Device simulation method based on mixed damping assisted convergence and related device

Abstract

The invention discloses a device simulation method based on mixed damping assisted convergence and a related device. The simulation method comprises the following steps: constructing an iterative calculation model; iteration is carried out based on the model, a current independent variable is obtained in each iteration, and an equation residual error and the iteration variable quantity of each independent variable are obtained through calculation; converting the iteration variable quantity of the Fermi potential to obtain a conversion variable quantity; based on the equation residual error, calculating to obtain the weight of the conversion variable quantity and the iteration variable quantity of the quasi Fermi potential, and obtaining the updated value of the quasi Fermi potential; updating the current independent variable, calculating to obtain an equation residual norm, and judging whether the equation residual norm meets a preset condition or not; and if yes, outputting a simulation result. According to the simulation method, the potential distribution and the iteration variable quantity of the quasi Fermi potential are synchronously calculated, the iteration variable quantity of the quasi Fermi potential is subjected to conversion and weight calculation, the updated value of the quasi Fermi potential is obtained, synchronous iteration updating of the quasi Fermi potential and the potential distribution is achieved, and the convergence of coupling solution is remarkably improved.

Description

Technical Field

[0001] This application belongs to the technical field of semiconductor device simulation, and particularly relates to a device simulation method and related device based on hybrid damping-assisted convergence. Background Art

[0002] TCAD device simulation is to solve the system of equations satisfied by the independent variables of electric potential ψ, electron concentration n, and hole concentration p on a designed semiconductor device, and then obtain the distribution of the independent variables in the device under given conditions through simulation, so as to judge whether the device design meets the expectations. It is an important part of semiconductor chip design technology.

[0003] In semiconductor device simulation, the coupled solution of the Poisson equation and the carrier continuity equation is one of the core challenges. The nonlinear characteristics of the two are significantly different, which directly affects the convergence of the Newton iteration method. Specifically, after discretization, the Poisson equation shows linear or weak nonlinearity, the condition number of the Jacobian matrix is relatively good, the diagonal dominance of the Jacobian matrix in Newton iteration is strong, the iteration step size is stable, and usually only a small number of iterations are required to converge; however, in the convergence of the carrier continuity equation, the carrier concentration has an exponential dependence on the electric potential, and the carrier concentration is extremely sensitive to small changes in the electric potential. In Newton iteration, the elements of the Jacobian matrix change violently with the electric potential, the matrix condition number is extremely high, and the convergence is difficult. Existing iteration methods adopt the Newton-damping strategy, the step size only considers the change in electric potential, and the carrier independent variables are restricted by the electric potential. However, since the relationship between carriers and electric potential is exponential, a small electric potential perturbation can cause the divergence of carriers, and the convergence is poor when dealing with high-bias, strong nonlinearity, or multi-physics field coupling problems. Summary of the Invention

[0004] The purpose of this application is to provide a device simulation method and related device based on hybrid damping-assisted convergence, so as to solve the technical problem that the existing device simulation iteration method adopts the Newton-damping strategy, the step size only considers the change in electric potential, restricts the carrier independent variables by the electric potential, and a small electric potential perturbation can cause the divergence of carriers, resulting in poor convergence when dealing with high-bias, strong nonlinearity, or multi-physics field coupling problems.

[0005] To achieve the above purpose, the first aspect of this application provides a device simulation method based on hybrid damping-assisted convergence, including:

[0006] Construct an iterative calculation model, where the iterative calculation model is used to represent the functional relationship between the electric potential distribution and the carrier concentration distribution inside the device;

[0007] Perform independent variable iteration based on the iterative calculation model. In each iteration, obtain the current independent variables of the semiconductor device, calculate the equation residual of the iterative calculation model and the iterative change amount of each independent variable, where the independent variables include the potential distribution and the quasi-Fermi potential, and the quasi-Fermi potential includes the electron quasi-Fermi potential and the hole quasi-Fermi potential;

[0008] Convert the iterative change amount of the quasi-Fermi potential to obtain a conversion change amount, and the conversion change amount of the quasi-Fermi potential is linearly related to the iterative change amount of the potential distribution;

[0009] Based on the equation residual, calculate the weights of the conversion change amount and the iterative change amount of the quasi-Fermi potential, and obtain the updated value of the quasi-Fermi potential based on the weights, the conversion change amount and the iterative change amount of the quasi-Fermi potential;

[0010] Update the current independent variables based on the updated value of the quasi-Fermi potential and the iterative change amount of the potential distribution, calculate the updated equation residual norm of the iterative calculation model, and determine whether the equation residual norm meets the preset conditions;

[0011] If so, output the simulation result.

[0012] In one or more embodiments, the iterative calculation model includes the Poisson equation and the carrier continuity equation, the carrier continuity equation includes the electron continuity equation and the hole continuity equation, and the iterative calculation model is specifically as follows:

[0013]

[0014]

[0015] In the formula, represents the Nabla operator, p is the hole concentration, n is the electron concentration, ε is the material permittivity, q is the elementary charge quantity, ND is the donor doping concentration, NA is the acceptor doping concentration, ψ is the potential, J n is the electron current density, J p is the hole current density.

[0016] In one or more embodiments, the steps of obtaining the current independent variables of the semiconductor device in each iteration and calculating the equation residual of the iterative calculation model and the iterative change amount of each independent variable include:

[0017] Input the current independent variables into the iterative calculation model to obtain the residual of the Poisson equation and the residual of the carrier continuity equation;

[0018] Construct a Jacobian matrix based on the iterative calculation model;

[0019] Based on the Jacobian matrix, the residual of the Poisson equation, and the residual of the carrier continuity equation, the iterative change amount of each independent variable is calculated as follows:

[0020] J(x k )Δx=-F(x k )

[0021] Wherein, F poisson is the residual of the Poisson equation, F continuity，n is the residual of the electron continuity equation, F continuity，p is the residual of the hole continuity equation, J(x k ) is the Jacobian matrix, Δψ is the iterative change amount of the electric potential distribution, is the iterative change amount of the electron quasi-Fermi potential, is the iterative change amount of the quasi-Fermi potential.

[0022] In one or more embodiments, in the step of converting the iterative change amount of the quasi-Fermi potential to obtain the conversion change amount, the conversion specifically includes: logarithmic conversion, piecewise linearization, logarithmic ratio transformation, or square root transformation.

[0023] In one or more embodiments, the conversion is a logarithmic conversion, and the conversion change amount of the quasi-Fermi potential is ln(1 + dx), where dx is the iterative change amount of the quasi-Fermi potential.

[0024] In one or more embodiments, based on the equation residual, calculating the weights of the conversion change amount and the iterative change amount of the quasi-Fermi potential, and based on the weights, the conversion change amount, and the iterative change amount of the quasi-Fermi potential, the steps of obtaining the updated value of the quasi-Fermi potential include:

[0025] Calculating the sum of the residual of the Poisson equation and the residual of the electron continuity equation to obtain a first sum value;

[0026] Calculating the ratio of the residual of the Poisson equation to the first sum value to obtain a first weight, and the first weight is the weight of the conversion change amount of the electron quasi-Fermi potential;

[0027] Calculating the ratio of the residual of the electron continuity equation to the first sum value to obtain a second weight, and the second weight is the weight of the iterative change amount of the electron quasi-Fermi potential;

[0028] Based on the first weight, the second weight, the conversion change amount, and the iterative change amount of the electron quasi-Fermi potential, obtaining the updated value of the electron quasi-Fermi potential;

[0029] Calculating the sum of the residual of the Poisson equation and the residual of the hole continuity equation to obtain a second sum value;

[0030] Calculate the ratio of the residual of the Poisson equation to the second sum value to obtain a third weight, where the third weight is the weight of the conversion change amount of the hole quasi-Fermi potential;

[0031] Calculate the ratio of the residual of the hole continuity equation to the second sum value to obtain a fourth weight, where the fourth weight is the weight of the iterative change amount of the hole quasi-Fermi potential;

[0032] Based on the third weight, the fourth weight, the conversion change amount and the iterative change amount of the hole quasi-Fermi potential, obtain an updated value of the hole quasi-Fermi potential.

[0033] In one or more embodiments, the step of updating the current independent variable based on the updated value of the quasi-Fermi potential and the iterative change amount of the electric potential distribution, and calculating the updated equation residual norm of the iterative calculation model includes:

[0034] Calculate the sum of the updated value of the electron quasi-Fermi potential and the current electron quasi-Fermi potential to obtain an iterative electron quasi-Fermi potential;

[0035] Calculate the sum of the updated value of the hole quasi-Fermi potential and the current hole quasi-Fermi potential to obtain an iterative hole quasi-Fermi potential;

[0036] Calculate the sum of the iterative change amount of the electric potential distribution and the current electric potential distribution to obtain an iterative electric potential distribution;

[0037] Input the iterative electron quasi-Fermi potential, the hole quasi-Fermi potential and the electric potential distribution into the iterative calculation model, and calculate the updated equation residual norm.

[0038] In one or more embodiments, it further includes:

[0039] If the equation residual norm does not meet the preset condition, perform the next iteration until the equation residual norm meets the preset condition or reaches the maximum number of iterations, and output the simulation result.

[0040] To achieve the above object, a second aspect of the present application provides a simulation device for a semiconductor device, including:

[0041] A construction module, configured to construct an iterative calculation model, where the iterative calculation model is used to characterize the functional relationship between the electric potential and the carrier concentration inside the device;

[0042] An iteration module, configured to perform independent variable iteration based on the iteration calculation model, obtain the current independent variables of the semiconductor device in each iteration, and calculate the equation residual of the iteration calculation model and the iteration change amount of each independent variable, where the independent variables include a potential distribution and quasi-Fermi potentials, and the quasi-Fermi potentials include an electron quasi-Fermi potential and a hole quasi-Fermi potential;

[0043] A conversion module, configured to convert the iteration change amount of the quasi-Fermi potential to obtain a conversion change amount, where the conversion change amount of the quasi-Fermi potential is linearly correlated with the iteration change amount of the potential distribution;

[0044] A weight calculation module, configured to calculate the weights of the conversion change amount and the iteration change amount of the quasi-Fermi potential based on the equation residual, and obtain an updated value of the quasi-Fermi potential based on the weights, the conversion change amount, and the iteration change amount of the quasi-Fermi potential;

[0045] An update module, configured to update the current independent variables based on the updated value of the quasi-Fermi potential and the iteration change amount of the potential distribution, calculate the updated equation residual norm of the iteration calculation model, and determine whether the equation residual norm satisfies a preset condition;

[0046] A result output module, configured to output a simulation result when the equation residual norm satisfies the preset condition.

[0047] To achieve the above object, a third aspect of the present application provides an electronic device, including:

[0048] At least one processor; and

[0049] A memory, where the memory stores instructions, and when the instructions are executed by the at least one processor, the at least one processor is caused to execute the simulation method as described in any of the above embodiments.

[0050] To achieve the above object, a fourth aspect of the present application provides a machine-readable storage medium, which stores executable instructions, and when the instructions are executed, the machine is caused to execute the simulation method as described in any of the above embodiments.

[0051] Different from the prior art, the beneficial effects of the present application are:

[0052] In the iteration process of the simulation method of the present application, the iteration change amount of the potential distribution and the iteration change amount of the quasi-Fermi potential of the carriers are synchronously calculated by using the equation residual, and the final updated value of the quasi-Fermi potential is obtained by converting and calculating the weights of the iteration change amount of the quasi-Fermi potential, realizing the synchronous iterative update of the quasi-Fermi potential and the potential distribution, significantly improving the convergence of the coupled solution, and avoiding the problem of solution divergence caused by the carrier concentration with exponential dependence. Description of the Drawings

[0053] To more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0054] Figure 1 It is a schematic flowchart of an implementation manner of the device simulation method based on hybrid damping-assisted convergence of the present application;

[0055] Figure 2 is Figure 1 a schematic flowchart of an implementation manner corresponding to S400 in

[0056] Figure 3 It is a schematic structural diagram of an implementation manner of the simulation device of the semiconductor device of the present application;

[0057] Figure 4 It is a schematic structural diagram of an implementation manner of the electronic device of the present application. Specific implementation manners

[0058] In order to enable those skilled in the art to better understand the technical solutions in the present application, the following will clearly and completely describe the technical solutions in the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0059] In the existing TCAD device simulation, Newton iteration usually requires designing a reasonable damping strategy (Damping) to improve the convergence stability, especially in complex scenarios such as high bias, strong non-equilibrium state, or multi-physics field coupling. The core idea of the current damping strategy is to dynamically adjust the step size of the potential update to ensure that the residual can effectively decrease after each iteration, thereby improving the convergence and stability of Newton iteration. By introducing an adjustment coefficient into the standard Newton step size, the change range of the potential independent variable in each Newton iteration is restricted to ensure that the residual of the Poisson equation gradually decreases. When the residual norms of both the Poisson and carrier continuity equations satisfy the convergence conditions, the equation is considered to converge and the iteration is terminated.

[0060] For the Poisson equation For this, the left side of the equation is the second derivative term of the electric potential, which shows linearity after discretization and only has weak non-linearity when the dielectric constant varies with space. Although the charge density on the right side of the equation depends on the carrier concentrations n and p, in the Newton iteration, the update of the electric potential is only achieved through the linear correction of the charge density, resulting in a relatively good condition number of the Jacobian matrix. Therefore, in the Newton iteration, the Jacobian matrix has strong diagonal dominance, the iteration step size is stable, and usually only a small number of iterations are required to converge.

[0061] However, the carrier concentration in the equation is exponentially dependent on the electric potential, and the carrier concentration is extremely sensitive to small changes in the electric potential. For example, when the electric potential changes by 60 mV, n / p changes by a factor of 10. In the Newton iteration, the elements of the Jacobian matrix change violently with the electric potential, the condition number of the matrix is extremely high, and it is difficult to converge; this leads to poor convergence when dealing with high-bias, strong non-linearity, or multi-physics field coupling problems.

[0062] To solve the above problems, the applicant has developed a new device simulation method based on hybrid damping-assisted convergence. This simulation method not only considers the change amount of the electric potential distribution but also synchronously calculates the change amount of the quasi-Fermi potential of the carriers, and then corrects the carrier concentration distribution, significantly improving the convergence of the coupled solution and avoiding the divergence of the solution caused by the exponentially dependent carrier concentration.

[0063] Specifically, please refer to Figure 1 , Figure 1 which is a schematic flow diagram of an embodiment of the device simulation method based on hybrid damping-assisted convergence of the present application.

[0064] As Figure 1 shown, this simulation method includes:

[0065] S100. Construct an iterative calculation model.

[0066] Among them, the iterative calculation model is used to characterize the functional relationship between the electric potential distribution and the carrier concentration distribution inside the device.

[0067] In one embodiment, the iterative calculation model may include the Poisson equation and the carrier continuity equation, where the carrier continuity equation includes the electron continuity equation and the hole continuity equation.

[0068] Specifically, the iterative calculation model may be as follows:

[0069]

[0070] In the formula, represents the Nabla operator, p is the hole concentration, n is the electron concentration, ε is the material permittivity, q is the elementary charge quantity, ND is the donor doping concentration, NA is the acceptor doping concentration, ψ is the electric potential, J n is the electron current density, Jp is the hole current density.

[0071] S200: Iterate the independent variables based on the iterative calculation model, obtain the current independent variables of the semiconductor device in each iteration, and calculate the equation residual of the iterative calculation model and the iterative change amount of each independent variable.

[0072] Among them, the independent variables include the potential distribution and the quasi-Fermi potential, and the quasi-Fermi potential includes the electron quasi-Fermi potential and the hole quasi-Fermi potential.

[0073] In this application, the quasi-Fermi potential is used as the independent variable, that is, the electron quasi-Fermi potential and the hole quasi-Fermi potential Iterate with the goal of minimizing the equation residual, and adjust the independent variables in each iteration magnitude.

[0074] Before the start of each iteration, first obtain the current independent variables, that is, the current potential distribution, the current electron quasi-Fermi potential, and the current hole quasi-Fermi potential.

[0075] Input the current independent variables into the iterative calculation model, and the residual of the Poisson equation, the residual of the electron continuity equation, and the residual of the hole continuity equation can be calculated.

[0076] The specific residual calculation formula can be as follows:

[0077]

[0078] In the Newton iteration algorithm, by constructing the Jacobian matrix, the change amount of the independent variables is calculated based on the residual. Among them, the Jacobian matrix is a matrix composed of the partial derivatives of the multivariable function of the potential distribution, the electron quasi-Fermi potential, and the hole quasi-Fermi potential, and can be calculated based on the above model, which will not be elaborated here.

[0079] Based on the Jacobian matrix and the residual, the iterative change amount of each independent variable can be calculated, specifically as follows:

[0080] J(x k )Δx=-F(x k )

[0081] In the formula, F poisson is the residual of the Poisson equation, F continuity，n is the residual of the electron continuity equation, F continuity，p is the residual of the hole continuity equation, J(x k ) is the Jacobian matrix, Δψ is the iterative change amount of the potential distribution, is the iterative change amount of the electron quasi-Fermi potential, is the iterative change of the hole quasi-Fermi potential.

[0082] S300. Convert the iterative change of the quasi-Fermi potential to obtain a converted change.

[0083] Among them, the converted change of the quasi-Fermi potential is linearly related to the iterative change of the electric potential distribution.

[0084] Different from the conventional device simulation method, the simulation method of this application synchronously considers the iterative change of the quasi-Fermi potential. From the pure mathematical form of the Poisson equation, the electric potential distribution is linearly related to the carrier concentration distribution, and at the same time, the quasi-Fermi potential is exponentially related to the carrier concentration distribution. Therefore, the electric potential distribution is exponentially related to the quasi-Fermi potential. So, it is necessary to convert the iterative change of the quasi-Fermi potential to obtain a converted change that is linearly related to the electric potential distribution.

[0085] In one embodiment, a logarithmic conversion method can be used to convert the iterative change of the quasi-Fermi potential. The converted change of the quasi-Fermi potential can be ln(1 + dx), where dx is the iterative change of the quasi-Fermi potential.

[0086] Specifically, when performing a logarithmic conversion on the iterative change of the quasi-Fermi potential, in the case where the iterative change of the quasi-Fermi potential is very small, the following formula is satisfied: ln(1 + dx) ≈ dx, and the converted change of the quasi-Fermi potential has a linear relationship with the electric potential distribution.

[0087] It should be understood that in other embodiments, other conversion methods can also be used, such as piecewise linearization, logarithmic ratio transformation, or square root transformation, etc., which can also achieve the effect of this embodiment.

[0088] S400. Based on the equation residual, calculate the weights of the converted change and the iterative change of the quasi-Fermi potential, and obtain the updated value of the quasi-Fermi potential based on the weights, the converted change, and the iterative change of the quasi-Fermi potential.

[0089] In S300, the converted change of the quasi-Fermi potential is obtained through conversion. Further, the weights of the converted change and the iterative change of the quasi-Fermi potential can be calculated using the equation residual, and then the final updated value of the quasi-Fermi potential can be obtained.

[0090] Specifically, in one embodiment, please refer to Figure 2 , Figure 2 is Figure 1 the flowchart of an embodiment corresponding to S400 in

[0091] As Figure 2 shown, the calculation method of the updated value of the quasi-Fermi potential includes:

[0092] S401. Calculate the sum of the residuals of the Poisson equation and the residuals of the electron continuity equation to obtain a first sum value.

[0093] S402. Calculate the ratio of the residuals of the Poisson equation to the first sum value to obtain a first weight.

[0094] Among them, the first weight is the weight of the conversion change amount of the electron quasi-Fermi potential.

[0095] Specifically, the calculation formula for the first weight x1 is as follows:

[0096]

[0097] In the formula, F poisson is the residual of the Poisson equation, and F continuity，n is the residual of the electron continuity equation.

[0098] S403. Calculate the ratio of the residuals of the electron continuity equation to the first sum value to obtain a second weight.

[0099] Among them, the second weight is the weight of the iterative change amount of the electron quasi-Fermi potential.

[0100] Specifically, the calculation formula for the second weight x2 is as follows:

[0101]

[0102] In the formula, F poisson is the residual of the Poisson equation, and F continuity，n is the residual of the electron continuity equation.

[0103] S404. Based on the first weight, the second weight, the conversion change amount and the iterative change amount of the electron quasi-Fermi potential, obtain an updated value of the electron quasi-Fermi potential.

[0104] The first weight represents the weight of the conversion change amount of the electron quasi-Fermi potential in the updated value, and the second weight represents the weight of the iterative change amount of the electron quasi-Fermi potential in the updated value. Therefore, the final updated value of the electron quasi-Fermi potential can be calculated.

[0105] Specifically, in one embodiment, the calculation formula for the updated value of the electron quasi-Fermi potential is as follows:

[0106]

[0107] In the formula, A n is the updated value of the electron quasi-Fermi potential.

[0108] S405. Calculate the sum of the residuals of the Poisson equation and the residuals of the hole continuity equation to obtain a second sum value.

[0109] S406. Calculate the ratio of the residual of the Poisson equation to the second sum value to obtain the third weight.

[0110] Among them, the third weight is the weight of the conversion change amount of the hole quasi-Fermi potential.

[0111] Specifically, the calculation formula of the third weight x3 is as follows:

[0112]

[0113] In the formula, F poisson is the residual of the Poisson equation, and F continuity，p is the residual of the hole continuity equation.

[0114] S407. Calculate the ratio of the residual of the hole continuity equation to the second sum value to obtain the fourth weight.

[0115] Among them, the fourth weight is the weight of the iterative change amount of the hole quasi-Fermi potential.

[0116] Specifically, the calculation formula of the fourth weight x4 is as follows:

[0117]

[0118] In the formula, F poisson is the residual of the Poisson equation, and F continuity，p is the residual of the hole continuity equation.

[0119] S408. Based on the third weight, the fourth weight, the conversion change amount and the iterative change amount of the hole quasi-Fermi potential, obtain the updated value of the hole quasi-Fermi potential.

[0120] Specifically, in one embodiment, the calculation formula of the updated value of the hole quasi-Fermi potential is as follows:

[0121]

[0122] In the formula, A p is the updated value of the hole quasi-Fermi potential.

[0123] S500. Update the current independent variable based on the updated value of the quasi-Fermi potential and the iterative change amount of the electric potential distribution, calculate the updated equation residual norm of the iterative calculation model, and determine whether the equation residual norm meets the preset conditions.

[0124] After obtaining the updated value of the quasi-Fermi potential, this updated value can be used to update the current quasi-Fermi potential to obtain the iterated quasi-Fermi potential.

[0125] Specifically, it may include: calculating the sum of the updated value of the electronic quasi-Fermi potential and the current electronic quasi-Fermi potential to obtain the iterated electronic quasi-Fermi potential; calculating the sum of the updated value of the hole quasi-Fermi potential and the current hole quasi-Fermi potential to obtain the iterated hole quasi-Fermi potential.

[0126] Similarly, the iterative change amount of the electric potential distribution and the current electric potential distribution can be calculated, and then the iterated electric potential distribution can be obtained.

[0127] Inputting the iterated electronic quasi-Fermi potential, hole quasi-Fermi potential and electric potential distribution into the iterative calculation model, the updated equation residual norm can be calculated.

[0128] Furthermore, it is determined whether the equation residual norm reaches a preset condition, where the preset condition can be set based on actual requirements. For example, the preset condition can be less than or equal to 0.01, etc.

[0129] When the equation residual norm reaches the preset condition, it includes:

[0130] S600a. Outputting the simulation result.

[0131] If the equation residual norm does not reach the preset condition, it includes:

[0132] S600b. Performing the next iteration until the equation residual norm meets the preset condition or reaches the maximum number of iterations, and outputting the simulation result.

[0133] The traditional simulation method restricts the carrier independent variable through the electric potential change amount, resulting in poor convergence. Based on the simulation methods of the above embodiments, during the iteration process, the iterative change amounts of the electric potential distribution and the carrier quasi-Fermi potential are synchronously calculated using the equation residual, and through the conversion and weight calculation of the iterative change amount of the quasi-Fermi potential, the final updated value of the quasi-Fermi potential is obtained, realizing the synchronous iterative update of the quasi-Fermi potential and the electric potential distribution, significantly improving the convergence of the coupled solution, and avoiding the problem of solution divergence caused by the carrier concentration with exponential dependence.

[0134] The present application also provides a simulation device for a semiconductor device. Please refer to Figure 3 , Figure 3 which is a schematic structural diagram of an embodiment of the simulation device for a semiconductor device of the present application.

[0135] As Figure 3 shown, the simulation device includes a construction module 21, an iteration module 22, a conversion module 23, a weight calculation module 24, an update module 25, and a result output module 26.

[0136] Among them, the construction module 21 is used to construct an iterative calculation model, where the iterative calculation model is used to characterize the functional relationship between the electric potential and the carrier concentration inside the device;

[0137] The iterative module 22 is configured to perform independent variable iteration based on an iterative calculation model, obtain the current independent variables of the semiconductor device in each iteration, calculate the equation residual of the iterative calculation model and the iterative change amount of each independent variable. The independent variables include the potential distribution and the quasi-Fermi potential, and the quasi-Fermi potential includes the electron quasi-Fermi potential and the hole quasi-Fermi potential;

[0138] The conversion module 23 is configured to convert the iterative change amount of the quasi-Fermi potential to obtain a conversion change amount, and the conversion change amount of the quasi-Fermi potential is linearly related to the iterative change amount of the potential distribution;

[0139] The weight calculation module 24 is configured to calculate the weights of the conversion change amount and the iterative change amount of the quasi-Fermi potential based on the equation residual, and obtain the updated value of the quasi-Fermi potential based on the weights, the conversion change amount of the quasi-Fermi potential, and the iterative change amount;

[0140] The update module 25 is configured to update the current independent variables based on the updated value of the quasi-Fermi potential and the iterative change amount of the potential distribution, calculate the updated equation residual norm of the iterative calculation model, and determine whether the equation residual norm satisfies a preset condition;

[0141] The result output module 26 is configured to output a simulation result when the equation residual norm satisfies a preset condition.

[0142] As described above with reference to Figures 1 to 2 , the device simulation method based on hybrid damping-assisted convergence according to the embodiments of the present specification has been described. The details mentioned in the above description of the method embodiments also apply to the device simulation apparatus of the embodiments of the present specification. The above device simulation apparatus can be implemented by hardware, or can be implemented by software or a combination of hardware and software.

[0143] The present application also provides an electronic device. Please refer to Figure 4 , Figure 4 is a schematic structural diagram of an embodiment of the electronic device of the present application. As Figure 4 shown, the electronic device 30 may include at least one processor 31, a memory 32 (such as a non-volatile memory), a memory 33, and a communication interface 34, and at least one processor 31, the memory 32, the memory 33, and the communication interface 34 are connected together via a bus 35. At least one processor 31 executes at least one computer-readable instruction stored or encoded in the memory 32.

[0144] It should be understood that the computer-executable instructions stored in the memory 32, when executed, cause at least one processor 31 to perform the various operations and functions described above in the respective embodiments of the present specification in conjunction with Figures 1 - 2 description.

[0145] In the embodiments of the present specification, the electronic device 30 may include, but is not limited to: a personal computer, a server computer, a workstation, a desktop computer, a laptop computer, a notebook computer, a mobile electronic device, a smart phone, a tablet computer, a cellular phone, a personal digital assistant (PDA), a handheld device, a messaging device, a wearable electronic device, a consumer electronic device, and the like.

[0146] According to one embodiment, there is provided a program product such as a machine-readable medium. The machine-readable medium may have instructions (i.e., the above elements implemented in software form), which when executed by a machine, cause the machine to perform the various operations and functions described above in connection with Figures 1 - 2 the various embodiments of the present specification. Specifically, a system or device equipped with a readable storage medium may be provided, on which software program code for implementing the functions of any one of the above embodiments is stored, and the computer or processor of the system or device reads and executes the instructions stored in the readable storage medium.

[0147] In this case, the program code read from the readable medium itself can implement the functions of any one of the above embodiments, so the machine-readable code and the readable storage medium storing the machine-readable code constitute a part of the present specification.

[0148] Examples of the readable storage medium include a floppy disk, a hard disk, a magneto-optical disk, an optical disk (such as a CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD-RW), a magnetic tape, a non-volatile memory card, and a ROM. Alternatively, the program code may be downloaded from a server computer or a cloud via a communication network.

[0149] Those skilled in the art should understand that the various embodiments disclosed above can be variously deformed and modified without departing from the essence of the invention. Therefore, the protection scope of the present specification should be defined by the appended claims.

[0150] It should be noted that not all steps and units in the above-mentioned various processes and system structure diagrams are necessary, and some steps or units can be ignored according to actual needs. The execution order of the steps is not fixed and can be determined as needed. The device structures described in the above embodiments can be physical structures or logical structures, that is, some units may be implemented by the same physical entity, or some units may be implemented separately by multiple physical entities, or some components in multiple independent devices may be jointly implemented.

[0151] In the above embodiments, the hardware units or modules may be implemented mechanically or electrically. For example, a hardware unit, module, or processor may include permanent dedicated circuitry or logic (such as a dedicated processor, FPGA, or ASIC) to perform the corresponding operations. The hardware unit or processor may also include programmable logic or circuitry (such as a general-purpose processor or other programmable processor) that can be temporarily configured by software to perform the corresponding operations. The specific implementation (mechanical, or dedicated permanent circuitry, or temporarily configured circuitry) may be determined based on cost and time considerations.

[0152] The specific embodiments described above in conjunction with the accompanying drawings describe exemplary embodiments, but do not represent all embodiments that can be implemented or fall within the scope of the claims. The term "exemplary" used throughout this specification means "serving as an example, instance, or illustration" and does not mean "preferred" or "advantageous" over other embodiments. For the purpose of providing an understanding of the described technology, the specific embodiments include specific details. However, the technology may be practiced without these specific details. In some instances, well-known structures and devices are shown in block diagram form to avoid obscuring the concepts of the described embodiments.

[0153] The foregoing description of the present disclosure has been provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to the present disclosure will be readily apparent to those skilled in the art, and the general principles herein described may be applied to other variations without departing from the scope of the present disclosure. Therefore, the present disclosure is not limited to the examples and designs described herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A device simulation method based on hybrid damping-assisted convergence, characterized in that, including: constructing an iterative calculation model, where the iterative calculation model is used to represent the functional relationship between the potential distribution and the carrier concentration distribution inside the device; performing independent variable iteration based on the iterative calculation model, obtaining the current independent variables of the semiconductor device in each iteration, and calculating the equation residual of the iterative calculation model and the iterative change amount of each independent variable, where the independent variables include the potential distribution and the quasi-Fermi potential, and the quasi-Fermi potential includes the electron quasi-Fermi potential and the hole quasi-Fermi potential; converting the iterative change amount of the quasi-Fermi potential to obtain a conversion change amount, and the conversion change amount of the quasi-Fermi potential is linearly related to the iterative change amount of the potential distribution; calculating the weights of the conversion change amount and the iterative change amount of the quasi-Fermi potential based on the equation residual, and obtaining the updated value of the quasi-Fermi potential based on the weights, the conversion change amount and the iterative change amount of the quasi-Fermi potential; updating the current independent variables based on the updated value of the quasi-Fermi potential and the iterative change amount of the potential distribution, calculating the updated equation residual norm of the iterative calculation model, and determining whether the equation residual norm meets a preset condition; if so, outputting the simulation result.

2. The device simulation method according to claim 1, wherein The iterative calculation model includes the Poisson equation and the carrier continuity equation, the carrier continuity equation includes the electron continuity equation and the hole continuity equation, and the iterative calculation model is specifically as follows: In the formula, represents the Nabla operator, p is the hole concentration, n is the electron concentration, ε is the material permittivity, q is the elementary charge quantity, ND is the donor doping concentration, NA is the acceptor doping concentration, ψ is the electric potential, J n is the electron current density, J p is the hole current density, R n is the net electron recombination rate, R p is the net hole recombination rate.

3. The device simulation method according to claim 2, wherein The steps of obtaining the current independent variables of the semiconductor device in each iteration and calculating the equation residual of the iterative calculation model and the iterative change amount of each independent variable include: inputting the current independent variables into the iterative calculation model to obtain the residual of the Poisson equation and the residual of the carrier continuity equation; constructing a Jacobian matrix based on the iterative calculation model; calculating the iterative change amount of each independent variable based on the Jacobian matrix, the residual of the Poisson equation and the residual of the carrier continuity equation, specifically as follows: J(x k )Δx=-F(x k ) In the formula, F poisson is the residual of the Poisson equation, and F continuity，n is the residual of the electron continuity equation, and F continuity，p is the residual of the hole continuity equation, J(x k ) is the Jacobian matrix, Δψ is the iterative change in the electric potential distribution, is the iterative change in the electron quasi-Fermi potential, is the iterative change in the quasi-Fermi potential.

4. The device simulation method according to claim 1, characterized in that In the step of converting the iterative change amount of the quasi-Fermi potential to obtain a conversion change amount, the conversion is specifically: logarithmic conversion, piecewise linearization, logarithmic ratio transformation or square root transformation.

5. The device simulation method according to claim 4, wherein The conversion is a logarithmic conversion, and the conversion change amount of the quasi-Fermi potential is ln(1 + dx), where dx is the iterative change amount of the quasi-Fermi potential.

6. The device simulation method according to claim 2, wherein The steps of calculating the weights of the conversion change amount and the iterative change amount of the quasi-Fermi potential based on the equation residual, and obtaining the updated value of the quasi-Fermi potential based on the weights, the conversion change amount and the iterative change amount of the quasi-Fermi potential include: calculating the sum of the residual of the Poisson equation and the residual of the electron continuity equation to obtain a first sum value; calculating the ratio of the residual of the Poisson equation to the first sum value to obtain a first weight, and the first weight is the weight of the conversion change amount of the electron quasi-Fermi potential; calculating the ratio of the residual of the electron continuity equation to the first sum value to obtain a second weight, and the second weight is the weight of the iterative change amount of the electron quasi-Fermi potential; obtaining the updated value of the electron quasi-Fermi potential based on the first weight, the second weight, the conversion change amount and the iterative change amount of the electron quasi-Fermi potential; Calculate the sum of the residuals of the Poisson equation and the residuals of the hole continuity equation to obtain a second sum value; Calculate the ratio of the residual of the Poisson equation to the second sum value to obtain a third weight, where the third weight is the weight of the conversion change amount of the hole quasi-Fermi potential; Calculate the ratio of the residual of the hole continuity equation to the second sum value to obtain a fourth weight, where the fourth weight is the weight of the iterative change amount of the hole quasi-Fermi potential; Based on the third weight, the fourth weight, the conversion change amount and the iterative change amount of the hole quasi-Fermi potential, obtain an updated value of the hole quasi-Fermi potential.

7. The device simulation method according to claim 1, characterized in that Based on the updated value of the quasi-Fermi potential and the iterative change amount of the electric potential distribution to update the current independent variable, the steps of calculating the updated equation residual norm of the iterative calculation model include: Calculate the sum of the updated value of the electron quasi-Fermi potential and the current electron quasi-Fermi potential to obtain the iterated electron quasi-Fermi potential; Calculate the sum of the updated value of the hole quasi-Fermi potential and the current hole quasi-Fermi potential to obtain the iterated hole quasi-Fermi potential; Calculate the sum of the iterative change amount of the electric potential distribution and the current electric potential distribution to obtain the iterated electric potential distribution; Input the iterated electron quasi-Fermi potential, the hole quasi-Fermi potential and the electric potential distribution into the iterative calculation model to calculate the updated equation residual norm.

8. The device simulation method according to claim 1, characterized in that Further includes: If the equation residual norm does not meet the preset condition, perform the next iteration until the equation residual norm meets the preset condition or reaches the maximum number of iterations, and output the simulation result.

9. A device simulation apparatus based on hybrid damping-assisted convergence, characterized in that, Includes: A construction module for constructing an iterative calculation model, where the iterative calculation model is used to characterize the functional relationship between the electric potential and the carrier concentration inside the device; An iteration module for performing independent variable iteration based on the iterative calculation model, obtaining the current independent variable of the semiconductor device in each iteration, and calculating the equation residual and the iterative change amount of each independent variable of the iterative calculation model, where the independent variables include the electric potential distribution and the quasi-Fermi potential, and the quasi-Fermi potential includes the electron quasi-Fermi potential and the hole quasi-Fermi potential; A conversion module for converting the iterative change amount of the quasi-Fermi potential to obtain a conversion change amount, where the conversion change amount of the quasi-Fermi potential is linearly related to the iterative change amount of the electric potential distribution; A weight calculation module for calculating the weights of the conversion change amount and the iterative change amount of the quasi-Fermi potential based on the equation residual, and obtaining the updated value of the quasi-Fermi potential based on the weights, the conversion change amount and the iterative change amount of the quasi-Fermi potential; An update module for updating the current independent variable based on the updated value of the quasi-Fermi potential and the iterative change amount of the electric potential distribution, calculating the updated equation residual norm of the iterative calculation model, and determining whether the equation residual norm meets the preset condition; A result output module for outputting the simulation result when the equation residual norm meets the preset condition.

10. An electronic device, including: At least one processor; And A memory that stores instructions which, when executed by the at least one processor, cause the at least one processor to perform the device simulation method according to any one of claims 1 to 8.

11. A machine-readable storage medium storing executable instructions which, when executed, cause the machine to perform the device simulation method according to any one of claims 1 to 8.

Images