JP7378692B1 - Method for manufacturing optical semiconductor device and method for designing low reflectance film - Google Patents

Abstract

The method for manufacturing an optical semiconductor device of the present disclosure is based on a characteristic matrix of a single-layer coating film (12) having a film thickness of λ0/4/nfl, and one material having a refractive index lower than the refractive index nfl and another material having a refractive index lower than the refractive index nfl. Calculate the minimum value Rmin0 of reflectance by equating the characteristic matrices of multilayer coating films (13, 14, 15) using two or more types of materials in which the refractive index of one material is higher than the refractive index nfl However, the characteristic matrix of the single layer coating film (12) with a film thickness of λ0/4/nfl1, the refractive index of one material is lower than the refractive index nfl1, and the refractive index of the other material is the refractive index nfl1 The minimum value Rmin at the wavelength λmin of the multilayer coating (13, 14, 15) is set equal to the characteristic matrix of the multilayer coating (13, 14, 15) using two types of materials with higher A multilayer coating film (13, 14, 15) is formed on the end face based on each film thickness obtained by matching the minimum reflectance R0.

Description

The present disclosure relates to a method for manufacturing an optical semiconductor device and a method for designing a low reflectance film.

As disclosed _{in Non-Patent Document 1, a refractive index n f ( =} 1.72, Al ₂ O ₃ ), the reflectance of the coating changes periodically with respect to the film thickness, and when the film thickness d _f is an integral multiple of λ ₀ /(4n _f ), the reflectance of the coating changes periodically. becomes the minimum value. The minimum reflectance R ₀ at this time is expressed by the following equation (1) and is uniquely determined.

つまり、波長λ₀に対する極小反射率Ｒ₀は、光半導体装置の実効屈折率ｎ_cと、光半導体装置の出射端面（前端面）に設けられた被覆膜の屈折率ｎ_fによって一義的に決定され、極小反射率Ｒ₀を変えることができなかった。

In other words, the minimum reflectance R ₀ for the wavelength λ ₀ is uniquely determined by the effective refractive index n _c of the optical semiconductor device and the refractive index n _f of the coating film provided on the output end face (front end face) of the optical semiconductor device. determined, and the minimum reflectance R ₀ could not be changed.

For example, in a semiconductor laser device, when controlling the mirror loss calculated from the end face reflectance and cavity length of the semiconductor laser device from the perspective of reducing threshold current or improving efficiency, the mirror loss value is set to the desired value. I couldn't change it.

I. Ladany et. al. , “Al2O3 half-wave films for long-life cw lasers,” Appl. Phys. Lett. , vol. 30, no. 2, pp. 87-88, 1977

Conventional optical semiconductor device manufacturing methods and low reflectance film designing methods have a problem in that the minimum reflectance R ₀ at a desired wavelength λ ₀ cannot be controlled to a desired minimum reflectance.

The present disclosure has been made to solve the above-mentioned problems, and by replacing the single-layer coating film with a multilayer coating film of three or more layers using a characteristic matrix, it is possible to obtain a desired wavelength at a desired wavelength. The present invention aims to obtain a method for manufacturing an optical semiconductor device having a low reflectance film controlled to a desired minimum reflectance, and also to obtain a method for designing a low reflectance film.

A method for manufacturing an optical semiconductor device according to the present disclosure includes:
A method for manufacturing an optical semiconductor device in which a low reflectance film having an effective refractive index n _c and a minimum reflectance R ₀ that is a desired minimum reflectance at a desired wavelength λ ₀ is formed,
The refractive index n _fl is expressed by the following formula,

膜厚がλ₀／４／ｎ_flである単層からなる被覆膜の特性行列と、少なくとも１つの材料の屈折率が前記屈折率ｎ_flよりも低く、少なくとも他の１つの材料の屈折率が前記屈折率ｎ_flよりも高い２種類以上の材料を用いた３層以上の被覆膜からなる多層被覆膜の特性行列とを等しいとすることにより、前記多層被覆膜の反射率の波長依存性を有する反射率の極小値Ｒ_min ⁰を算出し、
予め設定された設定反射率Ｒ₁を実現する単層からなる被覆膜の屈折率ｎ_fl ¹が、以下の式で表され、

A characteristic matrix of a coating film consisting of a single layer having a film thickness of λ ₀ /4/n _fl , a refractive index of at least one material lower than the refractive index n _fl , and a refractive index of at least one other material. is equal to the characteristic matrix of a multilayer coating consisting of three or more coating films using two or more types of materials having a refractive index higher than the refractive index n _fl , the reflectance of the multilayer coating is Calculate the minimum value R _min ⁰ of the reflectance that has wavelength dependence,
The refractive index n _fl ¹ of a coating film consisting of a single layer that realizes a preset set reflectance R ₁ is expressed by the following formula,

膜厚がλ₀／４／ｎ_fl ¹の単層からなる被覆膜の特性行列と、少なくとも１つの材料の屈折率が前記屈折率ｎ_fl ¹よりも低く、少なくとも他の１つの材料の屈折率が前記屈折率ｎ_fl ¹よりも高い２種類以上の材料を用いた３層以上の被覆膜からなる多層被覆膜の特性行列とを等しいとすることにより、前記多層被覆膜の反射率の波長依存性における波長λ_minにおける反射率の極小値Ｒ_minを前記極小反射率Ｒ₀と一致させ、
前記波長λ_minにおける前記極小値Ｒ_minを前記波長λ₀における前記極小反射率Ｒ₀と一致させることによって得られる前記３層以上の被覆膜の各膜厚に基づき多層被覆膜を端面に形成する。

A characteristic matrix of a coating film consisting of a single layer with a film thickness of λ ₀ /4/n _fl ¹ , a refractive index of at least one material lower than the refractive index n _fl ¹ , and a refraction of at least one other material. The reflection of the multilayer coating film is made equal to the characteristic matrix of a multilayer coating film consisting of three or more coating films using two or more types of materials whose refractive index is higher than the refractive index n _fl ¹ . In the wavelength dependence of the reflectance, the minimum value R _min of the reflectance at the wavelength λ _min is made to match the minimum reflectance R ₀ ,
A multilayer coating film is applied to the end face based on the thickness of each of the three or more coating films obtained by matching the minimum value R _min at the wavelength λ _min with the minimum reflectance R ₀ at the wavelength λ ₀ . Form.

A method for designing a low reflectance film according to the present disclosure includes:
A method of designing a low reflectance film having a minimum reflectance _R0 , which is a desired minimum reflectance other than zero, on an end face of an optical semiconductor device having an effective refractive index _nc , the method comprising:
a step of calculating _the refractive index n _fl by the following formula;

所望の波長λ₀において膜厚がλ₀／４／ｎ_flである単層からなる被覆膜の特性行列と、少なくとも１つの材料の屈折率が前記屈折率ｎ_flよりも低く、少なくとも他の１つの材料の屈折率が前記屈折率ｎ_flよりも高い２種類以上の材料を用いた３層以上の被覆膜からなる多層被覆膜の特性行列とを等しいとすることにより、前記多層被覆膜の反射率の波長依存性を有する反射率の極小値Ｒ_min ⁰を算出するステップと、
予め設定された設定反射率Ｒ₁を実現する単層からなる被覆膜の屈折率ｎ_fl ¹を、以下の式を用いて算出するステップと、

A characteristic matrix of a coating film consisting of a single layer having a film thickness of λ ₀ /4/n _fl at a desired wavelength λ ₀ and at least one material having a refractive index lower than the refractive index n fl and at least another material having a refractive index lower than the refractive index n _fl By making the characteristic matrices of a multilayer coating film made of three or more coating films using two or more types of materials in which the refractive index of one material is higher than the refractive index n _fl to be equal, the multilayer coating calculating a minimum value R _min ⁰ of the reflectance of the coating having wavelength dependence;
Calculating the refractive index n _fl ¹ of a coating film made of a single layer that achieves a preset set reflectance R ₁ using the following formula;

膜厚がλ₀／４／ｎ_fl ¹の単層からなる被覆膜の特性行列と、少なくとも１つの材料の屈折率が前記屈折率ｎ_fl ¹よりも低く、少なくとも他の１つの材料の屈折率が前記屈折率ｎ_fl ¹よりも高い２種類以上の材料を用いた３層以上の被覆膜からなる多層被覆膜の特性行列とを等しいとすることにより、前記多層被覆膜の反射率の波長依存性における波長λ_minにおける反射率の極小値Ｒ_minを前記極小反射率Ｒ₀と一致させるステップと、
前記波長λ_minにおける前記極小値Ｒ_minを前記波長λ₀における前記極小反射率Ｒ₀と一致させることによって得られる前記３層以上の被覆膜の各膜厚に基づき多層被覆膜の各膜厚を決定するステップと、
を備える。

A characteristic matrix of a coating film consisting of a single layer with a film thickness of λ ₀ /4/n _fl ¹ , a refractive index of at least one material lower than the refractive index n _fl ¹ , and a refraction of at least one other material. The reflection of the multilayer coating film is made equal to the characteristic matrix of a multilayer coating film consisting of three or more coating films using two or more types of materials whose refractive index is higher than the refractive index n _fl ¹ . a step of matching the minimum value R _min of the reflectance at the wavelength λ _min in the wavelength dependence of the reflectance with the minimum reflectance R ₀ ;
Each film of the multilayer coating film based on the thickness of each of the three or more coating films obtained by matching the minimum value R _min at the wavelength λ _min with the minimum reflectance R ₀ at the wavelength λ ₀ determining the thickness;
Equipped with

According to the method for manufacturing an optical semiconductor device and the method for designing a low reflectance film according to the present disclosure, a single-layer coating film is replaced with a multilayer coating film of three or more layers using a characteristic matrix, so that a desired It becomes possible to manufacture an optical semiconductor device having a low reflectance film whose reflectance is controlled to a desired minimal reflectance at a wavelength of 1, and also to obtain a method for designing a low reflectance film.

1 is an overview diagram of a quantum cascade laser device that is an example of an optical semiconductor device in Embodiment 1. FIG. 2 is a cross-sectional view taken along line AA in FIG. 1 of a quantum cascade laser device, which is an example of an optical semiconductor device in Embodiment 1. FIG. FIG. 2 is a schematic diagram for explaining a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 1. FIG. FIG. 3 is a diagram showing the wavelength dependence of the reflectance of a low reflectance film designed by the method for designing a low reflectance film having minimal reflectance of the optical semiconductor device in Embodiment 1; 2 is a schematic diagram showing a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 1. FIG. FIG. 2 is a schematic diagram for explaining a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 1. FIG. FIG. 3 is a diagram showing the wavelength dependence of the reflectance of a low reflectance film designed by the method for designing a low reflectance film having minimal reflectance of the optical semiconductor device in Embodiment 1; 7 is a schematic diagram for explaining a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 2. FIG. FIG. 7 is a diagram showing the wavelength dependence of the reflectance of a low reflectance film designed by the method of designing a low reflectance film having minimal reflectance of an optical semiconductor device in Embodiment 2; 7 is a schematic diagram for explaining a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 2. FIG. FIG. 7 is a diagram showing the wavelength dependence of the reflectance of a low reflectance film designed by the method of designing a low reflectance film having minimal reflectance of an optical semiconductor device in Embodiment 2; FIG. 7 is a schematic diagram for explaining a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 3; FIG. 7 is a diagram showing the wavelength dependence of the reflectance of a low reflectance film designed by the method of designing a low reflectance film having minimal reflectance of an optical semiconductor device in Embodiment 3; FIG. 7 is a schematic diagram for explaining a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 3; FIG. 7 is a diagram showing the wavelength dependence of the reflectance of a low reflectance film designed by the method of designing a low reflectance film having minimal reflectance of an optical semiconductor device in Embodiment 3; FIG. 7 is a schematic diagram for explaining a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 4; FIG. 7 is a diagram showing the wavelength dependence of the reflectance of a low reflectance film designed by the method for designing a low reflectance film having minimal reflectance of an optical semiconductor device in Embodiment 4; FIG. 7 is a schematic diagram for explaining a method of designing a low reflectance film having minimal reflectance for an optical semiconductor device in Embodiment 4; FIG. 7 is a diagram showing the wavelength dependence of the reflectance of a low reflectance film designed by the method for designing a low reflectance film having minimal reflectance of an optical semiconductor device in Embodiment 4;

Embodiment 1.
FIG. 1 is an overview diagram showing a quantum cascade laser device 100, which is an example of an optical semiconductor device according to the first embodiment. A quantum cascade laser device 100 according to the first embodiment includes an n-type first electrode 1, an n-type InP substrate 2, an n-type InP buffer layer 3, an n-type GaInAs first optical confinement layer 4, and 30 to 40 A core region 5 consisting of each stage, an n-type GaInAs second optical confinement layer 6, an n-type InP cladding layer 7, an n-type GaInAs contact layer 8, and an n-type second electrode 9. . Hereinafter, the quantum cascade laser device 100 may be referred to as an optical semiconductor device 11.

One stage of the core region 5 has a multi-quantum well (MQW) structure in which many GaInAs well layers and AlInAs barrier layers are laminated, and the oscillation wavelength is within the range of 3 to 24 μm. It is infrared light. Note that in FIG. 1, the low reflectance film 10 provided on the front end surface is not shown.

FIG. 2 is a cross-sectional view of the quantum cascade laser device 100 taken along line AA in FIG. A low reflectance film 10 is provided on the output end face of the quantum cascade laser device 100, which is composed of a plurality of coating films (hereinafter referred to as a multilayer coating film) and has a minimum reflectance at wavelength λ ₀ . .

An optical semiconductor device 11 having an effective refractive index n _c is coated with a single layer coating film (hereinafter referred to as a single layer) having a refractive index n _f at a wavelength λ ₀ and a film thickness set to λ ₀ /(4n _f ). When a single-layer coating film (referred to as a layer coating film) is provided, the reflectance of the single-layer coating film becomes the minimum reflectance R ₀ which is the minimum value. The minimum reflectance R ₀ is expressed by the above equation (1).

Conversely, from equation (1), the refractive index n _fl and n _fh of the coating film for realizing the desired minimum reflectance R ₀ are calculated using equation (2) below.

For example, when the effective refractive index n _c of the optical semiconductor device 11 is 3.2 and the minimum reflectance R ₀ =0.005 (0.5%), the refractive index n _fl and the refractive index n _fh are respectively , 1.666535 and 1.920152. However, there is currently no material constituting the coating film that has these refractive index values and is applicable to optical semiconductor devices. Therefore, in the present disclosure, the above-mentioned refractive index value is achieved by substituting a known material.

First, the case where the refractive index n _fl =1.666535 will be explained. Consider replacing the single-layer coating film with a three-layer coating film made of two materials: a material with a refractive index lower than the refractive index n _fl and a material with a refractive index higher than the refractive index n _fl .

FIG. 3 shows a single layer coating film 12 having a refractive index n _fl and a film thickness d _fl of λ ₀ /(4n _fl ), a film thickness d ₁ at a refractive index n ₁ , and a film thickness d at a refractive index n _2, respectively. ₂ and a three-layer coating film having a refractive index n ₁ and a film thickness d _3. FIG. As shown in FIG. 3, a film is formed on the end face of the optical semiconductor device 11 which emits light of wavelength λ ₀ with an effective refractive index n _c and a film thickness d _fl =λ ₀ / with a refractive index n _fl (=1.66535). (4n _fl ), a first coating 13 having a refractive index n ₁ and a thickness d ₁ , a second coating 14 having a refractive index n ₂ and a thickness d ₂ , It is replaced with a three-layer coating film of the third coating film 15 having a refractive index n ₁ and a film thickness d ₃ . If the single-layer coating film 12 can be replaced with a three-layer coating film, the characteristic matrices of both will be equal, as expressed by the following equation (3).

式（３）中の各被覆膜の位相項φ₁、φ₂及びφ₃は、以下の式（４）で表される。

The phase terms φ ₁ , φ ₂ and φ ₃ of each coating film in equation (3) are expressed by the following equation (4).

In equation (3), the refractive index n ₁ and refractive index n ₂ are known, so there are three unknowns: film thicknesses d ₁ , d ₂ and d ₃ , and each film thickness can be calculated by solving equation (3). It can be calculated.

The wavelength λ ₀ = 10 μm, the first coating film 13 and the third coating film 15 are YF 3 having a refractive index n ₁ = 1.40, which is lower than n _fl , and the second coating film ₁₄ is YF 3. When formula (3) is solved using ZnS, which has a refractive index n ₂ = 2.20, which is higher than n _fl , as an example, the thickness of each coating film is d ₁ =654.371 nm, d ₂ respectively. = 277.806 nm, d ₃ = 654.371 nm. The wavelength dependence of the reflectance in this case is shown by the dashed-dotted line 22 in FIG. Although the reflectance is 0.5% at a wavelength of 10 μm, this value is not a minimum value, and the minimum value R _min ⁰ of the reflectance of the three-layer coating film is 0.4857%.
In addition, in this disclosure, the meanings of R _min and R _min ⁰ are as follows.
(1) R _min : Minimum value of reflectance of multilayer coating when the set reflectance R ₁ of single layer coating is replaced with multilayer coating (2) R _min ⁰ : Due to single layer coating Minimum value of reflectance of multilayer coating film when desired minimum reflectance R ₀ is replaced with multilayer coating film

The minimum reflectance R _{min 0} of the three-layer coating is 0.4857%, compared to the minimum reflectance R ⁰ :0.5% of the single-layer coating. It will be lower than R ₀ . Therefore, the set reflectance R ₁ is set high in order to bring the minimum value R _min of the reflectance of the three-layer coating film to the desired minimum reflectance R ₀ . The guideline for the reflectance increment ΔR ₀ is R ₀ −R _min ⁰ =0.0143%, and the increment ΔR ₀ is adjusted until it matches the desired minimum reflectance R ₀ . In the first embodiment, the increment ΔR ₀ is 0.0146%, and the set reflectance R ₁ is 0.51460%. From the following equation (5), the refractive index n _fl ¹ of the single layer coating film for realizing the set reflectance R ₁ =0.51460% is calculated as 1.6648189.

That is, from equation (5), the refractive index n _fl ¹ of the single-layer coating film for realizing R ₁ =0.51460% is calculated as 1.6648189. When the film thickness of each coating film is calculated by solving the following equation (6), d ₁ =655.839 nm, d ₂ =276.062 nm, and d ₃ =655.839 nm, respectively.

The wavelength dependence of the reflectance in this case is shown by the two-dot chain line 23 in FIG. The minimum value R _min of the reflectance of the three-layer coating film is 0.5% at the wavelength λ _min =9.876 μm, which is the desired minimum reflectance of 0.5%.

Next, the wavelength λ _min at which the reflectance is minimal is set to the desired wavelength λ ₀ . Multiplying the thickness of each coating film by λ ₀ /λ _min yields d ₁ =664.074 nm, d ₂ =279.528 nm, and d ₃ =664.074 nm. The wavelength dependence of the reflectance in this case is shown by the solid line 24 in FIG. It can be seen that the minimum reflectance is 0.5% at the wavelength λ ₀ =10 μm.

Note that the broken line 21 in FIG. 4 shows the wavelength dependence of the reflectance for a single layer coating film having a refractive index n _fl and a film thickness λ ₀ /(4n _fl ). Although the solid line 24 and the broken line 21 in FIG. 4 do not completely match, they show almost the same wavelength dependence of reflectance, and the wavelengths at which the minimum reflectance and the minimum reflectance are reached completely match.

Minimum reflectance R ₀ =0.5% and wavelength λ ₀ =10 μm are examples, and the present invention is not limited to these values, and can be set to desired values. Further, in the above example, YF ₃ was used for the first coating film 13 and the third coating film 15, and ZnS was used for the second coating film 14, but the invention is not limited to these. It is sufficient to have at least one material whose refractive index is higher than _fl and n _fl ¹ and at least one material whose refractive index is lower than n _fl and n _fl ¹ , and the order of the materials can be arbitrarily selected.
From the above, it can be seen that a desired minimum reflectance at a desired wavelength can be achieved using a material with a known refractive index.

Figure 5 shows a method of replacing a single-layer coating film with a refractive index n _fl that has a minimal reflectance R ₀ at a wavelength λ ₀ and a film thickness of λ ₀ /(4n _fl ) with a three-layer coating film. It is a schematic diagram. In FIG. 5, a dotted line 21a represents the wavelength dependence of the reflectance of a single layer coating film having a refractive index n _fl and a film thickness λ ₀ /(4n _fl ), and shows the minimum reflectance R ₀ at the wavelength λ ₀ .

The above replacement method will be explained below.
(1) In order to replace the single-layer coating (broken line 21a) with a three-layer coating, the thickness of each of the three-layer coating is determined so that the characteristic matrices of both are equal. In this case, the minimum reflectance R ₀ is obtained at the wavelength λ ₀ , but the value of the minimum reflectance of the three-layer coating film (minimum value R _min ⁰ of the reflectance of the three-layer coating film) and the wavelength at which the minimum reflectance is (λ _min ) is off. The wavelength dependence of the reflectance in this case is represented by the dashed dotted line 22a in FIG.
(2) The set reflectance R ₁ of the single layer coating film is calculated as R ₁ = R ₀ + ΔR ₀ (dashed line 21b), and each film thickness of the 3-layer coating film whose characteristic matrix is equal is calculated, and the thickness is minimized at the wavelength λ _min . The reflectance is set so that the desired minimum value R _min of the reflectance of the three-layer coating film = minimum reflectance R ₀ . That is, the minimum reflectance R ₁ of the single-layer coating film is set to R ₀ +ΔR ₀ so that the minimum value R _min of the reflectance of the three-layer coating film matches the desired minimum reflectance R ₀ . The wavelength dependence of the reflectance in this case is represented by the two-dot chain line 23a in FIG.
(3) Each film thickness of the three-layer coating film is multiplied by λ ₀ /λ _min so that the reflectance R ₀ is minimal at the wavelength λ ₀ . The wavelength dependence of the reflectance in this case is represented by the solid line 24a in FIG.

The method for setting the set reflectance R ₁ will be explained in more detail below.
Assuming that the minimum reflectance of the three-layer coating film at the time of initial substitution is R _min ⁰⁽⁰⁾ ≠ R ₀ , the difference ΔR ₀ ⁽⁰⁾ from the desired reflectance R ₀ at this time is: ΔR ₀ ⁽⁰⁾ = R ₀ −R _min ⁰⁽⁰⁾ . Next, the set reflectance R ₁ ⁽¹⁾ of the single-layer coating film for the first loop is set to R ₁ ⁽¹⁾ = R ₀ +ΔR ₀ ⁽⁰⁾ , and the minimum reflectance is achieved by replacing it with a three-layer coating film. Calculate R _min ⁰⁽¹⁾ . As a result of the calculation, if R _min ⁰⁽¹⁾ = R ₀ , the calculation ends here. In this case, ΔR ₀ =ΔR ₀ ⁽⁰⁾ and R ₁ =R ₁ ⁽¹⁾ .

If R _min ⁰⁽¹⁾ ≠ R ₀ , the loop moves to the second time. The difference ΔR ₀ ⁽¹⁾ from the desired reflectance R ₀ at this time is ΔR ₀ ⁽¹⁾ =R ₀ -R _min ⁰⁽¹⁾ . The set reflectance R ₁ ⁽²⁾ of the single-layer coating film is set as R ₁ ⁽²⁾ = R ₀ +ΔR ₀ ⁽¹⁾ , and the minimum reflectance R _min ^{0 (2)} is obtained by replacing it with a three-layer coating film. calculate.

As a result of the calculation, if R _min ⁰⁽²⁾ = R ₀ , the calculation ends here. In this case, ΔR ₀ =ΔR ₀ ⁽¹⁾ and R ₁ =R ₁ ⁽²⁾ . If R _min ⁰⁽²⁾ ≠ R ₀ , the process moves to the third loop and repeats the calculation in the same way. In _other words, the set reflectance R 1 =R ^{1 (k)} can be determined by turning the loop k times until R _{min 0} ^(k ) = R ₀ .
The above is the method for setting the set reflectance _R1 .

Similarly, the case where the refractive index n _fh =1.920152 will be explained. Consider replacing the single-layer coating with a three-layer coating made of at least two materials: a material with a refractive index lower than the refractive index n _fh and a material with a refractive index higher than the refractive index n _fh .

FIG. 6 shows a single layer coating film 31 with a refractive index n _fh and a film thickness d _fh of λ ₀ /(4n _fh ), a film thickness d ₁ with a refractive index n ₁ and a film thickness d with a refractive index n _2, respectively. ₂ and a three-layer coating film having a refractive index n ₁ and a film thickness d _3. FIG. As shown in FIG. 6, the film thickness d _fh = λ ₀ / with refractive index n _fh (=1.920152) formed on the end face of the optical semiconductor device 11 that emits light of wavelength λ ₀ with effective refractive index n _c (4n _fh ), a first coating 32 with a refractive index n ₁ and a thickness d ₁ , a second coating 33 with a refractive index n ₂ and a thickness d ₂ , It is replaced with a three-layer coating film consisting of a third coating film 34 having a refractive index of n ₁ and a film thickness of d ₃ . The method for replacing the single-layer coating film with a three-layer coating film is the same as in the case of the low refractive index n _fl described above, and is performed by solving the following equation (7).

The wavelength λ ₀ =10 μm, the first coating film 32 and the third coating film 34 are YF 3 having a refractive index n ₁ =1.40, which is lower than n _fh , and the second coating film ₃₃ is YF 3 . When formula (7) is solved using ZnS, which has a refractive index n ₂ = 2.20, which is higher than n _fh , as an example, d ₁ = 434.257 nm, d ₂ = 547.934 nm, and d ₃ = 434, respectively. .257 nm. The wavelength dependence of the reflectance in this case is shown by the dashed-dotted line 36 in FIG. Although the reflectance is 0.5% at a wavelength of 10 μm, this value is not a minimum value, and the minimum value R _min ⁰ of the reflectance of the three-layer coating film is 0.4715%.

The minimum reflectance R _{min 0} of the three-layer coating is 0.4715%, which is the minimum reflectance of the single-layer coating, compared to the minimum reflectance R ⁰ :0.5% of the single-layer coating. It will be lower than R ₀ . Therefore, as in the case of the low refractive index n _fl described above, in order to make the minimum value R _min of the reflectance of the three-layer coating film the desired minimum reflectance R ₀ , the set reflectance R ₁ is set to 0.53032%. Set it high. From the following equation (8), the refractive index n _fh ¹ of the single layer coating film for realizing the set reflectance R ₁ =0.53032% is calculated as 1.9243333.

以下の式（９）を解いて各被覆膜の膜厚を計算すると、ｄ₁＝４３０．５１３ｎｍ、ｄ₂＝５５２．６９９ｎｍ、ｄ₃＝４３０．５１３ｎｍと、それぞれ算出される。

When the film thickness of each coating film is calculated by solving the following equation (9), d ₁ =430.513 nm, d ₂ =552.699 nm, and d ₃ =430.513 nm, respectively.

The wavelength dependence of the reflectance in this case is shown by the two-dot chain line 37 in FIG. The minimum value R _min of the reflectance of the three-layer coating film is 0.5% at the wavelength λ _min =10.174 μm, which is the desired minimum reflectance of 0.5%.

Next, the wavelength λ _min at which the reflectance is minimal is set to a desired wavelength λ ₀ . If each film thickness of the three-layer coating film is multiplied by λ ₀ /λ _min , then d ₁ =423.150 nm, d ₂ =543.247 nm. d ₃ =423.150 nm, respectively. The wavelength dependence of the reflectance in this case is shown by the solid line 38 in FIG. It can be seen that the minimum reflectance is 0.5% at the wavelength λ ₀ =10 μm.

Note that the broken line 35 in FIG. 7 shows the wavelength dependence of the reflectance for a single layer coating film having a refractive index n _fh and a film thickness λ ₀ /(4n _fh ). Although the solid line 38 and the broken line 35 in FIG. 7 do not completely match, they show almost the same wavelength dependence of the reflectance, and the wavelengths at which the minimum reflectance and the minimum reflectance are reached completely match.

Minimum reflectance R ₀ =0.5% and wavelength λ ₀ =10 μm are examples, and the present invention is not limited to these values, and can be set to desired values. Further, in the above example, YF ₃ was used for the first coating film 32 and the third coating film 34, and ZnS was used for the second coating film 33, but the invention is not limited to these. It is sufficient to have at least one material whose refractive index is higher than _fh and n _fh ¹ and at least one material whose refractive index is lower than n _fh and n _fh ¹ , and the order of the materials can be arbitrarily selected.
From the above, it can be seen that a desired minimum reflectance at a desired wavelength can be achieved using a material with a known refractive index.

<Effects of Embodiment 1>
As described above, according to the method for manufacturing an optical semiconductor device and the method for designing a low reflectance film according to Embodiment 1, a single layer coating film is replaced by a three-layer multilayer coating film using a characteristic matrix. This makes it possible to manufacture an optical semiconductor device having a low reflectance film controlled to a desired minimum reflectance at a desired wavelength, and also to obtain a method for designing a low reflectance film.

It should be noted that the method for manufacturing the optical semiconductor device described above utilizes the concept of the method for designing the low reflectance film described above, and each coating film of the multilayer coating film must not match exactly during manufacturing. I don't mind. In other words, the present disclosure includes a method of manufacturing a low reflectance film designed and provided in an optical semiconductor device by the following method.

First, in order to obtain the desired minimum reflectance (R ₀ ) at the desired wavelength (λ ₀ ), the single-layer coating that provides the desired minimum reflectance (R ₀ ) is replaced with a multilayer coating. The minimum value (R _min ⁰ ) of the reflectance of the coating film and the wavelength (λ _min ) at which the reflectance is the minimum are calculated. Next, the minimum reflectance R ₁ of the single layer coating is set to R ₀ +ΔR ₀ so that the minimum reflectance (R _min ) of the multilayer coating matches the desired minimum reflectance (R ₀ ). Set. Furthermore, the thickness of each layer of the multilayer coating film is calculated so that the desired minimum reflectance (R ₀ ) can be achieved at the desired wavelength (λ ₀ ).

Embodiment 2.
The minimum reflectance R ₀ can be set to any desired value. In the method for manufacturing an optical semiconductor device and the method for designing a low reflectance film according to the second embodiment, an example in which the minimum reflectance R ₀ =0.01 (1%) is shown. When the effective refractive index n _c of the optical semiconductor device is 3.2, n _fl and n _fh are calculated as 1.618080 and 1.977653, respectively, from the above equation (2).

First, the case where the refractive index n _fl =1.618080 will be explained. The single-layer coating film consists of three layers of three materials, at least one of which is a material with a refractive index lower than the refractive index n _fl , and at least one of which is a material with a refractive index higher than the refractive index n _fl Consider replacement with a coating film.

FIG. 8 shows a single layer coating film 41 having a refractive index n _fl and a film thickness d _fl of λ ₀ /(4n _fl ), a film thickness d ₁ at a refractive index n ₁ and a film thickness d ₂ at a refractive index n _2. , and a three-layer coating film having a refractive index n ₃ and a film thickness d ₃ . As shown in FIG. 8, the film thickness d fl =λ _{0 /} with refractive index n _fl (=1.618080) formed on the end face of the optical semiconductor device 11 that emits light of wavelength λ ₀ with effective refractive index n _c (4n _fl ), a first coating film 42 having a refractive index n ₁ and a film thickness d ₁ , a second coating film 43 having a refractive index n ₂ and a film thickness d ₂ , The third coating film 44 is replaced with a three-layer coating film having a refractive index of n ₃ and a film thickness of d ₃ . If the single-layer coating film 41 can be replaced with a three-layer coating film, the characteristic matrices of both will be equal, as expressed by the following equation (10).

式（１０）において、各被覆膜の位相項φ₁、φ₂及びφ₃は、以下の式（１１）と表される。

In equation (10), phase terms φ ₁ , φ ₂ and φ ₃ of each coating film are expressed as equation (11) below.

In equation (10), since the refractive index n ₁ , refractive index n ₂ and refractive index n ₃ are known, the three unknowns are the film thicknesses d ₁ , d ₂ and d ₃ , and solving equation (10) The thickness of each coating film can be calculated using

Wavelength λ ₀ = 10 μm, the first coating film 42 is YF 3 with a refractive index n ₁ = 1.40, which is lower than n _fl , and the second coating film 43 is YF ₃ , which has a refractive index higher than n _fl . Solving equation (10) using ZnS with a refractive index of n ₂ = 2.20 as an example and CeF ₃ with a refractive index of n ₃ = 1.45 lower than n _fl as the third coating film 44, each coating film The film thicknesses of d ₁ =640.642 nm, d ₂ =206.894 nm, and d ₃ =763.646 nm, respectively. The wavelength dependence of the reflectance in this case is shown by the dashed-dotted line 46 in FIG. Although the reflectance is 1.0% at a wavelength of 10 μm, this value is not a minimum value, and the minimum value R _min ⁰ of the reflectance of the three-layer coating film is 0.9836%.

The minimum reflectance R _{min 0} of the three-layer coating is 0.9836%, compared to the minimum reflectance R ⁰ of the single-layer coating: 1.0%, which is the minimum reflectance of the single-layer coating. It will be lower than R ₀ . Therefore, similarly to the first embodiment, the set reflectance R ₁ is set as high as 1.01648% in order to make the minimum value R _min of the reflectance of the three-layer coating film the desired minimum reflectance R ₀ . In this case, n _fl ¹ =1.616739 is calculated from equation (5). When the thickness of each coating film is calculated by solving equation (12) below, it is calculated as d ₁ =641.123 nm, d ₂ =205.474 nm, and d ₃ =765.332 nm.

The wavelength dependence of the reflectance in this case is shown by the two-dot chain line 47 in FIG. The minimum value R _min of the reflectance of the three-layer coating film is 1.0% at the wavelength λ _min =9.864 μm, which is the desired minimum reflectance of 1.0%.

Next, the wavelength λ _min at which the reflectance is minimal is set to the desired wavelength λ ₀ . When each film thickness is multiplied by λ ₀ /λ _min , d ₁ =649.962 nm, d ₂ =208.307 nm. It is calculated that d ₃ =775.884 nm. The wavelength dependence of the reflectance in this case is shown by the solid line 48 in FIG. It can be seen that the minimum reflectance is 1.0% at the wavelength λ ₀ . Note that a broken line 45 in FIG. 9 represents the wavelength dependence of reflectance for a single layer coating film having a refractive index n _fl and a film thickness λ ₀ /(4n _fl ). A solid line 48 and a broken line 45 in FIG. 9 show almost the same wavelength dependence of reflectance, and the wavelengths at which the minimum reflectance and the minimum reflectance are reached completely match.

Minimum reflectance R ₀ =1.0% and wavelength λ ₀ =10 μm are examples, and the present invention is not limited to these values, and can be set to desired values. Also. Although YF ₃ was used for the first coating film 42, ZnS was used for the second coating film 43, and CeF ₃ was used for the third coating film 44, the present invention is not _limited to _these. It is sufficient to have at least one material with a refractive index higher than ¹ and at least one material with a refractive index lower than n _fl and n _fl ¹ , and the order of the materials can be arbitrarily selected.
From the above, it can be seen that a desired minimum reflectance at a desired wavelength can be achieved using a material with a known refractive index.

Similarly, the case where n _fh =1.977653 will be explained. A three-layer coating film made of three materials in which the single-layer coating film is made of at least one material having a refractive index lower than the refractive index n _fh and at least one material having a refractive index higher than the refractive index n _fh . Consider the replacement by .

FIG. 10 shows a single layer coating film 49 having a refractive index n _fh and a film thickness d _fh of λ ₀ /(4n _fh ), a film thickness d ₁ at a refractive index n 1 and a film thickness d ₁ at a refractive index n _{2 ,} respectively. FIG. ₃ is a schematic diagram in the case of replacement with a three-layer coating film having a film thickness of d ₃ and a refractive index of n ₃ . As shown in FIG. 10, the film thickness d fh = λ _{0 /} with a refractive index n _fh (=1.977653) formed on the end face of an optical semiconductor device 11 that emits light with a wavelength λ ₀ and an effective refractive index n _c (4n _fh ), a first coating 50 having a refractive index n ₁ and a thickness d ₁ , a second coating 51 having a refractive index n ₂ and a thickness d ₂ , a refractive index n 1 and a thickness d 2 The third coating film 52 is replaced with a three-layer coating film having a ratio n ₃ and a thickness d ₃ . The method for replacing the single-layer coating film with a three-layer coating film is the same as in the case of the low refractive index described above, and is performed by solving the following equation (13).

The wavelength λ ₀ =10 μm, the first coating film 50 is YF 3 with a refractive index n ₁ =1.40, which is lower than n _fl , and the second coating film 51 is YF ₃ , which has a refractive index higher than n _fl . Solving Equation (13) using ZnS with a refractive index n ₂ = 2.20 and CeF ₃ with a refractive index n ₃ = 1.45, which is lower than n _fl , as an example of the third coating film 52, yields, respectively. , d ₁ =370.115 nm, d ₂ =607.246 nm, and d ₃ =395.897 nm. The wavelength dependence of the reflectance in this case is shown by the dashed line 54 in FIG. Although the reflectance is 1.0% at a wavelength of 10 μm, this value is not a minimum value, and the minimum value R _min ⁰ of the reflectance of the three-layer coating film is 0.94561%.

The minimum reflectance R _{min 0} of the single-layer coating is 1.0%, whereas the minimum reflectance R _min ⁰ of the three-layer coating is 0.94561%, which is the minimum reflectance of the single-layer coating. It will be lower than R ₀ . Therefore, similarly to the first embodiment, the set reflectance R ₁ is set as high as 1.057485% in order to make the minimum value R _min of the reflectance of the three-layer coating film the desired minimum reflectance R ₀ . The refractive index n _fh ¹ of the single layer coating film for realizing the set reflectance R ₁ =1.057485% is calculated as n _fh ¹ =1.9833241 from equation (8). When calculating the film thickness of each coating film by solving the following equation (14), each film thickness is calculated as d ₁ = 364.825 nm, d ₂ = 614.601 nm, and d ₃ = 390.009 nm. Ru.

The wavelength dependence of the reflectance in this case is shown by the two-dot chain line 55 in FIG. The minimum value R _min of the reflectance of the three-layer coating film is 1.0% at the wavelength λ _min =10.243 μm, which is the desired minimum reflectance of 1.0%.

Next, the wavelength λ _min at which the reflectance is minimal is set to the desired wavelength λ ₀ . When the film thickness of each coating film is multiplied by λ ₀ /λ _min , d ₁ =356.170 nm, d ₂ =600.021 nm, and d ₃ =380.757 nm are calculated, respectively. The wavelength dependence of the reflectance in this case is shown by the solid line 56 in FIG. It can be seen that the minimum reflectance is 1.0% at the wavelength λ ₀ .

Note that a broken line 53 in FIG. 11 indicates the wavelength dependence of the reflectance for a single-layer coating film having a refractive index n _fh and a film thickness λ ₀ /(4n _fh ). Although the solid line 56 and the broken line 53 in FIG. 11 do not completely match, they show almost the same wavelength dependence of reflectance, and the minimum reflectance and the wavelength at which the minimum reflectance is reached completely match.

Minimum reflectance R ₀ =1.0% and wavelength λ ₀ =10 μm are examples, and the present invention is not limited to these values, and can be set to desired values. Also. Although YF ₃ was used for the first coating film 50, ZnS was used for the second coating film 51, and CeF ₃ was used for the third coating film 52, the present invention is not _limited to these _. It is sufficient to have at least one material with a refractive index higher than ¹ and at least one material with a refractive index lower than n _fh and n _fh ¹ , and the order of the materials can be arbitrarily selected.
From the above, it can be seen that a desired minimum reflectance at a desired wavelength can be achieved using a material with a known refractive index.

<Effects of Embodiment 2>
As described above, according to the method for manufacturing an optical semiconductor device and the method for designing a low reflectance film according to the second embodiment, a single layer coating film is replaced by a three-layer multilayer coating film using a characteristic matrix. , it becomes possible to manufacture an optical semiconductor device having a low reflectance film controlled to a desired minimum reflectance at a desired wavelength, and it also becomes possible to obtain a method for designing a low reflectance film.

It should be noted that the method for manufacturing the optical semiconductor device described above utilizes the concept of the method for designing the low reflectance film described above, and each coating film of the multilayer coating film must not match exactly during manufacturing. I don't mind. In other words, a method of manufacturing a low reflectance film designed by the design method of Embodiment 2 and provided in an optical semiconductor device is included in the present disclosure.

Embodiment 3.
In Embodiment 3, a method of realizing a desired minimum reflectance at a desired wavelength using four or more materials with different refractive indexes will be described. A five-layer coating film will be described as an example of a multilayer coating film made of four or more materials.

In the third embodiment, the minimum reflectance R ₀ =0.01 (1%) will be explained as an example. Assuming that the effective refractive index n _c of the optical semiconductor device is 3.2, the refractive index n _fl and the refractive index n _fh are calculated as 1.618080 and 1.977653, respectively, from equation (2).

First, the case where the refractive index n _fl =1.618080 will be explained. A 5-layer coating film made of 5 materials in which the single-layer coating film is made of at least one material having a refractive index lower than the refractive index n _fl and at least one material having a refractive index higher than the refractive index n _fl Consider the replacement by .

FIG. 12 shows a single layer coating film 41 having a refractive index n _fl and a film thickness d _fl of λ ₀ /(4n _fl ), a film thickness d ₁ at a refractive index n ₁ and a film thickness d ₂ at a refractive index n _2. , is a schematic diagram in the case of replacing with a five-layer coating film having a refractive index n ₃ and a film thickness d ₃ , a refractive index n ₄ and a film thickness d ₄ , and a refractive index n ₅ and a film thickness d ₅ . As shown in FIG. 12, a film formed on the end face of the optical semiconductor device 11 which emits light of wavelength λ ₀ with an effective refractive index n _c has a refractive index n _fl and a film thickness d _fl of λ ₀ /(4n _fl ). The single layer coating film 41 is divided into a first coating film 61 having a refractive index n ₁ and a thickness d ₁ , a second coating film 62 having a refractive index n ₂ and a thickness d ₂ , and a film having a refractive index n ₃ . Five layers: a third coating film 63 with a thickness of d ₃ , a fourth coating film 64 with a refractive index of n ₄ and a thickness of d ₄ , and a _{fifth coating film 65 with a refractive index of n 5 and} a thickness of d 5. Replace with coating film. If the single-layer coating can be replaced with a five-layer coating, the characteristic matrices of both will be equal, as expressed by the following equation (15).

式（１５）中の各被覆膜の位相項φ₁、φ₂、φ₃、φ₄及びφ₅は、以下の式（１６）で表される。

The phase terms φ ₁ , φ ₂ , φ ₃ , φ ₄ and φ ₅ of each coating film in equation (15) are expressed by the following equation (16).

However, since the number of unknowns calculated from equation (15) is up to three, the film thicknesses of two of the five materials are set to preset film thicknesses. Here, as an example, the film thicknesses d ₁ and d ₂ of the first coating film 61 and the second coating film 62 are preset film thicknesses.

The wavelength λ ₀ =10 μm, the first coating film 61 is made of CeO ₂ with a refractive index n ₁ =1.70 higher than n _fl and a film thickness d ₁ =200 nm, and the second coating film 62 has a refractive index of is ZnS with a refractive index n ₂ = 2.20 higher than n _fl and a film thickness d ₂ = 100 nm, and the third coating film 63 has a refractive index n ₃ = 1.40 lower than n _fl and a film thickness d. _{3 ,} the fourth coating film 64 is ZnSe with a refractive index n ₄ =2.41 higher than n _fl and a film thickness d ₄ , and the fifth coating film 65 has a refractive index n _fl When solving equation (15) using as an example CeF ₃ with n ₅ = 1.45 and film thickness d ₅ lower than , the film thicknesses of each coating film are d ₃ = 738.670 nm and d ₄ = 151.598 nm, d ₅ =333.010 nm.

The wavelength dependence of the reflectance in this case is shown by the dashed line 67 in FIG. Although the reflectance is 1.0% at a wavelength of 10 μm, this value is not a minimum value, and the minimum value R _min ⁰ of the reflectance of the five-layer coating film is 0.998474%.

The minimum reflectance R _{min 0} of the five-layer coating is 0.998474%, compared to the minimum reflectance R ⁰ of the single-layer coating: 1.0%. It will be lower than R ₀ . Therefore, in order to set the minimum value R _min of the reflectance of the five-layer coating film to the desired minimum reflectance R ₀ , the set reflectance R ₁ is set as high as 1.00153%. In this case, the refractive index n _fl ¹ of the single layer coating film for realizing the set reflectance R ₁ =1.00153% is calculated as 1.617955 from equation (5). When the film thickness of each coating film is calculated by solving the following equation (17), d ₃ =738.955 nm, d ₄ =151.533 nm, and d ₅ =332.847 nm, respectively.

The wavelength dependence of the reflectance in this case is shown by the two-dot chain line 68 in FIG. The minimum value R _min of the reflectance of the five-layer coating film is 1.0% at the wavelength λ _min =10.040 μm, which is the desired minimum reflectance of 1.0%.

Next, the wavelength λ _min at which the reflectance is minimal is set to the desired wavelength λ ₀ . If the thickness of each coating film is multiplied by λ ₀ /λ _min , then d ₁ =199.203 nm, d ₂ =99.602 nm. d ₃ =736.011 nm, d ₄ =150.929 nm, and d ₅ =331.521 nm, respectively. Note that the first coating film 61 and the second coating film 62 are also multiplied by λ ₀ /λ _min . The wavelength dependence of the reflectance in this case is shown by the solid line 69 in FIG. It can be seen that at the wavelength λ ₀ =10 μm, the reflectance is minimal, 1.0%.

Note that a broken line 66 in FIG. 13 represents the wavelength dependence of reflectance for a single-layer coating film having a refractive index n _fl and a film thickness λ ₀ /(4n _fl ). Although the solid line 69 and the broken line 66 in FIG. 13 do not completely match, they show almost the same wavelength dependence of reflectance, and the wavelengths at which the minimum reflectance and minimum reflectance are reached completely match.

Minimum reflectance R ₀ =1.0% and wavelength λ ₀ =10 μm are examples, and the present invention is not limited to these values, and can be set to desired values. Also. In the above example, the first coating film 61 is made of CeO ₂ , the second coating film 62 is made of ZnS, the third coating film 63 is made of YF ₃ , the fourth coating film 64 is made of ZnSe, and the fifth coating film 64 is made of ZnSe. Although CeF ₃ is used for the coating film 65, it is not limited to this, and one or more materials with a refractive index higher than n _fl and n _fl ¹ and a material with a refractive index lower than n _fl and n _fl ¹ are used. One or more is sufficient, and the order of each material can be arbitrarily selected.

Further, the two coating films whose thicknesses are set in advance can also be arbitrarily selected from among the five-layer coating films. In Embodiment 3, a five-layer coating film was illustrated as an example of a coating film with four or more layers, but by performing the same process, even if the coating film is a multilayer coating, the desired minimal reflection at the desired wavelength can be achieved. rate can be achieved.

Similarly, the case where the refractive index n _fh =1.977653 will be explained. A 5-layer coating film made of 5 materials in which the single-layer coating film is made of a material in which at least one material has a refractive index lower than the refractive index n _fh and at least one material has a refractive index higher than the refractive index n _fh . Consider the replacement by .

FIG. 14 shows a single layer coating film 49 having a refractive index n _fh and a film thickness d _fh of λ ₀ /(4n _fh ), a film thickness d ₁ at a refractive index n ₁ and a film thickness d ₂ at a refractive index n _{2 .} , is a schematic diagram in the case of replacing with a five-layer coating film having a refractive index n ₃ and a film thickness d ₃ , a refractive index n ₄ and a film thickness d ₄ , and a refractive index n ₅ and a film thickness d ₅ . As shown in FIG. 14, the film thickness d fh = λ _{0 /} with a refractive index n _fh (=1.977653) formed on the end face of an optical semiconductor device 11 that emits light with a wavelength λ ₀ and an effective refractive index n _c (4n _fh ), a first coating 71 with a refractive index n ₁ and a thickness d ₁ , a second coating 72 with a refractive index n ₂ and a thickness d ₂ , A third coating film 73 having a refractive index n ₃ and a thickness d ₃ , a fourth coating film 74 having a refractive index n ₄ and a thickness d ₄ , and a fifth coating film 74 having a refractive index n ₅ and a thickness d ₅ . Replacement with a five-layer coating film of the coating film 75. The method for replacing the single-layer coating film with a five-layer coating film is the same as that for the low refractive index film described above, and is performed by solving the following equation (18).

The wavelength λ ₀ = 10 μm, the first coating film 71 is made of CeO ₂ with a refractive index n ₁ = 1.70 lower than n _fh and a film thickness d ₁ = 200 nm, and the second coating film 72 has a refractive index of is ZnS with a refractive index n ₂ = 2.20 higher than n _fh and a film thickness d ₂ = 100 nm, and the third coating film 73 has a refractive index n ₃ = 1.40 lower than n _fh and a film thickness d. _{The fourth} coating film 74 is made of ZnSe with a refractive index n ₄ =2.41 higher than n _fh and has a film thickness of d ₄ , and the fifth coating film 75 is made of YF 3 with a refractive index of n _fh When solving equation (18) using as an example CeF ₃ with n ₅ = 1.45 and film thickness d ₅ lower than , the film thicknesses of each coating film are d ₃ = 282.491 nm and d ₄ = 387.869 nm, d ₅ =366.354 nm.

The wavelength dependence of the reflectance in this case is shown by a dashed-dotted line 77 in FIG. Although the reflectance is 1.0% at a wavelength of 10 μm, this value is not a minimum value, and the minimum value R _min ⁰ of the reflectance of the five-layer coating film is 0.975517%.

Compared to the minimum reflectance R ₀ of the single-layer coating film: 1.0%, the minimum value R _min ⁰ of the 5-layer coating film is 0.975517%, which is from the minimum reflectance R ₀ of the single-layer coating film. will also be lower. Therefore, in order to make the minimum value R _min of the five-layer coating film the desired minimum reflectance R ₀ , the set reflectance R ₁ is set as high as 1.025357%. In this case, the refractive index n _fh ¹ of the single layer coating film for realizing the set reflectance R ₁ =1.025357% is calculated as n _fh ¹ =1.9801717 from equation (8). When the film thickness of each coating film is calculated by solving the following equation (19), d ₃ =280.332 nm, d ₄ =389.708 nm, and d ₅ =365.369 nm, respectively.

The wavelength dependence of the reflectance in this case is shown by the two-dot chain line 78 in FIG. The minimum value R _min of the five-layer coating film is 1.0% at the wavelength λ _min =10.159 μm, and the desired minimum reflectance of 1.0% can be obtained.

Next, the wavelength λ _min at which the reflectance is minimal is set to the desired wavelength λ ₀ . When each film thickness is multiplied by λ ₀ /λ _min , the film thickness of each coating film is d ₁ =196.870 nm, d ₂ =98.435 nm. d ₃ =275.944 nm, d ₄ =383.609 nm, and d ₅ =359.651 nm, respectively. Note that the first coating film 71 and the second coating film 72 are also multiplied by λ ₀ /λ _min . The wavelength dependence of the reflectance in this case is shown by a solid line 79 in FIG. It can be seen that the minimum reflectance is 1.0% at the wavelength λ ₀ =10 μm.

Note that a broken line 76 in FIG. 15 indicates the wavelength dependence of the reflectance of the single layer coating film 49 having a refractive index n _fh and a film thickness λ ₀ /(4n _fh ). Although the solid line 79 and the broken line 76 in FIG. 15 do not completely match, they show almost the same wavelength dependence of reflectance, and the minimum reflectance and the wavelength at which the minimum reflectance is reached completely match.

Minimum reflectance R ₀ =1.0% and wavelength λ ₀ =10 μm are examples, and the present invention is not limited to these values, and can be set to desired values. Also. The first coating film ₇₁ is made of CeO2, the second coating film 72 is made of ZnS, the third coating film 73 is made of YF3, the fourth coating film ₇₄ is made of ZnSe, and the fifth coating film 75 is made of CeF. ₃ was used, but is not limited to these, as long as there is one or more materials with a refractive index higher than n _fh and n _fh ¹ and one or more materials with a refractive index lower than n _fh and n _fh ¹ The order of each material can also be chosen arbitrarily.

Further, the two coating films whose thicknesses are set in advance can also be arbitrarily selected from among the five-layer coating films. In Embodiment 3, a five-layer coating film was illustrated as an example of a coating film with four or more layers, but by performing the same process, even if the coating film is a multilayer coating, the desired minimal reflection at the desired wavelength can be achieved. rate can be achieved.

<Effects of Embodiment 3>
As described above, according to the method for manufacturing an optical semiconductor device and the method for designing a low reflectance film according to the third embodiment, a single layer coating film is replaced by a five-layer multilayer coating film using a characteristic matrix. , it becomes possible to manufacture an optical semiconductor device having a low reflectance film controlled to a desired minimum reflectance at a desired wavelength, and it also becomes possible to obtain a method for designing a low reflectance film.

It should be noted that the method for manufacturing the optical semiconductor device described above utilizes the concept of the method for designing the low reflectance film described above, and each coating film of the multilayer coating film must not match exactly during manufacturing. I don't mind. In other words, the present disclosure includes a method of manufacturing a low reflectance film designed by the following design method and provided in an optical semiconductor device.

In the case of a multilayer coating film in which the number of coating films exceeds 3, the film thickness of the excess number of coating films is set in advance. Then, in order to obtain the desired minimum reflectance (R ₀ ) at the desired wavelength (λ ₀ ), the single-layer coating that provides the desired minimum reflectance (R ₀ ) is replaced with a multilayer coating. , the minimum reflectance value (R _min ⁰ ) of the multilayer coating film and the wavelength (λ _min ) at which the minimum reflectance occurs are calculated. Next, the minimum reflectance R ₁ of the single layer coating is set to R ₀ +ΔR ₀ so that the minimum reflectance (R _min ) of the multilayer coating matches the desired minimum reflectance (R ₀ ). Set. Furthermore, the thickness of each layer of the multilayer coating is calculated so that the desired minimum reflectance (R ₀ ) can be achieved at the desired wavelength (λ ₀ ).

Embodiment 4.
The mirror loss of the optical semiconductor device is defined by the following equation (20).

In equation (20), R _f , R _r and L are the front end face reflectance, the back end face reflectance and the resonator length, respectively. In applications that require a narrow band of mirror loss, it is necessary to narrow the band near the minimum reflectance.

FIG. 16 is a schematic diagram showing a method of narrowing the band near the minimum reflectance, taking the minimum reflectance shown in Embodiment 2 (FIG. 8) as an example. As shown in FIG. 16, the fourth embodiment is characterized in that a coating film 81 having a refractive index _na and a film thickness d _a of λ ₀ /(2na ₎ is provided. The other coating films are the same as those shown in FIG. 8 of the second embodiment.
The characteristic matrix of the four-layer coating film of Embodiment 4 is expressed by the following equation (21).

式（２１）において、各被覆膜の位相項φ₁、φ₂、φ₃及びφ_aは、以下の式（２２）で表され、挿入した被覆膜８１の膜厚ｄ_aは、以下の式（２３）で表される。

In formula (21), the phase terms φ ₁ , φ ₂ , φ ₃ and φ _a of each coating film are expressed by the following formula (22), and the thickness d _a of the inserted coating film 81 is as follows: It is expressed by the equation (23).

被覆膜の反射率は、行列成分ｍ₁₁、ｍ₁₂、ｍ₂₁、ｍ₂₂を用いて、以下の式（２４）で表される。

The reflectance of the coating film is expressed by the following equation (24) using matrix components m ₁₁ , m ₁₂ , m ₂₁ , and m ₂₂ .

An example of the material of the inserted coating film 81 is CeO ₂ having a refractive index n _a of 1.70. The thickness d _a of the coating film 81 is assumed to be 2941.176 nm, which is d _a =λ ₀ /(2n _a ) at the wavelength λ ₀ =10 μm.

In the second embodiment, the set reflectance R ₁ is 1.0165%, and the thickness of each coating film is calculated by solving equation (12), d ₁ =641.123 nm, d ₂ =205.474 nm, Wavelength dependence of reflectance when the above-mentioned coating film 81 is inserted between the second coating film and the third coating film of the three-layer coating film consisting of d ₃ = 765.332 nm is shown by a dashed line 82 in FIG. The minimum value R _min ⁰ of the reflectance of the four-layer coating film is 0.9609%.

Therefore, in order to set the minimum reflectance R ₀ to 1.0% at λ _min , the set reflectance R ₁ is set to 1.05761% and equation (12) is solved, and the film thickness of each coating film is d ₁ = 642.718 nm, d ₂ = 201.981 nm, and d ₃ = 769.510 nm, respectively, and the minimum value of the reflectance of the four-layer coating film R _min = 1.0% at the wavelength λ _min = 9.908 μm. (Two-dot chain line 83 in FIG. 17). At this time, the refractive index _na of the coating film 81 inserted between the second coating film 43 and the third coating film 44 is 1.70, and the film thickness d _a is 2941.176 nm.

Next, when the thickness of each coating film is multiplied by λ ₀ /λ _min , the thickness of each coating film is d ₁ =648.686 nm, d ₂ =203.856 nm, and d _a =2968.486 nm, respectively. , d ₃ =776.655 nm. The wavelength dependence of the reflectance in this case is shown by the solid line 84 in FIG. It can be seen that the minimum reflectance is 1.0% at the wavelength λ ₀ =10 μm.

For comparison, the wavelength dependence of the reflectance of the three-layer coating film of Embodiment 2 is shown by the broken line 48 in FIG. It can be seen that the reflectance band becomes narrow near the desired wavelength λ ₀ .

Similarly, using the minimum reflectance shown in Embodiment 2 (FIG. 10) as an example, a method for narrowing the band near the minimum reflectance when the refractive index is high (n _fh ) will be described below.

FIG. 18 is a schematic diagram showing the structure of the coating film. In FIG. 18, the coating film 81 has a refractive index _na and a film thickness _da of λ ₀ /(2na ₎ . The other coating films are the same as those in FIG. 10 of the second embodiment.

In Embodiment 2, the set reflectance R ₁ is 1.057485%, and the thicknesses of each coating film are calculated by solving equation (14), d ₁ =364.825 nm and d ₂ =614.601 nm, respectively. , d ₃ =390.009 nm Wavelength dependence of reflectance when the above-mentioned coating film 81 is inserted between the second coating film 51 and the third coating film 52 of the three-layer coating film consisting of 390.009 nm is shown by a dashed line 85 in FIG. The minimum value R _min ⁰ of the reflectance of the four-layer coating film is 0.9950%.

Therefore, in order to make the minimum reflectance 1.0% at the wavelength λ _min , the set reflectance R ₁ is set to 1.0627% and equation (14) is solved, and the film thickness of each coating film is d ₁ = 364.348 nm, d ₂ = 615.265 nm, d ₃ = 389.478 nm, and the minimum value of the reflectance of the four-layer coating film R _min = 1.0% at the wavelength λ _min = 10.110 μm ( (dotted chain line 86 in FIG. 19). At this time, the refractive index _na of the coating film 81 inserted between the second coating film 51 and the third coating film 52 is 1.70, and the film thickness d _a is 2941.176 nm.

Next, if the thickness of each coating film is multiplied by λ ₀ /λ _min , then d ₁ = 360.384 nm, d ₂ = 608.571 nm, d _a = 2909.175 nm, and d ₃ = 385.240 nm. Ru. The wavelength dependence of the reflectance in this case is shown by a solid line 87 in FIG. It can be seen that at the wavelength λ ₀ =10 μm, the reflectance is minimal, 1.0%.

For comparison, the wavelength dependence of the reflectance of the three-layer film of Embodiment 2 is shown by a broken line 56 in FIG. It can be seen that the reflectance band becomes narrow near the desired wavelength λ ₀ .

In the fourth embodiment, the coating film 81 having the desired refractive index n _a and the film thickness d _a of λ ₀ /(2n _a ) is inserted, but the film thickness of the covering film 81 is λ ₀ /(4n _{a ).} ) and thinner than 3λ ₀ /(4n _a ), it is possible to narrow the reflectance band.

In addition, in Embodiment 4, after solving the characteristic matrix of the three-layer coating film and deriving the film thickness of each coating film, the coating film is inserted and the wavelength dependence of the reflectance is calculated, and the four-layer coating film is inserted. The minimum value R _min ⁰ of the reflectance of the coating film was adjusted to a desired minimum reflectance R ₀ , and then the desired minimum reflectance R ₀ was set at a desired wavelength λ ₀ . However, as shown in Embodiment 3, assuming a four-layer coating film in advance, the thickness of the inserted coating film is determined as d _a =λ ₀ /(2n _a ) or d _a =λ _min /(2n _a ), and the thickness of each layer of the three-layer coating film may be determined.

Furthermore, in the fourth embodiment, a coating film with d _a =λ ₀ /(2n _a ) is inserted between the second coating film and the third coating film, but other interfaces, such as optical semiconductor It may be between the device and the first coating film, the first coating film and the second coating film, the third coating film and air (free space), or between the optical semiconductor device and the first coating film. It may be inserted at a plurality of interfaces such as between the gap and between the second coating film and the third coating film.

<Effects of Embodiment 4>
As described above, according to the method for manufacturing an optical semiconductor device and the method for designing a low reflectance film according to the fourth embodiment, a single layer coating film is replaced by a four-layer multilayer coating film using a characteristic matrix. , it becomes possible to manufacture an optical semiconductor device having a low reflectance film controlled to a desired minimum reflectance at a desired wavelength, and it also becomes possible to obtain a method for designing a low reflectance film.

It should be noted that the method for manufacturing the optical semiconductor device described above utilizes the concept of the method for designing the low reflectance film described above, and each coating film of the multilayer coating film must not match exactly during manufacturing. I don't mind. In other words, the present disclosure includes a method of manufacturing a low reflectance film designed by the following design method and provided in an optical semiconductor device.

When the desired wavelength is λ ₀ and the refractive index of the coating film to be inserted _{is na} , the thickness of the coating film to be inserted is thicker than λ ₀ /(4n _a ) and less than 3λ ₀ /(4n _a ). Set in advance in a thin range. Then, in order to obtain the desired minimum reflectance (R _{0 ) at the desired wavelength (λ 0 )} , the single-layer coating that provides the desired minimum reflectance (R ₀ ) is replaced with a multilayer coating. , the minimum reflectance value (R _min ⁰ ) of the multilayer coating film and the wavelength (λ _min ) at which the minimum reflectance occurs are calculated. Next, the minimum reflectance R ₁ of the single-layer coating film is set to R ₀ +ΔR ₀ so that the minimum reflectance value (R _min ) of the multilayer coating matches the desired minimum reflectance (R ₀ ). do. Furthermore, the thickness of each layer of the multilayer coating film is calculated so that the desired minimum reflectance (R ₀ ) can be achieved at the desired wavelength (λ ₀ ).

In Embodiments 1 to 4, the values of 0.5% and 1.0%, which are the desired minimum reflectance R ₀ , and 10 μm, which is the desired wavelength λ ₀ , are examples, and are not limited to these. , can be similarly designed at other desired minimum reflectances and desired wavelengths.

In Embodiments 1 to 4, when the multilayer coating is replaced with a multilayer coating, the minimum value R _min ⁰ of the reflectance of the multilayer coating is lower than the minimum reflectance R ₀ of the single layer coating, but if it is higher, In this case, a desired minimum reflectance can be achieved at a desired wavelength in the same manner.

Although this disclosure describes various exemplary embodiments and examples, the various features, aspects, and functions described in one or more embodiments may differ from those of a particular embodiment. The invention is not limited to application, and can be applied to the embodiments alone or in various combinations.

Accordingly, countless variations not illustrated are envisioned within the scope of the present disclosure. For example, this includes cases where at least one component is modified, added, or omitted, and cases where at least one component is extracted and combined with components of other embodiments.

1 n-type first electrode, 2 n-type InP substrate, 3 n-type InP buffer layer, 4 n-type GaInAs first optical confinement layer, 5 core region, 6 n-type GaInAs second optical confinement layer, 7 n-type InP cladding layer , 8 n-type GaInAs contact layer, 9 n-type second electrode, 10 low reflectance film, 11 optical semiconductor device, 12, 31, 41, 49 single layer coating film, 13, 32, 42, 50, 61, 71 First coating film, 14, 33, 43, 51, 62, 72 Second coating film, 15, 34, 44, 52, 63, 73 Third coating film, 21, 21a, 21b, 35, 45, 48, 53, 56, 66, 76 Broken line, 21a Dotted line, 22, 22a, 36, 46, 54, 67, 77, 82, 85 Dotted chain line, 23, 23a, 37, 47, 55, 68, 78, 83, 86 Two-dot chain line, 24, 24a, 38, 48, 56, 69, 79, 84, 87 Solid line, 64, 74 Fourth coating film, 65, 75 Fifth coating film, 81 Coating film, 100 Quantum cascade laser equipment

Claims (18)

A method for manufacturing an optical semiconductor device in which a low reflectance film having an effective refractive index n _c and a minimum reflectance R ₀ that is a desired minimum reflectance at a desired wavelength λ ₀ is formed,
The refractive index n _fl is expressed by the following formula,

A characteristic matrix of a coating film consisting of a single layer having a film thickness of λ ₀ /4/n _fl , a refractive index of at least one material lower than the refractive index n _fl , and a refractive index of at least one other material. is equal to the characteristic matrix of a multilayer coating consisting of three or more coating films using two or more types of materials having a refractive index higher than the refractive index n _fl , the reflectance of the multilayer coating is Calculate the minimum value R _min ⁰ of the reflectance that has wavelength dependence,
The refractive index n _fl ¹ of a coating film consisting of a single layer that realizes a preset set reflectance R ₁ is expressed by the following formula,

A characteristic matrix of a coating film consisting of a single layer with a film thickness of λ ₀ /4/n _fl ¹ , a refractive index of at least one material lower than the refractive index n _fl ¹ , and a refraction of at least one other material. The reflection of the multilayer coating film is made equal to the characteristic matrix of a multilayer coating film consisting of three or more coating films using two or more types of materials whose refractive index is higher than the refractive index n _fl ¹ . In the wavelength dependence of the reflectance, the minimum value R _min of the reflectance at the wavelength λ _min is made to match the minimum reflectance R ₀ ,
A multilayer coating film is applied to the end face based on the thickness of each of the three or more coating films obtained by matching the minimum value R _min at the wavelength λ _min with the minimum reflectance R ₀ at the wavelength λ ₀ . 1. A method of manufacturing an optical semiconductor device, comprising: forming an optical semiconductor device. A method for manufacturing an optical semiconductor device in which a low reflectance film having an effective refractive index n _c and a minimum reflectance R ₀ that is a desired minimum reflectance at a desired wavelength λ ₀ is formed,
The refractive index n _fh is expressed by the following formula,

A characteristic matrix of a coating film consisting of a single layer having a film thickness of λ ₀ /4/n _fh , a refractive index of at least one material lower than the refractive index n _fh , and a refractive index of at least one other material. is equal to the characteristic matrix of a multilayer coating film consisting of three or more coating films using two or more types of materials having a refractive index higher than the refractive index n _fh . Calculate the minimum value R _min ⁰ of the reflectance that has wavelength dependence,
The refractive index n _fh ¹ of a coating film consisting of a single layer that realizes a preset set reflectance R ₁ is expressed by the following formula,

A characteristic matrix of a coating film consisting of a single layer with a film thickness of λ ₀ /4/n _fh ¹ , a refractive index of at least one material lower than the refractive index n _fh ¹ , and a refraction of at least one other material. The reflection of the multilayer coating film is made equal to the characteristic matrix of the multilayer coating film consisting of three or more coating films using two or more types of materials whose refractive index is higher than the refractive index n _fh ¹ . In the wavelength dependence of the reflectance, the minimum value R _min of the reflectance at the wavelength λ _min is made to match the minimum reflectance R ₀ ,
A multilayer coating film is applied to the end face based on the thickness of each of the three or more coating films obtained by matching the minimum value R _min at the wavelength λ _min with the minimum reflectance R ₀ at the wavelength λ ₀ . 1. A method of manufacturing an optical semiconductor device, comprising: forming an optical semiconductor device. Three layers including a coating made of at least one material with a refractive index lower than n _fl and n _fl ¹ and a coating made of at least one other material with a refractive index higher than n _fl and n _fl ¹ 2. The method of manufacturing an optical semiconductor device according to claim 1, further comprising forming a coating film on an end face. Three layers comprising a coating made of at least one material with a refractive index lower than n _fh and n _fh ¹ and a coating made of at least one other material with a refractive index higher than n _fh and n _fh ¹ 3. The method of manufacturing an optical semiconductor device according to claim 2, further comprising forming a coating film on the end face. 3 comprising a coating film made of at least one material with a refractive index lower than n _fl and n _fl ¹ and a coating film made of at least one other material with a refractive index higher than n _fl and n _fl ¹ 2. The method of manufacturing an optical semiconductor device according to claim 1, wherein three layers of coating films made of different materials are formed on the end face. 3 comprising a coating film made of at least one material with a refractive index lower than n _fh and n _fh ¹ and a coating film made of at least one other material with a refractive index higher than n _fh and n _fh ¹ 3. The method of manufacturing an optical semiconductor device according to claim 2, wherein three layers of coating films made of different materials are formed on the end face. Consisting of four or more types of materials including at least one material with a refractive index lower than n _fl and n _fl ¹ and at least one other material with a refractive index higher than n _fl and n _fl ¹ , the above four types A multilayer coating film is formed on the end face, including a three-layer coating film each made of three types of materials among the above materials, and a coating film made of a material other than the three types and having a preset thickness. 2. The method of manufacturing an optical semiconductor device according to claim 1, further comprising: Consisting of four or more types of materials including at least one material with a refractive index lower than n _fh and n _fh ¹ and at least one other material with a refractive index higher than n _fh and n _fh ¹ , and the above four types A multilayer coating film is formed on the end face, including a three-layer coating film each made of three types of materials among the above materials, and a coating film made of a material other than the three types and having a preset thickness. 3. The method of manufacturing an optical semiconductor device according to claim 2. A coating film having a refractive index n _a and a film thickness greater than λ ₀ /(4n _a ) and thinner than 3λ ₀ /(4n _a ) is placed between the multilayer coating film and the end face, and the coating film is placed between the multilayer coating film and the end face. 9. The method for manufacturing an optical semiconductor device according to claim 3, wherein the method is provided between each coating film or on the outermost surface of the multilayer coating film. A method of designing a low reflectance film having a minimum reflectance _R0 , which is a desired minimum reflectance other than zero, on an end face of an optical semiconductor device having an effective refractive index _nc , the method comprising:
a step of calculating _the refractive index n _fl by the following formula;

A characteristic matrix of a coating film consisting of a single layer having a film thickness of λ ₀ /4/n _fl at a desired wavelength λ ₀ and at least one material having a refractive index lower than the refractive index n fl and at least another material having a refractive index lower than the refractive index n _fl By making the characteristic matrices of a multilayer coating film made of three or more coating films using two or more types of materials in which the refractive index of one material is higher than the refractive index n _fl to be equal, the multilayer coating calculating a minimum value R _min ⁰ of the reflectance of the coating having wavelength dependence;
Calculating the refractive index n _fl ¹ of a coating film made of a single layer that achieves a preset set reflectance R ₁ using the following formula;

A characteristic matrix of a coating film consisting of a single layer with a film thickness of λ ₀ /4/n _fl ¹ , a refractive index of at least one material lower than the refractive index n _fl ¹ , and a refraction of at least one other material. The reflection of the multilayer coating film is made equal to the characteristic matrix of a multilayer coating film consisting of three or more coating films using two or more types of materials whose refractive index is higher than the refractive index n _fl ¹ . a step of matching the minimum value R _min of the reflectance at the wavelength λ _min in the wavelength dependence of the reflectance with the minimum reflectance R ₀ ;
Each film thickness of the multilayer coating film based on each film thickness of the three or more layered coating film obtained by matching the minimum value R _min at the wavelength λ _min with the minimum reflectance R ₀ at the wavelength λ ₀ a step of determining
A method for designing a low reflectance film comprising: A method of designing a low reflectance film having a minimum reflectance _R0 , which is a desired minimum reflectance other than zero, on an end face of an optical semiconductor device having an effective refractive index _nc , the method comprising:
a step of calculating _the refractive index n _fh by the following formula;

A characteristic matrix of a coating film consisting of a single layer having a film thickness of λ ₀ /4/n _fh at a desired wavelength λ ₀ and at least one material having a refractive index lower than the refractive index n fh and at least another material having a refractive index lower than the refractive index n _fh By making the characteristic matrices of a multilayer coating film made of three or more coating films using two or more types of materials in which the refractive index of one material is higher than the refractive index n _fh to be equal, the multilayer coating calculating a minimum value R _min ⁰ of the reflectance of the coating having wavelength dependence;
Calculating the refractive index n _fh ¹ of a coating film made of a single layer that achieves a preset set reflectance R1 using the following formula;

A characteristic matrix of a coating film consisting of a single layer with a film thickness of λ ₀ /4/n _fh ¹ , a refractive index of at least one material lower than the refractive index n _fh ¹ , and a refraction of at least one other material. The reflectance of the multilayer coating film is equal to the characteristic matrix of a multilayer coating film consisting of three or more coating films using two types of materials whose refractive index is higher than the refractive index n _fh ¹ . Matching the minimum value R _min of the reflectance at the wavelength λ _min in the wavelength dependence of the reflectance R min with the minimum reflectance R ₀ ;
Each film of the multilayer coating film based on the thickness of each of the three or more coating films obtained by matching the minimum value R _min at the wavelength λ _min with the minimum reflectance R ₀ at the wavelength λ ₀ determining the thickness;
A method for designing a low reflectance film comprising: Three layers including a coating made of at least one material with a refractive index lower than n _fl and n _fl ¹ and a coating made of at least one other material with a refractive index higher than n _fl and n _fl ¹ 11. The method for designing a low reflectance film according to claim 10, further comprising forming a coating film on an end face. Three layers comprising a coating made of at least one material with a refractive index lower than n _fh and n _fh ¹ and a coating made of at least one other material with a refractive index higher than n _fh and n _fh ¹ 12. The method of designing a low reflectance film according to claim 11, wherein the coating film is formed on the end face. 3 comprising a coating film made of at least one material with a refractive index lower than n _fl and n _fl ¹ and a coating film made of at least one other material with a refractive index higher than n _fl and n _fl ¹ 11. The method of designing a low reflectance film according to claim 10, wherein a three-layer coating film made of different materials is formed on the end face. 3 comprising a coating film made of at least one material with a refractive index lower than n _fh and n _fh ¹ and a coating film made of at least one other material with a refractive index higher than n _fh and n _fh ¹ 12. The method for designing a low reflectance film according to claim 11, wherein a three-layer coating film made of different materials is formed on the end face. Consisting of four or more types of materials including at least one material with a refractive index lower than n _fl and n _fl ¹ and at least one other material with a refractive index higher than n _fl and n _fl ¹ , the above four types A multilayer coating film is formed on the end face, including a three-layer coating film each made of three types of materials among the above materials, and a coating film made of a material other than the three types and having a preset thickness. 11. The method for designing a low reflectance film according to claim 10. Consisting of four or more types of materials including at least one material with a refractive index lower than n _fh and n _fh ¹ and at least one other material with a refractive index higher than n _fh and n _fh ¹ , and the above four types A multilayer coating film is formed on the end face, including a three-layer coating film each made of three types of materials among the above materials, and a coating film made of a material other than the three types and having a preset thickness. 12. The method for designing a low reflectance film according to claim 11. A coating film having a refractive index n _a and a film thickness greater than λ ₀ /(4n _a ) and thinner than 3λ ₀ /(4n _a ) is placed between the multilayer coating film and the end face, and the coating film is placed between the multilayer coating film and the end face. 18. The method of designing a low reflectance film according to claim 12, wherein the method is provided between each coating film of the film or on the outermost surface of the multilayer coating film.

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