Semiconductor device numerical simulation method based on spatial discretization and uncoupling iteration

Abstract

The invention discloses a numerical simulation method for a semiconductor device based on spatial discretization and uncoupling iteration. The method comprises the following steps: establishing a basic equation set of the semiconductor device; spatial discretization is carried out on the non-uniform hexahedral mesh; discretizing the current equation to obtain a drift diffusion model equation set in a three-dimensional discrete format; and sequentially solving each equation in the drift diffusion model equation set by adopting a Gummel uncoupling method. According to the semiconductor device numerical simulation method based on spatial discretization and uncoupled iteration provided by the invention, a semiconductor partial differential equation is subjected to three-dimensional spatial discretization by adopting an FDM method, and a large-scale nonlinear equation set is solved by adopting a Gummel uncoupled iteration method, so that physical characteristics and internal physical images of the device are obtained; the occupied computer memory is relatively low, the method is not sensitive to an initial value, and the simulation speed is greatly improved.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor simulation technology, and in particular to a semiconductor device numerical simulation method based on spatial discretization and non-coupled iteration. Background Art

[0002] Computer numerical simulation of semiconductor devices refers to the selection of appropriate numerical methods and the development of computer programs through programming languages to numerically solve partial differential equations that can describe physical changes in semiconductors, thereby obtaining the physical characteristics of the device and the internal physical image. Since the 1960s, numerical simulation of semiconductor devices has played an increasingly important role in the integrated circuit industry, greatly reducing the development cycle of devices and reducing development costs. At present, the mainstream algorithm for semiconductor device simulation is based on the SG difference format proposed by Gummel and Scharfetter in 1969 for the classic drift-diffusion equation, which has good simulation accuracy for micron-sized devices. Currently, the numerical methods used for discretizing semiconductor equations mainly include the finite volume method (FVM), the finite element method (FEM), and the finite difference method (FDM). With the increase in the demand for device simulation from two-dimensional to three-dimensional, FVM and FEM generally use tetrahedral meshes, the mesh generation is relatively complex, and the simulation results strongly depend on the mesh quality. FDM uses non-uniform hexahedral meshes, the mesh generation is efficient and simple, and the process of discretizing partial differential equations in three-dimensional space using the seven-point difference format is concise and clear, which is simpler and more efficient for relatively regular semiconductor devices. After the spatial discretization is completed, it is necessary to solve a large-scale nonlinear system of equations. Currently, the most widely used method is the fully coupled Newton method, which solves the three basic equations of semiconductor devices at the same time. Its disadvantage is that it needs to construct and store a complex Jacobian matrix, which occupies a large amount of memory.

[0003] At present, there are also semiconductor multi-physics effect simulation methods, which use tetrahedral unit-based meshing to construct high-order basis functions, and use the hybridized discontinuous Galerkin method to discretize the differential equations in the carrier drift-diffusion model to obtain information such as the carrier concentration in the device. However, it is usually based on the finite element method, and the disadvantage is that for continuous test functions and basis functions, there is no local conservation, and only global conservation can be guaranteed; in addition, it cannot control local flux, and the discretization of flows dominated by stable convection is relatively complicated, and the amount of calculation may be very large.

[0004] Therefore, how to improve the speed and accuracy of semiconductor simulation and reduce the memory occupied by calculations is a technical problem that needs to be solved urgently. Summary of the invention

[0005] To solve the deficiencies of the prior art, the present invention provides a numerical simulation method for semiconductor devices based on spatial discretization and uncoupled iteration. The finite difference method (FDM) is used to discretize the semiconductor partial differential equations in three-dimensional space, and the Gummel uncoupled iteration method is used to solve large-scale nonlinear equations, thereby obtaining the physical characteristics of the device and the internal physical image. It occupies relatively low computer memory and is not sensitive to the initial value, greatly improving the simulation speed.

[0006] The embodiments of the present invention provide the following solutions:

[0007] The embodiments of the present invention provide a numerical simulation method for semiconductor devices based on spatial discretization and uncoupled iteration, and the method includes:

[0008] S1. Establish the basic equations of the semiconductor device, and the basic equations of the semiconductor device include the Poisson equation, the electron current continuity equation, the hole current continuity equation, the electron current density equation, and the hole current density equation;

[0009] S2. Use the three-dimensional seven-point central difference method to perform spatial discretization of the basic equations of the semiconductor device on a non-uniform hexahedral grid;

[0010] S3. Use the Scharfetter-Gummel format to discretize the basic equations of the semiconductor device to obtain the drift-diffusion model equations in three-dimensional discrete format, including the discretized Poisson equation, electron current equation, and hole current equation;

[0011] S4. Use the Gummel uncoupled method to sequentially solve each equation in the drift-diffusion model equations.

[0012] In an alternative embodiment, the basic equations of the semiconductor device described in step S1 include:

[0013]

[0014] Among them, the electrostatic potential ψ, the electron concentration n, and the hole concentration p are all independent variables. Equations (1) to (5) are the Poisson equation, the electron current continuity equation, the hole current continuity equation, the electron current density equation, and the hole current density equation in sequence; ε s is the material dielectric constant, q is the unit charge constant, is the donor doping concentration, is the acceptor doping concentration, J n is the electron current density inside the device, G n is the electron generation rate, R n is the electron recombination rate, Jp is the hole current density inside the device, G p is the hole generation rate, R pis the hole recombination rate, μ n is the electron mobility, E C is the conduction band energy level, m n is the electron effective mass, D n is the electron diffusion coefficient, μ p is the hole mobility, E V is the valence band energy level, m p is the hole effective mass, D p is the hole diffusion coefficient, k is the Boltzmann constant, T is the lattice temperature, and all are known quantities.

[0015] In an alternative embodiment, after step S2 performs spatial discretization using the three-dimensional seven-point central difference method, for each point O(x0, y0, z0) to be solved, six adjacent points (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), (x4, y4, z4), (x5, y5, z5), and (x6, y6, z6) around it are obtained, dx1 = x0 - x1, dx2 = x2 - x0, dy1 = y0 - y3, dy2 = y4 - y0, dz1 = z0 - z5, dz2 = z6 - z0.

[0016] In an alternative embodiment, the drift-diffusion model equations in the three-dimensional discrete format include:

[0017] (a0ψ0 + a1ψ1 + a2ψ2 + a3ψ3 + a4ψ4 + a5ψ5 + a6ψ6) j+1 = (n j - p j - C) - (n j + p j )ψ0 j (6)

[0018] (a0n0 + a1n1 + a2n2 + a3n3 + a4n4 + a5n5 + a6n6) j+1 - R(ψ j+1 , n j , p j ) = 0 (7)

[0019] (a0p0 + a1p1 + a2p2 + a3p3 + a4p4 + a5p5 + a6p6) j+1 - R(ψ j+1 , n j , p j ) = 0 (8)

[0020] Among them, Equation (6) is the discretized Poisson equation, Equation (7) is the discretized electron current equation, Equation (8) is the discretized hole current equation, ψ0, ψ1, ψ2, ψ3, ψ4, ψ5, and ψ6 are the electrostatic potentials of the point to be solved and its six adjacent points around it, n0, n1, n2, n3, n4, n5, and n6 are the electron concentrations of the point to be solved and its six adjacent points around it, p0, p1, p2, p3, p4, p5, and p6 are the hole concentrations of the point to be solved and its six adjacent points around it, j is the number of iterations, n j , p j and ψ j respectively represent the electron concentration, hole concentration, and electrostatic potential obtained after the j-th iteration, and a0, a1, a2, a3, a4, a5, and a6 are the coefficients of the drift-diffusion model equations in three-dimensional discretized format.

[0021] In an alternative embodiment, step S4 includes the following processes:

[0022] S4.1. Set the initial values of the electrostatic potential, electron concentration, and hole concentration as initial conditions;

[0023] S4.2. Solve the discretized Poisson equation. For the relationship between the electrostatic potential and the carrier concentration in this equation, use the statistical distribution of carriers to perform a first-order Taylor expansion for linear approximation to obtain the current electrostatic potential;

[0024] S4.3. Treat the electrostatic potential and hole concentration as constants, solve the discretized electron current equation, and obtain the current electron concentration;

[0025] S4.4. Continue to treat the electrostatic potential and electron concentration as constants, solve the discretized hole current equation, and obtain the current hole concentration;

[0026] S4.5. After this iteration ends, calculate the relative error of the solution of the unknowns. If the convergence condition is not met, use the current electrostatic potential, current electron concentration, and current hole concentration as the current conditions and return to step S4.2 for the next iteration, otherwise the iteration ends.

[0027] In an alternative embodiment, the initial conditions described in step S4.1 are obtained according to the charge balance condition. The acquisition of the initial conditions includes the following processes:

[0028] Let the initial values of the electrostatic potential, electron concentration, and hole concentration be (ψ 0 , n 0 , p 0 ). The initial value of the electrostatic potential is taken as the result of the quasi-Fermi potential of the majority carriers being adjusted by the built-in potential to ensure the overall electrical neutrality of the region. There is

[0029] ψ 0 = φ N + φin

[0030] Among them, the built-in potential

[0031]

[0032] n i,eff is the effective intrinsic concentration of the semiconductor material, and

[0033] is the net doping concentration;

[0034]

[0035] For an N-type semiconductor, C > 0:

[0036]

[0037] In an alternative embodiment, the convergence condition described in step S4.4 is determined according to the relative error of the solutions of the unknowns at all discrete lattice points for all equations,

[0038]

[0039] where z j (e, i) is the solution of equation e at the i-th lattice point in the j-th iteration, and the constant N is taken as the number of equations multiplied by the total number of lattice points, z ref (e) is for ensuring the numerical stability when |z j (e, i)| → 0, and the approximate value of the solution accuracy is z ref (e)ε R .

[0040] In an alternative embodiment, ε R takes the value of 10 -5 .

[0041] The beneficial effects of the present invention based on its technical solution are as follows:

[0042] (1) A numerical simulation method for semiconductor devices based on spatial discretization and uncoupled iteration provided by the present invention uses the uncoupled Gummel method to sequentially solve three equations, occupying relatively less computer memory compared to the Newton method and being insensitive to the initial value, thus greatly improving the simulation speed;

[0043] (2) The present invention provides a numerical simulation method for semiconductor devices based on spatial discretization and non-coupled iteration. The local expression can achieve local conservation. Compared with the finite element method, the discretization of the flow problem can achieve upwind stability more naturally and directly. In addition, the present invention adopts non-uniform hexahedral unit grid division, which is simpler than tetrahedral units in grid generation and quality control. In terms of the extensibility and compatibility of physical models (such as various band gap narrowing models, mobility models, composite models, collision ionization models, etc.), the present invention is also more advantageous. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1 A schematic flow chart of a semiconductor device numerical simulation method based on spatial discretization and non-coupled iteration provided by the present invention.

[0046] Figure 2 Schematic diagram of the three-dimensional seven-point central difference method.

[0047] Figure 3 It is a schematic diagram of the iteration process.

[0048] Figure 4 It is a schematic diagram for simulation comparison between the present invention and international mainstream semiconductor numerical simulation commercial software. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention belong to the scope of protection of the embodiments of the present invention.

[0050] The embodiment of the present invention provides a semiconductor device numerical simulation method based on spatial discretization and non-coupled iteration, referring to Figure 1 , the method comprising:

[0051] S1. Establish a basic set of equations for semiconductor devices, wherein the basic set of equations for semiconductor devices includes Poisson's equation, electron current continuity equation, hole current continuity equation, electron current density equation, and hole current density equation. The basic set of equations for semiconductor devices includes:

[0052]

[0053] Among them, the electrostatic potential ψ, the electron concentration n, and the hole concentration p are all independent variables. Equations (1) to (5) are the Poisson equation, the electron current continuity equation, the hole current continuity equation, the electron current density equation, and the hole current density equation in sequence; ∈ s is the material dielectric constant, q is the unit charge constant, is the donor doping concentration, is the acceptor doping concentration, J n is the electron current density inside the device, G n is the electron generation rate, R n is the electron recombination rate, Jp is the hole current density inside the device, G p is the hole generation rate, R p is the hole recombination rate, μ n is the electron mobility, E c is the conduction band energy level, m n is the electron effective mass, D n is the electron diffusion coefficient, μ p is the hole mobility, E V is the valence band energy level, m p is the hole effective mass, D p is the hole diffusion coefficient, k is the Boltzmann constant, and T is the lattice temperature, all of which are known quantities.

[0054] S2. The basic equations of the semiconductor device are discretized in space using the three-dimensional seven-point central difference method on a non-uniform hexahedral grid. Referring to Figure 2 , for each point O(x0, y0, z0) to be solved, its six adjacent points (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), (x4, y4, z4), (x5, y5, z5), and (x6, y6, z6) are obtained. dx1 = x0 - x1, dx2 = x2 - x0, dy1 = y0 - y3, dy2 = y4 - y0, dz1 = z0 - z5, dz2 = z6 - z0.

[0055] S3. The current equations are discretized using the Scharfetter-Gummel format to obtain a system of equations for the three-dimensional discretized drift-diffusion model, including:

[0056] (a0ψ0 + a1ψ1 + a2ψ2 + a3ψ3 + a4ψ4 + a5ψ5 + a6ψ6) j+1 = (n j - p j - C) - (n j + p j )ψ0 j (6)

[0057] (a0n0 + a1n1 + a2n2 + a3n3 + a4n4 + a5n5 + a6n6) j+1 -R(ψ j+1 , n j , p j ) = 0 (7)

[0058] (a0p0 + a1p1 + a2p2 + a3p3 + a4p4 + a5p5 + a6p6) j+1 -R(ψ j+1 , n j , p j ) = 0 (8)

[0059] Among them, C represents the net doping concentration. Equation (6) is the discretized Poisson equation, Equation (7) is the discretized electron current equation, and Equation (8) is the discretized hole current equation. ψ0, ψ1, ψ2, ψ3, ψ4, ψ5, and ψ6 are the electrostatic potentials of the point to be solved and its six adjacent points around it, respectively. n0, n1, n2, n3, n4, n5, and n6 are the electron concentrations of the point to be solved and its six adjacent points around it, respectively. p0, p1, p2, p3, p4, p5, and p6 are the hole concentrations of the point to be solved and its six adjacent points around it, respectively. j is the number of iterations. n j , p j and ψ j represent the electron concentration, hole concentration, and electrostatic potential obtained after the j-th iteration, respectively. a0, a1, a2, a3, a4, a5, and a6 are the coefficients of the drift-diffusion model equations in the three-dimensional discretization format. In Equation (6):

[0060]

[0061]

[0062] a0 = -(a1 + a2 + a3 + a4 + a5 + a6) - (n j + p j )

[0063] Among them

[0064] In Equation (7):

[0065]

[0066] Among them, D n | 01 is the average value of the electron diffusion coefficients of the point to be solved and the electron at the 1st adjacent point, given by the electron mobility model according to the Einstein relation. D n | 02is the average of the electron diffusion coefficients of the point to be solved and its adjacent point No. 2, and so on.

[0067] is the Bernoulli function.

[0068] In Equation (8):

[0069]

[0070] where D p | 01 is the average of the hole diffusion coefficients of the point to be solved and its adjacent point No. 1, which is given by the hole mobility model according to the Einstein relation. D p | 02 is the average of the hole diffusion coefficients of the point to be solved and its adjacent point No. 2, and so on.

[0071] S4. Use the Gummel non - coupled method to solve each equation in the drift - diffusion model equations in turn, referring to Figure 3 , which specifically includes the following process:

[0072] S4.1. Set the initial values of the electrostatic potential, electron concentration, and hole concentration as the initial conditions;

[0073] S4.2. Solve the discretized Poisson equation. For the relationship between the electrostatic potential and the carrier concentration in this equation, use the statistical distribution of carriers to perform a first - order Taylor expansion for linear approximation to obtain the current electrostatic potential;

[0074] S4.3. Treat the electrostatic potential and hole concentration as constants, and solve the discretized electron current equation to obtain the current electron concentration;

[0075] S4.4. Continue to treat the electrostatic potential and electron concentration as constants, and solve the discretized hole current equation to obtain the current hole concentration;

[0076] S4.5. After this iteration, calculate the relative error of the solution of the unknown quantity. If the convergence condition is not met, then use the current electrostatic potential, current electron concentration, and current hole concentration as the current conditions and return to step S4.2 for the next iteration. Otherwise, the iteration ends.

[0077] The initial conditions described in step S4.1 are obtained according to the charge balance condition. The acquisition of the initial conditions includes the following process:

[0078] Let the initial values of the electrostatic potential, electron concentration, and hole concentration be (ψ 0 , n 0 , p 0 ). The initial value of the electrostatic potential is taken as the result of the quasi - Fermi potential of the majority carriers adjusted by the built - in potential to ensure the electro - neutrality of the entire region. There is

[0079] ψ 0 = φ N + φ in

[0080] Let the initial values of the electrostatic potential, electron concentration, and hole concentration be (ψ 0 , n 0 , p 0 ). The initial value of the electrostatic potential is taken as the result of the quasi-Fermi potential of the majority carriers adjusted by the built-in potential to ensure electro-neutrality throughout the region. There is

[0081] ψ 0 = φ N + φ in

[0082] where the built-in electric potential

[0083]

[0084] n i,eff is the effective intrinsic concentration of the semiconductor material, is the net doping concentration;

[0085] For an N-type semiconductor, C > 0:

[0086]

[0087] For a P-type semiconductor, C < 0:

[0088]

[0089] The convergence condition described in step S4.4 is determined according to the relative error of the solution of the unknowns at all discrete grid points for all equations,

[0090]

[0091] where z j (e, i) is the solution of equation e at the i-th grid point in the j-th iteration. The constant N is taken as the number of equations multiplied by the total number of grid points. z ref (e) is for ensuring the numerical stability when |z j (e, i)| → 0. The approximate value of the solution accuracy is z ref (e)ε R . In this embodiment, ε R is taken as 10 -5 .

[0092] Through the built-in parallel computing technology, the present invention greatly improves the calculation efficiency of the electrical characteristics of semiconductor devices while maintaining the simulation accuracy, and can be used to quickly and stably simulate three-dimensional micron-scale semiconductor devices with regular boundaries. At the same time, the present invention can comprehensively and simply support a large number of complex semiconductor device physical models, including bandgap narrowing models, various mobility models, generation recombination models, impact ionization models, trap models, etc., so as to accurately describe the electrical characteristics and internal physical images of semiconductor devices. The comparison between the present invention and international mainstream commercial software is as follows Figure 4 As shown, the simulation device for comparison is a three-dimensional bipolar junction transistor (BJT). Figure 4 (a) shows its structure and non-uniformly meshed grid. Figure 4 (b) shows the output characteristic curve (Ic-Vc) under the base voltage (Vb = 0.5V), where the blue dashed line is the calculation result of the present invention, and the red solid circle line is the calculation result of the international mainstream commercial software. It can be seen that the overall trend of this electrical curve is consistent with the comparison software, and the relative error is within 1%. The total CPU time used by the present invention for this example calculation is 57 minutes and 20 seconds, and the memory usage is 2.583GB; the total CPU time used by the international mainstream commercial software for this example calculation is 2 hours, 10 minutes and 22 seconds, and the memory usage is 4.87GB. The above comparison can reflect that the present invention has more advantages in terms of calculation efficiency and memory occupancy under the condition of ensuring consistent calculation accuracy.

[0093] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can 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.

[0094] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (modules, systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows 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 the processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for realizing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0095] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to work in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction device that implements the functions specified in one or more of the procedures Figure 1 and / or boxes Figure 1 specified in one or more of the boxes.

[0096] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, such that a series of operational steps are performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one or more of the procedures Figure 1 and / or boxes Figure 1 specified in one or more of the boxes.

[0097] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made to these embodiments by those skilled in the art once they learn of the basic inventive concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications that fall within the scope of the present invention.

[0098] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A numerical simulation method for semiconductor devices based on spatial discretization and uncoupled iteration, characterized in that, The method includes the following steps: S1. Establish the basic equations of the semiconductor device. The basic equations of the semiconductor device include the Poisson equation, the electron current continuity equation, the hole current continuity equation, the electron current density equation, and the hole current density equation; S2. Use the three-dimensional seven-point central difference method to perform spatial discretization of the basic equations of the semiconductor device on a non-uniform hexahedral grid; S3. Use the Scharfetter-Gummel format to discretize the basic equations of the semiconductor device to obtain a drift-diffusion model equation set in three-dimensional discrete format, including the discretized Poisson equation, electron current equation, and hole current equation; S4. Use the Gummel decoupling method to solve each equation in the drift-diffusion model equation set in turn.

2. The numerical simulation method of semiconductor devices based on spatial discretization and uncoupled iteration according to claim 1, wherein: The basic equations of the semiconductor device described in step S1 include: Among them, the electrostatic potential ψ, the electron concentration n, and the hole concentration p are all independent variables. Equations (1) to (5) are the Poisson equation, the electron current continuity equation, the hole current continuity equation, the electron current density equation, and the hole current density equation in sequence; ∈ s is the dielectric constant of the material, q is the unit charge constant, is the donor doping concentration, is the acceptor doping concentration, J n is the electron current density inside the device, G n is the electron generation rate, R n is the electron recombination rate, Jp is the hole current density inside the device, G p is the hole generation rate, R p is the hole recombination rate, μ n is the electron mobility, E C is the conduction band energy level, m n is the electron effective mass, D n is the electron diffusion coefficient, μ p is the hole mobility, E V is the valence band energy level, m p is the hole effective mass, D p is the hole diffusion coefficient, k is the Boltzmann constant, and T is the lattice temperature.

3. The numerical simulation method of semiconductor devices based on spatial discretization and uncoupled iteration according to claim 2, characterized in that: After step S2 performs spatial discretization using the three-dimensional seven-point central difference method, for each point O(x0, y0, z0) to be solved, six adjacent points around it are obtained: (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), (x4, y4, z4), (x5, y5, z5), and (x6, y6, z6). dx1 = x0 - x1, dx2 = x2 - x0, dy1 = y0 - y3, d2 = y4 - y0, dz1 = z0 - z5, dz2 = z6 - z0.

4. The numerical simulation method of semiconductor devices based on spatial discretization and uncoupled iteration according to claim 3, characterized in that: The drift-diffusion model equation set in the three-dimensional discrete format includes: (a0ψ0 + a1ψ1 + a2ψ2 + a3ψ3 + a4ψ4 + a5ψ5 + a6ψ6) j+1 = (n j - p j - C) - (n j + p j )ψ0 j (6) (a0n0 + a1n1 + a2n2 + a3n3 + a4n4 + a5n5 + a6n6) j+1 -R(ψ j+1 , n j , p j ) = 0 (7) (a0p0 + a1p1 + a2p2 + a3p3 + a4p4 + a5p5 + a6p6) j+1 -R(ψ j+1 ,n j ,p j ) = 0 (8) Among them, Equation (6) is the discretized Poisson equation, Equation (7) is the discretized electron current equation, Equation (8) is the discretized hole current equation, C represents the net doping concentration, R represents the net recombination rate, ψ0, ψ1, ψ2, ψ3, ψ4, ψ5, and ψ6 are the electrostatic potentials of the point to be solved and its six adjacent points around it respectively, n0, n1, n2, n3, n4, n5, and n6 are the electron concentrations of the point to be solved and its six adjacent points around it respectively, p0, p1, p2, p3, p4, p5, and p6 are the hole concentrations of the point to be solved and its six adjacent points around it respectively, j is the number of iterations, n j , p j and ψ j respectively represent the electron concentration, hole concentration, and electrostatic potential obtained after the j-th iteration, and a0, a1, a2, a3, a4, a5, and a6 are the coefficients of the drift-diffusion model equations in three-dimensional discretized format.

5. The numerical simulation method of semiconductor devices based on spatial discretization and uncoupled iteration according to claim 4, wherein: Step S4 includes the following process: S4.

1. Set the initial values of the electrostatic potential, electron concentration, and hole concentration as the initial conditions; S4.

2. Solve the discretized Poisson equation. For the relationship between the electrostatic potential and the carrier concentration in this equation, use the statistical distribution of carriers to perform a first-order Taylor expansion for linear approximation to obtain the current electrostatic potential; S4.

3. Treat the electrostatic potential and the hole concentration as constants, and solve the discretized electron current equation to obtain the current electron concentration; S4.

4. Continue to treat the electrostatic potential and the electron concentration as constants, and solve the discretized hole current equation to obtain the current hole concentration; S4.

5. After this iteration ends, calculate the relative error of the solution of the unknown quantity. If the convergence condition is not satisfied, then use the current electrostatic potential, current electron concentration, and current hole concentration as the current conditions and return to step S4.2 for the next iteration. Otherwise, the iteration ends.

6. The numerical simulation method of semiconductor devices based on spatial discretization and uncoupled iteration according to claim 5, characterized in that: The initial conditions described in step S4.1 are obtained according to the charge balance condition. The acquisition of the initial conditions includes the following process: Set the initial values of the electrostatic potential, electron concentration, and hole concentration to (ψ 0 , n 0 , p 0 ). The initial value of the electrostatic potential is taken as the result of the quasi-Fermi potential of the majority carriers adjusted by the built-in potential to ensure overall charge neutrality in the region. There is ψ 0 = φ N + φ in where the built-in potential n i,eff is the effective intrinsic concentration of the semiconductor material, is the net doping concentration; For an N-type semiconductor, C > 0: For a P-type semiconductor, C < 0:

7. The numerical simulation method of semiconductor devices based on spatial discretization and uncoupled iteration according to claim 5, wherein: The convergence condition described in step S4.4 is determined according to the relative error of the solution of the unknown quantity at all discrete grid points of all equations. where z j (e, i) is the solution of equation e at the i-th lattice point in the j-th iteration. The constant N is taken as the number of equations multiplied by the total number of lattice points, z ref (e) is for ensuring the numerical stability when |z j (e, i)| → 0. The approximate value of the solution accuracy is z ref (e) ε R .

8. The numerical simulation method of semiconductor devices based on spatial discretization and uncoupled iteration according to claim 7, characterized in that: ε R The value is 10 -5 .

Images