JP7766929B2 - Anti-reflection coating for solar cells, and design method, manufacturing method, and design program for solar cells equipped with anti-reflection coating - Google Patents

Description

The present invention relates to an anti-reflective coating for solar cells, and a design method, manufacturing method, and design program for solar cells equipped with an anti-reflective coating.

To improve the power generation efficiency of solar cells, anti-reflective multilayer coatings that suppress light reflection on the cell surface are widely used. Figure 1 shows a cross-sectional schematic diagram illustrating the structure and function of an anti-reflective coating on a solar cell. If a solar cell does not have an anti-reflective coating, as shown in Figure 1(A), incident light is reflected and light energy is lost. However, if the solar cell has an anti-reflective coating on its surface, as shown in Figure 1(B), reflected light is suppressed, allowing the solar cell to efficiently absorb light and generate electricity.

In general, when designing an anti-reflective coating, the characteristics of each layer, such as the film thickness, are determined so that the amount of power generated is maximized when light is perpendicularly incident on the solar cell surface. This design method aims to maximize the effective use of light energy under conditions when the solar cell panel is installed so that sunlight at midday, when the light intensity is strongest, strikes it perpendicularly (Non-Patent Document 1, Non-Patent Document 2).

Mitsunobu Kohiyama, Optical Thin Film Filter Design, Optronics Co., Ltd. (2006). H. Angus Macleod, “Thin-film optical filters,” 4th ed., CRC Press, Boca Raton (2010).

In contrast, the inventors have discovered that when solar cells are used to generate electricity indoors, such as in factories or homes, as in IoT devices (various types of sensor equipment connected to the internet), which have become increasingly common in recent years, the direction of light relative to the solar cell varies depending on the position of the lighting and the orientation of the solar cell, making it inappropriate to design an anti-reflective coating that assumes a specific direction of light. Furthermore, indoor environments primarily consist of diffused light caused by multiple reflections on walls and ceilings, so it is necessary to consider the optical conditions in which light is incident from all directions simultaneously.

Therefore, there is a need for a method for designing anti-reflection coatings for solar cells that can improve anti-reflection performance when used indoors compared to conventional methods.

The gist of the present invention is as follows.
(1) (A) The energy density distribution g(θ) of a solar cell having an anti-reflection film with respect to the incident angle θ of isotropically diffused light on the surface of the anti-reflection film is calculated using the formula (1):
where θ is the angle of incidence of the isotropically diffused light on the surface of the solar cell, and g(θ) is the light energy density.
and determining a configuration of the anti-reflection coating that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ).
(2) determining a configuration of the anti-reflection film that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ);
(B) determining an nth configuration of the anti-reflection film;
(C) calculating the power generation amount J _SC (θ) of the solar cell with respect to the incident angle θ, or the reflectance R(λ, θ) of the entire solar cell having the anti-reflection film with respect to the incident angle θ and wavelength λ based on the n-th configuration of the anti-reflection film;
(D) calculating an average value J _SC ,ave of the amount of power generated by the solar cell or an average value R _ave of the reflectance of the solar cell using the relationship between the calculated energy density distribution g(θ) and the calculated J _SC (θ) or the calculated R(λ, θ); and (E) determining an (n+1)th configuration of the anti-reflection film that maximizes the calculated J _SC,ave or minimizes the calculated R _ave using an optimization engine,
The n is a natural number starting from 1,
and determining a final configuration of the anti-reflection coating by repeating (C) to (E) until a change in the J _{SC, ave} or the R _ave calculated using the optimization engine converges within a predetermined range.
The design method described in (1) above.
(3) The design method according to (2) above, wherein determining the first configuration of the antireflection film when n is 1 is performed using a random initial value.
(4) Maximizing the power generation efficiency of the solar cell is achieved by satisfying the formula (2):
(where θ _min and θ _max are the lower and upper limits of the integral range of the incident angle, and H(θ) is a function of the short-circuit current density J _SC (θ) generated by the solar cell at the incident angle θ, or a function of the reflectance R(λ, θ) at the incident angle θ and wavelength λ.)
The design method according to (1) or (2) above, wherein the evaluation function I is maximized.
(5) The H(θ) is expressed by the formula (3):
(where J _SC (θ) is the short circuit current density J _SC generated by the solar cell at the incident angle θ)
is expressed as
The evaluation function I is expressed by the formula (4):
This corresponds to J _SC,ave , which is the average value of J _SC due to isotropic diffused light,
The design method according to (4) above, wherein maximizing the evaluation function I means maximizing the J _SC,ave .
(6) The H(θ) is expressed by the formula (5):
(where R(λ, θ) is the value of reflectance R at wavelength λ and incident angle θ, F(λ) is expressed as the energy density at wavelength λ of the light source used in the design (e.g., sunlight, LED, fluorescent lamp, etc.), and λ _min and λ _max are the lower and upper limits of the wavelength range in which integration is performed.)
is expressed as
The evaluation function I is expressed by the formula (6):
The reflectance R _ave is the average reflectance under the condition of isotropic diffuse light, and the reflectance R ave is the negative value (−R _ave ),
The design method according to (4) above, wherein maximizing the evaluation function I is minimizing the −R _ave .
(7) The design method according to (2) above, wherein the nth configuration of the antireflection film is the number of layers of the antireflection film, the thickness of each layer, the refractive index, or a combination thereof.
(8) A method for producing an anti-reflection film for a solar cell, comprising the design method according to any one of (1) to (7) above.
(9) A method for manufacturing a solar cell provided with an anti-reflection film, including the design method according to any one of (1) to (7) above.
(10) To the computer:
(A) The energy density distribution g(θ) of a solar cell having an anti-reflection film with respect to the incident angle θ of isotropically diffused light on the surface of the anti-reflection film is calculated using the formula (1):
where θ is the angle of incidence of isotropically diffused light on the surface of the solar cell, and g(θ) is the light energy density.
and a configuration determination process for determining a configuration of the anti-reflection coating that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ).
(11) A configuration determination process for determining a configuration of the anti-reflection film that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ),
(B) an nth configuration determination process for determining an nth configuration of the antireflection film;
(C) a calculation process of J _{SC (θ) or reflectance R(λ, θ) for calculating the power generation amount J SC (} θ) of the solar cell with respect to the incident angle θ, or the reflectance R(λ, θ) of the entire solar cell having the anti-reflection film with respect to the incident angle θ and wavelength λ, based on the n-th configuration of the anti-reflection film;
(D) an R ave calculation process that calculates an average value J _SC ,ave of the power generation amount of the solar cell or an average value R _ave of the reflectance of the solar cell using the relationship between the calculated energy density distribution g(θ) and the calculated J _{SC (θ )} or the calculated R(λ, θ); and (E) an (n+1)th configuration determination process that determines an (n+1)th configuration of the anti-reflection film that maximizes the J _SC,ave or minimizes the R _ave calculated using an optimization engine,
The n is a natural number starting from 1,
and determining a final configuration of the anti-reflection coating by repeating (C) to (E) until a change in the J _{SC, ave} or the R _ave calculated using the optimization engine converges within a predetermined range.
The design program according to (10) above.
(12) The design program according to (11) above, wherein determining the first configuration of the antireflection film when n is 1 is performed using a random initial value.
(13) Maximizing the power generation efficiency of the solar cell is achieved by satisfying the formula (2):
(where θ _min and θ _max are the lower and upper limits of the integral range of the incident angle, and H(θ) is a function of the short-circuit current density J _SC (θ) generated by the solar cell at the incident angle θ, or a function of the reflectance R(λ, θ) at the incident angle θ and wavelength λ.)
The design program according to (10) or (11) above, wherein the evaluation function I is maximized.
(14) The H(θ) is expressed by the formula (3):
(where J _SC (θ) is the short circuit current density J _SC generated by the solar cell at the incident angle θ)
is expressed as
The evaluation function I is expressed by the formula (4):
This corresponds to J _SC,ave , which is the average value of J _SC due to isotropic diffused light,
The design program according to (13) above, wherein maximizing the evaluation function I is maximizing the J _SC,ave .
(15) The H(θ) is expressed by the formula (5):
(where R(λ, θ) is the value of reflectance R at wavelength λ and incident angle θ, F(λ) is represented by the energy density at wavelength λ of the light source used in the design (e.g., sunlight, LED, fluorescent lamp, etc.), and λ _min and λ _max are the lower and upper limits of the wavelength range in which integration is performed.)
is expressed as
The evaluation function I is expressed by the formula (6):
The reflectance R _ave is the average reflectance under the condition of isotropic diffuse light, and the reflectance R ave is the negative value (−R _ave ),
The design program according to (13) above, wherein maximizing the evaluation function I is minimizing the −R _ave .
(16) The design program according to (11) above, wherein the nth configuration of the antireflection film is the number of layers of the antireflection film, the thickness of each layer, the refractive index of each layer, or a combination thereof.

The present invention provides a method for designing an anti-reflection coating for solar cells that can improve anti-reflection performance when used indoors.

FIG. 1 is a cross-sectional view showing the structure and function of an anti-reflection film of a solar cell. FIG. 2 is a schematic diagram of isotropically diffused light on a solar cell in an indoor environment. FIG. 3 is a schematic diagram showing spherical coordinates (θ, φ). FIG. 4 is a graph of the light energy density g(θ) received by a solar cell due to isotropically diffused light with an incident angle θ. FIG. 5 shows an optimization algorithm showing the procedure for optimally designing an anti-reflection film. FIG. 6 is a schematic diagram of an example of an eight-layer anti-reflection coating design using SiO ₂ and TiO ₂ layers for an organic thin-film solar cell. FIG. 7 is a schematic diagram of an example of a four-layer anti-reflection coating designed using materials with adjusted refractive index for an organic thin-film solar cell.

The present disclosure provides (A) an energy density distribution g(θ) of a solar cell having an anti-reflection film with respect to an incident angle θ of isotropically diffused light on a surface of the anti-reflection film, expressed by the formula (1):
(where θ is the angle of incidence of isotropically diffused light with respect to the surface of the solar cell, and g(θ) is the light energy density), and determining a configuration of the anti-reflection coating that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ).

The design method disclosed herein (hereinafter also referred to as the present design method) essentially takes into account the indoor optical environment, which is completely different from that outdoors, and provides an anti-reflection coating configuration for solar cells that can substantially maximize the power generation efficiency of solar cells when used indoors, i.e., an anti-reflection coating for solar cells with improved anti-reflection performance compared to conventional coatings. The solar cells to which the anti-reflection coating provided by the present design method can be applied are not particularly limited, and can be, for example, organic thin-film solar cells, silicon solar cells, perovskite solar cells, etc.

In addition, this design method makes it possible to significantly improve efficiency during indoor use while roughly maintaining efficiency during outdoor use. Furthermore, because this design method is based on the design principle of increasing the average power generation (expected power generation) under optical conditions where light is received from various directions, it can be applied not only to indoor environments, but also to the design of anti-reflection coatings for solar cells installed in various mobile systems (electric vehicles, solar planes, etc.) where light is received from all directions and the direction of the light is unpredictable.

Furthermore, when manufacturing an anti-reflection coating with a multilayer structure obtained using this design method, adjusting the film thickness and refractive index of each layer to a certain extent can achieve a sufficient improvement in power generation efficiency compared to conventional methods. Adjusting the film thickness and refractive index of each layer essentially does not require changes to the sputtering equipment or other facilities used to deposit each layer, resulting in almost no increase in the cost of the solar cell. This design method makes it possible to significantly improve power generation efficiency, preferably by approximately 1.1 to 1.6%, when applied to various indoor devices (such as IoT devices) and mobile systems, while maintaining solar cell costs roughly the same as conventional methods.

Traditionally, when using solar cells in an indoor environment, the direction of incident light varies depending on the relative position of the light source (lighting and windows) and the orientation of the solar cell surface, making it very difficult to predict the direction of light when designing an anti-reflection coating.

This is especially true when designing anti-reflective coatings for solar cells used in mobile IoT devices such as active RFID tags, or when the same solar cell is used across multiple devices (e.g., different types of sensors). Furthermore, in indoor environments, scattered light occurs as light repeatedly bounces off various objects, floors, walls, etc., and scattered light coming from all directions typically accounts for a significant fraction of the incident light energy.

For this reason, when designing anti-reflection coatings for indoor optical environments, the assumption of isotropically diffused light, in which a solar cell receives light from various directions randomly and with equal probability, is generally appropriate. Figure 2 shows a schematic diagram of isotropically diffused light on a solar cell in an indoor environment. In Figure 2, light coming from a direction perpendicular to the solar cell surface has an incident angle θ = 0°.

The following explains the process of deriving equation (1), which represents the energy density distribution g(θ) relative to the incident angle θ of isotropically diffused light on the surface of an anti-reflection coating.

In an optical environment in which a solar cell receives isotropically diffused light, the light energy (irradiance) dE irradiated onto the surface of the solar cell by a ray of light contained in a solid angle dΩ at an incident angle θ is expressed by the following formula (A.1) based on the basic theory of electromagnetic waves:
(where L(λ) is the radiance of light of wavelength λ)
L(λ) is expressed as a function of only the wavelength λ under the condition of isotropic diffused light.

Here, in order to calculate the distribution of light energy received by a solar cell with respect to the angle of incidence, the spherical coordinates (θ, φ) shown in Figure 3 are introduced. The solid angle dΩ, the angle of incidence θ, and the azimuthal angle φ are expressed by the following equation (A.2):
Since the relationship of the above holds, by considering the integration of the right side of equation (A.1) with φ, the light energy corresponding to the region of the incident angle θ to θ + dθ is given by equation (A.3):
(where F _S (λ) is the irradiance spectrum of the incident light, and g(θ) is the probability distribution of the light energy received by the solar cell with respect to the incident angle θ)
It can be expressed as:

g(θ) is expressed by equation (A.4):
The constraints are satisfied.

By using this constraint, F _S (λ) = πL(λ) is established from equation (A.3), and by substituting this relationship into equation (A.3) again, equation (1):
The following relation is obtained:

In other words, assuming isotropic diffuse light, the light energy density distribution g(θ) (probability distribution of light energy with respect to the incident angle θ) actually received by a solar cell with respect to the incident angle θ is expressed by equation (1).

Figure 4 shows a graph of g(θ) versus the incident angle θ. Figure 4 shows the light energy density g(θ) actually received by a solar cell with isotropically diffused light. As can be seen from the function shape of g(θ) in Figure 4, under isotropically diffused light conditions, a solar cell receives the strongest light energy at an incident angle of θ = 45°, and receives almost no light energy near θ = 0° or 90°. This means that the conventional method of designing anti-reflection coatings to increase power generation efficiency at normal incidence (θ = 0°) is not appropriate for indoor use.

This design method makes it possible to design anti-reflection coatings for solar cells that maximize power generation efficiency when the solar cells are exposed to isotropically diffused light in an indoor environment or an equivalent environment.

Preferably, determining a configuration of the anti-reflection film that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ) includes:
(B) determining an nth configuration of the anti-reflection film;
(C) calculating the power generation amount J _SC (θ) of the solar cell with respect to the incident angle θ, or the reflectance R(λ, θ) of the entire solar cell having the anti-reflection film with respect to the incident angle θ and wavelength λ based on the n-th configuration of the anti-reflection film;
(D) calculating an average value J _SC ,ave of the amount of power generated by the solar cell or an average value R _ave of the reflectance of the solar cell using the relationship between the calculated energy density distribution g(θ) and the calculated J _SC (θ) or the calculated R(λ, θ); and (E) determining an (n+1)th configuration of the anti-reflection film that maximizes the calculated J _SC,ave or minimizes the calculated R _ave using an optimization engine,
The n is a natural number starting from 1,
and determining a final configuration of the anti-reflection coating by repeating (C) to (E) until a change in the J _{SC, ave} or the R _ave calculated using the optimization engine converges within a predetermined range.

Figure 5 shows an algorithm for determining the anti-reflection coating configuration, including the above (B) to (E). The algorithm shown in Figure 5 is an optimization algorithm for optimizing the anti-reflection coating configuration, and corresponds to steps α-1 to α-5 or steps β-2 to β-5 described below.

Step α-1
The initial value (initial configuration) of the antireflection film is determined. Step α-1 corresponds to (B) above when n = 1. The configuration of the antireflection film may include the number of layers constituting the antireflection film, the thickness of each layer, the wavelength dependence of the refractive index of each layer, etc. The nth configuration of the antireflection film is preferably the number of layers of the antireflection film, the thickness of each layer, the refractive index of each layer, or a combination thereof. The initial value (initial configuration) of the antireflection film may be determined by any method, such as by making it the same as a commonly used known configuration or by determining it based on a known configuration. A commonly used known configuration of an antireflection film is, for example, a multilayer film containing SiO ₂ with a low refractive index and TiO ₂ with a high refractive index. The refractive index of each layer constituting the antireflection film, such as SiO ₂ or TiO ₂ , is expressed as a function of the wavelength of incident light obtained by optical measurement.

A multilayer film containing _{SiO2, which} has a low refractive index, and _TiO2, which has a high refractive index, is preferable because it has a wide design range. The number of layers in the multilayer film is not particularly limited, but may be, for example, 2 to 10 layers or 4 to 8 layers. The initial value (initial configuration) of the anti-reflection film is preferably determined randomly as described in step β-1 below.

Step α-2
The solar cell's power generation current J _SC (θ) with respect to the incident angle θ (in case 1), or the relationship between the wavelength λ and the incident angle θ and the reflectance R(λ, θ) with respect to the wavelength λ and the incident angle θ (in case 2) is calculated by optical analysis that investigates light propagation using numerical calculations. Step α-2 corresponds to (C) above.

Step α-3
The value of the evaluation function I is calculated using formulas (1) to (4) (for case 1), or formulas (1), (2), (5) and (6) (for case 2). Step α-3 corresponds to (D) above.

Step α-4
The optimization engine is used to determine the configuration of the anti-reflection coating (such as the film thickness and refractive index of each layer) to be calculated next in order to increase the evaluation function I. The optimization engine can be any engine, such as a gradient method, a quasi-Newton method, or a simulated annealing method. Step α-4 corresponds to (E) above.

Step α-5
If the convergence condition for the solution is met, the search for the optimal solution ends. The convergence condition can be determined arbitrarily. If it is not met, return to step α-2 and repeat steps α-2 to α-4 until the convergence condition is met.

Preferably, an optimization method (multi-start method) can be applied, which repeats searches from a number of randomly selected initial values. The multi-start method can further improve performance without relying on the initial search values used in the optimization calculation. The algorithm for optimal design using the multi-start method is described in the following steps β-1 to β-6.

Step β-1
The initial values (initial configuration) of the anti-reflection film configuration (such as the film thickness and refractive index of each layer) are determined randomly within the design range. Step β-1 corresponds to (B) above when n=1.

Step β-2
The relationship J _SC (θ) of the generated current versus the incident angle θ (in case 1), or the relationship R(λ, θ) of the reflectance versus the incident angle θ and wavelength λ (in case 2) is calculated by optical analysis. Step β-2 corresponds to (C) above.

Step β-3
The evaluation function I is calculated using formulas (1) to (4) (for case 1), or formulas (1), (2), (5), and (6) (for case 2). Step β-3 corresponds to (D) above.

Step β-4
The optimization engine is used to determine the configuration of the anti-reflection coating (such as the film thickness and refractive index of each layer) to be calculated next in order to increase the evaluation function I. The optimization engine can be any engine, such as a gradient method, a quasi-Newton method, or a simulated annealing method. Step β-4 corresponds to (E) above.

Step β-5
If the convergence condition of the solution is satisfied, the obtained solution is saved and the process proceeds to step β-6. The convergence condition can be determined arbitrarily. If the convergence condition of the solution is not satisfied, the process returns to step β-2.

Step β-6
If the number of solutions saved in step β-5 is equal to or greater than a predetermined number, the solution with the largest evaluation function I among all the saved solutions is determined as the optimal solution, and the process ends. On the other hand, if the number of solutions saved in step β-5 has not yet reached the predetermined number, the process returns to step β-1. The predetermined number of solutions saved in step β-5 is not particularly limited, but may be, for example, 100 to 1000. In other words, the number of initial values (initial configurations) of the anti-reflection film randomly determined in step β-1 may be, for example, 100 to 1000.

Maximizing the power generation efficiency when a solar cell receives isotropically diffused light preferably means maximizing the evaluation function I expressed in the following formula (2). The structure of the multilayer anti-reflection coating can be determined so as to maximize the evaluation function I. The evaluation function I in formula (2) is related to the average value (expected value) of the amount of power generated by the solar cell. In this specification, the average value refers to the expected value, which is the weighted average of all values of random variables weighted by probability, and will hereinafter be referred to simply as the average value.

In the formula, θ _min and θ _max are the lower and upper limits of the integral range of the incident angle, and H(θ) is preferably a function of the short-circuit current density J _SC (θ) generated by the solar cell at the incident angle θ, or a function of the reflectance R(λ, θ) at the incident angle θ and wavelength λ. _{θ min} and θ _max can be determined depending on the optical environment of the solar cell for which the anti-reflection coating is designed. θ _min is preferably 0° or more. θ _max is preferably 90° or less. For the sake of explanation below, it is assumed that θ _min = 0° and θ _max = 90°. H(θ) is described by either Case 1 or Case 2 described below.

(Case 1) Maximizing the short-circuit current density (generated current) J _SC under isotropic diffuse light conditions If the optical characteristics of a solar cell (such as the thickness of each layer, the refractive index, and the wavelength dependence of absorption characteristics) can be understood, an anti-reflection coating suitable for indoor use can be designed to maximize the average generated current (expected value of generated current) J _SC,ave of the solar cell; this case is called Case 1. The optical characteristics of a solar cell can be understood, for example, by experimental measurements or by using a solar cell whose characteristics are understood. In Case 1, H(θ) is expressed by the following equation (3).

In the formula, J _SC (θ) represents the value of the short-circuit current density (generated current) J _SC generated by the solar cell at the incident angle θ.

In case 1, the evaluation function I in formula (2) coincides with J _SC,ave , which is the average value of J _SC due to isotropic diffused light, and J _SC,ave is expressed by formula (4):
Equation (4) can be obtained by substituting equation (3) into equation (2).

As described above, the design method for Case 1 aims to maximize J _SC,ave , which is the average value of the short-circuit current density J _SC due to isotropically diffused light. This means maximizing the average power generation (expected power generation) of indoor solar cells that receive light from various directions.

(Case 2) Minimizing reflectance under isotropic diffuse light conditions When it is difficult to accurately measure the optical properties of each layer constituting a solar cell device, it is possible to design an anti-reflection coating suitable for indoor use using the reflectance properties of the entire solar cell device equipped with an anti-reflection coating; this case is referred to as Case 2. The reflectance properties of the entire device refer to the reflectance when light is incident on the device surface. In Case 2, H(θ) is expressed by the following equation (5):

In the formula, R(λ, θ) is the value of reflectance R at wavelength λ and incident angle θ, F(λ) is the energy density at wavelength λ of the light source used in the design (e.g., sunlight, LED, fluorescent lamp, etc.), and λ _min and λ _max are the lower and upper limits of the wavelength range for which integration is performed. λ _min and λ _max can be determined depending on the wavelength range of the incident light and the absorption wavelength range of the solar cell. λ _min is preferably the lower limit (approximately 300 nm) of the wavelength range included in sunlight. λ _max is preferably a wavelength corresponding to the band gap of the power generation layer material, and for example, for a typical organic solar cell, it is approximately 600 to 800 nm. The wavelength corresponding to the band gap is the wavelength of the absorption limit.

In case 2, the evaluation function I in formula (2) coincides with the negative value (−R _ave ) of R _ave, which is the average value of reflectance under isotropic diffuse light conditions, and R _ave is expressed by the following formula (6). Formula (6) can be obtained by substituting formula (5) into formula (2).

Thus, the design method of Case 2 aims to minimize R _ave by maximizing the value of −R _ave , which means minimizing the average reflectance of indoor solar cells.

As such, the design objectives for Case 1 and Case 2 are to maximize the average power generation (expected power generation) and minimize the average reflectance (expected reflectance), respectively. In both cases, the objective is to maximize the average power generation efficiency expected under isotropic diffuse light conditions. When designing an anti-reflection coating, the choice between Case 1 and Case 2 may be made arbitrarily, or may be made based on information about the optical properties of the solar cell that is available when designing the anti-reflection coating.

In other words, if it is difficult to accurately grasp or measure the optical properties of each layer that makes up a solar cell device (such as the thickness of each layer, the refractive index, and the wavelength dependence of the absorption properties), it is possible to design an anti-reflection coating suitable for indoor use using the method in Case 2, using the reflectance properties of the entire device, which is relatively easy to obtain. On the other hand, if the detailed optical properties of the solar cell can be grasped or measured through experiments, etc., it is possible to design an anti-reflection coating with higher performance by calculating the average power generation current (expected value of power generation current) using the method in Case 1.

The present disclosure also relates to a method for manufacturing an anti-reflection film for a solar cell, including the above-mentioned method for designing an anti-reflection film for a solar cell. As described above, this design method makes it possible to manufacture an anti-reflection film for a solar cell using conventional manufacturing processes as is. Therefore, this manufacturing method makes it possible to manufacture an anti-reflection film that enables solar cells to be obtained with superior power generation efficiency compared to conventional methods, at a cost equivalent to conventional methods.

The present disclosure also relates to a method for manufacturing a solar cell equipped with an anti-reflective coating, including the above-described method for designing an anti-reflective coating for a solar cell. As described above, this design method allows the anti-reflective coating for a solar cell to be manufactured using conventional manufacturing processes, and the main body of the solar cell can be manufactured using the same method as conventional methods. Therefore, this manufacturing method allows solar cells equipped with an anti-reflective coating that has superior power generation efficiency to conventional methods to be manufactured at a cost equivalent to conventional methods.

The present disclosure also provides a method for calculating, on a computer, (A) an energy density distribution g(θ) of a solar cell having an anti-reflection coating with respect to an incident angle θ of isotropically diffused light with respect to a surface of the anti-reflection coating, using the formula (1):
(where θ is the angle of incidence of isotropically diffused light with respect to the surface of the solar cell, and g(θ) is the light energy density), and a configuration determination process that determines the configuration of the antireflection coating that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ).

Preferably, the configuration determination process for determining the configuration of the anti-reflection coating that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ) includes: (B) an n-th configuration determination process for determining the n-th configuration of the anti-reflection coating; (C) a J SC (θ) or reflectance R(λ, θ) calculation process for calculating the power generation amount J _SC (θ) of the solar cell with respect to the incident angle θ, or the reflectance R(λ, θ) of the entire solar cell having the anti-reflection coating with respect to the incident angle θ and the wavelength λ, based on the n-th configuration of the anti-reflection coating; (D) an R _ave calculation process for calculating the average power generation amount J _{SC ,ave} of the solar cell or the average reflectance R _ave of the solar cell, using the relationship between the calculated energy density distribution g(θ) and the calculated J _SC (θ) or the calculated R(λ, θ); and (E) a process for maximizing the J _SC,ave calculated using an optimization engine or for optimizing the R the (n+1)th configuration determination process for determining the (n+1)th configuration of the anti-reflection coating that minimizes J _{SC, ave ,} where n is a natural number starting from 1, and determining a final configuration of the anti-reflection coating by repeating (C) to (E) until changes in J SC, ave, or R _ave calculated using the optimization engine converge within a predetermined range.

The configurations related to the above design method can be applied to determining the first configuration of the anti-reflection film when n is 1, maximizing the power generation efficiency of the solar cell, J _SC (θ), J _SC,ave , R(λ,θ), R _ave , H(θ), evaluation function I, the nth configuration of the anti-reflection film, etc.

The computer that executes this program may be equipped with a communications unit, a memory unit, and a processing unit, and may be a mobile device or information terminal such as a smartphone, tablet, or PC, or a server.

The communication unit may be implemented as hardware, firmware, communication software such as a TCP/IP driver or a PPP driver, or a combination of these. The communication unit may be a wireless communication unit or a wired communication unit. The communication unit may receive data via serial communication using a USB cable. The communication unit may have an interface circuit for performing short-range wireless communication according to a communication method such as Bluetooth (registered trademark). The communication unit may have a receiving circuit for receiving various signals via infrared communication, etc. The communication unit may also have a wired LAN communication interface circuit.

The storage unit is, for example, a semiconductor memory device such as ROM or RAM. The storage unit may also be, for example, a magnetic disk, an optical disk, or any other storage device capable of storing data. The storage unit stores operating system programs, driver programs, application programs, data, this program, and other programs used for processing in the processing unit. Computer programs, including this program, stored in the storage unit may be installed into the storage unit using a known setup program from a computer-readable portable recording medium such as a CD-ROM or DVD-ROM, or may be installed into the storage unit via a network.

The processing unit has one or more processors and their peripheral circuits. The processing unit controls the overall operation of the server, and is, for example, a CPU (Central Processing Unit). The processing unit can control the operation of the communication unit and memory unit.

The processing unit executes various processes based on programs stored in the memory unit (driver programs, operating system programs, application programs, this program, etc.). The processing unit can also execute multiple programs (application programs, etc.) in parallel.

(Example 1, Comparative Example 1)
To verify the effects of the present invention, an optical design of an anti-reflection coating was performed using an organic thin-film solar cell, which has recently attracted attention as an indoor power generation device. The design involved using the characteristic matrix method, a typical electromagnetic field analysis method, and writing the algorithm in a C language program. The performance differences between (a) and (b) were compared by designing and analyzing an anti-reflection coating for the same solar cell device using both this design method (a: Example 1) and a conventional method (b: Comparative Example 1). Specifically, in (a), the design was performed to maximize the average power generation (expected power generation) obtained with isotropically diffused light (corresponding to Case 1). Meanwhile, in (b), the design was performed, as in the conventional method, to maximize the power generation when light is incident perpendicularly.

Figure 6 shows a schematic diagram of an example of an eight-layer anti-reflection coating designed for an organic thin-film solar cell using _SiO2 layers and _TiO2 layers, based on the algorithm using the random initial values described above. Figure 6(a) shows the result when the method of the present invention was applied, and Figure 6(b) shows the result when the conventional design method (a method for maximizing power generation at normal incidence) was applied.

As shown in Figure 6, when an eight-layer film composed of _SiO2 and _TiO2 , which are widely used materials for anti-reflection coatings, was designed, the thickness of each layer was optimized using this design method, and power generation efficiency in an indoor environment was improved by 3.97% (relative value) compared to a system without an anti-reflection coating. This is 1.09% higher than the conventional method, demonstrating that this design method has a significant advantage over the conventional method. Furthermore, since only the thickness of each layer of the anti-reflection coating is changed, there is no need to use new materials, and the same equipment can be used for manufacturing without changing the equipment used, so there is essentially no increase in cost.

(Example 2, Comparative Example 2)
Using the algorithm using the random initial values described above, optical design of an antireflection coating was carried out for a four-layer film using a refractive index-adjusted material (a material whose refractive index is adjusted arbitrarily by making the material porous).

Figure 7 shows a schematic diagram of an example of a four-layer anti-reflection coating with different refractive indices designed for an organic thin-film solar cell. Figure 7(a) (Example 2) shows the result when this design method was applied, while Figure 7(b) (Comparative Example 2) shows the result when the conventional design method (a method that maximizes power generation at normal incidence) was applied.

In Figure 7(b), the properties of the top layer (refractive index, thickness) are not shown because the thickness of the top layer converged to 0 as a result of the design (meaning that three layers are essentially sufficient). The refractive index n of the refractive index-matching material is limited to a generally adjustable range (1.05 to 2.66). This design method improved the power generation efficiency in an indoor environment by 8.57% (relative value) compared to solar cells without an anti-reflection coating. This is 1.64% higher than the conventional method, and it is clear that this design method has even greater advantages when a refractive index-matching material is used.

Claims (16)

(A) The energy density distribution g(θ) of a solar cell having an anti-reflection film with respect to the incident angle θ of isotropically diffused light on the surface of the anti-reflection film is calculated using the formula (1):
where θ is the angle of incidence of the isotropically diffused light on the surface of the solar cell, and g(θ) is the light energy density.
Calculating based on, and
determining a configuration of the anti-reflection coating that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ). determining a configuration of the anti-reflection film that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ);
(B) determining an nth configuration of the anti-reflection film;
(C) calculating the short-circuit current density J _SC (θ) of the solar cell with respect to the incident angle θ, or the reflectance R(λ, θ) of the entire solar cell having the anti-reflection film with respect to the incident angle θ and wavelength λ based on the n-th configuration of the anti-reflection film;
(D ) calculating an average value J _SC ,ave of the short-circuit current density of the solar cell or an average value R _ave of the reflectance of the solar cell using the calculated relationship between the energy density distribution g(θ) and the calculated J _{SC (θ} ) or the calculated R(λ, θ); and (E) determining an (n+1)th configuration of the anti-reflection film that maximizes the calculated J _SC,ave or minimizes the calculated R _ave using an optimization engine,
The n is a natural number starting from 1,
and determining a final configuration of the anti-reflection coating by repeating (C) to (E) until a change in the J _{SC, ave} or the R _ave calculated using the optimization engine converges within a predetermined range.
The design method according to claim 1 . The design method of claim 2, wherein determining the first configuration of the anti-reflection coating when n is 1 is performed using a random initial value. Maximizing the power generation efficiency of the solar cell is achieved by satisfying the formula (2):
(where θ _min and θ _max are the lower and upper limits of the integral range of the incident angle, and H(θ) is a function of the short -circuit current density J _SC (θ) generated by the solar cell at the incident angle θ, or a function of the reflectance R(λ, θ) at the incident angle θ and wavelength λ.)
3. The design method according to claim 2, wherein the evaluation function I is maximized. The H(θ) is expressed by the formula (3):
is expressed as
The evaluation function I is expressed by the formula (4):
The average value of the short-circuit current density due to the isotropic diffused light is expressed as J _SC,ave ,
5. The design method according to claim 4, wherein maximizing the evaluation function I is maximizing the J _SC,ave . The H(θ) is expressed by the formula (5):
(In the formula , F (λ) is represented by the energy density at the wavelength λ of the light source used in the design , and λ _min and λ _max are the lower and upper limits of the wavelength range in which integration is performed.)
is expressed as
The evaluation function I is expressed by the formula (6):
The reflectance R ave is the average reflectance under the condition of isotropic diffuse light, and the reflectance R _ave is the negative value (−R _ave ),
5. The design method according to claim 4, wherein maximizing the evaluation function I is minimizing −R _ave . The design method described in claim 2, wherein the nth configuration of the anti-reflection film is the number of layers of the anti-reflection film, the thickness of each layer, the refractive index, or a combination thereof. A method for manufacturing an anti-reflection coating for solar cells, comprising the design method described in any one of claims 1 to 7. A method for manufacturing a solar cell equipped with an anti-reflection coating, comprising the design method described in any one of claims 1 to 7. On the computer,
(A) The energy density distribution g(θ) of a solar cell having an anti-reflection film with respect to the incident angle θ of isotropically diffused light on the surface of the anti-reflection film is calculated using the formula (1):
where θ is the angle of incidence of the isotropically diffused light on the surface of the solar cell, and g(θ) is the light energy density.
A calculation process that calculates based on
a configuration determination process for determining a configuration of the anti-reflection coating that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ). a configuration determination process for determining a configuration of the anti-reflection film that maximizes the power generation efficiency of the solar cell based on the calculated energy density distribution g(θ),
(B) an nth configuration determination process for determining an nth configuration of the antireflection film;
(C) a calculation process of J _SC (θ) or reflectance R(λ, θ) for calculating the short-circuit current density J _SC (θ) of the solar cell with respect to the incident angle θ, or the reflectance R(λ, θ) of the entire solar cell having the anti-reflection film with respect to the incident angle θ and wavelength λ, based on the n-th configuration of the anti-reflection film;
(D ) an R ave calculation process that calculates an average value J _SC ,ave of the short-circuit current density of the solar cell or an average value R _ave of the reflectance of the solar cell using the relationship between the calculated energy density distribution g(θ) and the calculated J _{SC (θ) or} the calculated R(λ, θ); and (E) an (n+1)th configuration determination process that determines an (n+1)th configuration of the anti-reflection film that maximizes the J _SC,ave or minimizes the R _ave calculated using an optimization engine,
The n is a natural number starting from 1,
and determining a final configuration of the anti-reflection coating by repeating (C) to (E) until a change in the J _{SC, ave} or the R _ave calculated using the optimization engine converges within a predetermined range.
The design program according to claim 10. The design program described in claim 11, wherein determining the first configuration of the anti-reflection coating when n is 1 is performed using a random initial value. Maximizing the power generation efficiency of the solar cell is achieved by satisfying the formula (2):
(where θ _min and θ _max are the lower and upper limits of the integral range of the incident angle, and H(θ) is a function of the short -circuit current density J _SC (θ) generated by the solar cell at the incident angle θ, or a function of the reflectance R(λ, θ) at the incident angle θ and wavelength λ.)
The design program according to claim 11 , wherein the objective is to maximize an evaluation function I expressed as follows: The H(θ) is expressed by the formula (3):
is expressed as
The evaluation function I is expressed by the formula (4):
The average value of the short-circuit current density due to the isotropic diffused light is expressed as J _SC,ave ,
The design program according to claim 13, wherein maximizing the evaluation function I is maximizing the J _SC,ave . The H(θ) is expressed by the formula (5):
(where F (λ) is the energy density at wavelength λ of the light source used in the design , and λ _min and λ _max are the lower and upper limits of the wavelength range in which integration is performed).
is expressed as
The evaluation function I is expressed by the formula (6):
The reflectance R ave is the average reflectance under the condition of isotropic diffuse light, and the reflectance R _ave is the negative value (−R _ave ),
14. The design program according to claim 13, wherein maximizing the evaluation function I is minimizing −R _ave . The design program described in claim 11, wherein the nth configuration of the anti-reflection film is the number of layers of the anti-reflection film, the thickness of each layer, the refractive index of each layer, or a combination thereof.