Measurement method, measurement apparatus, and measurement program for measuring film thickness of thin film

Abstract

To measure a film thickness of an ultrathin film in a non-contact and non-destructive manner.SOLUTION: A measurement method for measuring a film thickness of a thin film includes: a detection step S1 of making light incident on the thin film and detecting reflected light from the thin film; a measurement step S2 of measuring a phase difference (▵) and an amplitude ratio (Ψ) between p-polarized light and s-polarized light of the reflected light; a first analysis step S3 of determining a sheet resistance value and scattering time of the thin film on the basis of the phase difference (▵) and amplitude ratio (Ψ); and a second analysis step S4 of determining the film thickness of the thin film on the basis of the sheet resistance value and scattering time with a model using Fresnel equations.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a technique for measuring the thickness of a thin film, and more particularly to a technique for measuring the thickness of a thin film by terahertz time-domain spectroscopic ellipsometry. [Background technology]

[0002] Terahertz time-domain spectroscopic ellipsometry (THz-TDSE) has been attracting attention as a non-destructive and non-contact characteristic evaluation method for semiconductor thin films. Measurement of the electrical characteristics (resistivity, carrier concentration, mobility) of semiconductors using THz-TDSE was proposed by Nagashima et al. of Osaka University in 2001 (Patent Document 1).

[0003] Furthermore, in 2013, Nippou Precision Co., Ltd. launched a terahertz ellipsometry device (product name: TeraEvaluator(registered trademark)) that can measure the electrical properties (resistivity, carrier concentration, mobility) and thickness of semiconductor substrates and epitaxial films in a non-contact and non-destructive manner. The TeraEvaluator(registered trademark) estimates the electrical properties of a sample from changes in the polarization state caused by the reflection of terahertz waves.

[0004] As shown in Fig. 10, in THz-TDSE, linearly polarized terahertz light (1 THz to 3 THz) is incident on a thin-film sample, and the amplitude ratio (Ψ) and phase difference (Δ) of p-polarized light and s-polarized light reflected from the sample are measured while changing the frequency. Fig. 11 (a) and (b) are graphs showing the frequency dependence (experimental values) of the amplitude reflection intensity ratio (tanΨ) and phase difference (Δ), respectively. These experimental values ​​are fitted (optimized by computer) with theoretical values ​​(FR model) using the Fresnel equation to estimate the electrical characteristics (Non-Patent Document 1).

[0005] For a thin film (two-layer structure) on a substrate as shown in FIG. 6, the relationship between the amplitude-reflection intensity ratio (tan Ψ) and the phase difference (Δ) is expressed by the following formula from the Fresnel equation.

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[0006] According to the Drude model, the complex refractive index is expressed by the following formula:

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[0007] In the conventional FR model, the film thickness and other parameters in these equations are estimated by fitting the parameters of film thickness (d), carrier density (N), and scattering time (τ) so that the amplitude reflection intensity ratio (tanΨ) and phase difference (Δ) measured by TeraEvaluator (registered trademark) are simultaneously established. The applicants have previously used this method to non-contact, non-destructively measure the electrical properties of epitaxial films on three-dimensional semiconductor substrates such as Si, GaAs, SiC, GaN, and InN, and reported the measurement results. These reports have revealed that the measurement results using the FR model are in good agreement with the measurement results using other methods for bulk crystals and epitaxial films with a certain thickness (approximately 1 μm or more). [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Patent No. 3550381 [Non-patent literature]

[0009] [Non-Patent Document 1] Edited by Noriyuki Iwamuro, "Challenges and Evaluation Technologies for Next-Generation Power Electronics," S&T Publishing Co., Ltd., July 2022, pp. 127-138 Summary of the Invention [Problem to be solved by the invention]

[0010] The applicants are studying a template in which a GaN thin film of approximately 1 μm or less is grown on a ScAlMgO4 (SAM) substrate by RF-MBE in order to create a free-standing GaN substrate. However, when they tried to analyze the thickness of such an extremely thin film using the conventional FR model, they found that there were multiple optimal solutions for the thickness, making it impossible to uniquely determine the thickness.

[0011] Figure 12 shows an example of an optimal solution for the electrical properties of an ultrathin film obtained by fitting using conventional THz-TDSE. In this example, fitting was performed using tanΨ to optimize three parameters: scattering time, carrier density, and film thickness. The initial film thickness was changed in the range of 0.5 μm to 1.1 μm. There are an infinite number of possible solutions that minimize the sum of squares of the residuals between the actual measured values ​​and the theoretical values, including the one shown in Figure 12, and it was found that it is difficult to simultaneously fit the three parameters of scattering time, carrier density, and film thickness using analysis using the conventional FR model.

[0012] The present invention has been made in view of the above problems, and an object of the present invention is to measure the thickness of an extremely thin film in a non-contact and non-destructive manner. [Means for solving the problem]

[0013] In order to solve the above problems, the present invention includes the following aspects. Section 1. A method for measuring a film thickness of a thin film, comprising the steps of: a detection step of directing light onto the thin film and detecting reflected light from the thin film; a measuring step of measuring a phase difference (△) and an amplitude ratio (Ψ) between p-polarized light and s-polarized light of the reflected light; a first analysis step of determining a sheet resistance value and a scattering time of the thin film based on the phase difference and the amplitude ratio; a second analysis step of determining a thickness of the thin film based on the sheet resistance and the scattering time using a model using Fresnel's equation; A measurement method having the following characteristics. Section 2. In the first analysis step, Item 2. The measurement method according to item 1, wherein the sheet resistance and the scattering time are determined without taking the film thickness into consideration by a model using characteristic impedance. Section 3. In the first analysis step, 3. The measurement method according to item 2, wherein fitting is performed using the sheet resistance and the scattering time as fitting parameters so that a theoretical amplitude reflection intensity ratio (tan Ψ) in a model using the characteristic impedance is consistent with an amplitude reflection intensity ratio (tan Ψ) corresponding to the amplitude ratio (Ψ) measured in the measurement step. Section 4. In the first analysis step, Item 2. The measurement method according to item 1, wherein the sheet resistance and the scattering time are determined by a model using Fresnel's equation, assuming that the film thickness is a predetermined value. Section 5. Item 5. The measurement method according to item 4, wherein the predetermined value is 1 μm or less. Section 6. 5. The measurement method according to item 4, wherein the first analysis step and the second analysis step are repeated by replacing the predetermined value with the film thickness obtained in the second analysis step until the film thickness obtained in the second analysis step converges. Section 7. In the second analysis step, Item 7. The measurement method according to any one of items 1 to 6, wherein fitting is performed using the film thickness as a fitting parameter so that a theoretical phase difference (△) in a model using the Fresnel equation is consistent with a phase difference (△) measured in the measurement step. Section 8. A measuring device for measuring the thickness of a thin film, a measurement unit that measures a phase difference (△) and an amplitude ratio (Ψ) between p-polarized light and s-polarized light reflected from the thin film; a first analysis unit that calculates a sheet resistance value and a scattering time of the thin film based on the phase difference and the amplitude ratio; a second analysis unit that calculates a thickness of the thin film based on the sheet resistance value and the scattering time using a model that uses a Fresnel equation; A measuring device having Section 9. A measurement program for measuring the thickness of a thin film, comprising: a measurement unit that measures the phase difference (△) and amplitude ratio (Ψ) between p-polarized light and s-polarized light reflected from the thin film; a first analysis unit that determines a sheet resistance value and a scattering time of the thin film based on the phase difference and the amplitude ratio; and a second analysis unit that calculates a thickness of the thin film based on the sheet resistance and the scattering time using a model that uses Fresnel's equation; A measurement program that causes a computer to operate as a Effect of the Invention

[0014] According to the present invention, the thickness of an extremely thin film can be measured in a non-contact and non-destructive manner. [Brief description of the drawings]

[0015] [Figure 1] FIG. 1 is a schematic diagram of a terahertz time-domain spectroscopic ellipsometry device. [Diagram 2] 1 is a block diagram showing functions of a measurement device according to an embodiment of the present invention. [Diagram 3] 4 is a flowchart showing a processing procedure of a first measurement method according to the embodiment of the present invention. [Figure 4] 14(a) to 14(d) are explanatory diagrams of the CI model. [Diagram 5] This is an example of fitting in the CI model. [Figure 6] FIG. 1 is an explanatory diagram of an FR model. [Figure 7] This is an example of fitting in the FR model. [Figure 8] 5 is a flowchart showing a processing procedure of a second measurement method according to the embodiment of the present invention. [Figure 9] 1 shows cross-sectional images of a sample taken by cross-sectional TEM observation. [Figure 10] FIG. 1 is an explanatory diagram of the measurement principle of THz-TDSE. [Figure 11] 1 is a graph showing the frequency dependence (experimental values) of the amplitude reflection intensity ratio (tan Ψ) and the phase difference (Δ). [Figure 12] This is an example of the optimum solution for the electrical properties of an ultra-thin film obtained by fitting the conventional THz-TDSE. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0016] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. Note that the present invention is not limited to the following embodiment, and various modifications are possible without departing from the spirit of the present invention.

[0017] (Device configuration) FIG. 1 is a schematic diagram of a terahertz time-domain spectroscopic ellipsometry device (THz-TDSE device) 1 according to this embodiment. In the THz-TDSE device 1, a femtosecond pulsed laser beam with a pulse width of about 100 fsec is emitted from a light source 2, and is split into a laser beam L1 (pump pulse) and a laser beam L2 (probe pulse) by a beam splitter 3. The laser beam L1 is incident on a photoconductive antenna 4 on the oscillation side, and an electromagnetic wave having a frequency in the terahertz wave region (100 GHz to 10 THz) is emitted from the photoconductive antenna 4. The electromagnetic wave passes through a polarizer 5 and is obliquely incident on a sample S. In this embodiment, the sample S is a GaN thin film of about 1 μm grown on a ScAlMgO4 (SAM) substrate by RF-MBE.

[0018] The reflected light from the sample S passes through an analyzer 6 and a polarizer 7 and is detected by a photoconductive antenna 8 on the detection side. A delay circuit 9 in the optical path on the detection side enables measurement in the time domain. The signal of the reflected light detected by the photoconductive antenna 8 is sent to a measurement device 10.

[0019] 2 is a block diagram showing the functions of the measurement device 10. The measurement device 10 can be configured as a general-purpose computer. The measurement device 10 includes, as its hardware configuration, a processor such as a CPU or GPU, a main storage device such as a DRAM or SRAM (not shown), and an auxiliary storage device 11 such as an HDD or SSD. A measurement program P is stored in the auxiliary storage device 11.

[0020] The measuring device 10 includes, as functional blocks, a measuring unit 12, a first analysis unit 13, and a second analysis unit 14. These functional blocks are realized by the processor of the measuring device 10 reading out a measurement program P into a main storage device and executing it. The measurement program P may be downloaded to the measuring device 10 via a communication network such as the Internet, or may be recorded in a computer-readable non-transitory recording medium such as a CD-ROM or an SD card and installed in the measuring device 10 via the recording medium. The functions of the above functional blocks will be described later.

[0021] (First measurement method) FIG. 3 is a flowchart showing the processing procedure of the first measurement method according to this embodiment.

[0022] In step S1 (detection step), the THz-TDSE device 1 causes light (linearly polarized in this embodiment) that has passed through the polarizer 5 to be incident on the sample S in which a GaN thin film is formed on a SAM substrate, and the photoconductive antenna 8 detects the light (elliptically polarized in this embodiment) reflected from the thin film. A signal of the detected reflected light is input to the measurement device 10.

[0023] In step S2 (measurement step), the measurement unit 12 of the measurement device 10 measures the phase difference (△) and amplitude ratio (Ψ) between the p-polarized light and the s-polarized light of the reflected light by a conventionally known method. (Ψ, △) are called the ellipsometric angle.

[0024] (CI analysis) In step S3 (first analysis step), the first analysis unit 13 of the measurement device 10 determines the GaN thin film (thin film sheet) resistance and scattering time based on the phase difference (△) and the amplitude ratio (Ψ). In the first measurement method, the first analysis unit 13 determines the DC sheet electrical conductivity (sheet resistance) and scattering time of the GaN thin film using a model using characteristic impedance (CI model) without considering the thickness of the GaN thin film.

[0025] First, we will explain the CI model (theory of radio waves). Characteristic impedance is the ratio of the voltage and current, or the electric field and magnetic field, that occurs in a propagation medium when AC electrical energy is transmitted to the medium. As shown in Figure 4(a), reflection occurs at the interface between two media with different refractive indices n1 and n2. As shown in Figure 4(b), a similar reflection occurs when an electrical signal propagates from a transmission line with impedance Z1 to a transmission line with impedance Z2.

[0026] As shown in Figure 4(c), when the GaN thin film formed on the SAM substrate is an extremely thin film with a thickness of 1 μm or less, the amplitude reflection intensity ratio (tanΨ) has almost no difference within the measurement variation range with respect to the amplitude reflection intensity ratio measured by THz-TDSE, even if the film thickness is 0 (on the other hand, the phase difference (△) has a large difference with respect to the phase difference measured by THz-TDSE, even if the film thickness is several tens of nm). Therefore, in the CI model, the structure shown in Figure 4(c) can be considered equivalent to the lumped constant circuit shown in Figure 4(d).

[0027] JPEG2025026116000005.jpg9135

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[0028] In the CI model, the relationship between the amplitude reflection intensity ratio (tan Ψ) and the phase difference (△) can be expressed by the following formula (2).

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[0029] The variables on the right side of the above formula (2) are expressed as in the following formulas (3) and (4).

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[0030] Using the DC sheet electrical conductivity (σ1) and scattering time (τ) in equation (1) representing the AC electrical conductivity as fitting parameters, fitting is performed so that the theoretical amplitude reflection intensity ratio (tanΨ) in the CI model is consistent with the amplitude reflection intensity ratio (tanΨ) corresponding to the amplitude ratio (Ψ) measured in step S2. This makes it possible to uniquely determine the DC sheet electrical conductivity (σ1) and scattering time (τ) of the GaN thin film. However, since the thickness of the GaN thin film is ignored, it is assumed that the DC sheet electrical conductivity is equivalent to the sheet resistance.

[0031] Figure 5 shows an example of fitting in the CI model (fitting range: 1 THz to 2.5 THz). This allows us to determine the DC sheet electrical conductivity (σ1) and scattering time (τ) that minimize the sum of squares of the residual between the theoretical value (fitting) and the measured value (GanonSAM).

[0032] In this manner, in step S3, the DC sheet electrical conductivity (σ1) and the scattering time (τ) can be obtained by applying the CI model to the amplitude reflection intensity ratio (tan Ψ).

[0033] (FR analysis) In step S4 (second analysis step), the second analysis unit 14 of the measurement apparatus 10 determines the thickness of the GaN thin film based on the DC sheet electrical conductivity (sheet resistance value) and scattering time using a model using Fresnel's equation (FR model).

[0034] 6 is an explanatory diagram of the FR model. In the FR model, the relationship between the amplitude reflection intensity ratio (tan Ψ) and the phase difference (Δ) can be expressed by the following formula (5).

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[0035] Each variable on the right side of the above formula (5) is expressed as in the following formulas (6) and (7).

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[0036] In step S3, since the DC sheet electrical conductivity (σ1) and scattering time (τ) have been determined, fitting is performed so that the theoretical phase difference (△) in the FR model matches the phase difference (△) measured in step S2, using the film thickness (d1) as a fitting parameter. This allows the film thickness (d1) of the GaN thin film to be uniquely determined.

[0037] Figure 7 shows an example of fitting in the FR model (fitting range: 1.5 THz to 2.5 THz). This allows us to determine the film thickness (d1) that minimizes the sum of squares of the residual between the theoretical value (fitting) and the actual measurement value (GanonSAM).

[0038] In this way, in step S4, the film thickness (d1) can be obtained by applying the FR model to the phase difference (△). Furthermore, once the film thickness (d1) is determined, the electrical properties of the GaN thin film, such as resistivity, carrier concentration, and mobility, can also be obtained.

[0039] (Summary) As described above, the first measurement method according to this embodiment is A step S1 of irradiating light onto the thin film and detecting reflected light from the thin film; Step S2 of measuring the phase difference (△) and amplitude ratio (Ψ) between the p-polarized light and the s-polarized light of the reflected light; A step S3 of determining the sheet resistance (DC sheet electrical conductivity) and scattering time of the thin film without taking the film thickness into account using a model using characteristic impedance; Step S4 of determining a thickness of the thin film based on the sheet resistance and the scattering time using a model using Fresnel's equation; has.

[0040] More specifically, In step S3, the sheet resistance value (DC sheet electrical conductivity) and the scattering time are used as fitting parameters to determine the sheet resistance value and the scattering time by fitting so that the theoretical amplitude reflection intensity ratio (tan Ψ) in the CI model matches the amplitude reflection intensity ratio (tan Ψ) corresponding to the amplitude ratio (Ψ) measured in step S2. In step S4, the film thickness is used as a fitting parameter to determine the film thickness by fitting so that the theoretical phase difference (△) in the FR model matches the phase difference (△) measured in step S2.

[0041] In this manner, in this embodiment, even if the film thickness is an extremely thin film of 1 μm or less, the film thickness can be obtained in one measurement by applying the CI model to the amplitude reflection intensity ratio (tan Ψ) and the FR model to the phase difference (△). Therefore, the film thickness of an extremely thin film can be measured non-contact and non-destructively.

[0042] The thickness of the thin film is not particularly limited as long as it is about 1 μm or less, and is preferably, for example, 100 nm to 1 μm. The wavelength of the light irradiated to the thin film is not particularly limited, but is preferably 100 GHz to 10 THz, and more preferably 1 THz to 4 THz.

[0043] (Second measurement method) FIG. 8 is a flowchart showing the processing procedure of the second measurement method according to this embodiment.

[0044] Steps S1 and S2 are the same as those in the first measurement method, and therefore a description thereof will be omitted.

[0045] In step S3' (first analysis step), the first analysis unit 13 of the measurement device 10 determines the GaN thin film (thin film sheet) resistance and scattering time based on the phase difference (△) and the amplitude ratio (Ψ). In the second measurement method, the first analysis unit 13 determines the DC sheet electrical conductivity (sheet resistance) and scattering time of the GaN thin film, assuming that the GaN thin film has a predetermined thickness, using a model using Fresnel's equation (FR model). The predetermined thickness is not particularly limited, but is preferably 1 μm or less, for example.

[0046] Specifically, for the thin film shown in FIG. 6, the relationship between the amplitude reflection intensity ratio (tan Ψ) and the phase difference (Δ) is expressed by the following formulas (12) to (14) from the Fresnel equation.

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[0047] According to the Drude model, the complex refractive index is expressed by the following equations (15) and (16).

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[0048] In step S3', in formulas (12) to (16), the film thickness (d) is set to a predetermined value, and the parameters of the carrier density (N) and scattering time (τ) are fitted so that the amplitude reflection intensity ratio (tan Ψ) and phase difference (Δ) measured in step S2 are simultaneously established. This allows the carrier density (N) and scattering time (τ) to be calculated, and further the sheet resistance value (DC sheet electrical conductivity) to be calculated from the carrier density (N).

[0049] In step S4 (second analysis step), the second analysis unit 14 of the measurement device 10 calculates the thickness of the GaN thin film based on the DC sheet electrical conductivity (sheet resistance value) and the scattering time using a model using Fresnel's equation (FR model). The method of calculating the thickness is the same as in step S4 in the first measurement method.

[0050] Furthermore, until the film thickness determined in step S4 converges (YES in step S5), the predetermined value is replaced with the film thickness determined in step S4 (step S6), and steps S3' and S4 are repeated. This makes it possible to uniquely determine the film thickness. There is no particular limitation on the method for determining whether or not convergence has occurred, but for example, it may be determined that convergence has occurred when the rate of change of the film thickness determined in step S4 relative to the film thickness determined in the immediately preceding step S4 becomes equal to or less than a certain value. EXAMPLES

[0051] In this example, similarly to the above embodiment, a GaN thin film was grown on a ScAlMgO4 (SAM) substrate by RF-MBE to fabricate a sample S. The thickness, resistivity, carrier concentration, and mobility of the GaN thin film were measured for this sample S by the first and second measurement methods according to the above embodiment. In the second measurement method, the predetermined value in step S3' was set to 1 μm.

[0052] As a comparative example, the SAM substrate of sample S was cut into 10 mm squares, and the Hall effect measurement and the film thickness measurement by cross-sectional TEM observation were performed. In the film thickness measurement by cross-sectional TEM observation, a transmission electron microscope (TEM) was used to photograph the cross section of the cut sample S, and the film thickness of the GaN thin film was measured from the image.

[0053] Figure 9 shows a cross-sectional image of sample S observed by cross-sectional TEM. From this cross-sectional image, it was confirmed that the thickness of the GaN thin film was 0.78 to 0.85 μm. In the Hall effect measurement, the resistivity, carrier concentration, and mobility of the GaN thin film were measured with a film thickness of 0.8 μm.

[0054] The measurement results of Example 1 and the Comparative Example are shown in Table 1. [Table 1]

[0055] From the above measurement results, it was found that even for an extremely thin film having a thickness of 1 μm or less, the film thickness, resistivity, carrier concentration, and mobility can be accurately measured by the first and second measurement methods according to this embodiment. [Explanation of symbols]

[0056] 1. Terahertz time-domain spectroscopic ellipsometry (THz-TDSE) device 2 light source 3 Beam splitter 4. Photoconductive antenna (radiator) 5 Polarizer 6. Analyzer 7 Polarizer 8 Photoconductive antenna (detector) 9 Delay Circuit 10. Measuring Equipment 11 Auxiliary storage 12 Measurement section 13 1st analysis section 14 2nd analysis section L1 Laser light L2 Laser light P Measurement Program S Sample

Claims

1. A method for measuring a film thickness of a thin film, comprising the steps of: a detection step of directing light onto the thin film and detecting reflected light from the thin film; a measuring step of measuring a phase difference (△) and an amplitude ratio (Ψ) between p-polarized light and s-polarized light of the reflected light; a first analysis step of determining a sheet resistance and a scattering time of the thin film based on the phase difference and the amplitude ratio; a second analysis step of determining a thickness of the thin film based on the sheet resistance and the scattering time using a model using Fresnel's equation; A measurement method having the following characteristics.

2. In the first analysis step, The measurement method according to claim 1 , wherein the sheet resistance and the scattering time are determined using a model that uses a characteristic impedance, without taking the film thickness into consideration.

3. In the first analysis step, 3. The measurement method according to claim 2, wherein fitting is performed using the sheet resistance and the scattering time as fitting parameters such that a theoretical amplitude reflection intensity ratio (tan Ψ) in a model using the characteristic impedance matches an amplitude reflection intensity ratio (tan Ψ) corresponding to the amplitude ratio (Ψ) measured in the measuring step.

4. In the first analysis step, 2. The measurement method according to claim 1, further comprising the steps of: determining the sheet resistance and the scattering time when the film thickness is assumed to be a predetermined value, using a model that uses Fresnel's equation.

5. The method according to claim 4, wherein the predetermined value is 1 μm or less.

6. 5. The measurement method according to claim 4, further comprising the steps of: replacing the predetermined value with the film thickness determined in the second analysis step, and repeating the first analysis step and the second analysis step until the film thickness determined in the second analysis step converges.

7. In the second analysis step, 7. The method according to claim 1, further comprising: performing fitting using the film thickness as a fitting parameter such that a theoretical phase difference (Δ) in a model using the Fresnel equation is consistent with a phase difference (Δ) measured in the measuring step.

8. A measuring device for measuring the thickness of a thin film, a measurement unit that measures a phase difference (△) and an amplitude ratio (Ψ) between p-polarized light and s-polarized light reflected from the thin film; a first analysis unit that calculates a sheet resistance value and a scattering time of the thin film based on the phase difference and the amplitude ratio; a second analysis unit that calculates a thickness of the thin film based on the sheet resistance and the scattering time using a model that uses a Fresnel equation; A measuring device having

9. A measurement program for measuring the thickness of a thin film, comprising: a measurement unit that measures the phase difference (△) and amplitude ratio (Ψ) between p-polarized light and s-polarized light reflected from the thin film; a first analysis unit that calculates a sheet resistance value and a scattering time of the thin film based on the phase difference and the amplitude ratio; and a second analysis unit that calculates a thickness of the thin film based on the sheet resistance and the scattering time using a model using Fresnel's equation; A measurement program that causes a computer to operate as a

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