Metalens, method for manufacturing metalens, electronic instrument, and method for designing metalens

Abstract

A method for manufacturing a metalens, according to the present invention, includes: a mask-pattern formation step for forming a mask pattern on a silicon layer of a substrate having the silicon layer on a surface thereof; an etching step for etching the silicon layer to form a silicon pattern layer having an array pattern comprising a plurality of silicon pillars or a plurality of unoxidized pores; and an oxidation treatment step for oxidizing at least a portion of the silicon in the silicon pattern layer to form a pattern layer comprising a plurality of oxidized silicon pillars or a plurality of pores. The pattern layer has a focal point for light that is incident on the pattern layer.

Description

Metalens, metalens manufacturing method, electronic device, and metalens design method

[0001] The present invention relates to a metalens, a method for manufacturing a metalens, an electronic device, and a method for designing a metalens. This application claims priority based on Japanese Patent Application No. 2022-114260, filed on July 15, 2022, the contents of which are incorporated herein by reference.

[0002] Thinner lenses are required for mobile camera modules, and lightweight lenses are required in the robotics field, as heavy lenses increase the moment of inertia.

[0003] Metalenses, for example, have been proposed as a thin, lightweight lens. A metalense is an optical element that functions as a lens by having a fine periodic structure that is small relative to the incident wavelength.

[0004] In Non-Patent Document 1, SiO ２ The present invention discloses a metalens manufactured by forming pillars of the above-mentioned metallization method.

[0005] Joon-Suh Park, Shuyan Zhang, Alan She, Wei Ting Chen, Peng Lin, Kerolos M. A. Yousef, Ji-Xin Cheng, and Federico Capasso, “All-Glass, Large Metalens at Visible Wavelength Using Deep-Ultraviolet Projection Lithography”, Nano Letters, Vol. 19, (2019), 8673-8682

[0006] In order to produce a metalens with a short focal length, it is effective to reduce the period (center-to-center distance) of the pillars, for example. To reduce the period of the pillars, pillars with a high aspect ratio are required. In conventional manufacturing methods, for example, in the metalens manufacturing method described in Non-Patent Document 1, SiO ２ By directly etching SiO ２ The pillars of SiO ２has low etching selectivity, so SiO ２ If an attempt is made to form pillars with a high aspect ratio by directly etching the above, the pillars will be damaged. Therefore, the method of Non-Patent Document 1 has the problem that pillars with an aspect ratio of up to 6.6 can only be formed, resulting in a long focal length.

[0007] The present invention has been made in consideration of the above circumstances, and aims to provide a metalens with a short focal length, a method for manufacturing a metalens, an electronic device, and a method for designing a metalens.

[0008] In order to solve the above problems, the present invention proposes the following measures. (1) A method for manufacturing a metalens according to aspect 1 of the present invention, comprising: a mask pattern formation step of forming a mask pattern on a silicon layer of a substrate having a silicon layer on its surface; an etching step of etching the silicon layer to form a silicon pattern layer having an array pattern consisting of a plurality of silicon pillars or a plurality of pre-oxidized holes; and an oxidation treatment step of oxidizing at least a portion of the silicon in the silicon pattern layer to form a pattern layer consisting of a plurality of oxidized silicon pillars or a plurality of holes, wherein the pattern layer has a focal point for light incident on the pattern layer. (2) Aspect 2 of the present invention is a method for manufacturing a metalens according to aspect 1, wherein the oxidation may be wet oxidation or dry oxidation. (3) Aspect 3 of the present invention is a method for manufacturing a metalens according to aspect 1 or 2, wherein, after the etching step, the method further comprises the step of annealing the substrate having the silicon pattern layer in a hydrogen atmosphere, an argon atmosphere, or a mixed atmosphere of hydrogen and argon. (4) Aspect 4 of the present invention relates to the method for manufacturing a metalens according to any one of aspects 1 to 3, wherein the mask pattern may be made of resin, silicon oxide, silicon nitride, or alumina. (5) Aspect 5 of the present invention relates to the method for manufacturing a metalens according to any one of aspects 1 to 3, wherein the mask pattern may be made of metal. (6) Aspect 6 of the present invention relates to the method for manufacturing a metalens according to any one of aspects 1 to 5, wherein the maximum aspect ratio of the silicon oxide pillars or the holes in the pattern layer may be greater than 6.7. (7) Aspect 7 of the present invention relates to the method for manufacturing a metalens according to any one of aspects 1 to 6, wherein the center-to-center distance between the silicon pillars may be 1.4 times or more the width of the silicon pillars. (8) Aspect 8 of the present invention relates to the method for manufacturing a metalens according to any one of aspects 1 to 7, wherein the etching step may involve etching the silicon pattern layer in consideration of silicon expansion during the oxidation treatment step.(9) A metalens according to a ninth aspect of the present invention comprises, in this order: a support substrate; and a patterned layer having an array pattern of a plurality of silicon oxide pillars or a plurality of holes, wherein the maximum aspect ratio of the silicon oxide pillars or the holes in the patterned layer is greater than 6.7, and the patterned layer is made of at least SiO. ２ (10) A tenth aspect of the present invention is the metalens of the ninth aspect, wherein the patterned layer is made of SiO ２ (11) Aspect 11 of the present invention relates to the metalens of aspect 9 or aspect 10, and may further include an intermediate layer between the support substrate and the patterned layer. (12) Aspect 12 of the present invention relates to the metalens of aspect 9 or aspect 10, and may further include a folded portion at a portion where the phase difference with respect to the center is 360°. (13) An electronic device of aspect 12 of the present invention is equipped with the metalens of any one of aspects 9 to 12. (14) A method of designing a metalens of aspect 13 of the present invention is a method of designing a metalens, comprising: a phase difference calculation step of calculating a phase difference φ(r) with respect to a distance r from the center of the metalens based on a set wavelength λ and focal length f of incident light; and a metalens design method comprising: a step of calculating a phase difference φ(r) with respect to a distance r from the center of the metalens based on a set wavelength λ and focal length f of incident light; and a step of calculating a height H and a width a of silicon oxide pillars constituting the metalens. ｘ , and period Λx and width a ｘ Phase difference φ(a ｘ ) by calculating the relationship between the height H and the width a ｘ and the period Λx, and after the step of determining the dimensions of the pillars, determining the phase difference φ(r) with respect to the distance r and the width a ｘ Phase difference φ(a ｘ ) the width a relative to the distance r from the center of the metalens ｘand a step of calculating the width of the pillars with respect to the distance r, where in the step of calculating the phase difference, if the phase difference φ(r) with respect to the distance r is 360° or greater, calculating φ'(r) so as to satisfy the following formulas (A) and (B): φ'(r)=φ(r)-360°×n (A) φ'(r)<360° (B) where, in formula (A), n is a natural number. (15) A fifteenth aspect of the present invention is the method for manufacturing a metalens according to any one of aspects 1 to 8, which may further include a step of carrying out the method for designing a metalens according to aspect 14.

[0009] According to the above aspects of the present invention, it is possible to provide a metalens with a short focal length, a metalens manufacturing method, an electronic device, and a metalens design method. In particular, it is possible to provide a metalens with an excellent etching selectivity of Si and SiO ２ It is possible to provide a manufacturing method that has an exceptional effect of enabling the production of a high-quality product.

[0010] 1(a) is an example of a plan view enlarging a portion of the array pattern of the metalens according to the first embodiment, and FIG. 1(b) is a cross-sectional view of the metalens of FIG. 1(a) taken along line A-A. The equivalent refractive index n ２Ｄ FIG. 1 is a diagram showing the relationship between the occupancy rate fx and the phase difference φ with respect to the distance from the lens center; FIG. 2 is a diagram showing an example of the calculation results of the phase difference φ with respect to the distance from the lens center; FIG. 3 is a diagram showing another example of the calculation results of the phase difference φ with respect to the distance from the lens center; and FIG. 4 is a diagram showing the relationship between the phase difference φ (a ｘ9(b) is a diagram showing an example of the calculation results of (a) the mask pattern formation step, (b) the etching step, and (c) the oxidation treatment step. FIG. 10(a) is a plan view showing an enlarged portion of the array pattern of a metalens according to a second embodiment, and FIG. 10(b) is a cross-sectional view of the metalens shown in FIG. 10(a) taken along line CC of the metalens shown in FIG. 10(a). FIG. 10(b) is a diagram showing the relationship between the width (nm) of silicon pillars and the expansion coefficient of the pillar width. FIG. 10(c) is a schematic diagram of a focal length evaluation device. FIG. 13(a) to FIG. 13(c) show the relationship between the distance r from the lens center and luminance when measured by changing the height of a metalens after one hour of oxidation. FIG. 13(a) shows the relationship between the distance r from the lens center and luminance from Z = 0 μm to Z = 500 μm. FIG. 13(b) shows the relationship between the distance r from the lens center and luminance from Z = 600 μm. FIG. 13(c) shows the relationship between the distance r from the lens center and luminance from Z = 700 μm to Z = 1400 μm. Similar to FIGS. 13(a) to 13(c), this figure shows the relationship between the distance r from the lens center and luminance when measured by changing the height of the metalens after 3 hours of oxidation. This figure also shows the results of linear approximation of the design value Wd of the pillars and the ratio γ of the actual measured value Wmp of the width of the silicon oxide pillars to the set value Wd. This figure also shows the relationship between the distance r from the lens center and luminance when measured by changing the height of the metalens of Example 2.

[0011] First Embodiment A metalens according to a first embodiment of the present invention will now be described with reference to the drawings. FIG. 1( a) is a plan view showing an enlarged portion of the array pattern of a metalens 100 according to the first embodiment. FIG. 1( b) is a cross-sectional view taken along line A-A of the metalens 100 in FIG. 1( a). The metalens 100 includes, in this order, a support substrate 15 and a patterned layer 20 having an array pattern of a plurality of silicon oxide pillars 22. The metalens 100 according to the first embodiment is a reflective metalens that reflects incident light. In the following description, in the first embodiment, the X direction is a direction parallel to the surface 12 a of an intermediate layer 12 provided between the support substrate 15 and the patterned layer 20, and is one of the directions in which the silicon oxide pillars 22 are arranged. Note that the intermediate layer 12 facing the surface 12 a across the support substrate 15 is formed when the support substrate 15 is subjected to a thermal oxidation treatment, and may not affect the optical function of the metalens 100. The Y direction is a direction parallel to the surface 12a of the intermediate layer 12 and intersects with the X direction. For example, the Y direction is approximately perpendicular to the X direction. The Z direction is a thickness direction of the support substrate 15 and intersects with the X and Y directions. Each component will be described below.

[0012] (Support substrate 15) The support substrate 15 may be made of any material that can form the reflective metalens 100. For example, silicon (Si) is preferably used as the material for the support substrate 15. The thickness of the support substrate 15 is not particularly limited as long as it can support the pattern layer 20.

[0013] (Intermediate layer 12) In the metalens 100, an intermediate layer 12 is provided between the support substrate 15 and the pattern layer 20. Specifically, the intermediate layer 12 is provided on the support substrate 15. There are no particular limitations on the material of the intermediate layer 12 as long as it can function as a reflective metalens 100. The material of the intermediate layer 12 is, for example, silicon dioxide (SiO ２ ). The thickness of intermediate layer 12 is not particularly limited as long as it can function as a reflective metalens 100. The thickness of intermediate layer 12 is, for example, 1 μm to 20 μm. In metalens 100, incident light that has passed through patterned layer 20 is reflected at the interface between intermediate layer 12 and supporting substrate 15.

[0014] (Pattern Layer 20) In the first embodiment, the pattern layer 20 is provided on the intermediate layer 12. The pattern layer 20 has an array pattern 26 consisting of a plurality of silicon oxide pillars 22. Here, the array pattern refers to a pattern in which microstructures (for example, silicon oxide pillars 22) are regularly arranged in the X and Y directions at a predetermined interval (center-to-center distance). The pattern layer 20 is made of at least SiO ２ The pattern layer 20 may include Si. ２ and Si, the refractive index of Si is ２ Since the pattern layer 20 is higher than SiO ２ The pattern layer 20 can have a larger equivalent refractive index than when it is made of SiO ２ The pattern layer 20 may be made of SiO ２ When the pattern layer 20 is made of SiO ２ Compared to a metalens made of Si and silicon, the transmittance of incident light can be increased. Patterned layer 20 has a folded portion at a location where the phase difference is 360° with respect to the center of metalens 100. The folded portion refers to a location where the phase difference changes from 360° to 0° in the radial direction from the center of metalens 100.

[0015] The pattern layer 20 has a focal point for incident light. The focal length of the pattern layer 20 is set appropriately depending on the design of the metalens 100. For example, when the wavelength of the incident light is a visible light wavelength (wavelength: 400 to 800 nm), the focal length of the pattern layer 20 is, for example, 500 μm to 2500 μm.

[0016] The shape (planar shape) of the silicon oxide pillars 22 as viewed in the Z direction is not particularly limited, and may be polygonal, circular, etc. In the first embodiment, the planar shape of the silicon oxide pillars 22 is a square. ｘ and the width in the Y direction a ｙ is set appropriately depending on the design of the metalens 100. The width a of the silicon oxide pillars 22 in the X direction ｘ The width a of the silicon oxide pillars 22 in the Y direction is, for example, 150 nm to 600 nm. ｙis, for example, 150 nm to 600 nm.

[0017] The center-to-center distance (period) Λ of the silicon oxide pillars 22 along the X direction as viewed from the Z direction ｘ and the center-to-center distance (period) Λ of the silicon oxide pillars 22 along the Y direction. ｙ is set appropriately depending on the design of the metalens 100. The period Λ of the silicon oxide pillars 22 along the X direction ｘ is, for example, 200 nm to 600 nm. The period Λ of the silicon oxide pillars 22 along the Y direction ｙ is, for example, 200 nm to 600 nm. ｘ and period Λ ｙ The center of the silicon oxide pillar 22 viewed from the Z direction is the center of the smallest inclusive circle when the planar shape of the silicon oxide pillar 22 is polygonal, and is the center of the circle when the planar shape of the silicon oxide pillar 22 is circular. Here, the smallest inclusive circle refers to the smallest circle that completely includes the polygon.

[0018] The length (height) H of the silicon oxide pillars 22 in the Z direction is set appropriately depending on the design of the metalens 100. The height H of the silicon oxide pillars 22 is 1.0 μm to 3.0 μm.

[0019] The height H of the silicon oxide pillar 22 and the width a of the silicon oxide pillar 22 in the X direction ｘ The aspect ratio (H / a ｘ The aspect ratio (H / a ｘ The maximum value of the aspect ratio (H / a) is more than 6.7. ｘ Similarly, the maximum value of the height H of the silicon oxide pillar 22 and the width a of the silicon oxide pillar 22 in the Y direction is 7.0 or more. ｙ The aspect ratio (H / a ｙ The maximum value of the aspect ratio (H / a) is also set appropriately depending on the design of the metalens 100. ｙ The maximum value of the aspect ratio (H / a) is more than 6.7. ｙ When the planar shape of the silicon oxide pillars 22 is square or circular, the maximum value of the aspect ratio (H / aｘ ) is the aspect ratio (H / a ｙ ) In other words, in this case, the aspect ratio of the silicon oxide pillars 22 is the ratio of the width to the height.

[0020] Next, the relationship between the array pattern 26 of the silicon oxide pillars 22 and the lens function will be described. The array pattern 26 of the silicon oxide pillars 22 has a small periodic structure relative to the incident wavelength. This periodic structure can be regarded as an optical medium with a uniform refractive index. Let the refractive index of the silicon oxide pillars 22 in Figures 1(a) and 1(b) be n １ , the refractive index of the surrounding medium is n ２ The refractive index of the TE wave (Transverse Electric Wave) is n ＴＥ The refractive index of the TM wave (Transverse Magnetic Wave) is n ＴＭ Then, the equivalent refractive index n ２Ｄ is expressed by the following formula (1): ＴＥ is expressed by the following formula (2), and n in formula (1) ＴＭ is expressed by the following formula (3). fx in the following formula (1) is the occupancy rate in the X direction, and is expressed by the following formula (4). fy in the following formula (1) is the occupancy rate in the Y direction, and is expressed by the following formula (5). a in the following formula (4) ｘ is the width of the silicon oxide pillar 22 in the X direction, and Λ ｘ is the center-to-center distance (period) of the silicon oxide pillars 22 along the X direction. ｙ is the width of the silicon oxide pillar 22 in the Y direction, and Λ ｙ is the center-to-center distance (period) of the silicon oxide pillars 22 along the Y direction.

[0021]

[0022] Figure 2 shows the equivalent refractive index n ２Ｄ 2 shows the relationship between n in the above formula (1) and the occupancy rate fx. １ SiO ２ The refractive index of the surrounding medium is n ２is calculated assuming that the refractive index of air is 1. In the first embodiment, since the shape is square, fx=fy. The vertical axis of FIG. 2 represents the equivalent refractive index n ２Ｄ , and the horizontal axis represents the occupancy rate fx. As shown in FIG. 2, the higher the occupancy rate fx, the lower the equivalent refractive index n ２Ｄ By changing the occupancy rate, the equivalent refractive index n ２Ｄ This refractive index distribution allows the metalens 100 to function as a lens. The optical path length when a light wave passes through the pattern layer 20 is determined by multiplying the height H of the silicon oxide pillars 22 by the equivalent refractive index n ２Ｄ n multiplied by ２Ｄ It is represented by H.

[0023] In the metalens 100 according to this embodiment, the silicon oxide pillars 22 have a high aspect ratio, so the focal length can be shortened to, for example, 500 μm to 2500 μm. A specific explanation will be given later.

[0024] In the first embodiment, the metalens 100 includes the intermediate layer 12, but the metalens 100 does not have to include the intermediate layer 12 as long as it is possible to reflect incident light.

[0025] The metalens 100 of the first embodiment may be warped. Furthermore, the silicon oxide pillars 22 are not limited to being completely perpendicular to the surface 12a of the intermediate layer 12. ｘ , a ｙ The average width a is not limited to being uniform, but may be non-uniform with a design error of about 1 to 5%. ｘ , a ｙ The aspect ratio of the height H of the silicon oxide pillar 22 to the surface may be greater than 6.7.

[0026] <Method of Designing Metalens 100> Next, an example of a method of designing the metalens 100 according to the first embodiment will be described. FIG. 3 is a flowchart of a method of designing the metalens 100 according to the first embodiment. Here, an example will be described in which the planar shape of the silicon oxide pillars 22 is square, but a metalens can also be designed in a similar manner in cases where the planar shape is different, such as circular. In this example, the planar shape of the silicon oxide pillars 22 is square, so the width a of the silicon oxide pillars 22 is ｘ is the width a of the silicon oxide pillar 22 in the Y direction ｙ In the case of a circle, the width a ｘ is the diameter. The period Λ of the silicon oxide pillars 22 in the X direction ｘ is the period Λ of the silicon oxide pillars 22 in the Y direction ｙ is the same as

[0027] (Initial Setting Step) The design method for metalens 100 includes an initial setting step S30 and a correction step S31. The initial setting step S30 will be described below. The initial setting step S30 includes a phase difference calculation step S10 for calculating the phase difference φ(r) with respect to distance r as a function of distance r from the center of the metalens based on the set wavelength λ of incident light and focal length f; ｘ , and period Λx and width a ｘ Phase difference φ(a ｘ ) the height H and width a of the silicon oxide pillars 22 are calculated. ｘ After the dimension determination step S11, the phase difference φ(r) with respect to the distance r and the width a of the silicon oxide pillar 22 are determined. ｘ Phase difference φ(a ｘ ) from the relationship between the width a of the pillar and the distance r from the center of the metalens, ｘ and a step S12 of calculating the width of the pillar with respect to the distance r. Each calculation step will be described below.

[0028] (Step of calculating phase difference φ(r)) In step S10 of calculating the phase difference φ, first, the wavelength of the incident light, the focal length f, and the lens diameter D are set. Here, as an example, a case will be described in which the wavelength λ of the incident light is 532 nm, the focal length f is 1000 μm, and the lens diameter D is 100 μm. These numerical values ​​can be changed appropriately depending on the purpose. The phase difference φ(r) relative to the distance r from the lens center (distance in the radial direction) is calculated using the following formula (6). In the following formula (6), λ represents the wavelength of the incident light, r represents the distance from the lens center, and f represents the focal length.

[0029]

[0030] Equation (6) shows that the shorter the focal length f, the larger the phase difference Φ(r). For example, when there are two focal lengths, fa and fb, the phase difference fb is larger than the phase difference fa at a distance r1 from the lens center. As described above, the optical path length (i.e., the phase difference) is calculated by multiplying the height of the silicon oxide pillars by the equivalent refractive index. Therefore, the higher the silicon oxide pillars are, the larger the phase difference obtained, and therefore a shorter focal length can be obtained.

[0031] FIG. 4 shows an example of the phase difference φ(r) calculated using the above formula (6). The horizontal axis of FIG. 4 represents the distance r (μm) from the lens center, and the vertical axis represents the phase difference (°). In calculating the phase difference φ, the phase difference can be folded back every 360° because the phase is equal before and after. Specifically, as the distance r increases, the phase difference φ(r) increases, and when the phase difference φ(r) is 360° or greater, φ'(r) is calculated to satisfy the following formulas (A) and (B). In the following formula (A), n is an arbitrary natural number. FIG. 5 shows an example in which the phase difference is folded back every 360°. The horizontal axis of FIG. 5 represents the distance r (μm) from the lens center, and the vertical axis represents the phase difference (°). By setting the phase difference within the metalens 100 to the range of 0 to 360°, it becomes possible to periodically and repeatedly use silicon oxide pillars 22 of the same width for the metalens, and the silicon oxide pillars 22 to be designed can be narrowed down to a specific range, so the width of the silicon oxide pillars 22 can be kept within a certain range. This improves the yield of the metalens 100. φ'(r) = φ(r) - 360° × n (A) φ'(r) < 360° (B)

[0032] (Determining Dimensions of Pillars S11) In the determining dimension of pillars S11, the height H and width a of the silicon oxide pillars 22 constituting the metalens 100 are determined. ｘ By calculating the relationship between the period Λx and the phase difference, the height H and width a of the silicon oxide pillars 22 are obtained. ｘ The width a of the silicon oxide pillars 22 and the period Λx are determined. ｘ , center-to-center distance (period) Λ ｘ , and the relationship between the height H and the phase difference can be calculated using, for example, rigorous coupled wave analysis. Here, the period Λx and the height H of the silicon oxide pillars 22 are fixed, and the equivalent refractive index n ２Ｄ However, the present invention is not limited to this.

[0033] The height H of the silicon oxide pillar 22 is fixed, and the width a of the silicon oxide pillar 22 is set as a reference. ｘis set as the lower limit, the period Λx is fixed, and the width a of the silicon oxide pillars 22 is set as the ｘ Phase difference φ(a ｘ The width a of the silicon oxide pillar 22 serving as a reference is calculated. ｘ The width a of the silicon oxide pillar 22 may be the minimum width that can be formed. ｘ Phase difference φ(a ｘ 6 shows the relationship between the width a of the silicon oxide pillar 22 and the period Λx when the height H of the silicon oxide pillar 22 is 2.5 μm and the wavelength of the incident light is 532 nm. ｘ The phase difference φ(a ｘ 6 is an example of calculating the width a of the silicon oxide pillar 22. ｘ (nm), the vertical axis is the phase difference φ (a ｘ ) (°). Phase difference φ(a ｘ ) is the width a ｘ a, which is the lower limit of the phase value at ｘ In FIG. 6, when the period Λx is set to 400 nm, the width a of the silicon oxide pillars 22 is ｘ By setting the period Λx to 192 nm to 340 nm, the phase difference can be controlled to be in the range of 0 to 360°. In this way, it is preferable to set the period Λx so that the phase difference φ is in the range of 0 to 360°. In addition, as shown in FIG. 6, ｘ cannot be greater than the value of the period, a large height means a large aspect ratio. Therefore, providing a metalens 100 of the present invention with an aspect ratio of greater than 6.7 is extremely valuable.

[0034] (Step of Calculating the Width of the Columnar Object with Respect to the Distance r) In step S12 of calculating the width of the columnar object with respect to the distance r, the phase difference φ(r) with respect to the distance r and the width a of the silicon oxide columnar object 22 are calculated. ｘ Phase difference φ(a ｘ The width of the pillars relative to the distance r from the center of the metalens is calculated from the relationship between the phase difference φ(r) relative to the distance r from the center of the lens and the width a of the silicon oxide pillars 22. ｘ Phase difference φ(a ｘSpecifically, the phase difference φ(r) at the distance r is calculated based on the width a of the silicon oxide pillars 22, which results in the phase difference. ｘ By doing so, the width a of the silicon oxide pillar 22 with respect to the distance r from the center of the metalens is ｘ is obtained, and metalens 100 can be designed. FIG. 7A is an example of a pattern model of a designed metalens. FIG. 7B is an enlarged view of the vicinity of the center of the metalens in FIG. 7A, and FIG. 7C is an enlarged view of the vicinity of the boundary where the width of the silicon oxide pillars 22 of the metalens changes. From FIG. 7, it can be seen that width a ｘ It can be seen that the phase difference Φ changes when the width a is changed. ｘ 7C shows the aforementioned folded portion where the phase is 360°, and the width a ｘ and the width of 0 degrees of the fold a ｘ In FIG. 7C, the width a ｘ are significantly different, but the phase is 360° and the turning point is 0°, so the phase is continuously connected.

[0035] (Correction Step S31) In the manufacturing method of the metalens 100 described below, silicon pillars are formed on a silicon layer by electron beam lithography and silicon dry etching, and then the silicon pillars are oxidized. The silicon pillars expand due to oxidation, and the measured values ​​of the silicon oxide pillars 22 after oxidation deviate from the set value. For this reason, it is preferable to correct the set value of the silicon pillars before oxidation based on the actual measured values ​​of the widths of the silicon oxide pillars 22. The correction step S31 for correcting the set value will be described below. In the correction step S31, a metalens made of silicon pillars with a predetermined width is fabricated, and the width a of the silicon oxide pillars 22 of the obtained metalens is ｘThe method includes a pillar width measurement step S13 for measuring the width of the silicon oxide pillar 22, a prediction function creation step S14 for creating a prediction function for predicting the actual measured width of the silicon oxide pillar 22 relative to the design value of the silicon pillar before oxidation from the set width value of the silicon oxide pillar 22 and the actual measured width value of the silicon oxide pillar 22 after the width measurement, and a feedback function creation step S15 for creating a feedback function from the obtained prediction function for calculating the actual measured width of the silicon oxide pillar 22 so that the silicon oxide pillar 22 becomes the set value, and correcting the set value of the silicon pillar. Each step will be described below.

[0036] (Step of Measuring the Width of the Columnar Objects) In step S13 of measuring the width of the columns, a metalens is fabricated based on the design of silicon columns having a predetermined width, and the width a of the silicon oxide columnar objects 22 of the obtained metalens is measured. ｘ Measure the width a ｘ The measurement can be made from an image observed using, for example, a scanning electron microscope.

[0037] (Prediction Function Creation) In the prediction function creation step S14, the width a of the columnar object 22 is calculated. ｘ After the measurement step S13, a prediction function is created that predicts the actual width of the silicon oxide pillars 22 relative to the design width, based on the original set value of the width of the silicon oxide pillars 22 and the actual measured width of the silicon oxide pillars 22. The method for creating the prediction function is not particularly limited. For example, the prediction function may be created by linear approximation based on the ratio of the actual measured width of the silicon oxide pillars 22 to the set value (actual value / set value) and the set value of the width of the silicon oxide pillars 22.

[0038] (Creating a Feedback Function) In the feedback function creating step S15, a feedback function is created from the prediction function obtained in the prediction function creating step S14, which calculates the set value of the silicon oxide pillars 22 from the actual measured value of the silicon oxide pillars 22, and the set value of the silicon pillars is corrected. The feedback function is created by inversely solving the prediction function. The feedback function is a function that returns the design value width of the silicon pillars for the desired silicon oxide pillars 22. A feedback function is created, and the initial width of the silicon pillars is designed and corrected so that the silicon oxide pillars reach the set value. In the above, the feedback function is used to create a metalens, and calculate the width a of the silicon oxide pillars 22 of the obtained metalens. ｘ However, the feedback function can also be calculated by measuring the width of silicon oxide pillars obtained by oxidizing silicon pillars of various widths and shapes without fabricating a metalens, and then measuring the width of the resulting silicon oxide pillars to determine the deviation from the set value. Fabricating a metalens is preferable because it allows for consideration of the influence of the surrounding area during oxidation, but it is time-consuming. On the other hand, fabricating only silicon pillars is simple and allows for a rough understanding of the expansion due to oxidation. From the calculated feedback function, by forming the silicon pillars thinner than the set width at the design stage, taking into account the expansion due to oxidation, the influence of deviation from the design value due to oxidation after the oxidation process can be reduced.

[0039] The method for designing the metalens 100 of the present disclosure has been described above. According to the method for designing the metalens 100 of the present disclosure, the width of the pillars of the metalens 100 can be kept within a predetermined range, and the yield of the metalens 100 can be improved. Furthermore, deviations from the design values ​​due to the effects of oxidation are corrected based on actual measured values, which can further improve the light-collecting properties.

[0040] Although the methods for designing metalenses of the present disclosure involve creating prediction functions and feedback functions, it is not necessary to create prediction functions and feedback functions.

[0041] <Method of manufacturing metalens> Next, a method of manufacturing the metalens 100 will be described. FIG. 8 is a flowchart of a method of manufacturing the metalens 100 according to the first embodiment. FIGS. 9( a) to 9(c) are cross-sectional views showing an example of the manufacturing steps of a method of manufacturing the metalens 100 of FIGS. 1(a) and 1(b). The method of manufacturing the metalens according to the first embodiment includes a mask pattern formation step S20 of forming a mask pattern 50 on the silicon layer 18 of a substrate 40 having a silicon layer 18 on its surface, an etching step S21 of etching the silicon layer 18 to form a silicon pattern layer 30 having an array pattern (silicon array pattern) 36 made of a plurality of silicon pillars 32, and an oxidation treatment step S22 of oxidizing at least a portion of the silicon in the silicon pattern layer 30 to form a pattern layer 20 made of a plurality of silicon oxide pillars 22.

[0042] (Mask Pattern Forming Step S20) In the mask pattern forming step S20, a mask pattern 50 is formed on the silicon layer 18 of the substrate 40 ( FIG. 9( a)). The thickness and material of the mask pattern 50 are not particularly limited as long as they can form the silicon pattern layer 30 after etching. The mask pattern 50 may be made of resin, silicon oxide, silicon nitride, or alumina. The method for forming the mask pattern 50 on the substrate 40 is not particularly limited. For example, when the mask pattern 50 is made of resist, the mask pattern 50 can be formed by the method described below. Resist is applied to the substrate 40, and patterning is performed by lithography (electron beam lithography, deep ultraviolet lithography, nanoimprint lithography, etc.). After lithography, the mask pattern 50 can be formed by development.

[0043] The mask pattern 50 may be formed from a metal. An example of a method for forming the mask pattern 50 when the mask pattern 50 is made of a metal such as Cr will be described below. First, a metal such as Cr is deposited on the substrate 40 by vapor deposition or the like. Then, a resist (resin) is applied onto the deposited metal. After the resist is applied, patterning is performed by lithography. The metal is then etched to form the mask pattern 50. By using a metal that is more difficult to etch than the resist as the mask pattern 50, it is possible to prevent the surfaces 32a on the tip side of the silicon pillars 32 from being scraped off during etching. This allows the planar shape of the silicon pillars 32 to be processed more precisely, and reduces the difference between the designed optical properties and the optical properties of the metalens 100.

[0044] The substrate 40 is not particularly limited as long as it has a silicon layer 18 on its surface and can reflect incident light. In the first embodiment, the substrate 40 includes a support substrate 15, an intermediate layer 12 provided on the support substrate 15, and a silicon layer 18 provided on the intermediate layer 12. The material of the support substrate 15 is not particularly limited. For example, it is silicon. The material of the intermediate layer 12 is preferably a material that has a lower etching rate than Si when etched. The material of the intermediate layer 12 is, for example, SiO ２ The material of the intermediate layer 12 is SiO ２ If the material has an etching rate lower than that of Si, such as silicon dioxide, etching in intermediate layer 12 is suppressed, making it easier to control the height of silicon pillars 32. The thickness of support substrate 15 is not particularly limited as long as it can function as reflective metalens 100. The thickness of intermediate layer 12 is also not particularly limited as long as it can function as reflective metalens 100. The thickness of intermediate layer 12 is, for example, 1 μm to 20 μm. Substrate 40 is, for example, a silicon-on-insulator (SOI) substrate.

[0045] There are no particular limitations on the crystallinity of the silicon layer 18. The silicon layer 18 may be single crystal, polycrystalline, or amorphous. The silicon layer 18 is preferably single crystal.

[0046] The thickness of the silicon layer 18 can be set as appropriate depending on the design of the metalens 100. For example, if the mask pattern 50 is not removed during etching, the thickness of the silicon layer 18 becomes the height H of the silicon oxide pillars 22. For example, the thickness of the silicon layer 18 is 1.0 μm to 3.0 μm.

[0047] (Etching Step S21) In the etching step S21, the silicon layer 18 is etched to form a silicon pattern layer 30 having an array pattern 36 composed of a plurality of silicon pillars 32 ( FIG. 9B ). In the etching step S21, the silicon pattern layer 30 may be etched taking into account silicon expansion during the oxidation treatment step S22. Because of the high etching selectivity of Si, silicon pillars 32 with a high aspect ratio can be formed. Dry etching is preferred. Dry etching can be performed by a known method, such as inductively coupled plasma etching. The etching preferably involves alternating a passivation step for forming a blocking layer and an etching step for etching silicon. This allows the formation of silicon pillars 32 with a high aspect ratio. When etching silicon, the silicon pillars 32 are formed with a width equal to the design value of the silicon pillars 32 calculated from a feedback function. Typically, the silicon pillars 32 are formed thinner than the set value, taking into account expansion during the oxidation treatment.

[0048] The center-to-center distance Λx1 between the silicon pillars 32 formed in the etching step S21 in the X direction is ｘ１ It is more preferable that the center-to-center distance Λ between the silicon pillars 32 in the X direction is 1.4 times or more. ｘ１ is the width a of the silicon pillar 32 ｘ１ When the silicon pillars 32 are completely oxidized, the width of the silicon pillars 32 becomes, for example, 1.4 to 1.6 times. Therefore, by making the center-to-center distance Λx1 in the X direction 1.4 to 1.6 times, it is possible to prevent the silicon oxide pillars 22 from connecting with each other. Similarly, the center-to-center distance Λy1 between the silicon pillars 32 in the Y direction is also 1.6 times or more larger than the width a of the silicon pillars 32 in the Y direction.ｙ１ It is more preferable that the center-to-center distance Λ between the silicon pillars 32 in the Y direction is 1.4 times or more. ｙ１ is the width a of the silicon pillar 32 ｙ１ This is more than 1.6 times the original amount.

[0049] (Oxidation Treatment Step S22) In the oxidation treatment step S22, after removing the mask pattern 50, at least a portion of the silicon in the silicon pattern layer 30 is oxidized to form a pattern layer 20 consisting of a plurality of silicon oxide pillars 22 (FIG. 9C). Since the feedback function is taken into consideration, the formed silicon oxide pillars 22 have a value close to a set value. The pattern layer 20 consisting of the silicon oxide pillars 22 has a focus for light incident on the pattern layer 20. By oxidizing the silicon pillars 32 to form the silicon oxide pillars 22, it is possible to form a high aspect ratio SiO 2 without damaging the silicon pillars. ２ It is possible to form pillars made of the above. The method for oxidizing silicon is not particularly limited. Thermal oxidation is a preferred oxidation method. Examples of thermal oxidation methods include dry oxidation, wet oxidation, and steam oxidation. Dry oxidation and wet oxidation are preferred. Wet oxidation is particularly preferred. By oxidizing the silicon pillars 32 by wet oxidation, it is possible to form silicon oxide pillars 22 in a short time.

[0050] The temperature during oxidation is not particularly limited, but is, for example, 800° C. to 1150° C. The time for oxidizing the silicon pattern layer 30 can be set appropriately. ２ All silicon in the silicon pattern layer 30 may be replaced with SiO ２ By doing so, the transparency of the pattern layer 20 can be improved.

[0051] The method for manufacturing a metalens according to the present embodiment has been described above. According to the method for manufacturing a metalens according to the first embodiment, a high aspect ratio SiO ２ Therefore, it is possible to manufacture a metalens 100 with a short focal length.

[0052] The method for manufacturing the metalens of the first embodiment may include, after the etching step S21, a step of annealing the substrate including the silicon pattern layer 30 in a hydrogen atmosphere, an argon atmosphere, or a mixed atmosphere of hydrogen and argon. By performing hydrogen annealing, argon annealing, or annealing in a mixed gas of hydrogen and argon after the etching step S21, it is possible to reduce unevenness on the side surfaces of the silicon pillars 32. The hydrogen annealing, argon annealing, or annealing in a mixed gas of hydrogen and argon can be performed, for example, in an atmosphere of 100% hydrogen, 100% argon, or a mixed atmosphere of hydrogen and argon, at a temperature of 800°C to 1200°C.

[0053] Second Embodiment The support substrate 15 of the metalens according to the first embodiment is a transparent substrate (e.g., silicon dioxide (SiO ２ )). This allows the metalens 100 according to the second embodiment to be a transmissive metalens that transmits incident light. In this case, the intermediate layer 12 may be present as long as it is transparent, or the intermediate layer 12 may be omitted. During production, a transparent SiO ２ Just use

[0054] The metalens 100 of the second embodiment may be warped.

[0055] Third Embodiment A metalens according to a third embodiment of the invention will now be described. FIG. 10( a) is an enlarged plan view of a portion of the array pattern of a metalens 100C according to the third embodiment. FIG. 10( b) is a cross-sectional view of the metalens 100C of FIG. 10( a) taken along line CC. The metalens 100C comprises, in this order, a support substrate 15 and a patterned layer 20C having an array pattern 26C consisting of a plurality of holes 24. The metalens 100C according to the third embodiment is a reflective metalens that reflects incident light.

[0056] (Pattern Layer 20C) In the third embodiment, the pattern layer 20C is provided on the intermediate layer 12. The pattern layer 20C has an array pattern 26C consisting of a plurality of holes 24. Here, the array pattern 26C is a pattern in which microstructures (holes 24 in the third embodiment) are regularly arranged in the X and Y directions at predetermined intervals. The pattern layer 20C is made of at least SiO ２ The pattern layer 20C may include Si.

[0057] The shape (planar shape) of the hole 24 as viewed from the Z direction is not particularly limited, and may be a polygon, a circle, etc. In the third embodiment, the planar shape of the hole 24 is a square. ｘｃ and the width in the Y direction a ｙｃ is set appropriately depending on the design of the metalens 100C. ｘｃ is, for example, 150 nm to 600 nm. ｙｃ is, for example, 150 nm to 600 nm.

[0058] The center-to-center distance (period) Λ of the holes 24 along the X direction as viewed from the Z direction ｘｃ and the center-to-center distance (period) Λ of the holes 24 along the Y direction ｙｃ is set appropriately depending on the design of the metalens 100C. The period Λ of the holes 24 along the X direction ｘｃ is, for example, 200 nm to 600 nm. The period Λ of the holes 24 along the Y direction ｙｃ is, for example, 200 nm to 600 nm. ｘｃ and period Λ ｙｃ It is preferable that the center of the hole 24 viewed from the Z direction is the center of the smallest encompassing circle when the planar shape (external shape) of the hole 24 is a polygon, and the center of the circle when the planar shape (external shape) of the hole 24 is a circle.

[0059] The length (depth) Hc of the holes 24 in the Z direction is set appropriately depending on the design of the metalens 100C. The depth Hc of the holes 24 is 1.0 μm to 3.0 μm.

[0060] The depth Hc of the hole 24 and the width a of the hole 24 in the X direction ｘｃ The aspect ratio (Hc / a ｘｃThe aspect ratio (Hc / a) is set appropriately depending on the design of the metalens 100C. ｘｃ The maximum value of the aspect ratio (Hc / a) is more than 6.7. ｘｃ ) is 7.0 or more. Similarly, the depth Hc of the hole 24 and the width a of the hole 24 in the Y direction ｙｃ The aspect ratio (Hc / a ｙ The maximum value of the aspect ratio (Hc / a) is also set appropriately depending on the design of the metalens 100C. ｙｃ The maximum value of the aspect ratio (Hc / a) is more than 6.7. ｙｃ When the planar shape of the hole 24 is square or circular, the maximum value of the aspect ratio (Hc / a ｘｃ ) is the aspect ratio (Hc / a ｙｃ ) In other words, in this case, the aspect ratio of the hole 24 is the ratio of the width to the depth.

[0061] As described above, the metalens 100C according to this embodiment has been described. Because the aspect ratio of the holes 24 in the metalens 100C is high, the focal length can be shortened to between 500 μm and 2500 μm.

[0062] Although metalens 100C was a reflective metalens, if a transmissive substrate is used as the substrate, it can be made into a transmissive metalens.

[0063] In the third embodiment, the metalens 100C includes the intermediate layer 12, but it does not have to include the intermediate layer 12 as long as it is possible to reflect incident light.

[0064] The metalens 100C of the third embodiment may be warped.

[0065] The manufacturing method for the metalens 100C of the third embodiment is the same as the manufacturing method for the first embodiment, except that the areas other than those that will become the holes 24 are covered with a mask pattern and then etching is performed to form the holes 24 with a high aspect ratio.

[0066] <First Modification> As a modification of the metalens according to the first embodiment, the shape (planar shape) of the silicon oxide pillars 22 may be circular. Even if the shape of the silicon oxide pillars 22 is circular, it can be made to function as a metalens by adjusting the occupancy rate fx, etc.

[0067] The metalens, metalens design method, and metalens manufacturing method according to the present embodiment have been described in detail above. Note that the technical scope of the present invention is not limited to the above embodiment, and various modifications can be made without departing from the spirit of the present invention. In addition, the components in the above embodiment can be replaced with known components as appropriate, and the above-described modifications can be combined as appropriate, without departing from the spirit of the present invention. Furthermore, the metalens according to the present embodiment can be incorporated into electronic devices. Examples of electronic devices incorporating the metalens according to the present embodiment include mobile phones.

[0068] Next, examples of the present invention will be described, but the conditions in the examples are merely examples adopted to confirm the feasibility and effects of the present invention, and the present invention is not limited to these examples. Various conditions can be adopted in the present invention as long as they do not deviate from the gist of the present invention and the object of the present invention is achieved.

[0069] Example 1 The focal length was 1000 μm and the wavelength was 532 nm. The metalens 100 was designed using the method described above in the design method for the metalens 100. The height H of the pillars was 2.5 μm, the pillar pitch was 400 nm, and the pillar width was 192 nm to 340 nm so that the phase difference was in the range of 0 to 360°. The pillar width at each position was determined from the phase difference in FIG. 5 and the distance r from the lens center, and a metalens like that shown in FIG. 7A was designed. Note that the metalens of this example was fabricated as a cylinder rather than a square pillar.

[0070] (Production of a reflective metalens) A 20 mm square SOI substrate was used. The handle layer (Si) had a thickness of 525 μm and a crystal orientation of (111), and the box layer (SiO ２The thickness of the device layer (Si) was 4 μm, and the crystal orientation of the device layer (Si) was (111). An electron beam (EB) resist (ZEP520A, manufactured by Zeon Corporation) and spacer were formed on the Si surface of the device by spin coating. The resist film thickness was approximately 140 nm.

[0071] EB lithography was performed using a JEOL EB lithography system JBX-6300SK. After EB lithography, development was performed. Pure water was used to rinse the spacer, ZED-N50 manufactured by Nippon Zeon Co., Ltd. was used as the resist developer, and isopropyl alcohol (IPA) was used to rinse the developer.

[0072] For dry etching, an inductively coupled plasma (ICP) etching device MUC-21 manufactured by SPP Technologies Co., Ltd. was used. ４ F ８ After passivation with gas for 2.5 seconds, ６ One cycle consisted of etching with gas for 3 seconds, and this cycle was repeated 20 times to process the Si pillars.

[0073] After etching, the substrate was subjected to ultrasonic cleaning with acetone for 15 minutes, rinsed with IPA, and dried on a hot plate at 110° C. for 15 minutes.

[0074] The substrate on which the Si pillars were formed was subjected to wet oxidation using a thermal oxidation furnace. The oxidation was performed at an oxidation temperature of 1100°C to fabricate a metalens. The oxidation was performed under two conditions: 1 hour and 3 hours.

[0075] (Expansion Coefficient of Width of Pillars) Silicon pillars before oxidation and silicon oxide pillars after oxidation were observed using a Hitachi High-Technologies Corporation scanning electron microscope (SEM) SU-70 to confirm the expansion coefficient of the pillar width. FIG. 11 shows the relationship between the obtained silicon pillar width (nm) and the expansion coefficient of the pillar width after oxidation. The horizontal axis of FIG. 11 represents the silicon pillar width (nm) (actually measured value of Si pillar), and the vertical axis represents the expansion coefficient of the pillar width (pillar width) (width after oxidation / width before oxidation). As shown in FIG. 11, the expansion coefficient tended to increase depending on the pillar width. At 200 to 280 nm, the expansion coefficient of the pillar width was 1.4 to 1.6 times.

[0076] (Evaluation of focal length) A schematic diagram of a focal length evaluation device is shown in FIG. 12. The solid line represents the path of light emitted from light source 51, and the dashed line represents the path of light observed by camera 52. The emitted light does not form an image on the metalens surface, but rather becomes parallel light and is irradiated onto the metalens. Camera 52 can confirm the image formed on the illuminated surface of metalens 100. The amount of light emitted from light source 51 is reduced by aperture stop 53. The light source light is redirected toward metalens 100 by half mirror 54, and then focused on the surface of metalens 100 by condenser lens 55. The image of the surface of metalens 100 is converted into parallel light by objective lens 55 and directed toward camera 52, where it is imaged via lens 56. This makes it possible to evaluate the focal length.

[0077] First, the sample (metalens) was placed on the stage and the focus was adjusted on the device layer surface. This was set as the reference stage height of 0 μm. Next, the aperture diaphragm was narrowed to its maximum in order to make the outline of the diaphragm image as clear as possible. While checking the height with a micrometer, the stage was lowered and imaging was repeated. The captured images were evaluated using image processing software. The evaluation performed was a luminance distribution evaluation, and the luminance distribution versus distance from the center of the metalens was analyzed from the captured images. The luminance value was calculated from the RGB values ​​of the obtained image data using the following equation (7). Note that RGB stands for R (red component), G (green component), and B (blue component).

[0078]

[0079] Figure 13 shows the relationship between the distance r from the lens center and brightness when measuring metalenses oxidized for one hour at different heights. The value Z in each graph in Figure 13 indicates the distance (μm) the stage was lowered. Figure 13(a) shows the relationship between the distance r from the lens center and brightness for Z = 0 μm to Z = 500 μm. The horizontal axis of Figure 13(a) shows the distance r from the lens center, and the vertical axis shows brightness. Figure 13(b) shows the relationship between the distance r from the lens center and brightness for Z = 600 μm. The horizontal axis of Figure 13(b) shows the distance r from the lens center, and the vertical axis shows brightness. Figure 13(c) shows the relationship between the distance r from the lens center and brightness for Z = 700 μm to Z = 1400 μm. The horizontal axis of Figure 13(c) shows the distance r from the lens center, and the vertical axis shows brightness. For metalenses oxidized for one hour, the highest brightness was achieved at Z = 500 μm. The bottom of the brightness distribution broadened at Z=600 μm, and the brightness decreased from Z=700 μm to 1400 μm.

[0080] Figure 14 shows the relationship between luminance and the distance r from the lens center, measured by changing the height of the metalens oxidized for three hours. The value of Z in each graph in Figure 14 indicates the distance (μm) the stage was lowered. Figure 14(a) shows the relationship between luminance and the distance r from the lens center for Z = 0 μm to Z = 500 μm. The horizontal axis of Figure 14(a) shows the distance r from the lens center, and the vertical axis shows the luminance. Figure 14(b) shows the relationship between luminance and the distance r from the lens center for Z = 600 μm. The horizontal axis of Figure 14(b) shows the distance r from the lens center, and the vertical axis shows the luminance. Figure 14(c) shows the relationship between luminance and the distance r from the lens center for Z = 700 μm to Z = 1400 μm. The horizontal axis of Figure 14(c) shows the distance r from the lens center, and the vertical axis shows the luminance. For the metalens oxidized for three hours, the highest luminance was achieved at Z = 500 μm. The brightness distribution broadened at Z=600 μm, and the brightness decreased from Z=700 μm to 1400 μm. The brightness was higher after 3 hours of oxidation. This is because the SiO ２It is speculated that the improvement in the ratio of SiO2 and the change in phase due to dimensional expansion caused by oxidation manifested as a change in brightness. The height of the pillars obtained was 1521 nm, and the width of the silicon oxide pillars was 200 nm to 350 nm. It was confirmed that pillars with a high aspect ratio (height / width) of 4.3 to 7.6 could be formed in metalenses oxidized for 3 hours.

[0081] Example 2 Next, the discrepancy between the measured and designed widths of the silicon oxide pillars of the obtained metalens was corrected, and a metalens was fabricated again. The correction was performed using the following procedure. First, the widths of the silicon oxide pillars of the metalens were measured using an SEM. Next, an approximate equation (8) was created by linear approximation based on the ratio of the measured and designed widths of the obtained silicon oxide pillars and the designed value of the pillars. FIG. 15 shows the results of linear approximation based on the ratio of the measured width Wmp of the silicon oxide pillars to the designed width Wd and the designed value of the pillars. The horizontal axis of FIG. 15 represents the pillar width (nm), and the vertical axis represents the ratio of the measured width Wmp of the pillars to the designed width Wd (measured value Wmp / design value Wd). Multiplying both sides of the obtained equation (8) by the designed width Wd of the pillars yielded the prediction function, equation (9). By inversely solving equation (9), equation (10) was obtained, which is a feedback function. In equation (10), Wd is the set value before correction, and Wdf is the set value after correction. Based on this correction, the width of each silicon oxide pillar was corrected. Next, using the same fabrication method as in Example 1, a metalens of Example 2 was fabricated based on the corrected design. Note that the metalens fabricated in Example 2 refracts light primarily in pattern layer 20 and then passes through an intermediate layer (SiO ２ The light passes through the intermediate layer 12, is reflected at the interface between the intermediate layer 12 and the support substrate 15, and is then secondarily refracted again at the pattern layer 20. Therefore, the lens is designed as a combination of two lenses with a combined focal length (reflection focal length). In Example 2, the reflection focal length was set to 835 μm.

[0082]

[0083] (Evaluation of Focal Length) Figure 16 shows a color map of the brightness measurement results for the metalens of Example 2. At height positions Z = 700-1100 μm, light focusing occurred near the center, resulting in high brightness (shown by a box in Figure 16). This demonstrates that the fabricated metalens layer functions as a light focusing element. Overall brightness was also high. Although not shown in the figure, when brightness was examined for each height position at r = 0.101 μm near the center, the highest brightness was obtained at Z = 1000 μm, with a maximum value of 245. The strongest light focusing occurred at this position, and the focal length of the fabricated reflective metalens was f = 1000 μm. These results suggest that the metalens of the present invention and metalenses obtained by the method for manufacturing a metalens can be widely used in electronic devices (including machinery, etc.) that use lenses, such as smartphones, VR glasses, microscopes, and cameras. As described above, experiments related to the examples demonstrate that embodiments of the present invention can provide metalens and methods for manufacturing metalens with short focal lengths. In particular, the excellent etching selectivity of Si and the thermal oxidation of SiO ２ It was confirmed that this has an exceptional effect of enabling

[0084] The foregoing has described the metalens, metalens manufacturing method, electronic device, and metalens design method according to the present embodiments. The metalens according to the present embodiments can shorten the focal length. Furthermore, the metalens manufacturing method and metalens design method according to the present embodiments can obtain a metalens with a short focal length.

[0085] The metalenses of the present disclosure have high industrial applicability due to their short focal lengths.

[0086] 12 Intermediate layer, 15 Support substrate, 20 Pattern layer, 22 Silicon oxide pillars, 24 Holes, 100 Metalens

Claims

1. A method for manufacturing a metalens, comprising: a mask pattern forming step of forming a mask pattern on a silicon layer of a substrate having a silicon layer on a surface thereof; an etching step of etching the silicon layer to form a silicon pattern layer having an array pattern of a plurality of silicon pillars or a plurality of pre-oxidation holes; an oxidation treatment step of oxidizing at least a portion of the silicon in the silicon pattern layer to form a pattern layer consisting of a plurality of silicon oxide pillars or a plurality of holes; Including, a patterned layer having a focal point for light incident on the patterned layer;

2. The method of making a metalens according to claim 1 , wherein the oxidation is wet oxidation or dry oxidation.

3. After the etching step, 3. A method for producing a metalens according to claim 1 or 2, further comprising the step of annealing the substrate carrying the silicon patterned layer under a hydrogen atmosphere, an argon atmosphere, or a mixed atmosphere of hydrogen and argon.

4. The method for producing a metalens according to claim 1 or 2, wherein the mask pattern is made of resin, silicon oxide, silicon nitride, or alumina.

5. The method for producing a metalens according to claim 1 or 2, wherein the mask pattern is made of a metal.

6. 3. A method for producing a metalens according to claim 1 or 2, wherein a maximum aspect ratio of the silicon oxide pillars or the holes in the patterned layer is greater than 6.

7.

7. 3. The method for producing a metalens according to claim 1 or 2, wherein the center-to-center distance between the silicon pillars is 1.4 times or more the width of the silicon pillars.

8. The method for producing a metalens according to claim 1 or 2, wherein in the etching step, the silicon pattern layer is etched taking into account expansion of silicon in an oxidation treatment step.

9. A support substrate; a pattern layer having an array pattern of silicon oxide pillars or holes; In this order, the maximum aspect ratio of the silicon oxide pillars or holes in the pattern layer is greater than 6.7; At least the surfaces of the silicon oxide pillars or the holes of the pattern layer are made of SiO ２ That is, metalens.

10. The pattern layer is made of SiO ２ The metalens of claim 9 , consisting of

11. Between the support substrate and the pattern layer, 11. The metalens of claim 9 or 10, further comprising an intermediate layer.

12. The metalens according to claim 9 or 10, wherein the patterned layer has a folded portion at a portion where the phase difference with respect to the center is 360°.

13. An electronic device equipped with the metalens according to claim 9 or 10.

14. 1. A method of designing a metalens, comprising: a phase difference calculation step of calculating a phase difference φ(r) with respect to a distance r from a center of the metalens based on a set wavelength λ of incident light and a focal length f; The height H and width a of the silicon oxide pillars constituting the metalens ｘ , and period Λx and width a ｘ Phase difference φ(a ｘ ) by calculating the relationship between the height H and the width a ｘ and the period Λx; After the step of determining the dimensions of the pillars, the phase difference φ(r) and the width a ｘ Phase difference φ(a ｘ ) the width a relative to the distance r from the center of the metalens ｘ a calculation step of calculating the width of the pillar with respect to the distance r, Including, In the phase difference calculation step, when the phase difference φ(r) with respect to the distance r is 360° or more, φ′(r) is calculated so as to satisfy the following formulas (A) and (B): The width a x of the silicon oxide pillar is corrected to take into account the expansion due to the oxidation of silicon. How to design a metalens. φ'(r)=φ(r)-360°×n...(A) φ'(r)<360°...(B) Here, in the above formula (A), n is a natural number.

15. A method for producing a metalens according to claim 1 or 2, further comprising the step of performing the method for designing a metalens according to claim 14.