 1 / 2 and a film thickness of λd / 4 / nc 1 / 2. [Figure 21] FIG. 10 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a fifth embodiment. [Figure 22]FIG. 11 is a diagram showing the wavelength dependency of the reflectance of an antireflection film in an optical semiconductor device according to the fifth embodiment. [Figure 23] FIG. 11 is a schematic diagram illustrating the configuration of an antireflection film having a wider reflectance band in an optical semiconductor device according to a fifth embodiment. [Figure 24] FIG. 13 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a sixth embodiment. [Figure 25] FIG. 13 is a diagram showing the wavelength dependency of reflectance in an optical semiconductor device according to the sixth embodiment. [Figure 26] FIG. 13 is a schematic diagram illustrating the configuration of an antireflection film having an even wider reflectance band in an optical semiconductor device according to a sixth embodiment. [Figure 27] FIG. 13 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a seventh embodiment. [Figure 28] FIG. 13 is a diagram showing the wavelength dependency of the reflectance of an antireflection film in an optical semiconductor device according to the seventh embodiment. [Figure 29] FIG. 13 is a schematic diagram illustrating the configuration of an antireflection film of an optical semiconductor device according to a seventh embodiment, which has a reflectance band wider than that of a single-layer coating film having a refractive index of nc 1 / 2 and a film thickness of λd / 4 / nc 1 / 2. [Figure 30] FIG. 13 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to an eighth embodiment. [Figure 31] FIG. 13 is a diagram showing the wavelength dependency of the reflectance of an antireflection film in an optical semiconductor device according to the eighth embodiment. [Figure 32] FIG. 13 is a schematic diagram illustrating the configuration of an antireflection film of an optical semiconductor device according to an eighth embodiment, which has a reflectance band wider than that of a single-layer coating film having a refractive index of nc 1 / 2 and a film thickness of λd / 4 / nc 1 / 2. [Figure 33] FIG. 13 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a ninth embodiment. [Figure 34] FIG. 13 is a diagram showing the wavelength dependency of the reflectance of an antireflection film in an optical semiconductor device according to the ninth embodiment. [Figure 35]FIG. 13 is a schematic diagram illustrating the configuration of an antireflection film having an even wider reflectance band in an optical semiconductor device according to a ninth embodiment. [Figure 36] FIG. 22 is a schematic diagram illustrating the configuration of an antireflection film in an optical semiconductor device according to a tenth embodiment. [Figure 37] FIG. 23 is a graph showing the wavelength dependence of the reflectance of an antireflection film in an optical semiconductor device according to the tenth embodiment. [Figure 38] FIG. 16 is a schematic diagram illustrating the configuration of an antireflection film of an optical semiconductor device according to a tenth embodiment, which has a reflectance band wider than that of a single-layer coating film having a refractive index of nc 1 / 2 and a film thickness of λd / 4 / nc 1 / 2. [Figure 39] FIG. 22 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to an eleventh embodiment. [Figure 40] FIG. 23 is a graph showing the wavelength dependence of the reflectance of an antireflection film in an optical semiconductor device according to an eleventh embodiment. [Figure 41] FIG. 16 is a schematic diagram illustrating the configuration of an antireflection film of an optical semiconductor device according to embodiment 11, which has a reflectance band wider than that of a single-layer coating film having a refractive index of nc 1 / 2 and a film thickness of λd / 4 / nc 1 / 2. [Figure 42] FIG. 22 is a schematic diagram illustrating a configuration of an antireflection film in an optical semiconductor device according to a twelfth embodiment. [Figure 43] FIG. 23 is a graph showing the wavelength dependence of the reflectance of an antireflection film in an optical semiconductor device according to the twelfth embodiment. [Figure 44] FIG. 16 is a schematic diagram illustrating the configuration of an antireflection film of an optical semiconductor device according to embodiment 12, which has a reflectance band wider than that of a single-layer coating film having a refractive index of nc 1 / 2 and a film thickness of λd / 4 / nc 1 / 2. [Figure 45] FIG. 22 is a schematic diagram showing the configuration of an antireflection film in an optical semiconductor device according to a thirteenth embodiment. [Figure 46] FIG. 23 is a diagram showing the wavelength dependence of the reflectance of an antireflection film in an optical semiconductor device according to the thirteenth embodiment. [Figure 47]FIG. 23 is a schematic diagram illustrating the configuration of an antireflection film having an even wider reflectance band in an optical semiconductor device according to a thirteenth embodiment. [Figure 48] FIG. 22 is a schematic diagram illustrating the configuration of an antireflection film in an optical semiconductor device according to a fourteenth embodiment. [Figure 49] FIG. 23 is a diagram showing the wavelength dependence of the reflectance of an antireflection film in an optical semiconductor device according to the fourteenth embodiment. [Figure 50] FIG. 22 is a schematic diagram illustrating the configuration of an antireflection film having an even wider reflectance band in an optical semiconductor device according to a fourteenth embodiment. [Figure 51] FIG. 22 is a schematic diagram illustrating the configuration of an antireflection film in an optical semiconductor device according to a fifteenth embodiment. [Figure 52] FIG. 23 is a graph showing the wavelength dependence of the reflectance of an antireflection film in an optical semiconductor device according to the fifteenth embodiment. [Figure 53] FIG. 22 is a schematic diagram illustrating the configuration of an antireflection film having an even wider reflectance band in an optical semiconductor device according to a fifteenth embodiment. [Figure 54] FIG. 23 is a flowchart illustrating a method for determining weighting coefficients in an antireflection film in an optical semiconductor device according to a sixteenth embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0014] Embodiment 1 1 is a schematic view showing a quantum cascade laser device as an example of an optical semiconductor device 500 according to the first embodiment. FIG. 2 is a schematic view showing the y-axis direction of the quantum cascade laser device as an example of an optical semiconductor device 500 according to the first embodiment. a -y b The quantum cascade laser device has a cavity length of L and a ridge width of W. The quantum cascade laser device has a buried ridge type waveguide structure.

[0015] As shown in FIGS. 1 and 2, a quantum cascade laser device, which is an example of an optical semiconductor device 500 according to the first embodiment, includes an n-type first electrode 1, an n-type InP substrate 2, an n-type InP buffer layer 3 having a layer thickness of 1.0 μm, and an n-type Ga 0.47 In 0.53 The device includes an n-type GaInAs (hereinafter abbreviated as GaInAs) first optical confinement layer 4, a core region 5 consisting of 35 stages 36 (details of the structure will be described later), an n-type GaInAs second optical confinement layer 6 having a layer thickness of 230 nm, an n-type InP cladding layer 7 having a layer thickness of 3.5 μm, an n-type GaInAs contact layer 8 having a layer thickness of 500 nm, an n-type second electrode 9, and an Fe-doped InP current blocking layer 10.

[0016] 2, an anti-reflection film 40 is provided on the emission end face of a quantum cascade laser device, which is an example of optical semiconductor device 500 according to embodiment 1. Note that anti-reflection film 40 is omitted in FIG.

[0017] FIG. 3 shows a quantum cascade laser device, which is an example of an optical semiconductor device 500 according to the first embodiment, in which a 5.0×10 6 3 is a schematic diagram showing the conduction band structure of one stage 36 when an electric field of 1000 V / m is applied. As shown in FIG. 3, the stage 36 is composed of two regions: an active region 34 and an injector region 35.

[0018] The active region 34, which constitutes a part of the stage 36, is made of undoped Al 0.48 In 0.52The semiconductor layer 10 is composed of an As (hereinafter abbreviated as AlInAs) barrier layer (undoped AlInAs barrier layer 11), an undoped GaInAs well layer 12 having a thickness of 3.7 nm, an undoped AlInAs barrier layer 13 having a thickness of 1.6 nm, an undoped GaInAs well layer 14 having a thickness of 4.8 nm, an undoped AlInAs barrier layer 15 having a thickness of 0.9 nm, an undoped GaInAs well layer 16 having a thickness of 5.2 nm, an undoped AlInAs barrier layer 17 having a thickness of 0.8 nm, an undoped GaInAs well layer 18 having a thickness of 5.3 nm, an undoped AlInAs barrier layer 19 having a thickness of 0.9 nm, an undoped GaInAs well layer 20 having a thickness of 1.5 nm, and a part of an undoped AlInAs barrier layer 21 having a thickness of 3.8 nm.

[0019] The injector region 35 constituting a remaining part of the stage 36 includes the remainder of the undoped AlInAs barrier layer 21 having a thickness of 3.8 nm, an undoped GaInAs well layer 22 having a thickness of 2.5 nm, an undoped AlInAs barrier layer 23 having a thickness of 3.1 nm, an undoped GaInAs well layer 24 having a thickness of 2.7 nm, an n-type AlInAs barrier layer 25 having a thickness of 2.5 nm and doped to the n-type, an n-type GaInAs well layer 26 having a thickness of 2.6 nm and doped to the n-type, and an n-type AlInAs well layer 27 having a thickness of 2.6 nm. The semiconductor layer 20 is made up of an n-type AlInAs barrier layer 27 doped to the n-type and having a thickness of 2.0 nm, an n-type GaInAs well layer 28 doped to the n-type and having a thickness of 2.7 nm, an undoped AlInAs barrier layer 29 having a thickness of 1.9 nm, an undoped GaInAs well layer 30 having a thickness of 2.8 nm, an undoped AlInAs barrier layer 31 having a thickness of 1.8 nm, an undoped GaInAs well layer 32 having a thickness of 3.0 nm, and an undoped AlInAs barrier layer 33 having a thickness of 2.2 nm.

[0020] The active region 34 is a region where electrons undergo transition between subbands formed within the active region 34 to emit light, and the injector region 35 is a region where electrons are injected into the active region 34 .

[0021] By applying a voltage between the n-type second electrode 9 and the n-type first electrode 1, electrons are injected from the injector region 35 into the active region 34, causing light to be emitted in the active region 34. The quantum cascade laser device according to the first embodiment has a laser oscillation wavelength λ d is in the vicinity of 9 μm (hereinafter also referred to as the desired wavelength). In addition, the effective refractive index n c is 3.21216.

[0022] 4 shows the configuration of the antireflection film 40a of the quantum cascade laser device according to the first embodiment. As shown in FIG. 4, the antireflection film 40a has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 42 made of a third material having a refractive index n3 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 42 made of a third material having a refractive index n1 and a film thickness d2 is provided on the light-emitting end surface 41 of the quantum cascade laser c 1 / 2 The second coating film 43 is made of a first material and has a thickness d1 that is higher than the refractive index n2. c 1 / 2 a third coating film 44 made of a second material having a thickness d2 lower than c 1 / 2 a fourth coating film 45 made of a first material having a thickness d1 higher than c 1 / 2 and a fifth coating film 46 made of a second material and having a thickness d2 lower than the thickness d1 of the first coating film 42. The thickness d3 of the first coating film 42 and the thickness d1 of the second coating film 43 are equal.

[0023] In the following explanation, d1, d2, d3, and d4 (described later) are simply referred to as film thicknesses when not multiplied by a weighting factor, but are referred to as reference film thicknesses when multiplied by a weighting factor. Also, a coating film made of a third material and a coating film made of a fourth material (described later) may be referred to as a single coating film.

[0024] The third material constituting the first coating film 42 is zinc sulfide (ZnS) and has a refractive index n3 of 2.270. The first material constituting the second coating film 43 and the fourth coating film 45 is germanium (Ge) and has a refractive index n1 of 4.085. The second material constituting the third coating film 44 and the fifth coating film 46 is yttrium fluoride (YF3) and has a refractive index n2 of 1.450. The refractive indexes of the respective materials were determined by reference to Non-Patent Document 1.

[0025] The second coating film 43 and the third coating film 44 form a first coating film pair 47, and the fourth coating film 45 and the fifth coating film 46 form a second coating film pair 48. That is, each coating film pair is composed of a coating film made of a first material and a coating film made of a second material. Therefore, the film thickness of each coating film pair is expressed as d1 + d2.

[0026] 4 is composed of a five-layer coating film, a first coating film 42 which is a single coating film, and two coating film pairs, a first coating film pair 47 and a second coating film pair 48. The total thickness of the antireflection film 40a is expressed as (d1+d2)×2+d3.

[0027] The thickness d1 (=d3) and thickness d2 of the antireflection film 40a are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are expressed by the following formula (1).

[0028]

number

[0029]

number

[0030]

number

[0031] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r described above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 59.025 nm and the film thickness d2 becomes 653.924 nm.

[0032] In the antireflection coating 40a, the first coating film 42 is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, and is composed of a ZnS film having a thickness of 59.025 nm, the second coating film 43 is formed of a Ge film having a thickness of 59.025 nm, the third coating film 44 is formed of a YF3 film having a thickness of 653.924 nm, the fourth coating film 45 is formed of a Ge film having a thickness of 59.025 nm, and the fifth coating film 46 is formed of a YF3 film having a thickness of 653.924 nm. By applying the antireflection coating 40a consisting of these five coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40a is zero at wavelengths around 9 μm.

[0033] 5 is a graph showing the wavelength dependency of the reflectance of the anti-reflection film 40a. In FIG. 5, a thin dotted line 51 indicates a wavelength where the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The thick dotted line 52 shows the wavelength dependence of the reflectance of a single-layer coating film with a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2The solid line 53 represents the wavelength dependence of the reflectance of the antireflection coating 40a consisting of five-layer coating films according to embodiment 1, and the dashed-dotted line 54 represents the wavelength dependence of the reflectance of the antireflection coating 40a consisting of five-layer coating films according to embodiment 1 when a third material (to be described later) and weighting coefficients of each coating film pair are taken into consideration.

[0034] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40a made of five coating layers according to the first embodiment is 1.859 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40a is sum Therefore, the sum (n×d) of the products of the refractive index and the film thickness of each coating film of the antireflection coating 40a made of five coating films according to the first embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.117, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40a has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0035] Refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band and film thickness of the single-layer coating film with a reflectance of less than 1% are 1.894 μm and 1255.405 nm, respectively. c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The reflectance band and film thickness of the single-layer coating film having a reflectance of less than 1% are 0.624 μm and 3766.216 nm, respectively. c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0036] Next, the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 This section describes an antireflection coating having a reflectance band wider than that of a single-layer coating film. In this antireflection coating, the thickness of the single coating film made of a third material and the weighting coefficients of each coating film pair are set using weighting coefficients q3, p1, and p2, at least one of which is a positive real number other than 1. Note that weighting coefficients p1 and p2 represent the weighting coefficients of each coating film pair, and weighting coefficient q3 represents the weighting coefficient of the single coating film made of the third material.

[0037] Figure 6 shows the refractive index of c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 6, the antireflection coating 40b has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 61 made of a third material having a refractive index n3 and a film thickness q3d3 and a second coating film 62 made of a third material having a refractive index n1 and a film thickness q3d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device. c 1 / 2 a second coating film 62 made of a first material having a thickness p1d1 higher than c 1 / 2 a third coating film 63 made of a second material having a thickness p1d2 lower than p1d2; and a refractive index n1 of n c 1 / 2 a fourth coating film 64 made of a first material having a thickness p2d1 higher than c 1 / 2 and a third coating film 63 made of a second material having a thickness p2d2 lower than p1, where d1, d2, and d3 each represent a reference film thickness, and the reference film thickness d3 of the first coating film 61 and the reference film thickness d1 of the second coating film 62 are equal.

[0038] The third material constituting the first coating film 61 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 62 and the fourth coating film 64 is Ge, and the refractive index n1 is 4.085. The second material constituting the third coating film 63 and the fifth coating film 65 is YF3, and the refractive index n2 is 1.450.

[0039] The second coating film 62 and the third coating film 63 constitute a first coating film pair 66 , and the fourth coating film 64 and the fifth coating film 65 constitute a second coating film pair 67 .

[0040] 6 is composed of a single coating film, that is, a first coating film 61, and two coating film pairs, that is, a first coating film pair 66 and a second coating film pair 67. The total thickness d sum is p i d1+p i It is expressed as d2+p2d1+p2d2+q3d3.

[0041] The overall characteristic matrix of the anti-reflection coating 40b is expressed by the following equation (4) using the characteristic matrix of each coating film.

[0042]

number

[0043] The weighting coefficients are set based on the setting method described below, and the reference film thickness d1 (= d3) and the reference film thickness d2 at which the real part and the imaginary part of the complex reflectance r in equation (3) are both zero are calculated. Then, the anti-reflection film 40b using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0044] As an example of the antireflection coating 40b, the case where the weighting factors are q3=2.00, p1=0.35, and p2=1.00 will be described below. In this case, the reference film thickness d1 (=d3) is 67.100 nm, and the reference film thickness d2 is 1083.500 nm.

[0045] 5, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40b is shown by the dashed-dotted line 54. The reflectance band of the anti-reflection coating 40b where the reflectance is less than 1% is 2.307 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0046] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40b (n×d) sum is 1687.509 nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 Therefore, the sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40b made of five coating films according to the first embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4)=1.242, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40b has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0047] In the antireflection coating 40b, the first coating film 61, which is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, is made of a ZnS film with a thickness of 134.199 nm, the second coating film 62 is made of a Ge film with a thickness of 23.485 nm, the third coating film 63 is made of a YF3 film with a thickness of 379.225 nm, the fourth coating film 64 is made of a Ge film with a thickness of 67.100 nm, and the fifth coating film 65 is made of a YF3 film with a thickness of 1083.500 nm. By applying the antireflection coating 40b made of these five coating films, it is possible to obtain a desired wavelength λ dThat is, the reflectance of the antireflection film 40b is zero at wavelengths around 9 μm.

[0048] Since this is common to each embodiment described below, the practical equivalence between the reference thickness d3 of the coating film made of the third material and the reference thickness d1 of the coating film made of the first material will be described here. Figure 7 shows the wavelength dependence of reflectance when the reference thickness d3 of the coating film made of the third material is changed relative to the reference thickness d1 of the coating film made of the first material. In Figure 7, the thick solid line 71 shows the wavelength dependence of reflectance when the reference thickness d3 of the coating film made of the third material is 30% thinner than the reference thickness d1 of the coating film made of the first material, and the thin solid line 72 shows the wavelength dependence of reflectance when the thickness d3 of the coating film made of the third material is 30% thicker than the reference thickness d1 of the coating film made of the first material. As can be seen from Figure 7, even if the reference thickness d3 changes by ±30%, the change in wavelength dependence of reflectance is negligible.

[0049] 8 shows the wavelength dependence of reflectance when the thickness of the coating film made of the first material and the coating film made of the third material is changed, and when the thickness of the coating film made of the second material is changed. In FIG. 8, the thin dotted line 73 shows the wavelength dependence of reflectance when the reference film thickness d1 (= d3) of the coating film made of the first material and the coating film made of the third material is changed to d1 (= d3) without any change in film thickness. 0 The thin dashed line 74 represents the wavelength dependency of the reflectance when the film thickness is 30% thinner than the film thickness of 59.025 nm. The thin dashed line 74 represents the difference between the reference film thickness d1 (= d3) of the coating film made of the first material and the coating film made of the third material and the reference film thickness d1 0 The thick dotted line 75 represents the wavelength dependence of the reflectance when the film thickness is 30% thicker than the standard film thickness d2 of the coating film made of the second material. 0 The thick dashed line 76 represents the wavelength dependency of the reflectance when the coating thickness is 10% thinner than the standard thickness d2 of the coating film made of the second material. 0 This shows the wavelength dependency of reflectance when the thickness is 10% for the desired wavelength λ = 653.924 nm. dThat is, the reflectance reaches a minimum around 9 μm, and the reflectance bands where the reflectance is less than 1% are 1.467 μm, 1.688 μm, 1.672 μm, and 1.988 μm, respectively.

[0050] From the above considerations, the refractive index is n c 1 / 2 For materials with a refractive index higher than n, the thickness change is within ±30%. c 1 / 2 In the case of materials with a lower temperature than this, it can be said that there are almost no practical problems if the film thickness change is within ±10%.

[0051] As will be described later, the reflectance spectrum itself can be shifted toward shorter or longer wavelengths by changing the film thickness of each layer at a certain rate, i.e., it can be adjusted, and the wavelength at which the reflectance is minimized is not a particular problem.

[0052] Next, we will explain the complex reflectance r. Figure 9 shows the complex reflectance r on the complex plane. The complex reflectance r can be expressed by the amplitude |r| and the phase θ. The power reflectance R (generally called reflectance) is |r| 2 The reflectance is the same all along the circumference of a circle with radius |r|.

[0053] First, we will explain the case where the reflectance R is 0.003 (0.3%). In this case, the radius |r| is 0.054772256. The phase θ can take any value greater than or equal to zero and less than 2π, but here we will explain the case where the phase θ is 0 and π. In this case, the real and imaginary parts of the complex reflectance r are 0.054772256 and -0.054772256, respectively. From equation (3), when the phase θ is zero, the reference film thickness d1 (= d3) is 45.634 nm and the reference film thickness d2 is 700.814 nm. When the phase θ is π, the reference film thickness d1 (= d3) is 71.156 nm and the reference film thickness d2 is 605.515 nm.

[0054] 10 shows the wavelength dependence of reflectance when the complex reflectance r is the above-mentioned value. The dotted line 77 shows the wavelength dependence of reflectance when the complex reflectance r is 0.054772256, and the dashed-dotted line 78 shows the wavelength dependence of reflectance when the complex reflectance r is -0.054772256. Desired wavelength λ d That is, the reflectance reaches a minimum around 9 μm, and the reflectance bands where the reflectance is less than 1% are 1.628 μm and 1.561 μm, respectively.

[0055] The reference film thickness can be calculated in a similar manner when the reflectance R is 0.005 (0.5%). When the phase θ is zero and π, the real and imaginary parts of the complex reflectance r are 0.070710678 and -0.070710678, respectively. From equation (3), when the phase θ is zero, the reference film thickness d1 (= d3) is calculated to be 41.437 nm, and the reference film thickness d2 is calculated to be 713.790 nm. When the phase θ is π, the reference film thickness d1 (= d3) is calculated to be 74.506 nm, and the reference film thickness d2 is calculated to be 591.333 nm.

[0056] 11 shows the wavelength dependency of reflectance when the complex reflectance r is the above-mentioned value. The dotted line 79 represents the wavelength dependency of reflectance when the complex reflectance r is 0.070710678, and the dashed-dotted line 80 represents the wavelength dependency of reflectance when the complex reflectance r is -0.070710678. Desired wavelength λ d That is, the reflectance becomes minimal near 9 μm, and the wavelength bands where the reflectance is less than 1% are 1.416 μm and 1.359 μm, respectively.

[0057] Although the above explanation illustrates cases where the phase θ is zero and π, the phase θ may be any value within the range of 0≦θ<2π. The complex reflectance r to be considered varies depending on the desired reflectance band. However, if the desired reflectance band is less than 1%, there is no practical problem as long as |r| is within the range of 0.070710678 or less.

[0058] In the following embodiments, the real and imaginary parts of the complex reflectance r are described as zero, but this is not particularly limited to this and can be any value other than zero within a range that does not cause practical problems.

[0059] To summarize the above, the laser oscillation wavelength is λ d and the effective refractive index is n c The anti-reflection coating is formed on an output end face, which is one end face of the optical semiconductor device, and is made up of a plurality of coating films, and the plurality of coating films are c 1 / 2 a first coating film made of a first material having a refractive index n1 smaller than n c 1 / 2 The coating film pair is composed of n (n≧2) coating film pairs each including a first coating film made of a second material having a refractive index n2 larger than the first coating film pair, and at least m (1≦m≦2) single coating films other than the coating film pairs, and the reference thickness of the first coating film is d1 and the reference thickness of the second coating film is d2, the thickness of the ith (2≦i≦n) coating film pair is weighted by p i Using p i d1+p i The reference thickness of the jth (1≦j≦m) single coating film is represented by d k When (k=j+2), the reference film thickness d k is the same thickness as the reference thickness d1 of the first coating film, and the refractive index of the jth single coating film is n k and the film thickness is determined by the weighting coefficient q j Using q j d k It is expressed as:

[0060] <Advantages of First Embodiment> As described above, according to the optical semiconductor device of the first embodiment, the antireflection film is configured as a five-layer coating film consisting of two pairs of coating films, each pair being a coating film made of a first material and a coating film made of a second material, and one single coating film made of a third material. The reference thickness d1 of the coating film made of the first material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving using a characteristic matrix with both the real part and the imaginary part of the complex reflectance set to zero. This produces the effect of obtaining an optical semiconductor device having an antireflection film that has a wide reflectance band and is thin.

[0061] Embodiment 2 In embodiment 1, the case where the reference thickness d3 of the coating film made of the third material is the same as the reference thickness d1 of the coating film made of the first material is shown, but in embodiment 2, the case where the reference thickness d3 of the coating film made of the third material is the same as the reference thickness d2 of the coating film made of the second material is described.

[0062] 12 shows the configuration of antireflection film 40c of the quantum cascade laser device according to the second embodiment. Antireflection film 40c of the quantum cascade laser device according to the second embodiment differs from antireflection film 40a of the quantum cascade laser device according to the first embodiment in that, while first coating film 42 made of a third material having a refractive index n3 has a reference thickness d3 equal to the reference thickness d1 in antireflection film 40a, it is replaced by first coating film 91 made of a third material having a refractive index n3 and a reference thickness d3 equal to the reference thickness d2. Note that first coating film 91 has a refractive index n3 of 2.270, and the third material is ZnS.

[0063] The reference film thickness d1 and the reference film thickness d2 (= d3) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are respectively expressed by the following equation (5).

[0064]

number

[0065] The overall characteristic matrix of the antireflection coating 40c is expressed by the above-mentioned formula (2) using the characteristic matrix of each coating film, as in the first embodiment. Furthermore, the components of the overall characteristic matrix of the antireflection coating 40c, m 11 , m 12 , m 21 , m 22 Using this formula, the complex reflectance r can also be expressed by the above formula (3) as in embodiment 1. As in embodiment 1, when the real and imaginary parts of the complex reflectance r are set to zero and solved, the reference film thickness d1 becomes 12.564 nm and the reference film thickness d2 becomes 565.076 nm.

[0066] That is, in the antireflection coating 40c, the first coating film 91 formed in this order from the emission end face 41 side of the quantum cascade laser device is made of a ZnS film with a film thickness of 565.076 nm, the second coating film 43 is made of a Ge film with a film thickness of 12.564 nm, the third coating film 44 is made of a YF3 film with a film thickness of 565.076 nm, the fourth coating film 45 is made of a Ge film with a film thickness of 12.564 nm, and the fifth coating film 46 is made of a YF3 film with a film thickness of 565.076 nm. By applying the antireflection coating 40c made of these five coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40c is zero at wavelengths around 9 μm.

[0067] The second coating film 43 and the third coating film 44 constitute a first coating film pair 47, and the fourth coating film 45 and the fifth coating film 46 constitute a second coating film pair 48.

[0068] Fig. 13 is a graph showing the wavelength dependence of the reflectance of antireflection coating 40c. In Fig. 13, a solid line 92 represents the wavelength dependence of the reflectance of antireflection coating 40c made of a five-layer coating film according to embodiment 2, and a dashed-dotted line 93 represents the wavelength dependence of the reflectance of the antireflection coating made of a five-layer coating film according to embodiment 2 when a single coating film made of a third material (described later) and weighting coefficients for each coating film pair are taken into consideration.

[0069] Assuming that the desired reflectance band is a band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40c made of five coating layers according to the second embodiment is 2.489 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40c is sum Therefore, the sum (n×d) of the products of the refractive index and the film thickness of each coating film of the antireflection coating 40c made of five coating films according to the second embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.344, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40c has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / nc 1 / 2 It can be seen that this is not a replacement for a single-layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 This is thinner than the monolayer coating film.

[0070] Next, further widening the reflectance band of the anti-reflection coating 40c will be described below. As in the first embodiment, the thickness of the single coating film made of the third material and the weighting coefficients of each coating film pair are set using weighting coefficients q3, p1, and p2, at least one of which is a positive real number other than 1.

[0071] 14 shows the configuration of antireflection film 40d of the quantum cascade laser device according to the second embodiment. Antireflection film 40d of the quantum cascade laser device according to the second embodiment differs from antireflection film 40b of the quantum cascade laser device according to the first embodiment in that, while first coating film 61 made of a third material having a refractive index n3 has a thickness d3 equal to thickness d1 in antireflection film 40b, antireflection film 40d is replaced by first coating film 94 made of a third material having a refractive index n3 and a reference thickness d3 equal to reference thickness d2. Note that first coating film 94 has a refractive index n3 of 2.270, and the third material is ZnS.

[0072] The overall characteristic matrix of the antireflection coating 40d is expressed by the above-mentioned formula (4) using the characteristic matrix of each coating film. Weighting coefficients are set based on a setting method described below, and reference film thicknesses d1 and d2 (=d3) that make both the real part and the imaginary part of the complex reflectance r in formula (3) zero are calculated. The antireflection coating 40d using the thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is then coated on the emission end face 41 of the quantum cascade laser device.

[0073] As an example of the antireflection coating 40d, the case where the weighting factors are q3=1.20, p1=1.00, and p2=1.00 will be described below. In this case, the reference film thickness d1 is 1.851 nm, and the reference film thickness d2 (=d3) is 567.551 nm.

[0074] 13, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40d is shown by a dashed line 93. The reflectance band of the anti-reflection coating 40d where the reflectance is less than 1% is 2.813 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0075] The sum of the products of the refractive index and thickness of each coating film of the antireflection film 40d (n×d) sum is 1819.866nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 Therefore, the sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40d made of five coating films according to the second embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4)=1.425, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40d has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0076] In the antireflection coating 40d, the first coating film 94, which is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, is made of a ZnS film with a film thickness of 681.061 nm, the second coating film 62 is made of a Ge film with a film thickness of 1.851 nm, the third coating film 63 is made of a YF3 film with a film thickness of 567.551 nm, the fourth coating film 64 is made of a Ge film with a film thickness of 1.851 nm, and the fifth coating film 65 is made of a YF3 film with a film thickness of 567.551 nm. By applying the antireflection coating 40d made of these five coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40d is zero at wavelengths in the vicinity of 9 μm.

[0077] <Advantages of the Second Embodiment> As described above, according to the optical semiconductor device of the second embodiment, the antireflection film is configured as a five-layer coating film consisting of two pairs of coating films, each pair being a coating film made of a first material and a coating film made of a second material, and one single coating film made of a third material. The reference thickness d2 of the coating film made of the second material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving using a characteristic matrix with both the real part and the imaginary part of the complex reflectance set to zero. This produces the effect of obtaining an optical semiconductor device having an antireflection film that has a wide reflectance band and is thin.

[0078] Embodiment 3 In the first and second embodiments, the first material has a refractive index of n c 1 / 2 The material with a refractive index higher than n is used as the second material. c 1 / 2 In the third embodiment, the first material has a refractive index of n c 1 / 2 The second material has a refractive index lower than n c 1 / 2 An anti-reflection film made of a material having a higher refractive index than the above will now be described.

[0079] 15 shows the configuration of the antireflection film 40e of the quantum cascade laser device according to the third embodiment. As shown in FIG. 15, the antireflection film 40e has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 42 made of a third material having a refractive index n3 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 42 made of a third material having a refractive index n1 and a film thickness d2 is provided on the light-emitting end surface 41 of the quantum cascade laser c 1 / 2 The second coating film 101 is made of a first material and has a thickness d1 that is smaller than the refractive index n2. c 1 / 2 a third coating film 102 made of a second material having a thickness d2 higher than d1; and a refractive index n1 of n c 1 / 2 A fourth coating film 103 made of a first material and having a thickness d1 that is smaller than c 1 / 2 and a fifth coating film 104 made of a second material having a thickness d2 higher than the thickness d1 of the first coating film 42. The thickness d3 of the first coating film 42 and the thickness d1 of the second coating film 101 are equal.

[0080] The third material constituting the first coating film 42 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 101 and the fourth coating film 103 is YF3, and the refractive index n1 is 1.450. The second material constituting the third coating film 102 and the fifth coating film 104 is Ge, and the refractive index n2 is 4.085.

[0081] The second coating film 101 and the third coating film 102 constitute a first coating film pair 105, and the fourth coating film 103 and the fifth coating film 104 constitute a second coating film pair 106.

[0082] The film thickness d1 (= d3) and the film thickness d2 are determined in the same manner as in embodiment 1. The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (1).

[0083] The overall characteristic matrix of the anti-reflection coating 40e is expressed by the above-mentioned formula (2) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0084] As in the first embodiment, when the real and imaginary parts of the complex reflectance r are set to zero, the film thickness d1 is 413.376 nm and the film thickness d2 is 28.087 nm.

[0085] That is, in the antireflection coating 40e, the first coating film 42 formed in this order from the emission end face 41 side of the quantum cascade laser device is made of a ZnS film with a film thickness of 413.376 nm, the second coating film 101 is made of a YF3 film with a film thickness of 413.376 nm, the third coating film 102 is made of a Ge film with a film thickness of 28.087 nm, the fourth coating film 103 is made of a YF3 film with a film thickness of 413.376 nm, and the fifth coating film 104 is made of a Ge film with a film thickness of 28.087 nm. By applying the antireflection coating 40e consisting of these five coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40e is zero at wavelengths around 9 μm.

[0086] Fig. 16 is a graph showing the wavelength dependence of the reflectance of antireflection coating 40e. In Fig. 16, solid line 107 represents the wavelength dependence of the reflectance of antireflection coating 40e made of five-layer coating films according to embodiment 3, and dashed-dotted line 108 represents the wavelength dependence of the reflectance of antireflection coating made of five-layer coating films according to embodiment 3 when a single coating film made of a third material (described later) and weighting coefficients for each coating film pair are taken into consideration.

[0087] Assuming that the desired reflectance band is a band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40e made of five coating layers according to the third embodiment is 2.022 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40e is sumTherefore, the sum (n×d) of the products of the refractive index and the film thickness of each coating film of the antireflection coating 40e made of five coating films according to the third embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.052, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40e has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0088] Next, further widening the reflectance band of the anti-reflection coating 40e will be described below. As in the first embodiment, the reference film thickness of a single coating film made of a third material and the weighting coefficients of each coating film pair are set using weighting coefficients q3, p1, and p2, at least one of which is a positive real number other than 1.

[0089] 17 shows the configuration of the antireflection film 40f of the quantum cascade laser device according to the third embodiment. As shown in FIG. 17, the antireflection film 40f has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 109 made of a third material having a refractive index n3 and a film thickness q3d3 and a second coating film 109 made of a third material having a refractive index n1 and a film thickness q3d3 are provided on the light-emitting end surface 41 of the quantum cascade laser device. c 1 / 2 The second coating 110 is made of a first material and has a thickness p1d1 that is lower than the refractive index n2 of the first material. c 1 / 2 a third coating film 111 made of a second material having a thickness p1d2 higher than c 1 / 2 The fourth coating 112 is made of a first material and has a thickness p2d1 that is smaller than the refractive index n2 of the first material. c 1 / 2 and a fifth coating film 113 made of a second material having a thickness p2d2 higher than the first coating film 42. The reference thickness d3 of the first coating film 42 and the reference thickness d1 of the second coating film 110 are equal to each other.

[0090] The third material constituting the first coating film 109 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 110 and the fourth coating film 112 is YF3, and the refractive index n1 is 1.450. The second material constituting the third coating film 111 and the fifth coating film 113 is Ge, and the refractive index n2 is 4.085.

[0091] The second coating film 110 and the third coating film 111 constitute a first coating film pair 114 , and the fourth coating film 112 and the fifth coating film 113 constitute a second coating film pair 115 .

[0092] The overall characteristic matrix of the antireflection coating 40f is expressed by the above-mentioned formula (4) using the characteristic matrix of each coating film. Weighting coefficients are set based on a setting method described below, and reference film thicknesses d1 (= d3) and d2 are calculated so that the real part and imaginary part of the complex reflectance r in formula (3) are both zero. The antireflection coating 40f using the thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is then coated on the emission end face 41 of the quantum cascade laser device.

[0093] As an example of the antireflection coating 40f, the case where the weighting factors are q3=1.00, p1=0.50, and p2=1.00 will be described below. In this case, the reference film thickness d1 (=d3) is 573.004 nm, and the reference film thickness d2 is 23.477 nm.

[0094] 16, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40f is shown by a dashed line 108. The reflectance band of the anti-reflection coating 40f where the reflectance is less than 1% is 2.340 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0095] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40f (n×d) sum is 1467.726nm, and the refractive index is n c 1 / 2and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40f made of five coating films according to the third embodiment is smaller than the thickness of the single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4)=1.196, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40f has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0096] In the antireflection coating 40f, the first coating film 109, which is formed in this order from the emission end face 41 side of the quantum cascade laser device, is made of a ZnS film with a thickness of 573.004 nm, the second coating film 110 is made of a YF3 film with a thickness of 286.502 nm, the third coating film 111 is made of a Ge film with a thickness of 11.739 nm, the fourth coating film 112 is made of a YF3 film with a thickness of 573.004 nm, and the fifth coating film 113 is made of a Ge film with a thickness of 23.477 nm. By applying the antireflection coating 40f consisting of these five coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40f is zero at wavelengths in the vicinity of 9 μm.

[0097] The first material has a refractive index of n c 1 / 2 The second material has a refractive index lower than n c 1 / 2 Even if a material with a refractive index higher than n is used, a thin anti-reflection coating with a wide reflectance band can be realized. c 1 / 2 Materials with refractive indexes lower than n c 1 / 2 The order of the coating film made of the first material and the coating film made of the second material may be any as long as they are made of a material having a higher resistance than the first material.

[0098] <Advantages of the Third Embodiment> As described above, in the optical semiconductor device according to the third embodiment, the antireflection film has a refractive index of n c 1 / 2 a coating film made of a first material having a refractive index higher than n c 1 / 2 The five-layer coating film is composed of two pairs of coating films, each pair consisting of a coating film made of a second material having a reflectance lower than the first material, and one single coating film made of a third material. The reference thickness d1 of the coating film made of the first material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving the characteristic matrix by setting both the real part and the imaginary part of the complex reflectance to zero. This provides the effect of obtaining an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0099] Embodiment 4 In the fourth embodiment, an anti-reflection coating is described that uses a coating film made of a third material and is made up of three pairs of coating films, each pair being made of a coating film made of a first material and a coating film made of a second material.

[0100] 18 shows the configuration of the antireflection film 40g of the quantum cascade laser device according to the fourth embodiment. As shown in FIG. 18, the antireflection film 40g has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n3 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n1 and a film thickness d2 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n2 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n3 and a film thickness d2 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n1 and a film thickness d2 is c 1 / 2 a second coating film 122 made of a first material having a thickness d1 higher than c 1 / 2 a third coating 123 made of a second material having a thickness d2 that is smaller than c 1 / 2 a fourth coating film 124 made of a first material having a thickness d1 higher than c 1 / 2 A fifth coating 125 made of a second material having a thickness d2 that is smaller than c 1 / 2A sixth coating 126 made of a first material having a thickness d1 higher than c 1 / 2 and a seventh coating film 127 made of a second material and having a thickness d2 lower than the thickness d1 of the first coating film 121. The thickness d3 of the first coating film 121 and the thickness d1 of the second coating film 122 are equal.

[0101] The third material constituting the first coating film 121 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 122, the fourth coating film 124, and the sixth coating film 126 is Ge, and the refractive index n1 is 4.085. The second material constituting the third coating film 123, the fifth coating film 125, and the seventh coating film 127 is YF3, and the refractive index n2 is 1.450.

[0102] The second coating film 122 and the third coating film 123 form a first coating film pair 128, the fourth coating film 124 and the fifth coating film 125 form a second coating film pair 129, and the sixth coating film 126 and the seventh coating film 127 form a third coating film pair 130. The reference film thickness d1 (= d3) and the reference film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (1).

[0103] The overall characteristic matrix of the anti-reflection coating 40g is expressed by the following equation (6) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0104]

number

[0105] Furthermore, the component of the overall characteristic matrix of the anti-reflection coating 40g, m 11 , m 12 , m 21 , m22 Using this, the complex reflectance r is expressed by the above equation (3).

[0106] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r mentioned above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 35.770 nm and the film thickness d2 becomes 418.651 nm.

[0107] In the antireflection coating 40g, first coating film 121 is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, and is composed of a ZnS film having a film thickness of 35.770 nm, second coating film 122 is formed of a Ge film having a film thickness of 35.770 nm, third coating film 123 is formed of a YF3 film having a film thickness of 418.651 nm, fourth coating film 124 is formed of a Ge film having a film thickness of 35.770 nm, fifth coating film 125 is formed of a YF3 film having a film thickness of 418.651 nm, sixth coating film 126 is formed of a Ge film having a film thickness of 35.770 nm, and seventh coating film 127 is formed of a YF3 film having a film thickness of 418.651 nm. By applying the antireflection coating 40g consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40g is zero at wavelengths in the vicinity of 9 μm.

[0108] 19 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40g. In FIG. 19, a solid line 131 represents the wavelength dependence of the reflectance of the antireflection coating 40g consisting of seven coating layers according to the fourth embodiment, a dashed-dotted line 132 represents the wavelength dependence of the reflectance of the antireflection coating consisting of seven coating layers according to the fourth embodiment when a single coating layer made of a third material and weighting coefficients of each coating layer pair are taken into consideration, as will be described later, and a two-dot-dashed line 133 represents the wavelength dependence of the reflectance of the antireflection coating consisting of seven coating layers according to the fourth embodiment when the thickness of each coating layer is multiplied by a constant on the dashed-dotted line 132, and the desired wavelength λ d 10 shows the wavelength dependency of the reflectance of the antireflection coating made of the seven-layer coating film according to the fourth embodiment when the wavelengths of the antireflection coatings and the seven-layer coating film are matched.

[0109] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40g made of seven coating layers according to the third embodiment is 1.878 μm. In addition, the sum (n×d) of the products of the refractive index and film thickness of each coating layer of the antireflection coating 40g is sum Therefore, the sum (n×d) of the products of the refractive index and film thickness of each coating film of the antireflection coating 40g made of seven coating films according to the fourth embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 0.998, which cannot be expressed as a positive odd number. From this result, it can be seen that the refractive index of the anti-reflection film 40g is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement for a single layer coating film with a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0110] Next, the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The following describes an antireflection coating having a reflectance band wider than that of a single-layer coating film of 1. As in the first embodiment, the thickness of the single coating film made of a third material and the weighting coefficients of each coating film pair are set using weighting coefficients q3, p1, p2, and p3, at least one of which is a positive real number other than 1.

[0111] 20 shows the configuration of the antireflection film 40h of the quantum cascade laser device according to the fourth embodiment. The antireflection film 40h has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2As shown in FIG. 20, the anti-reflection coating 40h has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 141 made of a third material having a refractive index n3 and a film thickness q3d3 and a second coating film 142 made of a third material having a refractive index n1 and a film thickness q3d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device having a refractive index n2 and a film thickness q3d3. c 1 / 2 The second coating film 142 is made of a first material and has a thickness p1d1 higher than the refractive index n2 of the first material. c 1 / 2 a third coating film 143 made of a second material having a thickness p1d2 lower than p1d2; and a refractive index n1 of n c 1 / 2 A fourth coating film 144 made of a first material having a thickness p2d1 higher than c 1 / 2 A fifth coating 145 made of a second material having a thickness p2d2 lower than c 1 / 2 A sixth coating film 146 made of a first material having a thickness p3d1 higher than c 1 / 2 and a seventh coating film 147 made of a second material having a thickness p3d2 lower than p3d1. The reference thickness d3 of the first coating film 141 and the reference thickness d1 of the second coating film 142 are equal.

[0112] The third material constituting the first coating film 141 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 142, the fourth coating film 144, and the sixth coating film 146 is Ge, and the refractive index n1 is 4.085. The second material constituting the third coating film 143, the fifth coating film 145, and the seventh coating film 147 is YF3, and the refractive index n2 is 1.450.

[0113] The second coating film 142 and the third coating film 143 constitute a first coating film pair 148, the fourth coating film 144 and the fifth coating film 145 constitute a second coating film pair 149, and the sixth coating film 146 and the seventh coating film 147 constitute a third coating film pair 150.

[0114] The overall characteristic matrix of the anti-reflection coating 40h is expressed by the following equation (7) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0115]

number

[0116] The weighting coefficients are set based on the setting method described below, and the reference film thickness d1 (= d3) and the reference film thickness d2 at which the real part and the imaginary part of the complex reflectance r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40h using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0117] As an example of the anti-reflection coating 40h, the case where the weighting factors are q3=1.15, p1=0.45, p2=0.85, and p3=6.74 will be described below. In this case, the reference film thickness d1 (=d3) is 22.227 nm, and the reference film thickness d2 is 245.138 nm.

[0118] 19, the wavelength dependency of the reflectance in the reflectance band of the antireflection coating 40h is shown by a dashed line 132. The reflectance band of the antireflection coating 40h where the reflectance is less than 1% is 4.513 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0119] In addition, the sum of the products of the refractive index and film thickness of each coating film of the anti-reflection film 40h (n × d) sum is 2175.178nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c1 / 2 Therefore, the sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40h made of seven coating films according to the fourth embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) = 1.445, which cannot be expressed as a positive odd number. From this result, it can be seen that the refractive index of the anti-reflection film 40h is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0120] In the antireflection coating 40h, a first coating film 141 formed in this order from the side of the emission end face 41 of the quantum cascade laser device is composed of a ZnS film having a film thickness of 25.561 nm, a second coating film 142 is composed of a Ge film having a film thickness of 10.002 nm, a third coating film 143 is composed of a YF3 film having a film thickness of 110.312 nm, a fourth coating film 144 is composed of a Ge film having a film thickness of 18.893 nm, a fifth coating film 145 is composed of a YF3 film having a film thickness of 208.368 nm, a sixth coating film 146 is composed of a Ge film having a film thickness of 149.811 nm, and a seventh coating film 147 is composed of a YF3 film having a film thickness of 1652.230 nm. By applying the antireflection coating 40h consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40h is zero at wavelengths in the vicinity of 9 μm.

[0121] The reflectance band of the anti-reflection coating 40h where the reflectance is less than 1% is 4.513 μm, which is the wavelength width of 6.886 μm to 11.399 μm. c is 9.143 μm, and the desired wavelength λ d The central wavelength λ of the reflectance band is different from (9 μm). c and the desired wavelength λ d To match the thickness of each coating, λ d / λ cThe wavelength dependency of the reflectance in this case is shown by the two-dot chain line 133 in Figure 19. It can be seen from Figure 19 that the center of the reflectance band is 9.0 µm.

[0122] In this case, the thickness of each coating film, from the emission end surface 41 side of the quantum cascade laser device, is as follows: first coating film 141 is 25.163 nm, second coating film 142 is 9.846 nm, third coating film 143 is 108.593 nm, fourth coating film 144 is 18.599 nm, fifth coating film 145 is 205.120 nm, sixth coating film 146 is 147.476 nm, and seventh coating film 147 is 1626.477 nm.

[0123] <Advantages of the Fourth Embodiment> As described above, according to the optical semiconductor device of the fourth embodiment, the antireflection film is configured as a seven-layer coating film consisting of three pairs of coating films, each pair being a coating film made of a first material and a coating film made of a second material, and one single coating film made of a third material. The reference film thickness d1 of the coating film made of the first material is set equal to the reference film thickness d3 of the single coating film, and the film thickness of each coating film is determined by solving using a characteristic matrix with both the real part and the imaginary part of the complex reflectance set to zero. This has the effect of providing an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0124] Embodiment 5. In the fourth embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d1 of the coating film made of the first material is described. In the fifth embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d2 of the coating film made of the second material is described.

[0125] FIG. 21 shows the configuration of antireflection coating 40i of the quantum cascade laser device according to the fifth embodiment. As shown in FIG. 21, antireflection coating 40i has a configuration in which first coating film 121 made of a third material having a refractive index n3 and a thickness d3 of antireflection coating 40g of the quantum cascade laser device according to the fourth embodiment is replaced with first coating film 161 made of a third material having a refractive index n3 and a thickness d3. While the thickness d3 of first coating film 121 and the thickness d1 of second coating film 122 of antireflection coating 40g according to the fourth embodiment are equal, antireflection coating 40i according to the fifth embodiment differs in that the thickness d3 of first coating film 161 is equal to the thickness d2 of third coating film 123. The third material constituting first coating film 161 is ZnS, which has a refractive index n3 of 2.270.

[0126] The reference film thickness d1 and the reference film thickness d2 (= d3) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned equation (5).

[0127] The overall characteristic matrix of the anti-reflection coating 40i is expressed by the above-mentioned formula (6) using the characteristic matrix of each coating film. Furthermore, the components of the overall characteristic matrix of the anti-reflection coating 40i, m 11 , m 12 , m 21 , m 22 When the above equation is used, the complex reflectance r is expressed by the above equation (3) as in the fourth embodiment.

[0128] As in the fourth embodiment, when the real and imaginary parts of the complex reflectance r are set to zero, the film thickness d1 is 19.368 nm and the film thickness d2 is 371.375 nm.

[0129] In the antireflection coating 40i, the first coating film 161 formed in this order from the side of the emission end face 41 of the quantum cascade laser device is composed of a ZnS film having a film thickness of 371.375 nm, the second coating film 122 is composed of a Ge film having a film thickness of 19.368 nm, the third coating film 123 is composed of a YF3 film having a film thickness of 371.375 nm, the fourth coating film 124 is composed of a Ge film having a film thickness of 19.368 nm, the fifth coating film 125 is composed of a YF3 film having a film thickness of 371.375 nm, the sixth coating film 126 is composed of a Ge film having a film thickness of 19.368 nm, and the seventh coating film 127 is composed of a YF3 film having a film thickness of 371.375 nm. By applying the antireflection coating 40i consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40i is zero at wavelengths in the vicinity of 9 μm.

[0130] Fig. 22 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40i. In Fig. 22, a solid line 162 represents the wavelength dependence of the reflectance of the antireflection coating 40i made of the seven-layer coating film according to the fifth embodiment, and a dashed-dotted line 163 represents the wavelength dependence of the reflectance of the antireflection coating made of the seven-layer coating film according to the fifth embodiment when a single coating film made of a third material, which will be described later, and weighting coefficients of each coating film pair are taken into consideration.

[0131] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40i made of seven coating layers according to the fifth embodiment is 2.138 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40i is sum Therefore, the sum (n×d) of the products of the refractive index and film thickness of each coating film of the antireflection coating 40i made of seven coating films according to the fifth embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.175, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40i has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2It can be seen that the anti-reflection coating 40i is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0132] Next, further widening the reflectance band of the anti-reflection coating 40i will be described below. As in the fourth embodiment, the thickness of the single coating film made of the third material and the weighting coefficients of each coating film pair are set using weighting coefficients q3, p1, p2, and p3, at least one of which is a positive real number other than 1.

[0133] FIG. 23 illustrates the configuration of an antireflection coating 40j having a wider reflectance band of a quantum cascade laser device according to the fifth embodiment. As illustrated in FIG. 23, the antireflection coating 40j has a configuration in which the first coating film 141 made of a third material having a refractive index n3 and a thickness q3d3 of the antireflection coating 40h of the quantum cascade laser device according to the fourth embodiment is replaced with a first coating film 164 made of a third material having a refractive index n3 and a thickness q3d3. The antireflection coating 40h according to the fourth embodiment differs in that the thickness d3 of the first coating film 141 and the thickness d1 of the second coating film 142 are equal to each other, whereas the antireflection coating 40j according to the fifth embodiment differs in that the reference thickness d3 of the first coating film 164 is equal to the reference thickness d2 of the third coating film 143. The third material constituting the first coating film 164 is ZnS, and the refractive index n3 is 2.270.

[0134] The reference film thickness d1 and the reference film thickness d2 (= d3) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned equation (5).

[0135] The overall characteristic matrix of the anti-reflection coating 40j is expressed by the above-mentioned formula (7) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m22 When the above equation is used, the complex reflectance r is expressed by the above equation (3) as in the fourth embodiment.

[0136] The weighting coefficients are set based on the setting method described below, and the reference film thicknesses d1 and d2 (= d3) at which the real and imaginary parts of the complex reflectivity r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40j using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0137] As an example of the anti-reflection coating 40j, the case where the weighting factors are q3=1.50, p1=0.50, p2=1.00, and p3=1.00 will be described below. In this case, the reference film thickness d1 is 1.667 nm, and the reference film thickness d2 (=d3) is 451.899 nm.

[0138] 22, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40j is shown by a dashed line 163. The reflectance band of the anti-reflection coating 40j where the reflectance is less than 1% is 2.783 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0139] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40j (n×d) sum is 1811.763 nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40j made of seven coating films according to the fifth embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.418, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40j has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0140] In the antireflection coating 40j, the first coating film 164 formed in this order from the side of the emission end face 41 of the quantum cascade laser device is composed of a ZnS film with a film thickness of 677.848 nm, the second coating film 142 is composed of a Ge film with a film thickness of 0.834 nm, the third coating film 143 is composed of a YF3 film with a film thickness of 225.949 nm, the fourth coating film 144 is composed of a Ge film with a film thickness of 1.667 nm, the fifth coating film 145 is composed of a YF3 film with a film thickness of 451.899 nm, the sixth coating film 146 is composed of a Ge film with a film thickness of 1.667 nm, and the seventh coating film 147 is composed of a YF3 film with a film thickness of 451.899 nm. By applying the antireflection coating 40j consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40j is zero at wavelengths in the vicinity of 9 μm.

[0141] <Effects of the Fifth Embodiment> As described above, according to the optical semiconductor device of the fifth embodiment, the antireflection film is configured as a seven-layer coating film consisting of three pairs of coating films, each pair being a coating film made of a first material and a coating film made of a second material, and one single coating film made of a third material. The reference thickness d2 of the coating film made of the second material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving using a characteristic matrix with both the real part and the imaginary part of the complex reflectance set to zero. This has the effect of providing an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0142] Embodiment 6 In the sixth embodiment, a coating film made of a third material is used, and three pairs of coating films each made of a first material and a second material are used. The first material has a refractive index of n c1 / 2 The second material has a refractive index lower than n c 1 / 2 In this example, an anti-reflection coating is described in which a material having a higher refractive index than that of the first material is used, and the thickness d3 of the coating film made of the third material is the same as the thickness d1 of the coating film made of the first material.

[0143] 24 shows the configuration of the antireflection film 40k of the quantum cascade laser device according to the sixth embodiment. The antireflection film 40k has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 As shown in FIG. 24, the anti-reflection coating 40k has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n3 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n1 and a film thickness d2 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n2 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 121 made of a third material having a refractive index n3 and a film thickness d2 .... c 1 / 2 A second coating film 171 made of a first material having a thickness d1 that is smaller than c 1 / 2 a third coating film 172 made of a second material having a thickness d2 higher than c 1 / 2 A fourth coating film 173 made of a first material and having a thickness d1 that is smaller than c 1 / 2 A fifth coating film 174 made of a second material having a thickness d2 higher than c 1 / 2 A sixth coating film 175 made of a first material and having a thickness d1 lower than c 1 / 2 and a seventh coating film 176 made of a second material having a thickness d2 that is higher than the thickness d1 of the first coating film 121. The thickness d3 of the first coating film 121 and the thickness d1 of the second coating film 171 are equal.

[0144] The third material constituting the first coating film 121 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 171, the fourth coating film 173, and the sixth coating film 175 is YF3, and the refractive index n2 is 1.450. The second material constituting the third coating film 172, the fifth coating film 174, and the seventh coating film 176 is Ge, and the refractive index n1 is 4.085.

[0145] The second coating film 171 and the third coating film 172 constitute a first coating film pair 177, the fourth coating film 173 and the fifth coating film 174 constitute a second coating film pair 178, and the sixth coating film 175 and the seventh coating film 176 constitute a third coating film pair 179.

[0146] The reference film thickness d1 (= d3) and the reference film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (1).

[0147] The overall characteristic matrix of the anti-reflection coating 40k is expressed by the above-mentioned formula (6) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0148] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r described above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 298.411 nm and the film thickness d2 becomes 22.823 nm.

[0149] In the antireflection coating 40k, first coating film 121, which is formed in this order from the side of emission facet 41 of the quantum cascade laser device, is made of a ZnS film with a film thickness of 298.411 nm, second coating film 171 is made of a YF3 film with a film thickness of 298.411 nm, third coating film 172 is made of a Ge film with a film thickness of 22.823 nm, fourth coating film 173 is made of a YF3 film with a film thickness of 298.411 nm, fifth coating film 174 is made of a Ge film with a film thickness of 22.823 nm, sixth coating film 175 is made of a YF3 film with a film thickness of 298.411 nm, and seventh coating film 176 is made of a Ge film with a film thickness of 22.823 nm. By applying the antireflection coating 40k made of these seven coating films, it is possible to obtain a desired wavelength λ d In other words, the reflectance of the anti-reflection film 40k is zero at wavelengths around 9 μm.

[0150] Fig. 25 is a graph showing the wavelength dependence of the reflectance of antireflection coating 40i. In Fig. 25, a solid line 180 represents the wavelength dependence of the reflectance of antireflection coating 40k made of seven-layer coating films according to embodiment 6, and a dashed-dotted line 181 represents the wavelength dependence of the reflectance of the antireflection coating made of seven-layer coating films according to embodiment 6 when a single coating film made of a third material, which will be described later, and weighting coefficients for each coating film pair are taken into consideration.

[0151] Assuming that the desired reflectance band is a band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40k made of seven coating layers according to the sixth embodiment is 1.945 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40i is sum Therefore, the sum (n×d) of the products of the refractive index and film thickness of each coating film of the antireflection coating 40k made of seven coating films according to the sixth embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.002, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40k is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2It can be seen that this is not a replacement for a single layer coating film with a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0152] Next, further widening the reflectance band of the anti-reflection coating 40k will be described below. In this case, the thickness of the single coating film made of the third material and the weighting coefficients of each coating film pair are set using weighting coefficients q3, p1, p2, and p3, at least one of which is a positive real number other than 1.

[0153] 26 shows the configuration of the antireflection film 40l of the quantum cascade laser device according to the fourth embodiment. The antireflection film 40l has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 As shown in FIG. 26, the anti-reflection coating 40l has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 141 made of a third material having a refractive index n3 and a film thickness q3d3 and a second coating film 142 made of a third material having a refractive index n1 and a film thickness q3d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device having a refractive index n2 and a film thickness q3d3. c 1 / 2 The second coating film 182 is made of a first material and has a thickness p1d1 that is lower than the refractive index n2 of the first material. c 1 / 2 a third coating film 183 made of a second material having a thickness p1d2 higher than c 1 / 2 A fourth coating film 184 made of a first material having a thickness p2d1 lower than c 1 / 2 A fifth coating film 185 made of a second material having a thickness p2d2 higher than c 1 / 2 A sixth coating film 186 made of a first material having a thickness p3d1 lower than c 1 / 2and a seventh coating film 187 made of a second material having a thickness p3d2 higher than the first coating film 141. The reference thickness d3 of the first coating film 141 and the reference thickness d1 of the second coating film 182 are equal to each other.

[0154] The third material constituting the first coating film 141 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 182, the fourth coating film 184, and the sixth coating film 186 is YF3, and the refractive index n2 is 1.450. The second material constituting the third coating film 183, the fifth coating film 185, and the seventh coating film 187 is Ge, and the refractive index n1 is 4.085.

[0155] The second coating film 182 and the third coating film 183 constitute a first coating film pair 188, the fourth coating film 184 and the fifth coating film 185 constitute a second coating film pair 189, and the sixth coating film 186 and the seventh coating film 187 constitute a third coating film pair 190.

[0156] The reference film thickness d1 (= d3) and the reference film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (1).

[0157] The overall characteristic matrix of the anti-reflection coating 40l is expressed by the above-mentioned formula (7) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0158] The weighting coefficients are set based on the setting method described below, and the reference film thickness d1 (= d3) and the reference film thickness d2 at which the real part and the imaginary part of the complex reflectance r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40l using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0159] As an example of the anti-reflection coating 40l, the case where the weighting factors are q3=1.50, p1=1.00, p2=1.00, and p3=1.00 will be described below. In this case, the reference film thickness d1 (=d3) is 296.016 nm, and the reference film thickness d2 is 16.678 nm.

[0160] 25, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40l is shown by a dashed line 181. The reflectance band of the anti-reflection coating 40l where the reflectance is less than 1% is 2.093 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0161] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40l (n×d) sum is 1382.106 nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40l made of seven coating films according to the sixth embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.111, which cannot be expressed as a positive odd number. From this result, the anti-reflection film 40l has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0162] In antireflection coating 40l, first coating film 141, which is formed in this order from the side of emission facet 41 of the quantum cascade laser device, is made of a ZnS film with a film thickness of 444.023 nm, second coating film 182 is made of a YF3 film with a film thickness of 296.016 nm, third coating film 183 is made of a Ge film with a film thickness of 16.678 nm, fourth coating film 184 is made of a YF3 film with a film thickness of 296.016 nm, fifth coating film 185 is made of a Ge film with a film thickness of 16.678 nm, sixth coating film 186 is made of a YF3 film with a film thickness of 296.016 nm, and seventh coating film 187 is made of a Ge film with a film thickness of 16.678 nm. By applying antireflection coating 40l made of these seven coating layers, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40l is zero at wavelengths in the vicinity of 9 μm.

[0163] <Advantages of Sixth Embodiment> As described above, in the optical semiconductor device according to the sixth embodiment, the antireflection film has a refractive index of n c 1 / 2 a coating film made of a first material having a refractive index lower than n c 1 / 2 The seven-layer coating film is composed of three coating film pairs, each pair consisting of a coating film made of a second material having a reflectance higher than the first coating film, and one single coating film made of a third material. The reference thickness d1 of the coating film made of the first material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving using a characteristic matrix with both the real and imaginary parts of the complex reflectance set to zero. This provides the effect of obtaining an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0164] Embodiment 7 In the sixth embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d1 of the coating film made of the first material is described. In the seventh embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d2 of the coating film made of the second material is described.

[0165] FIG. 27 shows the configuration of antireflection coating 40m of the quantum cascade laser device according to the seventh embodiment. As shown in FIG. 27, antireflection coating 40m has a configuration in which first coating film 121 made of a third material having a refractive index n3 and a thickness d3 of antireflection coating 40k of the quantum cascade laser device according to the sixth embodiment is replaced with first coating film 164 made of a third material having a refractive index n3 and a thickness d3. While the thickness d3 of first coating film 121 and the thickness d1 of second coating film 171 of antireflection coating 40k according to the sixth embodiment are equal, antireflection coating 40m according to the seventh embodiment differs in that the reference thickness d3 of first coating film 164 is equal to the reference thickness d2 of third coating film 172. The third material constituting first coating film 164 is ZnS, and the refractive index n3 is 2.270.

[0166] The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (5).

[0167] The overall characteristic matrix of the anti-reflection coating 40m is expressed by the above-mentioned formula (6) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 When using the above formula, the complex reflectance r is expressed by the above formula (3) as in the sixth embodiment.

[0168] The weighting coefficients are set based on the setting method described below, and the film thicknesses d1 and d2 (= d3) at which the real and imaginary parts of the complex reflectivity r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40m using the film thicknesses of the coating films determined based on the film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0169] As in the sixth embodiment, when the real and imaginary parts of the complex reflectance r are set to zero, the film thickness d1 is 1339.793 nm and the film thickness d2 is 29.394 nm.

[0170] In the antireflection coating 40m, the first coating film 164, which is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, is composed of a ZnS film having a film thickness of 29.394 nm, the second coating film 171 is composed of a YF3 film having a film thickness of 339.793 nm, the third coating film 172 is composed of a Ge film having a film thickness of 29.394 nm, the fourth coating film 173 is composed of a YF3 film having a film thickness of 339.793 nm, the fifth coating film 174 is composed of a Ge film having a film thickness of 29.394 nm, the sixth coating film 175 is composed of a YF3 film having a film thickness of 339.793 nm, and the seventh coating film 176 is composed of a Ge film having a film thickness of 29.394 nm. By applying the antireflection coating 40m consisting of these seven coating films, it is possible to obtain a desired wavelength λ d In other words, the reflectance of the anti-reflection film 40 mm is zero at wavelengths around 9 μm.

[0171] Fig. 28 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40m. In Fig. 28, a solid line 191 represents the wavelength dependence of the reflectance of the antireflection coating 40m made of the seven-layer coating film according to the seventh embodiment, and a dashed-dotted line 192 represents the wavelength dependence of the reflectance of the antireflection coating made of the seven-layer coating film according to the seventh embodiment when a single coating film made of a third material, which will be described later, and weighting coefficients of each coating film pair are taken into consideration.

[0172] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40m made of a seven-layer coating according to the seventh embodiment is 1.863 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40m is sum Therefore, the sum (n×d) of the products of the refractive index and film thickness of each coating film of the antireflection coating 40m made of seven coating films according to the seventh embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 0.847, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40m is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2It can be seen that this is not a replacement for a single layer coating film with a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0173] Next, the reflectance band of the anti-reflection coating 40 m is c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The following describes how to further widen the reflectance band beyond that of a single coating film, which is 1. As in the sixth embodiment, the thickness of the single coating film made of the third material and the weighting coefficients of each coating film pair are set using weighting coefficients q3, p1, p2, and p3, at least one of which is a positive real number other than 1.

[0174] 29 shows the configuration of the antireflection film 40n of the quantum cascade laser device according to the seventh embodiment. The antireflection film 40n has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The antireflection coating 40n has a reflectance band wider than that of a single-layer coating having a refractive index of n3 and a thickness of q3d3. As shown in FIG. 29, the antireflection coating 40n has a configuration in which the first coating film 141 made of a third material having a refractive index of n3 and a thickness of q3d3 of the antireflection coating 40l of the quantum cascade laser device according to the sixth embodiment is replaced with a first coating film 164 made of a third material having a refractive index of n3 and a thickness of q3d3. The antireflection coating 40n according to the seventh embodiment differs in that the thickness d3 of the first coating film 141 and the thickness d1 of the second coating film 182 of the antireflection coating 40l according to the sixth embodiment are equal to each other, whereas the reference thickness d3 of the first coating film 164 is equal to the reference thickness d2 of the third coating film 183. The third material constituting the first coating film 164 is ZnS, and the refractive index n3 is 2.270.

[0175] The weighting coefficients are set based on the setting method described below, and the reference film thicknesses d1 and d2 (= d3) at which the real and imaginary parts of the complex reflectivity r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40n using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0176] As an example of the anti-reflection coating 40n, the case where the weighting factors are q3=20.00, p1=1.00, p2=1.00, and p3=1.00 will be described below. In this case, the reference film thickness d1 is 294.650 nm, and the reference film thickness d2 (=d3) is 19.323 nm.

[0177] 28, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40n is shown by a dashed line 192. The reflectance band of the anti-reflection coating 40n where the reflectance is less than 1% is 2.024 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0178] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40n (n×d) sum is 1328.370nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40n consisting of seven coating films according to the seventh embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.065, which cannot be expressed as a positive odd number. From this result, the anti-reflection film 40n has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2It can be seen that this is not a replacement of the monolayer coating film.

[0179] In the antireflection coating 40n, the first coating film 164, which is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, is made of a ZnS film with a film thickness of 386.452 nm, the second coating film 182 is made of a YF3 film with a film thickness of 294.650 nm, the third coating film 183 is made of a Ge film with a film thickness of 19.323 nm, the fourth coating film 184 is made of a YF3 film with a film thickness of 294.650 nm, the fifth coating film 185 is made of a Ge film with a film thickness of 19.323 nm, the sixth coating film 186 is made of a YF3 film with a film thickness of 294.650 nm, and the seventh coating film 187 is made of a Ge film with a film thickness of 19.323 nm. By applying the antireflection coating 40n made of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40n is zero at wavelengths in the vicinity of 9 μm.

[0180] <Effects of the Seventh Embodiment> As described above, in the optical semiconductor device according to the seventh embodiment, the antireflection film has a refractive index of n c 1 / 2 a coating film made of a first material having a refractive index lower than n c 1 / 2 The seven-layer coating film is composed of three coating film pairs, each pair consisting of a coating film made of a second material having a reflectance higher than that of the first coating film, and one single coating film made of a third material. The reference thickness d2 of the coating film made of the second material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving the characteristic matrix by setting both the real part and the imaginary part of the complex reflectance to zero. This produces the effect of obtaining an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0181] Embodiment 8 In the eighth embodiment, Y2O3 is used as the third material, and three pairs of coating films each consisting of a coating film made of a first material and a coating film made of a second material are used, and a coating film having a refractive index of n c 1 / 2 The second material has a refractive index higher than nc 1 / 2 In this example, an antireflection coating is described in which a material having a lower refractive index than that of the first material is used, and the thickness d3 of the coating film made of the third material is the same as the thickness d1 of the coating film made of the first material.

[0182] 30 shows the configuration of the antireflection film 40o of the quantum cascade laser device according to the eighth embodiment. As shown in FIG. 30, the antireflection film 40o has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 201 made of a third material having a refractive index n3 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 201 made of a third material having a refractive index n1 and a film thickness d2 is provided on the light-emitting end surface 41 of the quantum cas c 1 / 2 The second coating film 202 is made of a first material and has a thickness d1 that is higher than the refractive index n2. c 1 / 2 a third coating film 203 made of a second material having a thickness d2 lower than c 1 / 2 The fourth coating film 204 is made of a first material and has a thickness d1 that is higher than the refractive index n2. c 1 / 2 A fifth coating film 205 made of a second material having a thickness d2 that is lower than c 1 / 2 A sixth coating film 206 made of a first material having a thickness d1 higher than c 1 / 2 and a seventh coating film 207 made of a second material having a thickness d2 lower than the thickness d1 of the first coating film 201. The thickness d3 of the first coating film 201 and the thickness d1 of the second coating film 202 are equal.

[0183] The third material constituting the first coating film 201 is Y2O3, and the refractive index n3 is 1.884115. The first material constituting the second coating film 202, the fourth coating film 204, and the sixth coating film 206 is Ge, and the refractive index n1 is 4.085. The second material constituting the third coating film 203, the fifth coating film 205, and the seventh coating film 207 is YF3, and the refractive index n2 is 1.450. Note that the refractive index of Y2O3 was determined by referring to Non-Patent Document 2.

[0184] The second coating film 202 and the third coating film 203 constitute a first coating film pair 208, the fourth coating film 204 and the fifth coating film 205 constitute a second coating film pair 209, and the sixth coating film 206 and the seventh coating film 207 constitute a third coating film pair 210.

[0185] The film thickness d1 (= d3) and the film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (1).

[0186] The overall characteristic matrix of the anti-reflection coating 40o is expressed by the above-mentioned formula (6) using the characteristic matrix of each coating film. Furthermore, the components m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0187] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r mentioned above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 35.429 nm and the film thickness d2 becomes 416.369 nm.

[0188] In the antireflection coating 40o, the first coating film 201 is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, and is composed of a YO film having a film thickness of 35.429 nm, a second coating film 202 is formed of a Ge film having a film thickness of 35.429 nm, a third coating film 203 is formed of a YF film having a film thickness of 416.369 nm, a fourth coating film 204 is formed of a Ge film having a film thickness of 35.429 nm, a fifth coating film 205 is formed of a YF film having a film thickness of 416.369 nm, a sixth coating film 206 is formed of a Ge film having a film thickness of 35.429 nm, and a seventh coating film 207 is formed of a YF film having a film thickness of 416.369 nm. By applying the antireflection coating 40o composed of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40o is zero at wavelengths in the vicinity of 9 μm.

[0189] Fig. 31 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40o. In Fig. 31, a solid line 211 represents the wavelength dependence of the reflectance of the antireflection coating 40o made of the seven-layer coating film according to the eighth embodiment, and a dashed-dotted line 212 represents the wavelength dependence of the reflectance of the antireflection coating made of the seven-layer coating film according to the eighth embodiment when a single coating film made of a third material and weighting coefficients for each coating film pair are taken into account.

[0190] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40o made of seven coating layers according to the eighth embodiment is 1.881 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40o is sum Therefore, the sum (n×d) of the products of the refractive index and film thickness of each coating film of the antireflection coating 40o made of seven coating films according to the eighth embodiment is 1390.824 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.028, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40o is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0191] Next, the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2The following describes an antireflection coating having a reflectance band wider than that of a single coating film of , where q3, p1, p2, and p3, at least one of which is a positive real number other than 1, are used to set the reference thickness of the single coating film made of a third material and the weighting coefficients for each coating film pair.

[0192] FIG. 32 shows the configuration of the antireflection film 40p of the quantum cascade laser device according to the eighth embodiment. The antireflection film 40p has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 As shown in FIG. 32, the anti-reflection coating 40p has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 213 made of a third material having a refractive index n3 and a film thickness q3d3 and a second coating film 214 made of a third material having a refractive index n1 and a film thickness q3d3 are provided on the light-emitting end surface 41 of the quantum cascade laser device. c 1 / 2 The second coating film 214 is made of a first material and has a thickness p1d1 higher than the refractive index n2 of the first material. c 1 / 2 a third coating film 215 made of a second material having a thickness p1d2 lower than p1d2; and a refractive index n1 of n c 1 / 2 A fourth coating film 216 made of a first material having a thickness p2d1 higher than c 1 / 2 A fifth coating film 217 made of a second material having a thickness p2d2 lower than c 1 / 2 A sixth coating film 218 made of a first material having a thickness p3d1 higher than c 1 / 2 and a seventh coating film 219 made of a second material having a thickness p3d2 lower than p3d1. Note that the reference thickness d3 of the first coating film 213 and the reference thickness d1 of the second coating film 214 are equal.

[0193] The third material constituting the first coating film 213 is Y2O3 and has a refractive index n3 of 1.884115. The first material constituting the second coating film 214, the fourth coating film 216, and the sixth coating film 218 is Ge and has a refractive index n2 of 4.085. The second material constituting the third coating film 215, the fifth coating film 217, and the seventh coating film 219 is YF3 and has a refractive index n1 of 1.450.

[0194] The second coating film 214 and the third coating film 215 constitute a first coating film pair 220, the fourth coating film 216 and the fifth coating film 217 constitute a second coating film pair 221, and the sixth coating film 218 and the seventh coating film 219 constitute a third coating film pair 222.

[0195] The reference film thickness d1 (= d3) and the reference film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (1).

[0196] The overall characteristic matrix of the anti-reflection coating 40p is expressed by the above-mentioned formula (7) using the characteristic matrix of each coating film. Furthermore, the components of the overall characteristic matrix of the anti-reflection coating 40p, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0197] The weighting coefficients are set based on the setting method described below, and the reference film thickness d1 (= d3) and the reference film thickness d2 are calculated so that the real part and the imaginary part of the complex reflectance r in the above-mentioned equation (3) become zero. Then, the anti-reflection film 40p using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0198] As an example of the antireflection coating 40p, the case where the weighting factors are q3=1.00, p1=1.00, p2=1.00, and p3=3.00 will be described below. In this case, the reference film thickness d1 (=d3) is 17.625 nm, and the reference film thickness d2 is 284.204 nm.

[0199] 31, the wavelength dependency of the reflectance in the reflectance band of the antireflection coating 40p is shown by the dashed-dotted line 212. The reflectance band of the antireflection coating 40p where the reflectance is less than 1% is 2.022 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0200] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40p (n×d) sum is 1526.769 nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40p consisting of seven coating films according to the eighth embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.091, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40p is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0201] In the antireflection coating 40p, the first coating film 213 formed in this order from the emission end face 41 side of the quantum cascade laser device is composed of a YO film having a film thickness of 17.625 nm, the second coating film 214 is composed of a Ge film having a film thickness of 17.625 nm, the third coating film 215 is composed of a YF film having a film thickness of 284.204 nm, the fourth coating film 216 is composed of a Ge film having a film thickness of 17.625 nm, the fifth coating film 217 is composed of a YF film having a film thickness of 284.204 nm, the sixth coating film 218 is composed of a Ge film having a film thickness of 52.874 nm, and the seventh coating film 219 is composed of a YF film having a film thickness of 852.612 nm. By applying the antireflection coating 40p consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40p is zero at wavelengths in the vicinity of 9 μm.

[0202] <Effects of the Eighth Embodiment> As described above, in the optical semiconductor device according to the eighth embodiment, the antireflection film has a refractive index of n c 1 / 2 a coating film made of a first material having a refractive index higher than n c 1 / 2 The seven-layer coating film is composed of three coating film pairs, each pair consisting of a coating film made of a second material having a reflectance lower than the first material, and one single coating film made of a third material, Y2O3. The reference thickness d1 of the coating film made of the first material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving the characteristic matrix by setting both the real and imaginary parts of the complex reflectance to zero, thereby achieving the effect of obtaining an optical semiconductor device having an anti-reflection film with a wide reflectance band and thin layers.

[0203] Embodiment 9 In the eighth embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d1 of the coating film made of the first material is described. In the ninth embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d2 of the coating film made of the second material is described.

[0204] FIG. 33 shows the configuration of antireflection coating 40q of a quantum cascade laser device according to the ninth embodiment. As shown in FIG. 33, antireflection coating 40q has a configuration in which first coating film 201 made of a third material having a refractive index n3 and a thickness d3 of antireflection coating 40o of the quantum cascade laser device according to the sixth embodiment is replaced with first coating film 223 made of a third material having a refractive index n3 and a thickness d3. While the thickness d3 of first coating film 201 and the thickness d1 of second coating film 202 of antireflection coating 40o according to the sixth embodiment are equal, antireflection coating 40q according to the ninth embodiment differs in that the reference thickness d3 of first coating film 223 is equal to the reference thickness d2 of third coating film 203. The third material constituting first coating film 223 is YO, and the refractive index n3 is 1.884115.

[0205] The reference film thickness d1 and the reference film thickness d2 (= d3) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned equation (5).

[0206] The overall characteristic matrix of the anti-reflection coating 40q is expressed by the above-mentioned formula (6) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 When the above equation is used, the complex reflectance r is expressed by the above equation (3) as in the eighth embodiment.

[0207] As in the eighth embodiment, when the real and imaginary parts of the complex reflectance r are set to zero, the film thickness d1 is 22.501 nm and the film thickness d2 is 334.422 nm.

[0208] In antireflection coating 40q, first coating film 223 is formed in this order from the side of emission facet 41 of the quantum cascade laser device, and is composed of a Y2O3 film having a film thickness of 334.422 nm, second coating film 202 is formed of a Ge film having a film thickness of 22.501 nm, third coating film 203 is formed of a YF3 film having a film thickness of 334.422 nm, fourth coating film 204 is formed of a Ge film having a film thickness of 22.501 nm, fifth coating film 205 is formed of a YF3 film having a film thickness of 334.422 nm, sixth coating film 206 is formed of a Ge film having a film thickness of 22.501 nm, and seventh coating film 207 is formed of a YF3 film having a film thickness of 334.422 nm. By applying antireflection coating 40q consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40q is zero at wavelengths in the vicinity of 9 μm.

[0209] Fig. 34 is a graph showing the wavelength dependence of the reflectance of antireflection coating 40q. In Fig. 34, a solid line 224 represents the wavelength dependence of the reflectance of antireflection coating 40q consisting of seven coating layers according to embodiment 9, and a dashed-dotted line 225 represents the wavelength dependence of the reflectance of the antireflection coating consisting of seven coating layers according to embodiment 9 when a single coating layer made of a third material and weighting coefficients for each coating layer pair are taken into account.

[0210] Assuming that the desired reflectance band is a band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40q made of seven coating layers according to the ninth embodiment is 1.977 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40q is sum Therefore, the sum (n×d) of the products of the refractive index and the film thickness of each coating film of the antireflection coating 40i made of seven coating films according to the ninth embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.049, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40q has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2It can be seen that the anti-reflection film 40q is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0211] Next, further widening the reflectance band of the antireflection coating 40q will be described below. As in the eighth embodiment, the thickness of the single coating film made of the third material and the weighting coefficients of each coating film pair are set using weighting coefficients q3, p1, p2, and p3, at least one of which is a positive real number other than 1.

[0212] FIG. 35 shows the configuration of antireflection coating 40r of the quantum cascade laser device according to the ninth embodiment. As shown in FIG. 35, antireflection coating 40r has a configuration in which first coating film 213 made of a third material having a refractive index n3 and a thickness q3d3 of antireflection coating 40p of the quantum cascade laser device according to the eighth embodiment is replaced with first coating film 226 made of a third material having a refractive index n3 and a thickness q3d3. While the thickness d3 of first coating film 213 and the thickness d1 of second coating film 214 of antireflection coating 40p according to the eighth embodiment are equal, antireflection coating 40r according to the ninth embodiment differs in that the reference thickness d3 of first coating film 226 is equal to the reference thickness d2 of third coating film 215. The third material constituting first coating film 226 is YO, and the refractive index n3 is 1.884115.

[0213] The reference film thickness d1 and the reference film thickness d2 (= d3) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned equation (5).

[0214] The overall characteristic matrix of the anti-reflection coating 40r is expressed by the above-mentioned formula (7) using the characteristic matrix of each coating film. Furthermore, the components of the overall characteristic matrix of the anti-reflection coating 40r, m 11 , m 12 , m 21 , m 22When the above equation is used, the complex reflectance r is expressed by the above equation (3) as in the eighth embodiment.

[0215] The weighting coefficients are set based on the setting method described below, and the reference film thicknesses d1 and d2 (= d3) at which the real and imaginary parts of the complex reflectance r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40r using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0216] As an example of the anti-reflection coating 40r, the case where the weighting factors are q3=2.00, p1=0.50, p2=1.00, and p3=6.00 will be described below. In this case, the reference film thickness d1 is 8.218 nm, and the reference film thickness d2 (=d3) is 162.225 nm.

[0217] 34, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40r is shown by the dashed-dotted line 225. The reflectance band of the anti-reflection coating 40r where the reflectance is less than 1% is 2.190 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0218] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40r (n×d) sum is 1602.766nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40r made of seven coating films according to the ninth embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.168, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40r has a refractive index of nc 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0219] In the antireflection coating 40r, the first coating film 223 formed in this order from the side of the emission end face 41 of the quantum cascade laser device is composed of a Y2O3 film having a film thickness of 324.449 nm, the second coating film 202 is composed of a Ge film having a film thickness of 4.109 nm, the third coating film 203 is composed of a YF3 film having a film thickness of 81.112 nm, the fourth coating film 204 is composed of a Ge film having a film thickness of 8.218 nm, the fifth coating film 205 is composed of a YF3 film having a film thickness of 162.225 nm, the sixth coating film 206 is composed of a Ge film having a film thickness of 49.305 nm, and the seventh coating film 207 is composed of a YF3 film having a film thickness of 973.348 nm. By applying the antireflection coating 40r consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40r is zero at wavelengths in the vicinity of 9 μm.

[0220] <Effects of the 9th embodiment> As described above, in the optical semiconductor device according to the ninth embodiment, the antireflection film has a refractive index of n c 1 / 2 a coating film made of a first material having a refractive index higher than n c 1 / 2 The seven-layer coating film is composed of three coating film pairs, each pair consisting of a coating film made of a second material having a reflectance lower than the first coating film, and one single coating film made of a third material, Y2O3. The reference thickness d2 of the coating film made of the second material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving using a characteristic matrix with both the real and imaginary parts of the complex reflectance set to zero, thereby achieving the effect of obtaining an optical semiconductor device having an anti-reflection film with a wide reflectance band and thin layers.

[0221] Embodiment 10 In the tenth embodiment, Y2O3 is used as the third material, and three pairs of coating films each consisting of a coating film made of a first material and a coating film made of a second material are provided, and a coating film having a refractive index of n c 1 / 2 The second material has a refractive index lower than n c 1 / 2 In this example, an antireflection coating is described in which a material having a higher refractive index than that of the first material is used, and the thickness d3 of the coating film made of the third material is the same as the thickness d1 of the coating film made of the first material.

[0222] 36 shows the configuration of an antireflection film 40s of a quantum cascade laser device according to embodiment 10. As shown in FIG. 36, the antireflection film 40s has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 201 made of a third material having a refractive index n3 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 201 made of a third material having a refractive index n1 and a film thickness d2 is provided on the light-emitting end surface 41 of the quantum cas c 1 / 2 The second coating film 231 is made of a first material and has a thickness d1 that is smaller than the refractive index n2 of the first material. c 1 / 2 a third coating film 232 made of a second material having a thickness d2 higher than c 1 / 2 A fourth coating film 233 made of a first material and having a thickness d1 that is smaller than c 1 / 2 a fifth coating film 234 made of a second material having a thickness d2 higher than c 1 / 2 A sixth coating film 235 made of a first material having a thickness d1 lower than c 1 / 2 and a seventh coating film 236 made of a second material having a thickness d2 that is higher than the thickness d1 of the first coating film 201. The thickness d3 of the first coating film 201 and the thickness d1 of the second coating film 231 are equal.

[0223] The third material constituting the first coating film 201 is Y2O3 and has a refractive index n3 of 1.884115. The first material constituting the second coating film 231, the fourth coating film 233, and the sixth coating film 235 is YF3 and has a refractive index n2 of 1.450. The second material constituting the third coating film 232, the fifth coating film 234, and the seventh coating film 236 is Ge and has a refractive index n1 of 4.085.

[0224] The second coating film 231 and the third coating film 232 constitute a first coating film pair 237, the fourth coating film 233 and the fifth coating film 234 constitute a second coating film pair 238, and the sixth coating film 235 and the seventh coating film 236 constitute a third coating film pair 239.

[0225] The reference film thickness d1 (= d3) and the reference film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (1).

[0226] The overall characteristic matrix of the anti-reflection coating 40s is expressed by the above-mentioned formula (6) using the characteristic matrix of each coating film. Furthermore, the components of the overall characteristic matrix of the anti-reflection coating 40s, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0227] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r described above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 270.371 nm and the film thickness d2 becomes 25.020 nm.

[0228] In the antireflection coating 40s, the first coating film 201, which is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, is made of a YO film having a film thickness of 270.371 nm, the second coating film 231 is made of a YF film having a film thickness of 270.371 nm, the third coating film 232 is made of a Ge film having a film thickness of 25.020 nm, the fourth coating film 233 is made of a YF film having a film thickness of 270.371 nm, the fifth coating film 234 is made of a Ge film having a film thickness of 25.020 nm, the sixth coating film 235 is made of a YF film having a film thickness of 270.371 nm, and the seventh coating film 236 is made of a Ge film having a film thickness of 25.020 nm. By applying the antireflection coating 40s made of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40s is zero at wavelengths in the vicinity of 9 μm.

[0229] Fig. 37 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40s. In Fig. 37, a solid line 240 represents the wavelength dependence of the reflectance of the antireflection coating 40s made of the seven-layer coating film according to embodiment 10, and a dashed-dotted line 241 represents the wavelength dependence of the reflectance of the antireflection coating made of the seven-layer coating film according to embodiment 10 when a single coating film made of a third material (described later) and weighting coefficients for each coating film pair are taken into consideration.

[0230] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40s made of seven coating layers according to the tenth embodiment is 1.859 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40s is sum Therefore, the sum (n×d) of the products of the refractive index and film thickness of each coating film of the antireflection coating 40s made of seven coating films according to the tenth embodiment is 1156.543 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 0.885, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40k is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2It can be seen that the anti-reflection coating 40s is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0231] Next, the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The following describes an antireflection coating having a reflectance band wider than that of a single coating film of , where q3, p1, p2, and p3, at least one of which is a positive real number other than 1, are used to set the thickness of the single coating film made of a third material and the weighting coefficients for each coating film pair.

[0232] FIG. 38 shows the configuration of the antireflection film 40t of the quantum cascade laser device according to the tenth embodiment. The antireflection film 40t has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 As shown in FIG. 38, the anti-reflection coating 40t has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 251 made of a third material having a refractive index n3 and a film thickness q3d3 and a second coating film 252 made of a third material having a refractive index n1 and a film thickness q3d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device. c 1 / 2 The second coating film 252 is made of a first material and has a thickness p1d1 that is lower than the refractive index n2 of the first material. c 1 / 2 a third coating film 253 made of a second material having a thickness p1d2 higher than p1d2; and a refractive index n1 of n c 1 / 2 A fourth coating film 254 made of a first material having a thickness p2d1 lower than c 1 / 2 A fifth coating film 255 made of a second material having a thickness p2d2 higher than c1 / 2 A sixth coating film 256 made of a first material having a thickness p3d1 lower than c 1 / 2 and a seventh coating film 257 made of a second material having a thickness p3d2 higher than the first coating film 251. The reference thickness d3 of the first coating film 251 and the reference thickness d1 of the second coating film 252 are equal to each other.

[0233] The third material constituting the first coating film 251 is Y2O3 and has a refractive index n3 of 1.884115. The first material constituting the second coating film 252, the fourth coating film 254, and the sixth coating film 256 is YF3 and has a refractive index n1 of 1.450. The second material constituting the third coating film 253, the fifth coating film 255, and the seventh coating film 257 is Ge and has a refractive index n2 of 4.085. The second coating film 252 and the third coating film 253 constitute a first coating film pair 258, the fourth coating film 254 and the fifth coating film 255 constitute a second coating film pair 259, and the sixth coating film 256 and the seventh coating film 257 constitute a third coating film pair 260.

[0234] The reference film thickness d1 (= d3) and the reference film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (1).

[0235] The overall characteristic matrix of the anti-reflection coating 40t is expressed by the above-mentioned formula (7) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0236] The weighting coefficients are set based on the setting method described below, and the reference film thickness d1 (= d3) and the reference film thickness d2 at which the real part and the imaginary part of the complex reflectance r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40t using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0237] As an example of the anti-reflection coating 40t, the case where the weighting factors are q3=5.00, p1=1.00, p2=1.00, and p3=1.00 will be described below. In this case, the reference film thickness d1 (=d3) is 180.297 nm, and the reference film thickness d2 is 2.578 nm.

[0238] 37, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40t is shown by a dashed line 241. The reflectance band of the anti-reflection coating 40t where the reflectance is less than 1% is 2.037 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0239] In addition, the sum (n×d) of the products of the refractive index and film thickness of each coating film of the anti-reflection film 40t sum is 1450.110nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40t made of seven coating films according to the tenth embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.118, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40t is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0240] In the antireflection coating 40t, a first coating film 251 formed in this order from the side of the emission end face 41 of the quantum cascade laser device is composed of a Y2O3 film having a film thickness of 901.486 nm, a second coating film 252 is composed of a YF3 film having a film thickness of 180.297 nm, a third coating film 253 is composed of a Ge film having a film thickness of 2.578 nm, a fourth coating film 254 is composed of a YF3 film having a film thickness of 180.297 nm, a fifth coating film 255 is composed of a Ge film having a film thickness of 2.578 nm, a sixth coating film 256 is composed of a YF3 film having a film thickness of 180.297 nm, and a seventh coating film 257 is composed of a Ge film having a film thickness of 2.578 nm. By applying the antireflection coating 40t consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40t is zero at wavelengths in the vicinity of 9 μm.

[0241] <Advantages of the Tenth Embodiment> As described above, in the optical semiconductor device according to the tenth embodiment, the antireflection film has a refractive index of n c 1 / 2 a coating film made of a first material having a refractive index lower than n c 1 / 2 The seven-layer coating film is composed of three coating film pairs, each pair consisting of a coating film made of a second material having a reflectance higher than that of the first material, and one single coating film made of a third material, Y2O3. The reference thickness d1 of the coating film made of the first material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving the characteristic matrix by setting both the real and imaginary parts of the complex reflectance to zero, thereby achieving the effect of obtaining an optical semiconductor device having an anti-reflection film with a wide reflectance band and thin layers.

[0242] Embodiment 11 In the tenth embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d1 of the coating film made of the first material is described. In the eleventh embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d2 of the coating film made of the second material is described.

[0243] FIG. 39 shows the configuration of antireflection coating 40u of a quantum cascade laser device according to the eleventh embodiment. As shown in FIG. 39, antireflection coating 40u has a configuration in which first coating film 201 made of a third material having a refractive index n3 and a thickness q3d3 of antireflection coating 40s of the quantum cascade laser device according to the tenth embodiment is replaced with a first coating film 271 made of a third material having a refractive index n3 and a thickness q3d3. The antireflection coating 40s according to the tenth embodiment differs in that the thickness d3 of first coating film 201 and the thickness d1 of second coating film 231 are equal, whereas the antireflection coating 40u according to the eleventh embodiment differs in that the reference thickness d3 of first coating film 271 is equal to the reference thickness d2 of third coating film 232. The third material constituting first coating film 271 is YO, and the refractive index n3 is 1.884115.

[0244] The film thickness d1 and film thickness d2 (= d3) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned formula (5).

[0245] The overall characteristic matrix of the anti-reflection coating 40u is expressed by the above-mentioned formula (6) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 When the above equation is used, the complex reflectance r is expressed by the above equation (3) as in the tenth embodiment.

[0246] As in the tenth embodiment, when the real and imaginary parts of the complex reflectance r are set to zero, the film thickness d1 is 377.553 nm and the film thickness d2 is 29.341 nm.

[0247] In the antireflection coating 40u, the first coating film 271 formed in this order from the emission end face 41 side of the quantum cascade laser device is made of a Y2O3 film having a film thickness of 29.341 nm, the second coating film 231 is made of a YF3 film having a film thickness of 337.553 nm, the third coating film 232 is made of a Ge film having a film thickness of 29.341 nm, the fourth coating film 233 is made of a YF3 film having a film thickness of 337.553 nm, the fifth coating film 234 is made of a Ge film having a film thickness of 29.341 nm, the sixth coating film 235 is made of a YF3 film having a film thickness of 337.553 nm, and the seventh coating film 236 is made of a Ge film having a film thickness of 29.341 nm. By applying the antireflection coating 40u consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40u is zero at wavelengths in the vicinity of 9 μm.

[0248] Fig. 40 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40u. In Fig. 40, a solid line 272 represents the wavelength dependence of the reflectance of the antireflection coating 40u consisting of the seven-layer coating film according to embodiment 11, and a dashed-dotted line 273 represents the wavelength dependence of the reflectance of the antireflection coating consisting of the seven-layer coating film according to embodiment 11 when a single coating film made of a third material and weighting coefficients for each coating film pair are taken into consideration.

[0249] Assuming that the desired reflectance band is a band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40u made of seven coating layers according to the eleventh embodiment is 1.861 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40u is sum Therefore, the sum (n×d) of the products of the refractive index and the film thickness of each coating film of the antireflection coating 40u made of seven coating films according to the eleventh embodiment is 1130.021 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 0.837, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40u has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2It can be seen that the anti-reflection film 40u is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0250] Next, the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The following describes an antireflection coating having a reflectance band wider than that of a single-layer coating film of 1. As in the tenth embodiment, the reference film thickness of a single coating film made of a third material and the weighting coefficients for each coating film pair are set using weighting coefficients q3, p1, p2, and p3, at least one of which is a positive real number other than 1.

[0251] FIG. 41 shows the configuration of antireflection coating 40v of the quantum cascade laser device according to the eleventh embodiment. As shown in FIG. 41, antireflection coating 40v has a configuration in which first coating film 251 made of a third material having a refractive index n3 and a thickness q3d3 of antireflection coating 40t of the quantum cascade laser device according to the tenth embodiment is replaced with a first coating film 274 made of a third material having a refractive index n3 and a thickness q3d3. While the thickness d3 of first coating film 251 and the thickness d1 of second coating film 252 of antireflection coating 40t according to the tenth embodiment are equal, antireflection coating 40v according to the eleventh embodiment differs in that the reference thickness d3 of first coating film 274 is equal to the reference thickness d2 of third coating film 253. The third material constituting first coating film 274 is YO, and the refractive index n3 is 1.884115.

[0252] The reference film thickness d1 and the reference film thickness d2 (= d3) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, and the coating film made of the third material are each expressed by the above-mentioned equation (5).

[0253] The overall characteristic matrix of the anti-reflection coating 40v is expressed by the above-mentioned formula (7) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 When the above equation is used, the complex reflectance r is expressed by the above equation (3) as in the fourth embodiment.

[0254] The weighting coefficients are set based on the setting method described below, and the reference film thicknesses d1 and d2 (= d3) at which the real and imaginary parts of the complex reflectivity r in the above-mentioned equation (3) are both zero are calculated. Then, the anti-reflection film 40v using the film thicknesses of the coating films determined based on each reference film thickness and each weighting coefficient is coated on the emission end surface 41 of the quantum cascade laser device.

[0255] As an example of the anti-reflection coating 40v, the case where the weighting factors are q3=100.00, p1=1.00, p2=1.00, and p3=1.00 will be described below. In this case, the reference film thickness d1 is 172.82 nm, and the reference film thickness d2 (=d3) is 7.995 nm.

[0256] 40, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40v is shown by the dashed-dotted line 273. The reflectance band of the anti-reflection coating 40v where the reflectance is less than 1% is 1.997 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0257] In addition, the sum of the products of the refractive index and film thickness of each coating film of the anti-reflection film 40v (n × d) sum is 1341.996 nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40v consisting of seven coating films according to the eleventh embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.047, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40v is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0258] In the antireflection coating 40v, the first coating film 274, which is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, is composed of a Y2O3 film with a film thickness of 799.532 nm, the second coating film 252 is composed of a YF3 film with a film thickness of 172.826 nm, the third coating film 253 is composed of a Ge film with a film thickness of 7.995 nm, the fourth coating film 254 is composed of a YF3 film with a film thickness of 172.826 nm, the fifth coating film 255 is composed of a Ge film with a film thickness of 7.995 nm, the sixth coating film 256 is composed of a YF3 film with a film thickness of 172.826 nm, and the seventh coating film 257 is composed of a Ge film with a film thickness of 7.995 nm. By applying the antireflection coating 40v consisting of these seven coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40v is zero at wavelengths around 9 μm.

[0259] <Effects of the Eleventh Embodiment> As described above, in the optical semiconductor device according to the eleventh embodiment, the antireflection film has a refractive index of n c 1 / 2 a coating film made of a first material having a refractive index lower than n c 1 / 2The seven-layer coating film is composed of three coating film pairs, each pair consisting of a coating film made of a second material having a reflectance higher than that of the first material, and one single coating film made of a third material, Y2O3. The reference thickness d2 of the coating film made of the second material is set equal to the reference thickness d3 of the single coating film, and the thickness of each coating film is determined by solving the characteristic matrix by setting both the real and imaginary parts of the complex reflectance to zero, thereby achieving the effect of obtaining an optical semiconductor device having an anti-reflection film with a wide reflectance band and thin layers.

[0260] Embodiment 12 In the twelfth embodiment, a fourth material is used in addition to a third material, and an antireflection coating is described that includes three pairs of coating films, each of which is made up of a coating film made of a first material and a coating film made of a second material. When a fourth material is used, there are four methods for matching the thicknesses of the coating films made of the third material and the fourth material with the thicknesses of the coating films made of the first material and the second material. In the twelfth embodiment, an example is described in which the thicknesses of the coating films made of the third material and the fourth material are both made the same as the thickness of the coating film made of the first material.

[0261] 42 shows the configuration of the antireflection film 40w of the quantum cascade laser device according to the twelfth embodiment. The antireflection film 40w has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 As shown in FIG. 42, the anti-reflection coating 40w has an effective refractive index of n c , that is, 3.21216, is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 281 made of a third material having a refractive index n3 and a film thickness d3 is provided on the light-emitting end surface 41 of the quantum cascade laser device, and a first coating film 281 made of a third material having a refractive index n1 and a film thickness d2 is provided on the light-emitting end surface 41 of the quantum cas c 1 / 2 a second coating film 282 made of a first material having a thickness d1 higher than c 1 / 2 a third coating film 283 made of a second material having a thickness d2 lower than c1 / 2 A fourth coating film 284 made of a first material having a thickness d1 higher than c 1 / 2 A fifth coating film 285 made of a second material having a thickness d2 lower than c 1 / 2 A sixth coating film 286 made of a first material having a thickness d1 higher than c 1 / 2 The seventh coating film 287 is made of a second material and has a thickness d2, and the eighth coating film 288 is made of a fourth material and has a refractive index n4 and a thickness d4. The thickness d3 of the first coating film 281 is equal to the thickness d1 of the second coating film 282, and the thickness d4 of the eighth coating film 288 is equal to the thickness d1 of the second coating film 282.

[0262] The third material constituting the first coating film 281 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 282, the fourth coating film 284, and the sixth coating film 286 is Ge, and the refractive index n1 is 4.085. The second material constituting the third coating film 283, the fifth coating film 285, and the seventh coating film 287 is YF3, and the refractive index n2 is 1.450. The fourth material constituting the eighth coating film 288 is CeO2, and the refractive index n4 is 1.650. Note that the refractive index of CeO2 was determined by referring to Patent Document 3.

[0263] The second coating film 282 and the third coating film 283 form a first coating film pair 289, the fourth coating film 284 and the fifth coating film 285 form a second coating film pair 290, and the sixth coating film 286 and the seventh coating film 287 form a third coating film pair 291.

[0264] The film thickness d1 (= d3 = d4) and the film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, the coating film made of the third material, and the coating film made of the fourth material are expressed by the following equation (8).

[0265]

number

[0266]

number

[0267] Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0268] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r described above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 35.512 nm and the film thickness d2 becomes 408.067 nm.

[0269] In the antireflection coating 40w, a first coating film 281 formed in this order from the side of the emission end face 41 of the quantum cascade laser device is composed of a ZnS film having a film thickness of 35.512 nm, a second coating film 282 is composed of a Ge film having a film thickness of 35.512 nm, a third coating film 283 is composed of a YF3 film having a film thickness of 408.067 nm, a fourth coating film 284 is composed of a Ge film having a film thickness of 35.512 nm, a fifth coating film 285 is composed of a YF3 film having a film thickness of 408.067 nm, a sixth coating film 286 is composed of a Ge film having a film thickness of 35.512 nm, a seventh coating film 287 is composed of a YF3 film having a film thickness of 408.067 nm, and an eighth coating film 288 is composed of a CeO2 film having a film thickness of 35.512 nm. By applying the antireflection coating 40w consisting of these eight coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40w is zero at wavelengths around 9 μm.

[0270] Fig. 43 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40w. In Fig. 43, a solid line 292 represents the wavelength dependence of the reflectance of the antireflection coating 40w consisting of eight coating layers according to the twelfth embodiment, and a dashed-dotted line 293 represents the wavelength dependence of the reflectance of the antireflection coating consisting of eight coating layers according to the twelfth embodiment when the weighting coefficients of the single coating layers and the respective coating layer pairs made of the third and fourth materials described below are taken into consideration.

[0271] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40w made of eight coating layers according to the twelfth embodiment is 1.890 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40w is sum Therefore, the sum (n×d) of the products of the refractive index and the film thickness of each coating film of the antireflection coating 40w made of eight coating films according to the twelfth embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.044, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40w is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that the anti-reflection film 40w is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0272] Next, the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The following describes an antireflection coating having a reflectance band wider than that of a single coating film of , where q3, p1, p2, p3, and q4, at least one of which is a positive real number other than 1, are used to set the thicknesses of the single coating films made of the third and fourth materials and the weighting coefficients for each coating film pair.

[0273] 44 shows the configuration of an antireflection film 40x of a quantum cascade laser device according to embodiment 12. The antireflection film 40x has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 As shown in FIG. 44, the anti-reflection coating 40x has an effective refractive index of n c , that is, 3.21216, on the emission end surface 41 of the quantum cascade laser device, a first coating film 294 made of a third material having a refractive index n3 and a film thickness q3d3 and a second coating film 294 made of a third material having a refractive index n1 and a film thickness q3d3 are provided. c 1 / 2 A second coating film 295 made of a first material having a thickness p1d1 higher than c 1 / 2 a third coating film 296 made of a second material having a thickness p1d2 lower than p1d2; and a refractive index n1 of n c 1 / 2 A fourth coating film 297 made of a first material having a thickness p2d1 higher than c 1 / 2 A fifth coating film 298 made of a second material having a thickness p2d2 lower than c 1 / 2 A sixth coating film 299 made of a first material having a thickness p3d1 higher than c 1 / 2 The seventh coating film 300 is made of a second material with a refractive index of n4 and a thickness of q4d2, and an eighth coating film 301 is made of a fourth material with a refractive index of n4 and a thickness of q4d4. The reference thickness d3 of the first coating film 294 is equal to the reference thickness d1 of the second coating film 295, and the reference thickness d4 of the eighth coating film 301 is equal to the reference thickness d1 of the second coating film 295.

[0274] The third material constituting the first coating film 294 is ZnS, and the refractive index n3 is 2.270. The first material constituting the second coating film 295, the fourth coating film 297, and the sixth coating film 299 is Ge, and the refractive index n1 is 4.085. The second material constituting the third coating film 296, the fifth coating film 298, and the seventh coating film 300 is YF3, and the refractive index n2 is 1.450. The fourth material constituting the eighth coating film 301 is CeO2, and the refractive index n4 is 1.650.

[0275] The second coating film 295 and the third coating film 296 constitute a first coating film pair 302, the fourth coating film 297 and the fifth coating film 298 constitute a second coating film pair 303, and the sixth coating film 299 and the seventh coating film 300 constitute a third coating film pair 304.

[0276] The reference film thickness d1 (= d3 = d4) and the reference film thickness d2 are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, the coating film made of the third material, and the coating film made of the fourth material are expressed by the above-mentioned equation (8).

[0277] The overall characteristic matrix of the anti-reflection coating 40x is expressed by the following formula (10) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0278]

number

[0279] The weighting coefficients are set based on the setting method described below, and the reference film thicknesses d1 (= d3 = d4) and d2 at which the real and imaginary parts of the complex reflectivity r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40x using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0280] As an example of the anti-reflection coating 40l, the case where the weighting factors are q3=1.00, p1=1.00, p2=1.00, p3=5.00, and q4=1.00 will be described below. In this case, the reference film thickness d1 (=d3=d4) is 13.829 nm, and the reference film thickness d2 is 218.373 nm.

[0281] 43, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40x is shown by the dashed-dotted line 293. The reflectance band of the anti-reflection coating 40x where the reflectance is less than 1% is 2.318 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0282] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40x (n×d) sum is 1653.063nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40x made of eight coating films according to the twelfth embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.185, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40x is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0283] In the antireflection coating 40x, a first coating film 294 is formed in this order from the side of the emission end face 41 of the quantum cascade laser device, and is composed of a ZnS film having a film thickness of 13.829 nm, a second coating film 295 is formed of a Ge film having a film thickness of 13.829 nm, a third coating film 296 is formed of a YF3 film having a film thickness of 218.373 nm, a fourth coating film 297 is formed of a Ge film having a film thickness of 13.829 nm, a fifth coating film 298 is formed of a YF3 film having a film thickness of 218.373 nm, a sixth coating film 299 is formed of a Ge film having a film thickness of 69.143 nm, a seventh coating film 300 is formed of a YF3 film having a film thickness of 1091.860 nm, and an eighth coating film 301 is formed of a CeO2 film having a film thickness of 13.829 nm. By applying the antireflection coating 40x composed of these eight coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40x is zero at wavelengths around 9 μm.

[0284] <Effects of the twelfth embodiment> As described above, according to the optical semiconductor device of the twelfth embodiment, the antireflection film is composed of an eight-layer coating film consisting of three pairs of coating films, each pair being a coating film made of a first material and a coating film made of a second material, and two single coating films made of a third material and a fourth material, respectively, and the reference thickness d1 of the coating film made of the first material is set equal to both the reference thickness d3 of the single coating film made of the third material and the reference thickness d4 of the single coating film made of the fourth material, and the thickness of each coating film is determined by solving using a characteristic matrix with both the real part and the imaginary part of the complex reflectance set to zero, thereby achieving the effect of obtaining an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0285] Embodiment 13 In the twelfth embodiment, the case where the thickness d3 of the coating film made of the third material and the thickness d4 of the coating film made of the fourth material are the same as the thickness d1 of the coating film made of the first material is described. In the thirteenth embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d1 of the coating film made of the first material and the thickness d4 of the coating film made of the fourth material is the same as the thickness d2 of the coating film made of the second material is described.

[0286] FIG. 45 shows the configuration of antireflection coating 40y of a quantum cascade laser device according to the thirteenth embodiment. As shown in FIG. 45, antireflection coating 40y has a configuration in which eighth coating film 288 made of a fourth material having a refractive index n4 and a thickness d4 of antireflection coating 40w of the quantum cascade laser device according to the thirteenth embodiment is replaced with eighth coating film 311 made of a fourth material having a refractive index n4 and a thickness d4. While the thickness d4 of eighth coating film 288 of antireflection coating 40w according to the thirteenth embodiment is equal to the thickness d1 of second coating film 282, antireflection coating 40y according to the thirteenth embodiment differs in that the thickness d4 of eighth coating film 311 is equal to the thickness d2 of third coating film 283. The fourth material constituting eighth coating film 311 is CeO2, and the refractive index n4 is 1.650.

[0287] The film thickness d1 (= d3) and the film thickness d2 (= d4) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, the coating film made of the third material, and the coating film made of the fourth material are expressed by the following equation (11).

[0288]

number

[0289] The overall characteristic matrix of the anti-reflection coating 40y is expressed by the above-mentioned formula (9) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0290] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r described above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 33.695 nm and the film thickness d2 becomes 322.724 nm.

[0291] In the antireflection coating 40y, a first coating film 281 formed in this order from the emission end face 41 side of the quantum cascade laser device is composed of a ZnS film having a film thickness of 33.695 nm, a second coating film 282 is composed of a Ge film having a film thickness of 33.695 nm, a third coating film 283 is composed of a YF3 film having a film thickness of 322.724 nm, a fourth coating film 284 is composed of a Ge film having a film thickness of 33.695 nm, a fifth coating film 285 is composed of a YF3 film having a film thickness of 322.724 nm, a sixth coating film 286 is composed of a Ge film having a film thickness of 33.695 nm, a seventh coating film 287 is composed of a YF3 film having a film thickness of 322.724 nm, and an eighth coating film 311 is composed of a CeO2 film having a film thickness of 322.724 nm. By applying the antireflection coating 40y consisting of these eight coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40y is zero at wavelengths in the vicinity of 9 μm.

[0292] Fig. 46 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40y. In Fig. 46, a solid line 312 represents the wavelength dependence of the reflectance of the antireflection coating 40y consisting of eight coating layers according to the thirteenth embodiment, and a dashed-dotted line 313 represents the wavelength dependence of the reflectance of the antireflection coating consisting of eight coating layers according to the thirteenth embodiment when the weighting coefficients of the single coating layers and the respective coating layer pairs made of the third and fourth materials described later are taken into consideration.

[0293] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40y made of eight coating layers according to the thirteenth embodiment is 1.981 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40y is sum Therefore, the sum (n×d) of the products of the refractive index and the film thickness of each coating film of the antireflection coating 40y made of eight coating films according to the thirteenth embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.078, which cannot be expressed as a positive odd number. From this result, it can be seen that the refractive index of the anti-reflection film 40y is n c 1 / 2 and the film thickness is λd / 4 / n c 1 / 2 It can be seen that the anti-reflection film 40y is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0294] Next, we will discuss an anti-reflection coating with a wider reflectance band. In this case, the reference film thicknesses of the single coating films made of the third and fourth materials and the weighting coefficients for each coating pair are set using weighting coefficients q3, p1, p2, p3, and q4, at least one of which is a positive real number other than 1.

[0295] 47 shows the configuration of antireflection coating 40z of a quantum cascade laser device according to the thirteenth embodiment. As shown in FIG. 47, antireflection coating 40z has a configuration in which eighth coating film 301 made of a fourth material having a refractive index of n4 and a thickness of d4 of antireflection coating 40x of the quantum cascade laser device according to the thirteenth embodiment is replaced with eighth coating film 314 made of a fourth material having a refractive index of n4 and a thickness of d4. While antireflection coating 40x according to the thirteenth embodiment has a reference thickness d4 of thickness q4d4 of eighth coating film 301 equal to the reference thickness d1 of thickness p1d1 of second coating film 295, antireflection coating 40z according to the thirteenth embodiment differs in that a reference thickness d4 of thickness q4d4 of eighth coating film 314 equals a reference thickness d2 of thickness p1d2 of third coating film 296. The fourth material constituting eighth coating film 314 is CeO2, and the refractive index n4 is 1.650.

[0296] The reference film thickness d1 (= d3) and the reference film thickness d2 (= d4) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, the coating film made of the third material, and the coating film made of the fourth material are expressed by the above-mentioned equation (11).

[0297] The overall characteristic matrix of the anti-reflection coating 40z is expressed by the above-mentioned formula (10) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0298] The weighting coefficients are set based on the setting method described below, and the reference film thicknesses d1 (= d3) and d2 (= d4) at which the real and imaginary parts of the complex reflectivity r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40z using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0299] As an example of the antireflection coating 40z, the case where the weighting factors are q3=1.50, p1=1.00, p2=1.00, p3=4.00, and q4=1.00 will be described below. In this case, the reference film thickness d1 (=d3) is 16.734 nm, and the reference film thickness d2 (=d4) is 207.793 nm.

[0300] 46, the wavelength dependency of the reflectance in the reflectance band of the antireflection coating 40z is shown by a dashed line 313. The reflectance band of the antireflection coating 40z where the reflectance is less than 1% is 2.315 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0301] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40z (n×d) sum is 1580.056 nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40z made of eight coating films according to the thirteenth embodiment is smaller than the thickness of the single-layer coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.163, which cannot be expressed as a positive odd number. From this result, the refractive index of the anti-reflection film 40z is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0302] In the antireflection coating 40z, the first coating film 294 is formed in this order from the emission end face 41 side of the quantum cascade laser device, and is composed of a ZnS film with a film thickness of 25.101 nm, the second coating film 295 is formed of a Ge film with a film thickness of 16.734 nm, the third coating film 296 is formed of a YF3 film with a film thickness of 207.793 nm, the fourth coating film 297 is formed of a Ge film with a film thickness of 16.734 nm, the fifth coating film 298 is formed of a YF3 film with a film thickness of 207.793 nm, the sixth coating film 299 is formed of a Ge film with a film thickness of 66.937 nm, the seventh coating film 300 is formed of a YF3 film with a film thickness of 831.171 nm, and the eighth coating film 314 is formed of a CeO2 film with a film thickness of 207.793 nm. By applying the antireflection coating 40z composed of these eight coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40z is zero at wavelengths in the vicinity of 9 μm.

[0303] <Effects of the Thirteenth Embodiment> As described above, according to the optical semiconductor device of the thirteenth embodiment, the antireflection film is composed of an eight-layer coating film consisting of three pairs of coating films, each pair being a coating film made of a first material and a coating film made of a second material, and two single coating films made of a third material and a fourth material, respectively. The reference thickness d1 of the coating film made of the first material is equal to the reference thickness d3 of the single coating film made of the third material, and the reference thickness d2 of the coating film made of the second material is equal to the reference thickness d4 of the single coating film made of the fourth material. The thickness of each coating film is determined by solving using a characteristic matrix, assuming that both the real part and the imaginary part of the complex reflectance are zero. This produces the effect of providing an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0304] Embodiment 14 In the twelfth embodiment, the case where the thickness d3 of the coating film made of the third material and the thickness d4 of the coating film made of the fourth material are the same as the thickness d1 of the coating film made of the first material is described. In the fourteenth embodiment, the case where the thickness d3 of the coating film made of the third material is the same as the thickness d2 of the coating film made of the second material, and the thickness d4 of the coating film made of the fourth material is the same as the thickness d1 of the coating film made of the first material is described.

[0305] 48 shows the configuration of antireflection coating 40aa of a quantum cascade laser device according to embodiment 14. As shown in FIG. 48, antireflection coating 40aa has a configuration in which first coating film 281 made of a third material having a refractive index of n3 and a thickness of d3 of antireflection coating 40w of the quantum cascade laser device according to embodiment 12 is replaced with first coating film 321 made of a third material having a refractive index of n3 and a thickness of d3. While thickness d3 of first coating film 281 and thickness d4 of eighth coating film 288 of antireflection coating 40w according to embodiment 12 are equal to thickness d1 of second coating film 282, antireflection coating 40aa according to embodiment 14 differs in that thickness d3 of first coating film 321 is equal to thickness d2 of third coating film 283 and thickness d4 of eighth coating film 288 is equal to thickness d1 of second coating film 282. The third material constituting first coating film 321 is ZnS, and the refractive index n3 is 2.270.

[0306] The film thickness d1 (= d4) and the film thickness d2 (= d3) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, the coating film made of the third material, and the coating film made of the fourth material are expressed by the following equation (12).

[0307]

number

[0308] The overall characteristic matrix of the anti-reflection coating 40aa is expressed by the above-mentioned formula (9) using the characteristic matrix of each coating film. Furthermore, the components m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0309] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r described above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 19.554 nm and the film thickness d2 becomes 364.894 nm.

[0310] In the antireflection coating 40aa, the first coating film 321 formed in this order from the side of the emission end face 41 of the quantum cascade laser device is composed of a ZnS film with a film thickness of 364.894 nm, the second coating film 282 is composed of a Ge film with a film thickness of 19.554 nm, the third coating film 283 is composed of a YF3 film with a film thickness of 364.894 nm, the fourth coating film 284 is composed of a Ge film with a film thickness of 19.554 nm, the fifth coating film 285 is composed of a YF3 film with a film thickness of 364.894 nm, the sixth coating film 286 is composed of a Ge film with a film thickness of 19.554 nm, the seventh coating film 287 is composed of a YF3 film with a film thickness of 364.894 nm, and the eighth coating film 288 is composed of a CeO2 film with a film thickness of 19.554 nm. By applying the antireflection coating 40aa consisting of these eight coating films, it is possible to obtain a desired wavelength λ dThat is, the reflectance of the antireflection film 40aa is zero at wavelengths around 9 μm.

[0311] Fig. 49 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40aa. In Fig. 49, a solid line 322 represents the wavelength dependence of the reflectance of the antireflection coating 40aa consisting of eight coating layers according to the fourteenth embodiment, and a dashed-dotted line 323 represents the wavelength dependence of the reflectance of the antireflection coating consisting of eight coating layers according to the fourteenth embodiment when the weighting coefficients of the single coating layers and the respective coating layer pairs made of the third and fourth materials described below are taken into consideration.

[0312] Assuming that the desired reflectance band is a band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40aa made of eight coating layers according to the fourteenth embodiment is 2.135 μm. In addition, the sum (n×d) of the products of the refractive index and thickness of each coating layer of the antireflection coating 40aa is sum Therefore, the sum (n×d) of the products of the refractive index and the film thickness of each coating film of the antireflection coating 40aa made of eight coating films according to the fourteenth embodiment is sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.194, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40aa has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that the anti-reflection film 40aa is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0313] Next, an antireflection coating having a wider reflectance band will be described below, in which the reference film thicknesses of the single coating films made of the third and fourth materials and the weighting coefficients for each coating pair are set using weighting coefficients q3, p1, p2, p3, and q4, at least one of which is a positive real number other than 1.

[0314] Fig. 50 shows the configuration of antireflection film 40ab of a quantum cascade laser device according to embodiment 14. As shown in Fig. 50, antireflection film 40ab has a configuration in which first coating film 294 made of a third material having a refractive index of n3 and a thickness of q3d3 of antireflection film 40z of the quantum cascade laser device according to embodiment 13 is replaced with first coating film 324 made of a third material having a refractive index of n3 and a thickness of q3d3, and eighth coating film 314 made of a fourth material having a thickness of q4d4 of antireflection film 40z is replaced with eighth coating film 301 made of the fourth material having a thickness q4d4. The antireflection coating 40z according to embodiment 13 differs in that the reference thickness d4 of the thickness q4d4 of the eighth coating film 314 is equal to the reference thickness d2 of the thickness p1d2 of the third coating film 296, whereas the antireflection coating 40ab according to embodiment 14 differs in that the reference thickness d3 of the thickness q3d3 of the first coating film 324 is equal to the reference thickness d2 of the thickness p1d2 of the third coating film 296, and the reference thickness d4 of the thickness q4d4 of the eighth coating film 301 is the same as the reference thickness d1 of the thickness p1d1 of the second coating film 295. The third material constituting the first coating film 324 is ZnS, and the refractive index n3 is 2.270.

[0315] The weighting coefficients are set based on the setting method described below, and the reference film thickness d1 (= d3) and the reference film thickness d2 (= d4) at which the real part and the imaginary part of the complex reflectance r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40z using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0316] As an example of the anti-reflection coating 40ab, the case where the weighting factors are q3=1.50, p1=1.00, p2=1.00, p3=1.00, and q4=1.00 will be described below. In this case, the reference film thickness d1 (=d4) is 9.742 nm, and the reference film thickness d2 (=d3) is 360.658 nm.

[0317] 49, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40ab is shown by a dashed line 323. The reflectance band of the anti-reflection coating 40ab where the reflectance is less than 1% is 2.388 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0318] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40ab (n×d) sum is 1661.928nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40ab made of eight coating films according to the fourteenth embodiment is smaller than the thickness of a single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.303, which cannot be expressed as a positive odd number. From this result, it can be seen that the anti-reflection film 40ab has a refractive index of n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0319] In the antireflection coating 40ab, the first coating film 324 formed in this order from the emission end face 41 side of the quantum cascade laser device is composed of a ZnS film with a film thickness of 540.987 nm, the second coating film 295 is composed of a Ge film with a film thickness of 9.742 nm, the third coating film 296 is composed of a YF3 film with a film thickness of 360.658 nm, the fourth coating film 297 is composed of a Ge film with a film thickness of 9.742 nm, the fifth coating film 298 is composed of a YF3 film with a film thickness of 360.658 nm, the sixth coating film 299 is composed of a Ge film with a film thickness of 9.742 nm, the seventh coating film 300 is composed of a YF3 film with a film thickness of 360.658 nm, and the eighth coating film 301 is composed of a CeO2 film with a film thickness of 9.742 nm. By applying the antireflection coating 40ab consisting of these eight coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40ab is zero at wavelengths in the vicinity of 9 μm.

[0320] <Advantages of the Fourteenth Embodiment> As described above, according to the optical semiconductor device of the fourteenth embodiment, the antireflection film is composed of an eight-layer coating film consisting of three pairs of coating films, each pair being a coating film made of a first material and a coating film made of a second material, and two single coating films made of a third material and a fourth material, respectively, and the reference thickness d2 of the coating film made of the second material is equal to the reference thickness d3 of the single coating film made of the third material, and the reference thickness d1 of the coating film made of the first material is equal to the reference thickness d4 of the single coating film made of the fourth material, and the thickness of each coating film is determined by solving using a characteristic matrix with both the real part and the imaginary part of the complex reflectance set to zero, thereby achieving the effect of obtaining an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0321] Embodiment 15 In the twelfth embodiment, the case where the thickness d3 of the coating film made of the third material and the thickness d4 of the coating film made of the fourth material are both the same as the thickness d1 of the coating film made of the first material is described. In the fifteenth embodiment, the case where the thickness d3 of the coating film made of the third material and the thickness d4 of the coating film made of the fourth material are both the same as the thickness d2 of the coating film made of the second material is described.

[0322] 51 shows the configuration of antireflection coating 40ac of the quantum cascade laser device according to the fifteenth embodiment. As shown in FIG. 51, antireflection coating 40ac has a configuration in which eighth coating film 288 made of a fourth material, having a refractive index of n4 and a thickness of d4, of antireflection coating 40aa of the quantum cascade laser device according to the fourteenth embodiment is replaced with eighth coating film 311 made of a fourth material, having a refractive index of n4 and a thickness of d4. In antireflection coating 40aa according to the fourteenth embodiment, thickness d3 of first coating film 321 is equal to thickness d2 of third coating film 283 and thickness d4 of eighth coating film 288 is equal to thickness d1 of second coating film 282. In contrast, antireflection coating 40ac according to the fifteenth embodiment differs in that thickness d3 of first coating film 321 is equal to thickness d2 of third coating film 283 and thickness d4 of eighth coating film 288. The fourth material constituting eighth coating film 311 is CeO2, and the refractive index n4 is 1.650.

[0323] The film thickness d1 and film thickness d2 (= d3 = d4) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, the coating film made of the third material, and the coating film made of the fourth material are expressed by the following equation (13).

[0324]

number

[0325] The overall characteristic matrix of the anti-reflection coating 40ac is expressed by the above-mentioned formula (9) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0326] Since the reflectance of the anti-reflection coating is assumed to be zero, it is sufficient that both the real and imaginary parts of the complex reflectance r described above are zero. In fact, when the real and imaginary parts of the complex reflectance r are solved as zero, the film thickness d1 becomes 21.008 nm and the film thickness d2 becomes 284.936 nm.

[0327] In the antireflection coating 40ac, the first coating film 321 formed in this order from the side of the emission end face 41 of the quantum cascade laser device is composed of a ZnS film having a film thickness of 284.936 nm, the second coating film 282 is composed of a Ge film having a film thickness of 21.008 nm, the third coating film 283 is composed of a YF3 film having a film thickness of 284.936 nm, the fourth coating film 284 is composed of a Ge film having a film thickness of 21.008 nm, the fifth coating film 285 is composed of a YF3 film having a film thickness of 284.936 nm, the sixth coating film 286 is composed of a Ge film having a film thickness of 21.008 nm, the seventh coating film 287 is composed of a YF3 film having a film thickness of 284.936 nm, and the eighth coating film 311 is composed of a CeO2 film having a film thickness of 284.936 nm. By applying the antireflection coating 40ac consisting of these eight coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the anti-reflection film 40ac is zero at wavelengths in the vicinity of 9 μm.

[0328] Fig. 52 is a graph showing the wavelength dependence of the reflectance of the antireflection coating 40ac. In Fig. 52, a solid line 331 represents the wavelength dependence of the reflectance of the antireflection coating 40ac consisting of the eight-layer coating film according to the fifteenth embodiment, and a dashed-dotted line 332 represents the wavelength dependence of the reflectance of the antireflection coating consisting of the eight-layer coating film according to the fifteenth embodiment when the weighting coefficients of the single coating film and each coating film pair made of the third and fourth materials described below are taken into consideration.

[0329] Assuming that the desired reflectance band is a reflectance band with a reflectance of less than 1%, the reflectance band of the antireflection coating 40ac made of eight coating layers according to the fifteenth embodiment is 2.108 μm. In addition, the sum (n×d) of the products of the refractive index and film thickness of each coating layer of the antireflection coating 40ac is sum Therefore, the sum (n×d) of the products of the refractive index and film thickness of each coating film of the antireflection coating 40ac made of eight coating films according to the fifteenth embodiment is 1487.703 nm.sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.162, which cannot be expressed as a positive odd number. From this result, it can be seen that the refractive index of the anti-reflection film 40ac is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that the anti-reflection film 40ac is not a replacement for a single layer coating film having a refractive index of n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 It can be seen that the thickness is thinner than the single-layer coating film.

[0330] Next, an antireflection coating having a wider reflectance band will be described below, in which the reference film thicknesses of the single coating films made of the third and fourth materials and the weighting coefficients for each coating pair are set using weighting coefficients q3, p1, p2, p3, and q4, at least one of which is a positive real number other than 1.

[0331] Fig. 53 shows the configuration of antireflection film 40ad of a quantum cascade laser device according to embodiment 15. As shown in Fig. 53, antireflection film 40ad has a configuration in which eighth coating film 301 made of a fourth material and having a thickness of q4d4 of antireflection film 40ab of the quantum cascade laser device according to embodiment 14 is replaced with eighth coating film 314 made of a fourth material and having a thickness of q4d4. In the antireflection coating 40ab according to the fourteenth embodiment, the reference thickness d3 of the thickness q3d3 of the first coating film 324 is equal to the reference thickness d2 of the thickness p1d2 of the third coating film 296, and the reference thickness d4 of the thickness q4d4 of the eighth coating film 301 is equal to the reference thickness d1 of the thickness p1d1 of the second coating film 295. In contrast, the antireflection coating 40ad according to the fifteenth embodiment differs in that the reference thickness d3 of the thickness q3d3 of the first coating film 324 and the reference thickness d2 of the thickness p1d2 of the third coating film 296 are equal to the reference thickness d4 of the thickness q4d4 of the eighth coating film 314. The fourth material constituting the eighth coating film 314 is CeO2, and the refractive index n4 is 1.650.

[0332] The reference film thickness d1 and the reference film thickness d2 (= d3 = d4) are determined as follows: The phase terms of the coating film made of the first material, the coating film made of the second material, the coating film made of the third material, and the coating film made of the fourth material are expressed by the above-mentioned equation (13).

[0333] The overall characteristic matrix of the anti-reflection coating 40ad is expressed by the above-mentioned formula (10) using the characteristic matrix of each coating film. Furthermore, m 11 , m 12 , m 21 , m 22 Using this, the complex reflectance r is expressed by the above-mentioned equation (3).

[0334] The weighting coefficients are set based on the setting method described below, and the reference film thicknesses d1 and d2 (= d3 = d4) at which the real and imaginary parts of the complex reflectivity r in the above-mentioned equation (3) become zero are calculated. Then, the anti-reflection film 40ad using the film thicknesses of the coating films determined based on the reference film thicknesses and the weighting coefficients is coated on the emission end surface 41 of the quantum cascade laser device.

[0335] As an example of the anti-reflection coating 40ad, the case where the weighting factors are q3=1.50, p1=1.00, p2=1.00, p3=5.00, and q4=1.00 will be described below. In this case, the reference film thickness d1 is 10.084 nm, and the reference film thickness d2 (=d3=d4) is 162.478 nm.

[0336] 52, the wavelength dependency of the reflectance in the reflectance band of the anti-reflection coating 40ad is shown by a dashed line 332. The reflectance band of the anti-reflection coating 40ad where the reflectance is less than 1% is 2.309 μm, and the refractive index is n c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 The reflectance band is wider than the reflectance band of 1.894 μm of the single-layer coating film.

[0337] The sum of the products of the refractive index and film thickness of each coating film of the antireflection film 40ad (n×d) sum is 1614.130 nm, and the refractive index is n c 1 / 2 and the film thickness is 3λ d / 4 / n c 1 / 2 The sum (n×d) of the products of the refractive index and thickness of each coating film of the antireflection coating 40ad made of eight coating films according to the fifteenth embodiment is smaller than the thickness of the single coating film, 3766.216 nm. sum λ d When divided by / 4, that is, (n×d) sum / (λ d / 4) is 1.226, which cannot be expressed as a positive odd number. c 1 / 2 and the film thickness is λ d / 4 / n c 1 / 2 It can be seen that this is not a replacement of the monolayer coating film.

[0338] In the antireflection coating 40ad, the first coating film 324 formed in this order from the emission end face 41 side of the quantum cascade laser device is composed of a ZnS film with a film thickness of 243.718 nm, the second coating film 295 is composed of a Ge film with a film thickness of 10.084 nm, the third coating film 296 is composed of a YF3 film with a film thickness of 162.478 nm, the fourth coating film 297 is composed of a Ge film with a film thickness of 10.084 nm, the fifth coating film 298 is composed of a YF3 film with a film thickness of 162.478 nm, the sixth coating film 299 is composed of a Ge film with a film thickness of 50.419 nm, the seventh coating film 300 is composed of a YF3 film with a film thickness of 812.392 nm, and the eighth coating film 314 is composed of a CeO2 film with a film thickness of 162.478 nm. By applying the antireflection coating 40ad consisting of these eight coating films, it is possible to obtain a desired wavelength λ d That is, the reflectance of the antireflection film 40ad is zero at wavelengths in the vicinity of 9 μm.

[0339] <Effects of the 15th embodiment> As described above, according to the optical semiconductor device of the fifteenth embodiment, the antireflection film is composed of an eight-layer coating film consisting of three pairs of coating films, each pair being a coating film made of a first material and a coating film made of a second material, and two single coating films made of a third material and a fourth material, respectively, and the reference thickness d2 of the coating film made of the second material is set equal to both the reference thickness d3 of the single coating film made of the third material and the reference thickness d4 of the single coating film made of the fourth material, and the thickness of each coating film is determined by solving using a characteristic matrix with both the real part and the imaginary part of the complex reflectance set to zero, thereby achieving the effect of obtaining an optical semiconductor device having an antireflection film with a wide reflectance band and thin layers.

[0340] Embodiment 16 In the method for manufacturing an optical semiconductor device according to the sixteenth embodiment, a method for determining the weight coefficient q of a single coating film made of a third or subsequent material, and the weight coefficient p of a coating film pair consisting of a coating film made of a first material and a coating film made of a second material, which is a characteristic step in the method for manufacturing an optical semiconductor device, will be described. As an example of the method for determining the weight coefficients, the weight coefficients p1, p2, and p3 of the three coating film pairs are calculated. 3、 The following describes the case of a weighting factor q3 of the first coating film (single coating film) made of the third material and a weighting factor q4 of the eighth coating film (single coating film) made of the fourth material.

[0341] 54 is a flowchart illustrating a method for determining weighting coefficients in a method for manufacturing an optical semiconductor device according to Embodiment 16. Each step will be described below in order with reference to FIG. (1) Desired reflectance band Δλ d Step (ST001) of setting in advance (2) Weighting coefficient p i and weighting factor q j A step (ST002) of calculating the reflectance band Δλ0 by calculating the reference film thickness d1 and the reference film thickness d2, assuming all of these to be 1.00. (3) Reflectance band Δλ d and the reflectance band Δλ0, Δλ0 ≥ Δλ d If Δλ0<Δλ, it is determined that the calculation is finished. dIf so, proceed to step (4) (ST003) (4) Weighting coefficient p i and weighting factor q j By setting one of the weighting coefficients to be greater than 1.00 or smaller than 1.00, the reference film thickness d1 and the reference film thickness d2 are calculated, and the reflectance band Δλ h Step (ST004) of calculating (h≧1) (5) Reflectance band Δλ d and reflectance band Δλ h Compared with Δλ h ≧Δλ d If , it is determined that the calculation is finished, and Δλ h <Δλ d If yes, proceed to step (6) (ST005) (6)Δλ h If Δλ 0 or greater, the weighting coefficient is further increased if it is selected to increase it in step (4), or the weighting coefficient is further decreased if it is selected to decrease it in step (4), thereby calculating the reference film thickness d1 and the reference film thickness d2, thereby obtaining the reflectance band Δλ h+1 Calculate Δλ h If it is determined that the reflectance band Δλ is less than Δλ0, the weighting coefficient is decreased if it is determined in step (4) that the weighting coefficient is increased, and the reference film thickness d1 and the reference film thickness d2 are calculated by increasing the weighting coefficient if it is determined in step (4) that the weighting coefficient is decreased. h+1 A step of calculating (ST006) (7) Desired reflectance band Δλ d and reflectance band Δλ h+1 Compared with Δλ h+1 ≧Δλ d If , it is determined that the calculation is finished, and Δλ h+1 <Δλ d If yes, proceed to step (8) (ST007) (8)Δλ h+1 ≧Δλ hIn the case of (4), if the weighting coefficient is selected to be increased, the weighting coefficient is further increased, and if the weighting coefficient is selected to be decreased in the step (4), the weighting coefficient is further decreased to calculate the reference film thickness d1 and the reference film thickness d2, and the reflectance band Δλ h+2 Calculate Δλ h+1 <Δλ h In the case of (4), if it is selected to increase the weighting coefficient in step (4), the weighting coefficient is decreased conversely, and if it is selected to decrease the weighting coefficient in step (4), the weighting coefficient is increased conversely, thereby calculating the reference film thickness d1 and the reference film thickness d2, and the reflectance band Δλ h+2 A step of calculating (ST008) (9) Desired reflectance band Δλ d and reflectance band Δλ h+2 Compared with Δλ h+2 ≧Δλ d If , it is determined that the calculation is finished, and Δλ h+2 <Δλ d If yes, proceed to step (10) (ST009) (10) Absolute value |Δλ h+2 -Δλ h+1 | and determine the absolute value |Δλ h+2 -Δλ h+1 If |<1 nm, proceed to step (12) and calculate the absolute value |Δλ h+2 -Δλ h+1 If |≧1 nm, a step (ST010) of determining to proceed to step (11) (11) Return to step (8) and repeat the calculation (ST011). (12) A step (ST012) of returning to step (4) and performing the same calculation using a weighting factor other than the weighting factor selected in step (4).

[0342] In the above step (10), the absolute value |Δλ h+2 -Δλ h+1 Although | is judged based on a standard of 1 nm, it is not limited to this and can be arbitrarily changed depending on the likelihood of a desired reflectance band.

[0343] Each of the above steps can be executed by using, for example, a computer. When setting weighting factors in each of the above steps, the weighting factors may be set by sequentially adding or subtracting a step size preset by the computer to each weighting factor.

[0344] In each of the above embodiments, a quantum cascade laser device has been described as an example of an optical semiconductor device, but the subject matter of the present disclosure is not limited to this and can be applied to optical semiconductor devices in general, such as semiconductor lasers, light-emitting diodes, and photodiodes.

[0345] In the above embodiments, Ge and YF3 are specifically described as materials for forming the coating film pair. However, the materials for forming the coating film pair are not limited to these, and the effective refractive index n c Square root of n c 1 / 2 The effective refractive index n of a material and an optical semiconductor device having a refractive index greater than c Square root of n c 1 / 2 It would be good if a combination of materials with refractive indices smaller than 10 ...

[0346] The refractive index of the materials constituting the single coating film, such as the third material and the fourth material, may be any value. c Square root of n c 1 / 2 It may be larger, smaller, or the same as

[0347] In the present disclosure, a single coating film made of a material such as a third material or a fourth material is provided from the light-emitting end face side of the optical semiconductor device as a first coating film and, in some cases, as a final coating film, but this is not limited to these configurations and may be provided between any pair of coating films, or multiple coating films may be provided between any pair of coating films, or may be provided between multiple pairs of any pair of coating films.

[0348] Furthermore, as described in the first embodiment, the film thickness and complex reflectance values ​​of each coating film are not limited to one, but include any values ​​within the practically acceptable range as long as they are based on the technical concept of the present disclosure.

[0349] Although the present disclosure describes various exemplary embodiments and examples, the various features, aspects, and functions described in one or more embodiments are not limited to application to a particular embodiment, but may be applied to the embodiments alone or in various combinations.

[0350] Therefore, countless variations not illustrated are conceivable within the scope of the technology of the present disclosure, including, for example, cases where at least one component is modified, added, or omitted, and cases where at least one component is extracted and combined with a component of another embodiment. [Explanation of symbols]

[0351] 1 n-type first electrode, 2 n-type InP substrate, 3 n-type InP buffer layer, 4 first optical confinement layer, 5 core region, 6 second optical confinement layer, 7 n-type InP cladding layer, 8 n-type GaInAs contact layer, 9 n-type second electrode, 10 Fe-doped InP current blocking layer, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33 undoped AlInAs barrier layer, 12, 14, 16, 18, 20, 22, 24, 30, 32 undoped GaInAs well layer, 25, 27 n-type AlInAs barrier layer, 26, 28 n-type GaInAs well layer, 34 active region, 35 injector region, 36 Stage, 40, 40a, 40b, 40c, 40d, 40e, 40f, 40g, 40h, 40i, 40j, 40k, 40l, 40m, 40n, 40o, 40p, 40q, 40r, 40s, 40t, 40u, 40x, 40y, 40z, 40aa, 40ab, 40ac, 40ad Anti-reflection coating, 41 Output end face, 42, 61, 91, 94, 109, 121, 141, 161, 164, 201, 213, 223, 226, 251, 271, 274, 281, 294, 321, 324 First coating film, 43, 62, 101, 110, 122, 142, 171, 182, 202, 214, 231, 252, 282, 295 Second coating film, 44, 63, 102, 111, 123, 143, 172, 183, 203, 215, 232, 253, 283, 296 Third coating film, 45, 64, 103, 112, 124, 144, 173, 184, 204, 216, 233, 254, 284, 297 Fourth coating film, 46, 65, 104, 113, 125, 145, 174, 185, 205, 217, 234, 255, 285, 298 Fifth coating, 126, 146, 175, 186, 206, 218, 235, 256, 286, 299 Sixth coating, 127, 147, 176, 187, 207, 219, 236, 257, 287, 300 Seventh coating, 301, 311, 314, 288 Eighth coating, 47, 66, 105, 114, 128, 148, 177, 188, 208, 220, 237, 258, 289, 302 First coating pair, 48, 67, 106, 115, 129, 149, 178, 189, 209, 221, 238, 259, 290, 303Second coated film pair, 130, 150, 179, 190, 210, 222, 239, 260, 291, 304 Third coated film pair, 51, 73 Thin dotted line, 52, 75 Thick dotted line, 53, 92, 107, 131, 162, 180, 191, 211, 224, 240, 272, 292, 312, 322, 331 Solid line, 54, 78, 80, 93, 108, 132, 163, 181, 192, 212, 225, 241, 273, 293, 313, 323, 332 Dash-dotted line, 71 Thick solid line, 72 Thin solid line, 74 Thin dot-dotted line, 76 Thick dot-dotted line, 77, 79 Dotted line, 133 Two-dot chain line, 500 Optical semiconductor device

Claims

1. The laser oscillation wavelength is λ d and the effective refractive index is n c An optical semiconductor device comprising: an anti-reflection film formed on one end surface of the optical semiconductor device and including a plurality of coating films; The plurality of coating films are c 1 / 2 A refractive index n smaller than 1 a coating film made of a first material having n c 1 / 2 A refractive index n greater than 2 and at least m (1≦m≦2) single coating films other than the coating film pairs, The reference thickness of the coating film made of the first material is d 1 , the reference thickness of the coating film made of the second material is d 2 , the thickness of the ith (2≦i≦n) coating film pair is given by the weighting coefficient p i Using p i d 1 +p i d 2 is expressed as The reference film thickness of the jth (1≦j≦m) single coating film is defined as d k (k=j+2), the reference film thickness d k is the reference film thickness d of the coating film made of the first material 1 or the reference film thickness d of the coating film made of the second material 2 The refractive index of the j-th single coating film is n k and the refractive index n k is the refractive index n 1 and the refractive index n 2 Unlike, the film thickness is weighted by the weighting coefficient q j Using q j d k An optical semiconductor device characterized by being represented by the formula:

2. 2. The optical semiconductor device according to claim 1, wherein among the pairs of coating films, a first pair of coating films is provided closest to the end face, and the first pair of coating films to the nth pair of coating films are formed in order in a direction away from the end face.

3. 3. The optical semiconductor device according to claim 1, wherein in each of the pairs of coating films, the coating film made of the first material is disposed on the end face side.

4. 3. The optical semiconductor device according to claim 1, wherein in each of the pairs of coating films, the coating film made of the second material is disposed on the end face side.

5. The elements of the characteristic matrix of the plurality of coating films consisting of the n coating film pairs and the m single coating films are defined as m 11 , m 12 , m 21 , m 22 In this case, the real and imaginary parts of the complex reflectance r expressed by the following formula (1) are d 3. The optical semiconductor device according to claim 1, wherein both of the above are zero. [Equation 1]

6. The weighting coefficient p i and the weighting coefficient q j 3. The optical semiconductor device according to claim 1, wherein each of

7. The weighting coefficient p i and the weighting coefficient q j is a positive real number, and the weighting coefficient p i and the weighting coefficient q j 3. The optical semiconductor device according to claim 1, wherein one or more of the following is a numerical value other than 1:

8. The thickness of the anti-reflection film is 3λ d / 4 / n c 1 / 2 3. The optical semiconductor device according to claim 1, wherein the thickness of the single-layer coating film is smaller than that of the single-layer coating film represented by the formula (1).

9. The reflectance band set by the antireflection coating is λ d / 4 / n c 1 / 2 3. The optical semiconductor device according to claim 1, wherein the reflectance band is wider than the reflectance band set by a single-layer coating film represented by the formula:

10. The preset laser oscillation wavelength is λ d and the preset reflectance band is Δλ d and the Δλ d The central wavelength of λ c In the optical semiconductor device, the thickness of each of the pair of coating films and the single coating film is λ d / λ c 3. The optical semiconductor device according to claim 1, wherein the anti-reflection film is provided on the end face of the optical semiconductor device to a thickness twice as thick as that of the anti-reflection film.

11. The first material is Ge and the second material is YF 3 or the first material is YF 3 3. The optical semiconductor device according to claim 1, wherein the second material is Ge.

12. The material constituting the single coating film is Y 2 O 3 3. The optical semiconductor device according to claim 1, wherein the material is ZnS.

13. 3. The optical semiconductor device according to claim 1, wherein the optical semiconductor device is a quantum cascade laser device.

14. The laser oscillation wavelength is λ d and the effective refractive index is n c A method for manufacturing an optical semiconductor device, comprising: forming an anti-reflection film made of a plurality of coating films on one end face of the optical semiconductor device; The plurality of coating films are c 1 / 2 A refractive index n smaller than 1 a coating film made of a first material having n c 1 / 2 A refractive index n greater than 2 and at least m (1≦m≦2) single coating films other than the coating film pairs, The reference thickness of the coating film made of the first material is d 1 , the reference thickness of the coating film made of the second material is d 2 , the thickness of the ith (2≦i≦n) coating film pair is given by the weighting coefficient p i Using p i d 1 +p i d 2 is expressed as The reference film thickness of the jth (1≦j≦m) single coating film is defined as d k (k=j+2), the reference film thickness d k is the reference film thickness d of the coating film made of the first material 1 or the reference film thickness d of the coating film made of the second material 2 The refractive index of the j-th single coating film is n k and the refractive index n k is the refractive index n 1 and the refractive index n 2 Unlike, the film thickness is weighted by the weighting coefficient q j Using q j d k is expressed as The elements of the characteristic matrix of the plurality of coating films consisting of the n coating film pairs and the m single coating films are defined as m 11 , m 12 , m 21 , m 22 In this case, the real and imaginary parts of the complex reflectance r expressed by the following equation (2) are d and (c) the number of optical semiconductor devices is zero. [Equation 2]

15. The weighting coefficient p i and the weighting coefficient q j is a positive real number, and the weighting coefficient p i and the weighting coefficient q j 15. The method for manufacturing an optical semiconductor device according to claim 14, wherein one or more of the following is a numerical value other than 1:

16. The weighting coefficient p i and the weighting coefficient q j but, (1) Desired reflectance band Δλ d A step of setting in advance (2) The weighting coefficient p i and the weighting coefficient q j are all set to 1.00, and the reference film thickness d 1 and reference film thickness d 2 By calculating the reflectance band Δλ 0 The process of calculating (3) The reflectance band Δλ d and the reflectance band Δλ 0 Compared with Δλ 0 ≧Δλ d If , it is determined that the calculation is finished, and Δλ 0 <Δλ d If so, proceed to step (4) (4) The weighting coefficient p i and the weighting coefficient q j By setting one of the weighting coefficients to be greater than 1.00 or smaller than 1.00, the reference film thickness d 1 and reference film thickness d 2 Calculate the reflectance band Δλ h Calculating (h≧1) (5) The reflectance band Δλ d and the reflectance band Δλ h Compared with Δλ h ≧Δλ d If , it is determined that the calculation is finished, and Δλ h <Δλ d If yes, proceed to step (6) (6) Δλ h ≧Δλ 0 In the case of step (4), if the weighting coefficient is selected to be increased, the weighting coefficient is further increased, and if the weighting coefficient is selected to be decreased in step (4), the weighting coefficient is further decreased, thereby 1 and reference film thickness d 2 By calculating the reflectance band Δλ h+1 Calculate Δλ h <Δλ 0 In the case of step (4), if it is selected to increase the weighting coefficient, the weighting coefficient is decreased, and if it is selected to decrease the weighting coefficient, the weighting coefficient is increased, thereby reducing the reference film thickness d 1 and reference film thickness d 2 Calculate the reflectance band Δλ h+1 The process of calculating (7) the desired reflectance band Δλ d and the reflectance band Δλ h+1 Compared with Δλ h+1 ≧Δλ d If , it is determined that the calculation is finished, and Δλ h+1 <Δλ d If so, proceed to step (8) (8) Δλ h+1 ≧Δλ i In the case of step (4), if the weighting coefficient is selected to be increased, the weighting coefficient is further increased, and if the weighting coefficient is selected to be decreased in step (4), the weighting coefficient is further decreased, thereby 1 and reference film thickness d 2 Calculate the reflectance band Δλ h+2 Calculate Δλ h+1 <Δλ i In the case of step (4), if it is selected to increase the weighting coefficient, the weighting coefficient is decreased, and if it is selected to decrease the weighting coefficient, the weighting coefficient is increased, thereby reducing the reference film thickness d 1 and reference film thickness d 2 Calculate the reflectance band Δλ h+2 The process of calculating (9) the desired reflectance band Δλ d and the reflectance band Δλ h+2 Compared with Δλ h+2 ≧Δλ d If , it is determined that the calculation is finished, and Δλ h+2 <Δλ d If so, proceed to step (10) (10) Absolute value |Δλ h+2 -Δλ h+1 | is determined, and the absolute value |Δλ h+2 -Δλ h+1 If |<1 nm, proceed to step (12), and the absolute value |Δλ h+2 -Δλ h+1 | If ≧1 nm, determine to proceed to step (11). (11) A step of returning to the step (8) and repeating the calculation (12) returning to step (4) and performing calculations using weighting factors other than the weighting factors selected in step (4); 16. The method for manufacturing an optical semiconductor device according to claim 14, wherein the thickness is determined by the above steps.

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