Method, system, device and storage medium for predicting optoelectronic characteristics of semiconductor devices

Abstract

The present invention provides a method for predicting the photoelectric characteristics of semiconductor devices, including constructing the Maxwell equations of the optical model and the diffusion drift equations of the electrical model; simplifying the Maxwell equations according to the vector magnetic potential and the scalar potential to obtain the first Maxwell equations; processing the first Maxwell equations according to the frequency domain Lorentz norm by the frequency domain finite difference method to obtain the D'Alembert equation, and then discretizing the five-point central difference grid to obtain the vector magnetic potential; calculating the absorption energy density and the carrier generation rate according to the vector magnetic potential; substituting the generation rate into the drift equation, and solving the current continuity equations of electrons and holes by the finite difference method and the exponential difference approximation method to obtain the prediction results of the electrical characteristics. This solution solves the problem that the prior art may face low-frequency breakdown, and the problem that the prediction of the photoelectric characteristics of semiconductor devices is not accurate enough due to the large amount of calculation and complex calculation principle in the process of coupling the optical model and the electrical model.

Description

Technical Field

[0001] The present invention belongs to the field of optoelectronic characteristics of semiconductor devices, and in particular relates to a prediction method, system, equipment and storage medium for optoelectronic characteristics of semiconductor devices. Background Art

[0002] With the advancement of nanotechnology, the length of semiconductor devices has gradually shrunk to the nanoscale. Semiconductor devices usually involve the interaction of electromagnetic fields. The finite difference method can be used to simulate the distribution of electromagnetic fields in these devices, help understand the distribution of electric and magnetic fields inside the device, and then optimize the device design. It can also simulate the transmission process of light in semiconductor devices, including the propagation, reflection, and refraction of light in the medium, which helps to analyze the optical properties of the device, such as transmittance, reflectivity, and dispersion properties. At the same time, semiconductor devices may generate heat when working, affecting device performance. The finite difference method can simulate processes such as heat conduction and thermal radiation inside the device to help evaluate the thermal management of the device and avoid overheating damage.

[0003] In finite difference simulation, it is very important to consider the multi-scale phenomena determined by Maxwell's equations. The frequency domain finite difference method is widely used to solve Maxwell's equations because of its simplicity and intuitiveness and its significant advantages in dealing with optical dispersive media and complex structures. At the same time, the photoelectric coupling phenomenon plays a vital role in modern optoelectronics and optical communication systems. Its accurate simulation and understanding are of great significance for the design of high-performance semiconductor devices and systems.

[0004] The FDFD algorithm is one of the easiest numerical methods to derive and implement. By solving Maxwell's equations in the frequency domain using the finite difference method, researchers can obtain relevant field values ​​and further solve the optical parameters through post-processing methods. This method has significant advantages in solving periodic and oblique incidence problems, so it is widely used in the field of organic solar cells. However, this method may face low-frequency breakdown problems and has challenges in coupling the optical model and the electrical model. The coupling process involves large amounts of calculations and complex calculation principles. Summary of the invention

[0005] In order to solve the problem that the method for solving Maxwell's equations in the prior art may face low-frequency breakdown, and the problem that the photoelectric characteristics of semiconductor devices are not accurately predicted due to the large amount of calculation and complex calculation principles in the process of coupling optical models and electrical models, the present invention provides a method, system, device and storage medium for predicting the photoelectric characteristics of semiconductor devices.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for predicting the optoelectronic characteristics of a semiconductor device comprises the following steps:

[0008] According to the material parameters of the semiconductor device, the Maxwell equations of the optical model and the diffusion drift equations of the electrical model of the simulation area of ​​the semiconductor device are constructed;

[0009] Substitute the vector magnetic potential and scalar potential of the semiconductor device into the Maxwell equations, simplify the Maxwell equations after substitution according to Gauss's theorem of electric field and Ampere's loop law to obtain the first Maxwell equations; express the scalar potential with the vector magnetic potential according to the Lenz gauge condition in the frequency domain to obtain the scalar potential expression, substitute the scalar potential expression into the first Maxwell equations, simplify the first Maxwell equations after substitution by the frequency domain finite difference method to obtain the D'Alembert equations, discretize the D'Alembert equations by five-point central difference grids and solve them to obtain the vector magnetic potential of the optical model; calculate the absorbed energy density and carrier generation rate of the semiconductor material according to the vector magnetic potential;

[0010] The carrier generation rate is coupled to the diffusion drift equation, and the expressions of electrons and holes in the diffusion drift equation are substituted into the current continuity equation of electrons and holes to obtain the first current continuity equation of electrons and holes. The first current continuity equation of electrons and holes is discretized using the same meshing system as the optical model to obtain a one-dimensional finite difference discrete format. The exponential difference approximation method is used to approximate the potential in the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes, and the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes after the approximate calculation is solved to obtain the prediction results of the electrical characteristics of the semiconductor device.

[0011] Furthermore, the step of solving the D'Alembert equation by five-point central difference grid discretization to obtain the vector magnetic potential of the optical model includes:

[0012] The differential form of the Maxwell equations is as follows:

[0013] (1);

[0014] in, , , and represent the electric displacement vector, electric field intensity, magnetic induction intensity and magnetic field intensity respectively, and denote the charge and current density, respectively, is the gradient operator, It is represented as the divergence of the vector D; Expressed as the curl of vector E;

[0015] According to the vector magnetic potential and scalar potential To solve Maxwell's equations, the electric and magnetic fields are related as follows:

[0016] (2);

[0017] Substituting equation (2) into equation (1), the first Maxwell equation can be obtained from Gauss's theorem of electric field and Ampere's circuit law:

[0018] (3);

[0019] in, and They are the dielectric constant and magnetic permeability of the material, respectively. The Lorentz specification is used to measure the magnetic potential A and the scalar potential Uniquely determined, if the time harmonic factor is , the frequency domain Lorentz gauge condition is introduced as: , the Lorentz gauge condition is obtained Substitute the expression into the second formula in equation (3), and simplify the obtained D'Alembert equation by the frequency domain finite difference method, and discretize the D'Alembert equation by five-point central difference grid. The specific discretization formula is as follows:

[0020] (4);

[0021] in, is the wave number in free space, x and y are the horizontal and vertical coordinates of the five-point central difference grid in the plane rectangular coordinate system, Represents the total field, by transforming the vector magnetic potential in formula (4) The five-point central differential grid discretization is performed to obtain the differential discretization formula for the vector magnetic potential A. The specific formula is as follows:

[0022] (5);

[0023] (6);

[0024] in, , , , Represents the dielectric constant of the four mesh materials around the center point, is the dielectric constant of the material at the center point, , are the length and width of each grid, , , , , Five point vector magnetic potentials of the optical model;

[0025] The incident field is input as the excitation, and the vector magnetic potential A is expressed by the incident field and the scattered field. The vector magnetic potential A is substituted into equation (5), and the corresponding scattered field is obtained by solving equation (5) after translation simplification. The vector magnetic potential of the electromagnetic-optical model is calculated based on the incident field and the scattered field.

[0026] Furthermore, when the D'Alembert equation is discretized by a five-point central difference grid, the output wave is absorbed by using a coordinate stretched perfect matching layer as a boundary condition, and the formula (4) is modified according to the coordinate stretching parameter to obtain the modified Maxwell equation. The modified Maxwell equation is as follows:

[0027] (7);

[0028] in, is the coordinate stretching parameter, ;

[0029] After discretizing the modified Maxwell equations using a five-point central difference grid, the vector magnetic potential A at the boundary is obtained.

[0030] Further, the step of calculating the absorbed energy density and carrier generation rate of the semiconductor material according to the vector magnetic potential includes:

[0031] Substituting the vector magnetic potential obtained by solving formula (5) into the calculation formula of absorption energy density and carrier generation rate, the average absorption energy density of the semiconductor material and the carrier generation rate at each point are calculated. The specific calculation formula is as follows:

[0032] (8);

[0033] (9);

[0034] in, is the average absorbed energy , is the carrier generation rate at each point, is the reduced Planck constant, is the imaginary part of the complex dielectric constant of the semiconductor material, is the atmospheric mass 1.5G solar spectrum, is the vector magnetic potential, is the scalar potential, S is the total area of ​​the semiconductor material, is the wavelength, and are the upper and lower limits of the wavelength interval integral.

[0035] Furthermore, the step of solving the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes after approximate calculation to obtain the prediction result of the electrical characteristics of the semiconductor device includes:

[0036] The current continuity equation is solved according to the electron current density and hole current density in the semiconductor. The relevant formulas for the electron current density and hole current density in the diffusion drift equation are as follows:

[0037] (10);

[0038] Where q is the electron charge, n and p are the electron and hole concentrations, and are the mobilities of electrons and holes, respectively, is the Boltzmann constant;

[0039] The electron current in formula (10) and hole current Substituting the expression into the current continuity equation of electrons and holes, we get the first current continuity equation of electrons and holes, which is as follows:

[0040] (11);

[0041] in, and are the acceptor and donor concentrations, respectively; is the carrier generation rate inside the semiconductor device, is the total recombination rate inside the device;

[0042] The carrier concentrations n and p, and the potential Discretize on the grid points. If the discretization grid size is set to , then the finite difference discrete format of the electron concentration n in one dimension is:

[0043] (12);

[0044] Among them, i+1 / 2 represents the middle position between the i-th intersection point and the i+1-th intersection point on the discrete grid, and i-1 / 2 represents the middle position between the i-1-th intersection point and the i-th intersection point on the discrete grid. is the exciton generation rate at the ith point, is the material recombination rate at the ith point. The potential in formula (12) is approximated by exponential difference and an auxiliary variable is introduced. , the specific calculation formula is as follows:

[0045] (13);

[0046] (14);

[0047] Among them, the potential , the electron n and hole p concentrations at the grid points, the vector magnetic potential A and the current is the vector connecting the grid points, and are the electron and hole diffusion coefficients respectively, according to and The charge carrier mobility of electrons and holes and Satisfying the Einstein relation, we get the following formula:

[0048] (15);

[0049] (16);

[0050] (17);

[0051] in, Indicates temperature, is the thermal voltage, is the Boltzmann constant;

[0052] By jointly solving equations (13), (14), (15) and (17), we can obtain the electron concentration n and the potential , and then according to the electric potential By solving the formula , is the dielectric constant, and the current density is ;

[0053] Similarly, the iterative difference format of holes is derived, and the approximate solution formula for the hole concentration p is as follows:

[0054] (18);

[0055] By jointly solving equations (13), (18), (16) and (17), the hole concentration p and the potential can be obtained: ;

[0056] According to the current density and potential The volt-ampere characteristic curve of the device is obtained, and the corresponding electron and hole distribution inside the device is obtained according to the electron concentration n and the hole concentration p.

[0057] Furthermore, the predicted results of the electrical characteristics include a volt-ampere characteristic curve, and corresponding electron and hole concentrations and distributions inside the semiconductor device.

[0058] A prediction system for optoelectronic characteristics of semiconductor devices, comprising:

[0059] A model building module, used for building the Maxwell equations of the optical model and the diffusion drift equations of the electrical model of the simulation area of ​​the semiconductor device according to the material parameters of the semiconductor device;

[0060] An optical property prediction module is used to substitute the vector magnetic potential and scalar potential of the semiconductor device into the Maxwell equations, simplify the Maxwell equations after substitution according to Gauss's theorem of electric field and Ampere's loop law to obtain the first Maxwell equations; express the scalar potential with the vector magnetic potential according to the Lenz gauge condition in the frequency domain to obtain the scalar potential expression, substitute the scalar potential expression into the first Maxwell equations, simplify the first Maxwell equations after substitution by the frequency domain finite difference method to obtain the D'Alembert equation, discretize the D'Alembert equation into a five-point central difference grid and solve it to obtain the vector magnetic potential of the optical model; calculate the absorption energy density and carrier generation rate of the semiconductor material according to the vector magnetic potential;

[0061] The electrical characteristics prediction module is used to couple the carrier generation rate to the diffusion drift equation, substitute the expressions of electrons and holes in the diffusion drift equation into the current continuity equation of electrons and holes to obtain the first current continuity equation of electrons and holes, use the same grid partitioning system as the optical model, discretize the first current continuity equation of electrons and holes to obtain a one-dimensional finite difference discrete format; use the exponential difference approximation method to approximate the potential in the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes, solve the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes after the approximate calculation, and obtain the prediction results of the electrical characteristics of the semiconductor device.

[0062] A computer device comprises a memory and a processor, wherein the memory stores computer-executable instructions, and the processor executes the computer-executable instructions stored in the memory to implement a method for predicting optoelectronic characteristics of a semiconductor device as described above.

[0063] A computer-readable storage medium is used to store computer-executable instructions. When the computer-executable instructions are executed by a processor, they are used to implement the above-mentioned method for predicting the optoelectronic characteristics of a semiconductor device.

[0064] The method for predicting the optoelectronic characteristics of a semiconductor device provided by the present invention has the following beneficial effects:

[0065] The invention simplifies the Maxwell equations according to the electric field Gauss's theorem, Ampere's loop law, vector magnetic potential and scalar potential to obtain the first Maxwell equations; processes the first Maxwell equations according to the frequency domain Lorentz norm by the frequency domain finite difference method to obtain the D'Alembert equations, discretizes the D'Alembert equations by five-point central difference grids, and solves them to obtain the total field value of the optical model; calculates the absorbed energy density and the carrier generation rate of the semiconductor material according to the total field value; couples the carrier generation rate to the diffusion drift equation, uses the same grid partitioning system in the optical model and the electrical model, adopts the finite difference method and the exponential difference approximation method, solves the current continuity equations of the electrons and the current continuity equations of the holes, and obtains the prediction results of the electrical characteristics of the semiconductor device.

[0066] The present invention transforms the Maxwell equations by introducing vector magnetic potential and scalar electric potential; and after discretization according to the frequency domain Lorentz norm and the five-point central differential grid, the total field value of the optical model is approximately solved, which significantly reduces the complexity of directly solving the Maxwell equations by the frequency domain finite difference method in the existing method. The method of the present invention is more suitable for multi-scale problems because it is stable in the long wavelength range and does not need to extract the electric potential at each time step, which saves running time and solves the problem of low-frequency breakdown.

[0067] The finite difference method and the exponential difference approximation method are used to solve the current continuity equation for electrons and the current continuity equation for holes to simplify the calculation process of the function, improve numerical stability, and accelerate the calculation speed of the calculation process, thereby improving the accuracy of the prediction of the optoelectronic characteristics of semiconductor devices. Through accurate prediction of the optoelectronic characteristics, the structural design and material selection of the device can be guided to achieve the optimization of device performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the embodiment of the present invention and its design scheme, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0069] Figure 1 A flowchart of a prediction method according to an embodiment of the present invention;

[0070] Figure 2 A schematic diagram of a five-point center differential grid and non-uniform material processing in an embodiment of the method of the present invention;

[0071] Figure 3 A schematic diagram of an electromagnetic and semiconductor discrete grid for an embodiment of the method of the present invention;

[0072] Figure 4A schematic diagram of the structure of a perovskite battery according to an embodiment of the method of the present invention;

[0073] Figure 5 A comparison diagram of reflectivity simulation results of an embodiment of the method of the present invention;

[0074] Figure 6 A comparison diagram of the absorption rate simulation results of an embodiment of the method of the present invention;

[0075] Figure 7 A comparison diagram of the simulation results of the generation rate of the embodiment of the method of the present invention;

[0076] Figure 8 It is a comparison diagram of the simulation results of the volt-ampere curves of the method embodiment of the present invention. DETAILED DESCRIPTION

[0077] In order to enable those skilled in the art to better understand the technical solution of the present invention and implement it, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the scope of protection of the present invention.

[0078] Method Embodiment

[0079] The present invention provides a method for predicting the optoelectronic characteristics of a semiconductor device, specifically Figure 1 As shown, including the direct use of vector potential and scalar potential (A and ) significantly reduces the solution complexity. And this new method is more suitable for multiscale problems because it is stable in the long wavelength range and does not require the extraction of the electric potential at each time step, thus establishing the proposed method as a better algorithm in electromagnetic simulation.

[0080] At the same time, in terms of photoelectric coupling, the scalar potential in the electromagnetic model (optical model) The potential in the semiconductor model (electrical model) , which can effectively simplify the model complexity by designing the position of physical quantities in the grid and using the same grid division system.

[0081] 1) Optical model: Maxwell equations

[0082] Maxwell's equations are the most basic mathematical expressions in macroscopic electromagnetic theory. Their differential form can describe the changing law of the field at any point in space. The evolution of the electromagnetic response characteristics inside the device in the time domain and space domain is described by using the derived form of Maxwell's equations and its auxiliary equations. The differential form of Maxwell's equations is as follows:

[0083] (1).

[0084] in, , , and represent the electric displacement vector, electric field intensity, magnetic induction intensity and magnetic field intensity respectively, and denote the charge and current density, respectively, is the gradient operator, It is represented as the divergence of the vector D; Expressed as the curl of the vector E.

[0085] In order to solve the diffusion drift equation of semiconductor carriers in a self-consistent manner, the present invention proposes a method using vector magnetic potential A and scalar potential to deal with Maxwell's equations, Represented as a scalar The gradient of is related to the electric and magnetic fields as follows:

[0086] (2).

[0087] Substituting equation (2) into equation (1), we can obtain from Gauss's law of electric field and Ampere's circuit law:

[0088] (3).

[0089] in, and are the dielectric constant and magnetic permeability of the material. In the solar cell structure, all materials are non-magnetic materials, so = 1. In the above formula (3), the vector magnetic potential A and the scalar potential To determine the vector field, it is necessary to specify both the divergence and curl of the field. However, in equation (2), only the curl of the vector magnetic potential A is specified, without specifying the divergence. Therefore, the Lorentz specification is used to make A and Uniquely determined, if the time harmonic factor is , the frequency domain Lorentz gauge condition is introduced as: , and the Lorentz gauge condition will Substitute the expression into the second formula in formula (3) and use the finite difference frequency domain method to substitute The D'Alembert equation (4) obtained by processing the second formula in the formula (3) is discretized using a five-point central difference grid, as Figure 2 shown.

[0090] (4).

[0091] in, is the wave number in free space, and the vector magnetic potential in equation (4) is Perform five-point central difference grid discretization, That is , x and y are the horizontal and vertical coordinates of the five-point central difference grid in the plane rectangular coordinate system, Representing the total field (the total field is equal to the incident field plus the scattered field), the differential discrete equation about the vector magnetic potential A is obtained, and the specific formula is as follows:

[0092] (5).

[0093] (6).

[0094] in, , , , Represents the dielectric constant of the four mesh materials around the center point, is the dielectric constant of the material at the center point, , are the length and width of each grid, , , , , They are the vector magnetic potentials of the five points, that is, the total field of the five points.

[0095] Input the incident field as the excitation, represent the total field A by the incident field and the scattered field, substitute it into equation (5), and solve equation (5) to obtain the corresponding scattered field after translation simplification. If the discrete grid size is set to , the total field of the electromagnetic optical model is calculated from the incident field and the scattered field. Substitute the corresponding dielectric constant of the material into formulas (5) and (6) to solve for the scattered field, and finally get the total field value of the structure based on the known incident field plus the scattered field , and then substitute the total field value into formula (8) and formula (9) to calculate the relevant optical parameters.

[0096] Due to limited computer resources, the simulation area cannot be infinite, and a perfectly matched layer (PML) is required as a boundary condition to absorb the output wave. In the prior art, a very simple method of realizing PML using the idea of ​​coordinate stretching has been proposed, which will not be described here. The same method is also used in the present invention to realize A- The PML of the equation. The electromagnetic optical model formula at the boundary is obtained by modifying equation (4) as follows using the coordinate stretching parameter:

[0097] (7).

[0098] These coordinate stretching parameters are defined as: , the conductivity in PML is set to the following form to simulate infinite space:

[0099] (A).

[0100] (B).

[0101] , is the number of layers of PML, is the order of the polynomial, is a constant. Similarly, by solving formula (7), the total field value at the boundary of the simulation area can be obtained.

[0102] Average absorbed energy density of semiconductor materials and the carrier generation rate at each discrete point It can be expressed as:

[0103] (8).

[0104] (9).

[0105] in, is the reduced Planck constant, is the imaginary part of the complex dielectric constant of the semiconductor material, is the atmospheric mass 1.5G solar spectrum, is the total field value at a point, is the scalar potential, is the total area of ​​semiconductor material, , and are the upper and lower limits of the wavelength interval integral. =300nm, =900nm.

[0106] Substituting the total field value and other related parameters obtained by solving formula (5) into formulas (8) and (9), after post-processing, the electromagnetic-optical model can give the electrical model input parameters such as the average absorption energy density of the semiconductor material and the exciton generation rate at each discrete point.

[0107] The generation rate obtained by solving Maxwell's equations will be coupled into the semiconductor equations, which is a bridge between optics and electricity.

[0108] (2)) Electrical model: semiconductor diffusion drift equation.

[0109] Applying the drift-diffusion model to semiconductors, the flow of carriers is divided into drift motion and diffusion motion. Drift motion refers to the directional movement of carriers under the action of an external field, which generates a drift current; diffusion motion refers to the movement of carriers from a higher concentration to a lower concentration, which generates a diffusion current. The electron current density of the semiconductor diffusion drift equation is obtained from the semiconductor equation and hole current density The specific expressions are as follows:

[0110] (10).

[0111] in, is the dielectric constant, q is the electron charge, n and p are the electron and hole concentrations, and are the mobility of electrons and holes, respectively; is the Boltzmann constant. The electron current density and hole current density Substituting the expression (10) into the current continuity equation, we get the equation group (11), which is:

[0112] (11).

[0113] In the above formula, and are the acceptor and donor concentrations respectively; G is the carrier generation rate inside the semiconductor device, and R is the total recombination rate inside the device. Figure 3 As shown, the carrier concentration (n, p) and potential Discretized on the grid points, the current density J and the vector magnetic potential A are the vectors connecting the grid points. By designing the position of the physical quantity in the grid, the optical model and the electrical model can use the same grid partitioning system, simplifying the model complexity. If the discrete grid size is set to , and are the length and width of each grid respectively. Taking the current continuity equation of electrons as an example, its finite difference discrete format in one dimension is:

[0114] (12).

[0115] Among them, i+1 / 2 represents the middle position between the i-th intersection point and the i+1-th intersection point on the discrete grid, and i-1 / 2 represents the middle position between the i-1-th intersection point and the i-th intersection point on the discrete grid. is the exciton generation rate at the ith point, is the material recombination rate at the i-th point. The exponential difference approximation is used for formula (12). The exponential difference approximation can simplify the calculation of the function, improve the numerical stability, and accelerate the calculation process, thereby more effectively solving the current transport problem in semiconductor devices. And introduce auxiliary variables:

[0116] (13).

[0117] (14).

[0118] The electric potential , electron n and hole p concentrations are at the grid points, and the vector magnetic potential A and current density J are the vectors connecting the grid points. and are the electron and hole diffusion coefficients, and the carrier mobility and Satisfies the Einstein relation, that is:

[0119] (15).

[0120] (16).

[0121] (17).

[0122] in, Indicates temperature, is the thermal voltage, is the Boltzmann constant;

[0123] By jointly solving the above formulas (13), (14), (15) and (17), we can obtain the electron concentration n and the potential Then according to the electric potential By solving the formula we get , is the dielectric constant, and the current density is .

[0124] Because the methods for solving electron n and hole p are the same, the iterative difference format for holes can be derived by the same logic, so the approximate solution formula for hole p is as follows:

[0125] (18).

[0126] By jointly solving the above formulas (13), (18), (16) and (17), we can obtain the hole concentration p and the potential .

[0127] According to the current density and potential The volt-ampere characteristic curve of the device is obtained, and the corresponding electron and hole distribution inside the device is obtained according to the electron concentration n and the hole concentration p. Among them, under the light condition, is defined as the current density when the externally applied voltage is zero. When the current density is zero, Defined as open circuit voltage. Obtaining the distribution of electrons and holes through carrier dynamics is an important way to study the characteristics and physical mechanisms of semiconductor devices, and provides technical support for more effective electrical regulation.

[0128] (3) Photoelectric coupling model verification

[0129] In order to verify the correctness of the photovoltaic coupling model in calculating the photovoltaic performance of solar cells, the solar cell structure calculated in this example is shown in the following figure. Figure 4 As shown, the thicknesses of indium tin oxide, nickel oxide, perovskite layer, carbon 60, and silver are 50nm, 20nm, 500nm, 50nm, and 120nm, respectively, with a period of 5nm. Perfectly matched layers PML and absorption boundary conditions Mur mixed boundaries are set at the top and bottom of the organic solar cell structure to simulate infinite space. Periodic boundary conditions are set on the left and right sides. The structure is as shown in Figure 4 As shown. This embodiment numerically solves Maxwell's equations and semiconductor equations by finite difference method. SolarDesign is a photovoltaic power station design software. Figure 5 and Figure 7 The SolarDesign simulation absorptivity curve in the incident wave Hz mode coincides with the absorptivity curve of the incident wave Hz mode; Figure 6 Curve 3 is the SolarDesign simulation absorption rate. Figure 6 Curve 4 is the simulated absorption rate of the incident wave Hz mode. When the wavelength of the horizontal axis is 600nm, the two curves overlap; Figure 8 Curve 1 in the figure is the COMSOL simulation JV curve, and curve 2 is the vector potential A calculation simulation JV curve; Figure 5 - Figure 8 As shown, the optical parameters of the structure are calculated based on the photoelectric coupling model: reflectivity, absorption rate and generation rate, as well as the JV curve related to the electrical parameters. The simulation results in the figure are basically consistent with the results in the literature, which verifies the correctness of the photoelectric coupling model proposed in the present invention.

[0130] System Example

[0131] The present invention provides a prediction system for photoelectric characteristics of a semiconductor device, comprising:

[0132] The model building module is used to build the Maxwell equations of the optical model and the diffusion drift equations of the electrical model of the simulation area of ​​the semiconductor device according to the material parameters of the semiconductor device.

[0133] An optical property prediction module is used to substitute the vector magnetic potential and scalar potential of a semiconductor device into Maxwell equations, simplify the Maxwell equations after substitution according to Gauss's theorem of electric field and Ampere's circuit law to obtain the first Maxwell equations; express the scalar potential with the vector magnetic potential according to the Lenz gauge condition in the frequency domain to obtain the scalar potential expression, substitute the scalar potential expression into the first Maxwell equations, simplify the first Maxwell equations after substitution by the frequency domain finite difference method to obtain the D'Alembert equations, discretize the D'Alembert equations by five-point central difference grids and solve them to obtain the vector magnetic potential of the optical model; calculate the absorption energy density and carrier generation rate of the semiconductor material according to the vector magnetic potential.

[0134] The electrical characteristics prediction module is used to couple the carrier generation rate to the current continuity equations of electrons and holes in the diffusion drift equation. The current continuity equations of electrons and holes are discretized using the same grid partitioning system as the optical model to obtain a one-dimensional finite difference discrete format. The exponential difference approximation method is used to approximate the electric potential in the one-dimensional finite difference discrete format of the current continuity equations of electrons and holes. The one-dimensional finite difference discrete format of the current continuity equations of electrons and holes after the approximate calculation is solved to obtain the prediction results of the electrical characteristics of the semiconductor device.

[0135] Device Embodiment

[0136] The present invention provides a computer device, including a memory and a processor, wherein the memory stores computer execution instructions, and the processor executes the computer execution instructions stored in the memory to implement a method for predicting the optoelectronic characteristics of a semiconductor device as described above, wherein the method has been described in detail in the method embodiment and will not be repeated here.

[0137] Storage Medium Embodiments

[0138] The present invention provides a computer-readable storage medium, which is used to store computer execution instructions. When the computer execution instructions are executed by a processor, they are used to implement a method for predicting the optoelectronic characteristics of a semiconductor device as described above, wherein the method has been described in detail in the method embodiment and will not be repeated here.

[0139] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0140] The present invention is described with reference to flowcharts and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as a combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0141] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0142] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0143] It should be noted that the above-described specific implementation methods can enable those skilled in the art to more fully understand the invention, but do not limit the invention in any way. Therefore, although the present specification and embodiments have described the invention in detail, those skilled in the art should understand that the invention can still be modified or replaced by equivalents; and all technical solutions and improvements that do not deviate from the spirit and scope of the invention are included in the protection scope of the patent for the invention. Any figure mark in the claims should not be regarded as limiting the claims involved.

Claims

1. A method for predicting optoelectronic characteristics of a semiconductor device, characterized in that: The steps include: According to the material parameters of the semiconductor device, the Maxwell equations of the optical model and the diffusion drift equations of the electrical model of the simulation area of ​​the semiconductor device are constructed; Substitute the vector magnetic potential and scalar potential of the semiconductor device into the Maxwell equations, simplify the Maxwell equations after substitution according to Gauss's theorem of electric field and Ampere's circuit law to obtain the first Maxwell equations; express the scalar potential with the vector magnetic potential according to the Lenz gauge condition in the frequency domain to obtain the scalar potential expression, substitute the scalar potential expression into the first Maxwell equations, simplify the first Maxwell equations after substitution by the frequency domain finite difference method to obtain the D'Alembert equations, discretize the D'Alembert equations by five-point central difference grids and solve them to obtain the vector magnetic potential of the optical model; calculate the absorption energy density and carrier generation rate of the semiconductor material according to the vector magnetic potential; The carrier generation rate is coupled to the diffusion drift equation, and the expressions of electrons and holes in the diffusion drift equation are substituted into the current continuity equations of electrons and holes to obtain the first current continuity equations of electrons and holes. The first current continuity equations of electrons and holes are discretized using the same meshing system as the optical model to obtain a one-dimensional finite difference discretized format. Using the exponential difference approximation method, the potential in the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes is approximately calculated, and the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes after the approximate calculation is solved to obtain the prediction results of the electrical characteristics of the semiconductor device; The step of solving the D'Alembert equation by five-point central difference grid discretization to obtain the vector magnetic potential of the optical model comprises: The differential form of the Maxwell equations is as follows: Where D, E, B and H represent the electric displacement vector, electric field intensity, magnetic induction intensity and magnetic field intensity respectively, ρ and J represent the charge and current density respectively. is the gradient operator, It is represented as the divergence of the vector D; Expressed as the curl of vector E; Maxwell's equations are solved based on the vector magnetic potential A and the scalar potential φ, which are related to the electric and magnetic fields as follows: Substituting equation (2) into equation (1), the first Maxwell equation can be obtained from Gauss's theorem of electric field and Ampere's circuit law: Among them, ε r and μ r are the dielectric constant and magnetic permeability of the material respectively. The Lorentz specification is used to uniquely determine the magnetic potential A and the scalar potential φ. If the time harmonic factor is e jωt , the frequency domain Lorentz gauge condition is introduced as: Substitute the expression of φ obtained by the Lorentz gauge condition into the second formula in equation (3), and simplify the obtained D'Alembert equation by the frequency domain finite difference method, and discretize the D'Alembert equation by five-point central difference grid. The specific discretization formula is as follows: Where k0 is the wave number in free space, x and y are the horizontal and vertical coordinates of the five-point central difference grid in the plane rectangular coordinate system, Representing the total field, the differential discretization formula for the vector magnetic potential A in formula (4) is obtained by discretizing the vector magnetic potential A with a five-point central differential grid. The specific formula is as follows: Among them, ε1, ε2, ε3, and ε4 represent the dielectric constants of the four mesh materials around the center point. is the dielectric constant of the material at the center point, Δx, Δy are the length and width of each grid, A0, A1, A2, A3, A4 are the five point vector magnetic potentials of the optical model; The incident field is input as the excitation, and the vector magnetic potential A is represented by the incident field and the scattered field, which is then substituted into equation (5). After translation simplification, equation (5) is solved to obtain the corresponding scattered field. The vector magnetic potential of the electromagnetic-optical model is calculated based on the incident field and the scattered field.

2. The method for predicting the optoelectronic characteristics of a semiconductor device according to claim 1, characterized in that: When the five-point central difference grid is discretized for the D'Alembert equation, the output wave is absorbed by using a coordinate stretched perfect matching layer as a boundary condition, and the formula (4) is modified according to the coordinate stretching parameter to obtain the modified Maxwell equation. The modified Maxwell equation is as follows: Among them, s r is the coordinate stretching parameter, s r =1-jσ / ωε r ; After discretizing the modified Maxwell equations using a five-point central difference grid, the vector magnetic potential A at the boundary is obtained.

3. The method for predicting the optoelectronic characteristics of a semiconductor device according to claim 1, characterized in that: The step of calculating the absorbed energy density and carrier generation rate of the semiconductor material according to the vector magnetic potential comprises: Substituting the vector magnetic potential obtained by solving formula (5) into the calculation formula of absorption energy density and carrier generation rate, the average absorption energy density of the semiconductor material and the carrier generation rate at each point are calculated. The specific calculation formula is as follows: Where η is the average absorbed energy density, G is the carrier generation rate at each point, is the reduced Planck constant, Im[ε r ] is the imaginary part of the complex dielectric constant of the semiconductor material, is the atmospheric mass 1.5G solar spectrum, A is the vector magnetic potential, φ is the scalar potential, S is the total area of ​​the semiconductor material, λ is the wavelength, and c1 and c2 are the upper and lower limits of the wavelength interval integration.

4. The method for predicting the optoelectronic characteristics of a semiconductor device according to claim 3, characterized in that: The step of solving the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes after approximate calculation to obtain the prediction result of the electrical characteristics of the semiconductor device comprises: The current continuity equation is solved according to the electron current density and hole current density in the semiconductor. The relevant formulas for the electron current density and hole current density in the diffusion drift equation are as follows: Where q is the electron charge, n and p are the electron and hole concentrations, and μ n and μ p are the mobility of electrons and holes, respectively, k b is the Boltzmann constant; The electron current J in formula (10) n and hole current J p Substituting the expression into the current continuity equation of electrons and holes, we get the first current continuity equation of electrons and holes, which is as follows: Among them, N A and N D are the acceptor and donor concentrations, respectively; G is the carrier generation rate inside the semiconductor device, and R is the total recombination rate inside the device; The carrier concentrations n and p, and the potential φ are discretized on the grid points. If the discretization grid size is set to Δx×Δy, the finite difference discretization format of the electron concentration n in one dimension is: Among them, i+1 / 2 represents the middle position between the i-th intersection point and the i+1-th intersection point on the discrete grid, i-1 / 2 represents the middle position between the i-1-th intersection point and the i-th intersection point on the discrete grid, and G i is the exciton generation rate at the ith point, R i is the material recombination rate at the i-th point. The potential in formula (12) is approximated by exponential difference and an auxiliary variable B(x) is introduced. The specific calculation formula is as follows: Among them, the potential φ, the electron n and hole p concentrations are at the grid points, the vector magnetic potential A and the current J are the vectors connecting the grid points, Dn and Dp are the electron and hole diffusion coefficients, respectively. According to Dn and Dp and the electron and hole carrier mobility μ n and μ p Satisfying the Einstein relation, we get the following formula: Where T represents temperature, U t is the thermal voltage, k b is the Boltzmann constant; By jointly solving formulas (13), (14), (15) and (17), the electron concentration n and the potential φ can be obtained. Then, according to the potential φ, the formula ε is the dielectric constant, and the current density J is obtained; Similarly, the iterative difference format of holes is derived, and the approximate solution formula for the hole concentration p is as follows: By jointly solving the formulas (13), (18), (16) and (17), the hole concentration p and the potential φ can be obtained; The volt-ampere characteristic curve of the device is obtained based on the current density J and the potential φ, and the corresponding electron and hole distribution inside the device is obtained based on the electron concentration n and the hole concentration p.

5. The method for predicting the optoelectronic characteristics of a semiconductor device according to claim 1, characterized in that: The predicted results of the electrical characteristics include the volt-ampere characteristic curve, and the corresponding electron and hole concentrations and distributions inside the semiconductor device.

6. A prediction system for optoelectronic characteristics of semiconductor devices, characterized in that: include: A model building module, used for building the Maxwell equations of the optical model and the diffusion drift equations of the electrical model of the simulation area of ​​the semiconductor device according to the material parameters of the semiconductor device; An optical property prediction module is used to substitute the vector magnetic potential and scalar potential of the semiconductor device into the Maxwell equations, simplify the Maxwell equations after substitution according to Gauss's theorem of electric field and Ampere's loop law to obtain the first Maxwell equations; express the scalar potential with the vector magnetic potential according to the Lenz gauge condition in the frequency domain to obtain the scalar potential expression, substitute the scalar potential expression into the first Maxwell equations, simplify the first Maxwell equations after substitution by the frequency domain finite difference method to obtain the D'Alembert equation, discretize the D'Alembert equation into a five-point central difference grid and solve it to obtain the vector magnetic potential of the optical model; calculate the absorption energy density and carrier generation rate of the semiconductor material according to the vector magnetic potential; The electrical property prediction module is used to couple the carrier generation rate to the diffusion drift equation, substitute the expressions of electrons and holes in the diffusion drift equation into the current continuity equations of electrons and holes to obtain the first current continuity equations of electrons and holes, and discretize the first current continuity equations of electrons and holes using the same meshing system as the optical model to obtain a one-dimensional finite difference discrete format; Using the exponential difference approximation method, the potential in the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes is approximately calculated, and the one-dimensional finite difference discrete format of the first current continuity equation of electrons and holes after the approximate calculation is solved to obtain the prediction results of the electrical characteristics of the semiconductor device; The step of solving the D'Alembert equation by five-point central difference grid discretization to obtain the vector magnetic potential of the optical model comprises: The differential form of the Maxwell equations is as follows: Where D, E, B and H represent the electric displacement vector, electric field intensity, magnetic induction intensity and magnetic field intensity respectively, ρ and J represent the charge and current density respectively. is the gradient operator, It is represented as the divergence of the vector D; Expressed as the curl of vector E; Maxwell's equations are solved based on the vector magnetic potential A and the scalar potential φ, which are related to the electric and magnetic fields as follows: Substituting equation (2) into equation (1), the first Maxwell equation can be obtained from Gauss's theorem of electric field and Ampere's circuit law: Among them, ε r and μ r are the dielectric constant and magnetic permeability of the material respectively. The Lorentz specification is used to uniquely determine the magnetic potential A and the scalar potential φ. If the time harmonic factor is e jωt , the frequency domain Lorentz gauge condition is introduced as: Substitute the expression of φ obtained by the Lorentz gauge condition into the second formula in equation (3), and simplify the obtained D'Alembert equation by the frequency domain finite difference method, and discretize the D'Alembert equation by five-point central difference grid. The specific discretization formula is as follows: Where k0 is the wave number in free space, x and y are the horizontal and vertical coordinates of the five-point central difference grid in the plane rectangular coordinate system, Representing the total field, the differential discretization formula for the vector magnetic potential A in formula (4) is obtained by discretizing the vector magnetic potential A with a five-point central differential grid. The specific formula is as follows: Among them, ε1, ε2, ε3, and ε4 represent the dielectric constants of the four mesh materials around the center point. is the dielectric constant of the material at the center point, Δx, Δy are the length and width of each grid, A0, A1, A2, A3, A4 are the five point vector magnetic potentials of the optical model; The incident field is input as the excitation, and the vector magnetic potential A is represented by the incident field and the scattered field, which is then substituted into equation (5). After translation simplification, equation (5) is solved to obtain the corresponding scattered field. The vector magnetic potential of the electromagnetic-optical model is calculated based on the incident field and the scattered field.

7. A computer device comprising a memory and a processor, characterized in that: The memory stores computer-executable instructions, and the processor executes the computer-executable instructions stored in the memory to implement a method for predicting optoelectronic characteristics of a semiconductor device according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium is used to store computer-executable instructions, and when the computer-executable instructions are executed by a processor, they are used to implement a method for predicting the optoelectronic characteristics of a semiconductor device as described in any one of claims 1 to 5.

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