Iterative initial value determination method and apparatus for device simulation, and device and storage medium

Abstract

Disclosed in the present invention are an iterative initial value determination method and apparatus for device simulation, and a device and a storage medium. The method comprises: on the basis of Newton's method, establishing an iterative calculation model for device simulation; on the basis of a change step length of an external voltage, determining a boundary-value condition ψi for an i-th instance of simulation; inputting into the iterative calculation model an iterative initial value yi for the i-th instance of simulation and the boundary-value condition ψi for the i-th instance of simulation, and determining an iterative optimal solution xi for the i-th instance of simulation; on the basis of the iterative optimal solution xi for the i-th instance of simulation, performing conversion to obtain a quasi-Fermi potential, performing Jacobian extrapolation on the quasi-Fermi potential obtained by performing conversion on the basis of the iterative optimal solution xi for the i-th instance of simulation, and determining an iterative initial value yi+1 for an (i+1)th instance of simulation; and repeating the execution of determining the boundary-value condition ψi for the i-th instance of simulation, so as to perform the next simulation process. The technical solution in the embodiments of the present invention can effectively improve the convergence speed of performing solving on the basis of Newton's method in each simulation process.

Description

Iterative initial value determination method, device, equipment and storage medium for device simulation

[0001] This invention claims priority to Chinese patent application number 202410338766.4, filed with the Patent Office of China on March 25, 2024, entitled “Method, device, apparatus and storage medium for iterative initial value determination for device simulation”, the entire contents of which are incorporated herein by reference. Technical Field

[0002] Embodiments of the present invention relate to the technical field of semiconductor device simulation, and in particular to a method, apparatus, device, and storage medium for iterative initial value determination for device simulation. Background Art

[0003] When simulating semiconductor devices using Technology Computer Aided Design (TCAD) software, the Newton iteration algorithm is used to calculate the carrier concentration and potential distribution within the semiconductor device at a series of grid points under external voltages on a specific device grid. The initial value of the iterative calculation has a significant impact on the convergence speed of the algorithm.

[0004] Assume that the external voltage of the semiconductor device to be simulated is calculated from 0V to 5V. When the external voltage is 0, a better initial value can be obtained by the Poisson equation in the Newton iteration algorithm equation group, and then after Newton iteration, the independent variable distribution inside the device is matched. The external voltage changes from 0V to 5V with a step size of 0.1V, and each change step size is simulated and calculated once. If all parameters are taken as 0 as the initial value for each calculation, the distance between this initial value and the iterative optimal solution is relatively far, and multiple iterations are required to obtain the optimal solution, resulting in a long iterative calculation time, and even the situation where the iterative calculation result does not converge. However, the method of using the previous simulation calculation result as the iterative initial value for the next simulation calculation in the prior art is conducive to improving the calculation convergence speed, reducing the algorithm calculation time, and improving the robustness of the algorithm. On this basis, the prior art proposes a differential equation based on the Newton iteration algorithm, using the Jacobian matrix according to the optimal solution of the previous simulation calculation to predict the iterative initial value for the next simulation calculation, thereby further reducing the number of simulation solution algorithm iterations and improving the convergence speed. However, the above-mentioned method for determining the initial value still has room for improvement in reducing the number of iterative solutions in each simulation to improve the convergence speed of the algorithm.

[0005] Summary of the Invention

[0006] The present invention provides a method, apparatus, device and storage medium for determining iterative initial values ​​of device simulation, so as to effectively improve the convergence speed of the Newton iterative algorithm and reduce the number of iterations.

[0007] According to one aspect of the present invention, there is provided an iterative initial value determination method for device simulation, which is applied to calculate the carrier concentration and potential distribution inside a semiconductor device;

[0008] The iterative initial value determination method for device simulation includes:

[0009] An iterative calculation model for device simulation is established based on the Newton iteration algorithm; wherein the iterative calculation model characterizes the relationship between the external voltage and the internal potential and carrier concentration distribution of the semiconductor device;

[0010] According to the change step of the external voltage, the boundary condition ψ of the i-th simulation is determined i ; Wherein, the boundary condition ψ of the i-th simulation i The external voltage applied to the semiconductor device for the i-th simulation;

[0011] The initial value y of the iteration of the i-th simulation i and the boundary condition ψ of the i-th simulation i Input the iterative calculation model to perform simulation and determine the iterative optimal solution x of the i-th simulation i ;

[0012] According to the iterative optimal solution x of the i-th simulation i The quasi-Fermi potential is converted and the optimal solution x for the iterative simulation of the i-th simulation is obtained. i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 ;

[0013] Repeat the execution to determine the boundary condition ψ of the i-th simulation i Step , and proceed to the next simulation process.

[0014] Optionally, the iterative optimal solution x according to the i-th simulation i The quasi-Fermi potential is converted and the optimal solution x for the iterative simulation of the i-th simulation is obtained. i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 ,include:

[0015] According to the quasi-Fermi potential and the preset conversion relationship, the iterative optimal solution x i The optimal solution of the carrier concentration in is converted to obtain the carrier quasi-Fermi potential value; wherein the preset conversion relationship represents the relationship between the carrier concentration inside the semiconductor device and the quasi-Fermi potential;

[0016] According to the carrier quasi-Fermi potential value, converting the iterative optimal solution of the i-th simulation simulation into an iterative conversion solution of the (i+1)-th simulation simulation after Jacobian extrapolation; wherein the iterative conversion solution includes the potential inside the semiconductor device, the electron quasi-Fermi potential conversion expression and the hole quasi-Fermi potential distribution;

[0017] According to the iterative conversion solution, the initial value y of the iteration of the i+1 simulation is determined after conversion. i+1 .

[0018] Optionally, the preset conversion relationship includes: a conversion relationship between electron concentration and the electron quasi-Fermi potential, and a conversion relationship between hole concentration and the hole quasi-Fermi potential.

[0019] Optionally, the conversion relationship between the electron concentration and the electron quasi-Fermi potential includes:

[0020] Where n represents the electron concentration, n i represents the intrinsic carrier concentration, ψ represents the potential inside the semiconductor device, represents the electron quasi-Fermi potential, V T It represents the ratio of carrier diffusivity to carrier mobility;

[0021] The conversion relationship between the hole concentration and the hole quasi-Fermi potential includes:

[0022] Where p represents the hole concentration, represents the hole quasi-Fermi potential.

[0023] Optionally, the electron quasi-Fermi potential conversion expression includes:

[0024] Among them, n i represents the optimal solution of electron concentration in the i-th simulation, ψ i represents the optimal solution of the electric potential of the i-th simulation, represents the optimal solution of the electron quasi-Fermi potential of the i-th simulation, represents the electron quasi-Fermi potential conversion expression;

[0025] The hole quasi-Fermi potential distribution includes:

[0026] Among them, p i represents the hole concentration of the optimal solution of the i-th simulation, represents the hole quasi-Fermi potential of the optimal solution of the i-th simulation, represents the hole quasi-Fermi potential conversion expression.

[0027] According to another aspect of the present invention, there is provided an apparatus for determining iterative initial values ​​for device simulation, comprising:

[0028] A model building module is used to establish an iterative calculation model for device simulation based on the Newton iteration algorithm; wherein the iterative calculation model represents the relationship between the external voltage and the internal potential and carrier concentration distribution of the semiconductor device;

[0029] The boundary condition determination module is used to determine the boundary condition ψ of the i-th simulation according to the change step of the external voltage i ; Wherein, the boundary condition ψ of the i-th simulation i The external voltage applied to the semiconductor device for the i-th simulation;

[0030] Iterative calculation module, used to convert the initial value y of the iteration of the i-th simulation i and the boundary condition ψ of the i-th simulation i Input the iterative calculation model to perform iterative calculation to determine the iterative optimal solution x of the i-th simulation i ;

[0031] Iterative initial value determination module, used for iterative optimal solution x according to the i-th simulation i The quasi-Fermi potential is converted and the optimal solution x for the iterative simulation of the i-th simulation is obtained. i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 ;

[0032] A loop calculation module is used to repeatedly determine the boundary value condition ψ of the i-th simulation i Step , and proceed to the next simulation process.

[0033] According to another aspect of the present invention, an electronic device is provided, comprising:

[0034] at least one processor; and

[0035] a memory communicatively connected to the at least one processor; wherein,

[0036] The memory stores a computer program that can be executed by the at least one processor, and the computer program is executed by the at least one processor so that the at least one processor can execute the iterative initial value determination method for device simulation described in any embodiment of the first aspect.

[0037] According to another aspect of the present invention, a computer-readable storage medium is further provided, characterized in that the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to implement the iterative initial value determination method for device simulation described in any embodiment of the first aspect when executed.

[0038] The technical solution of the embodiment of the present invention is based on the Newton iteration algorithm, which establishes an iterative calculation model for device simulation and determines the boundary value condition ψ of the i-th simulation according to the change step of the external voltage. i . The initial value y of the iteration of the i-th simulation i and the boundary condition ψ of the ith simulation i Input the iterative calculation model to perform simulation and determine the iterative optimal solution x of the i-th simulation i According to the iterative optimal solution x of the i-th simulation i The quasi-Fermi potential is obtained by conversion, and the iterative optimal solution is converted into an expression represented by the quasi-Fermi potential. The Jacobian extrapolation of the quasi-Fermi potential is performed using the extrapolation algorithm, and the initial value y of the iteration of the i+1 simulation is determined accordingly. i+1 Returns the boundary condition ψ for the i-th simulation. i Steps to determine the boundary conditions of the i+1th simulation, and according to the determined iterative initial value y of the i+1th simulation i+1 The i+1th simulation process is performed. In this way, the carrier concentration in the iterative optimal solution of the previous simulation process is converted into a representation by the quasi-Fermi potential. Since the quasi-Fermi potential and the electric potential have the same physical quantity unit, the physical quantities in the iterative optimal solution have a good linear correlation. Therefore, the initial value of the next simulation process determined according to the iterative optimal solution can effectively reduce the number of iterations, improve the convergence speed of the iterative calculation, and quickly determine the initial value of the iteration.

[0039] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present invention, nor is it intended to limit the scope of the present invention. Other features of the present invention will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, 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.

[0041] FIG1 is a schematic flow chart of an iterative initial value determination method for device simulation according to an embodiment of the present invention;

[0042] FIG2 is a schematic diagram of a specific flow chart of step S140 in an iterative initial value determination method for device simulation according to an embodiment of the present invention;

[0043] 3 is a schematic structural diagram of an apparatus for determining iterative initial values ​​for device simulation according to an embodiment of the present invention;

[0044] FIG4 is a schematic structural diagram of an electronic device provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0046] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0047] An embodiment of the present invention provides an iterative initial value determination method for device simulation. Figure 1 is a flow chart of an iterative initial value determination method for device simulation provided by an embodiment of the present invention. This embodiment is applicable to the case of calculating the carrier concentration and potential distribution inside a semiconductor device. The method can be executed by an iterative initial value determination device for device simulation, which can be implemented in the form of hardware and / or software, and can be configured in electronic devices such as computers or servers. As shown in Figure 1, the iterative initial value determination method for device simulation specifically includes the following steps:

[0048] S110. Establish an iterative calculation model for device simulation based on the Newton iteration algorithm; wherein the iterative calculation model represents the relationship between the external voltage and the internal potential and carrier concentration distribution of the semiconductor device.

[0049] For example, the iterative calculation model used to simulate the semiconductor device can be a differential equation of the Newton iterative algorithm, which represents the relationship between the potential of the internal grid position of the device and the corresponding carrier concentration. The carrier concentration can include the electron concentration and the hole concentration. The iterative calculation model can be expressed by formula (1), which can be expressed in the following form:

[0050] Formula (1) can be transformed into formula (2), which can be expressed as follows:

[0051] Where ε represents the permittivity of the semiconductor device material; ψ represents the potential at the lattice point of the semiconductor device; q represents the charge of the element, and q = 1.6021892 × 10 19 C; n represents the electron concentration; p represents the hole concentration; NA represents the doping concentration at the lattice site of the semiconductor device; t represents time; G represents the carrier generation rate, and R represents the carrier recombination rate. Since the total amount of charge in the semiconductor device remains unchanged, the amount of electrons and holes generated and the amount of recombination must be equal; J n Represents the current density of electrons in semiconductor devices, J p Represents the hole current density in semiconductor devices; μ n Represents the mobility of electrons in semiconductor devices, μ p Indicates the mobility of holes in semiconductor devices; D n Represents the diffusion rate of electrons in semiconductor devices, D p Represents the diffusion rate of holes in semiconductor devices.

[0052] For each parameter in the above iterative calculation model, x=(ψ, n, p) is the independent variable to be determined, and the other parameters are constants determined by the semiconductor device material.

[0053] S120, according to the change step of the external voltage, determine the boundary condition ψ of the i-th simulation i ; Among them, the boundary condition ψ of the i-th simulation i The external voltage applied to the semiconductor device for the i-th simulation.

[0054] For example, the boundary condition in the simulation process is the external voltage applied to the semiconductor device. The simulation needs to iteratively calculate the results of the carrier concentration and potential distribution of the semiconductor device within an external voltage range. The change step of the external voltage, that is, the external voltage changes in a certain step size, and an iterative calculation is required for each change of the step size. Therefore, the boundary condition ψ of the i-th simulation is i , which is the external voltage value of the semiconductor device after the external voltage changes by one step in the (i-1)th simulation.

[0055] S130, the initial value y of the iteration of the i-th simulation i and the boundary condition ψ of the ith simulation i Input the iterative calculation model to perform simulation and determine the iterative optimal solution x of the i-th simulation i .

[0056] For example, the initial value y of the iteration of the i-th simulation is determined i And the boundary condition ψ of the ith simulation i Input the iterative calculation model and perform multiple simulations until the calculation converges, that is, the iterative optimal solution x of the i-th simulation is obtained. i . Among them, the iterative optimal solution x i The values ​​include the potential, electron concentration, and hole concentration at the lattice point of the semiconductor device. It should be noted that the iterative initial value determination method for device simulation provided by the embodiment of the present invention is a method for performing iterative calculations to obtain an iterative optimal solution based on the iterative initial value determination of the previous simulation, and predicting and determining the initial value of the next simulation based on the iterative optimal solution. For the iterative initial value of the first simulation process, the user can set an initial value according to the actual situation to facilitate subsequent iterative calculations and obtain the iterative optimal solution of the first simulation process.

[0057] S140, based on the iterative optimal solution x of the i-th simulation i Convert to obtain the quasi-Fermi potential, and the optimal solution x for the iterative simulation of the i-th simulation is i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 .

[0058] For example, since the physical units of the electron concentration, hole concentration and electric potential in the iterative optimal solution are different, their linear correlation is poor. Therefore, according to the differential equation based on the Newton iteration algorithm in the related art, the method of using the Jacobian matrix to perform linear calculation on the iterative optimal solution, the accuracy of the initial value of the next simulation simulation still needs to be improved. In an embodiment of the present invention, an extrapolation algorithm is used to convert the electron concentration in the iterative optimal solution into an expression represented by the electron quasi-Fermi potential, and the hole concentration into an expression represented by the hole quasi-Fermi potential. Since the physical units of the quasi-Fermi potential and the electric potential are both volts, there is a good linear correlation between the quasi-Fermi potential and the electric potential. In this way, the Jacobian matrix of the electric potential and the quasi-Fermi potential at the lattice position is used to simulate the iterative optimal solution x of the i-th simulation of the quasi-Fermi potential. i The converted quasi-Fermi potential is extrapolated by Jacobi to obtain the initial value y of the iterative simulation of the i+1th simulation i+1, which can effectively reduce the number of subsequent Newton iterations and improve the convergence speed of iterative calculations.

[0059] S150, repeatedly executing to determine the boundary condition ψ of the i-th simulation i Steps to proceed to the next simulation process.

[0060] For example, after determining the initial value y of the iteration of the i+1th simulation i+1 After that, the process returns to step S120 to determine the boundary condition ψ for the i+1th simulation. i+1 . The boundary condition ψ i+1 and the initial value y of the iteration of the i+1th simulation i+1 An iterative calculation model is input and an i+1th simulation process is performed to determine an iterative optimal solution of the i+1th simulation process.

[0061] The technical solution of the embodiment of the present invention is based on the Newton iteration algorithm, which establishes an iterative calculation model for device simulation and determines the boundary value condition ψ of the i-th simulation according to the change step of the external voltage. i . The initial value y of the iteration of the i-th simulation i and the boundary condition ψ of the ith simulation i Input the iterative calculation model to perform simulation and determine the iterative optimal solution x of the i-th simulation i According to the iterative optimal solution x of the i-th simulation i The quasi-Fermi potential is obtained by conversion, and the iterative optimal solution is converted into an expression represented by the quasi-Fermi potential. The Jacobian extrapolation of the quasi-Fermi potential is performed using the extrapolation algorithm, and the initial value y of the iteration of the i+1 simulation is determined accordingly. i+1 Returns the boundary condition ψ for the i-th simulation. i Steps to determine the boundary conditions of the i+1th simulation, and according to the determined iterative initial value y of the i+1th simulation i+1 The i+1th simulation process is performed. In this way, the carrier concentration in the iterative optimal solution of the previous simulation process is converted into a representation of the quasi-Fermi potential. Since the quasi-Fermi potential and the electric potential have the same physical quantity unit, the physical quantities in the iterative optimal solution have a good linear correlation. Therefore, the initial value of the next simulation process determined according to the iterative optimal solution can effectively reduce the number of iterations, improve the convergence speed of the simulation, and quickly determine the initial value of the iteration.

[0062] Alternatively, FIG2 is a schematic diagram of a specific flow chart of step S140 in a method for determining an iterative initial value of a device simulation provided by an embodiment of the present invention. Based on the above embodiment, as shown in FIG2 , the iterative optimal solution x of the i-th simulation in step S140 is iThe quasi-Fermi potential is obtained by transformation, and the optimal solution x for the iterative simulation of the i-th simulation is i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 , specifically including the following steps:

[0063] S141. According to the quasi-Fermi potential and the preset conversion relationship, the iterative optimal solution x i The optimal solution of the carrier concentration in is converted to obtain the carrier quasi-Fermi potential value; wherein the preset conversion relationship represents the relationship between the carrier concentration and the quasi-Fermi potential inside the semiconductor device.

[0064] Exemplarily, a preset conversion relationship between carrier concentration and quasi-Fermi potential is used to convert the optimal solution of carrier concentration in the iterative optimal solution into an expression represented by quasi-Fermi potential, thereby obtaining the carrier quasi-Fermi potential value. Exemplarily, the preset conversion relationship includes: a conversion relationship between electron concentration and electron quasi-Fermi potential, and a conversion relationship between hole concentration and hole quasi-Fermi potential. Among them, the conversion relationship between electron concentration and electron quasi-Fermi potential can be expressed by formula (3), and formula (3) can include the following form:

[0065] Where n represents the electron concentration, n i represents the intrinsic carrier concentration, ψ represents the potential inside the semiconductor device, represents the electron quasi-Fermi potential, V T It represents the ratio of carrier diffusivity to carrier mobility;

[0066] The conversion relationship between hole concentration and hole quasi-Fermi potential can be expressed by formula (4), which can include the following forms:

[0067] Where p represents the hole concentration, represents the hole quasi-Fermi potential.

[0068] S142. Based on the carrier quasi-Fermi potential value, convert the iterative optimal solution of the i-th simulation into an iterative conversion solution of the (i+1)-th simulation after Jacobian extrapolation; wherein the iterative conversion solution includes the electric potential inside the semiconductor device, the electron quasi-Fermi potential conversion expression and the hole quasi-Fermi potential distribution.

[0069] For example, according to the electron concentration conversion value, the method of converting the electron concentration in the iterative optimal solution into the electron quasi-Fermi potential conversion solution can be represented by the electron quasi-Fermi potential conversion expression, and the electron quasi-Fermi potential conversion expression can be represented by formula (5), which can be expressed as follows:

[0070] Among them, n irepresents the optimal solution of electron concentration in the i-th simulation, ψ i represents the optimal solution of the electric potential of the i-th simulation, represents the optimal solution of the electron quasi-Fermi potential of the i-th simulation, represents the electron quasi-Fermi potential conversion expression;

[0071] in, is the electron concentration conversion value.

[0072] According to the hole concentration conversion value, the method of converting the hole concentration in the iterative optimal solution into the hole quasi-Fermi potential conversion solution can be expressed by the hole quasi-Fermi potential distribution. The hole quasi-Fermi potential distribution can be expressed by formula (6), which can be expressed as follows:

[0073] Among them, p i represents the hole concentration of the optimal solution of the i-th simulation, represents the hole quasi-Fermi potential of the optimal solution of the i-th simulation, represents the hole quasi-Fermi potential conversion expression.

[0074] in, This is the hole concentration conversion value.

[0075] For example, taking x0 = (ψ0, n0, p0) as an example to represent the iterative optimal solution of the i-th simulation, the iterative transformation solution of the iterative optimal solution according to the quasi-Fermi potential can be expressed as

[0076] S143, according to the iterative conversion solution, determine the initial value y of the iteration of the i+1 simulation after conversion i+1 .

[0077] Exemplarily, the Taylor expansion calculation is performed on the transformed independent variables of the equation group to be solved, and the optimal solution of the iterative simulation of the i+1th simulation is predicted. According to the predicted optimal solution of the iterative simulation of the i+1th simulation, the initial value of the iterative simulation of the i+1th simulation is obtained by conversion calculation. Exemplarily, based on the above step S142, y1=(ψ1,φ n,1 ,φ p,1 ) represents the iterative optimal solution of the predicted i+1th simulation containing the quasi-Fermi potential independent variable, and x1 represents the iterative initial value of the i+1th simulation containing the carrier independent variable, then

[0078] It should be noted that, by comparing the iterative initial value determination method for device simulation provided by the embodiment of the present invention with the method for determining initial values ​​in related technologies, it can be clearly seen that the carrier concentration change calculated by the iterative initial value determination method for device simulation provided by the embodiment of the present invention is greater than that calculated by the method for determining initial values ​​in related technologies. For example: That is, the independent variable of the quasi-Fermi potential changes from y0=(ψ0,φ n,0 ,φ p,0 ) changes to y1=(ψ0+a1,φ n,0 +a2,φ p,0 +a3), the independent variable of carrier concentration changes from x0 = (ψ0, n0, p0) to From this we can see that the carrier change is In the related art, only the Jacobian matrix is ​​used to predict the iterative initial value. The carrier concentration change can be expressed by formula (7), which can be expressed as follows:

[0079] Where V0 represents the boundary condition for the i-th simulation, V1 represents the boundary condition for the i+1-th simulation, and other physical quantity parameters are described in the above embodiments. Thus, it can be seen that there is an approximate difference between the iterative initial value determination method for device simulation provided by the embodiment of the present invention and the initial value determination method in the related art. Therefore, the iterative initial value determination method for device simulation provided by the embodiment of the present invention can effectively improve the convergence speed of the simulation and reduce the number of iterations.

[0080] The iterative initial value determination method for device simulation provided in this embodiment adopts an extrapolation algorithm to perform Jacobian extrapolation on the quasi-Fermi potential converted from the iterative optimal solution, so that the electric potential in the independent variable to be determined and the quasi-Fermi potential have the same physical quantity unit and have a good linear correlation. Therefore, the initial value of the next simulation process determined according to the iterative optimal solution can effectively improve the convergence speed of the iterative calculation and reduce the number of iterative calculations.

[0081] An embodiment of the present invention further provides an iterative initial value determination device for device simulation. FIG3 is a schematic structural diagram of an iterative initial value determination device for device simulation provided by an embodiment of the present invention. As shown in FIG3 , the iterative initial value determination device 100 for device simulation includes:

[0082] The model building module 101 is used to build an iterative calculation model for device simulation based on the Newton iteration algorithm; wherein the iterative calculation model represents the relationship between the external voltage and the internal potential and carrier concentration distribution of the semiconductor device;

[0083] The boundary condition determination module 102 is used to determine the boundary condition ψ of the i-th simulation according to the change step of the external voltage. i; Among them, the boundary condition ψ of the i-th simulation i The external voltage applied to the semiconductor device for the i-th simulation;

[0084] Iterative calculation module 103 is used to convert the initial value y of the iteration of the i-th simulation i and the boundary condition ψ of the ith simulation i Input the iterative calculation model to perform iterative calculation and determine the iterative optimal solution x of the i-th simulation i ;

[0085] Iterative initial value determination module 104 is used to determine the optimal solution x of the iterative simulation of the i-th simulation. i Convert to obtain the quasi-Fermi potential, and the optimal solution x for the iterative simulation of the i-th simulation is i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 ;

[0086] The loop calculation module 105 is used to repeatedly determine the boundary condition ψ of the i-th simulation i Steps to proceed to the next simulation process.

[0087] The device simulation iterative initial value determination device provided by the embodiment of the present invention can execute the device simulation iterative initial value determination method provided by any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method. Specifically, the model establishment module 101 establishes an iterative calculation model for device simulation based on the Newton iteration algorithm; the boundary condition determination module 102 determines the boundary condition ψ of the i-th simulation based on the change step size of the external voltage. i The iterative calculation module 103 takes the initial value y of the iteration of the i-th simulation as i and the boundary condition ψ of the ith simulation i Input the iterative calculation model to perform simulation and determine the iterative optimal solution x of the i-th simulation i The iterative initial value determination module 104 is based on the iterative optimal solution x of the i-th simulation. i Convert to obtain the quasi-Fermi potential, perform extrapolation calculation on the converted quasi-Fermi potential, and determine the initial value y of the iteration of the i+1 simulation i+1 The loop calculation module 105 repeatedly executes to determine the boundary condition ψ of the i-th simulation i The iterative initial value determination device for device simulation provided by the embodiment of the present invention is used to perform the iterative initial value determination method for device simulation provided by any embodiment of the present invention, which can effectively improve the convergence speed of iterative calculation and reduce the number of iterative calculations.

[0088] Optionally, based on the above embodiment, the iterative initial value determination module 104 includes:

[0089] Parameter conversion unit, used to convert the iterative optimal solution x according to the quasi-Fermi potential and the preset conversion relationship i The optimal solution of the carrier concentration in is converted to obtain the carrier quasi-Fermi potential value; wherein the preset conversion relationship represents the relationship between the carrier concentration and the quasi-Fermi potential inside the semiconductor device;

[0090] a conversion solution determining unit, configured to convert the iterative optimal solution of the i-th simulation into an iterative conversion solution of the i+1-th simulation after Jacobian extrapolation based on the carrier quasi-Fermi potential value; wherein the iterative conversion solution includes the potential inside the semiconductor device, the electron quasi-Fermi potential conversion expression, and the hole quasi-Fermi potential distribution;

[0091] The iterative initial value determination unit is used to determine the iterative initial value y of the i+1th simulation according to the iterative conversion solution. i+1 .

[0092] An embodiment of the present invention further provides an electronic device. FIG4 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or claimed herein.

[0093] As shown in FIG4 , the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 and a random access memory (RAM) 13, that is communicatively connected to the at least one processor 11. The memory stores a computer program that can be executed by the at least one processor, and the processor 11 can perform various appropriate actions and processes according to the computer program stored in the read-only memory (ROM) 12 or the computer program loaded from the storage unit 18 into the random access memory (RAM) 13. Various programs and data required for the operation of the electronic device 10 can also be stored in the RAM 13. The processor 11, ROM 12, and RAM 13 are connected to each other via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0094] Multiple components in the electronic device 10 are connected to the I / O interface 15, including an input unit 16, such as a keyboard, a mouse, etc.; an output unit 17, such as various types of displays, speakers, etc.; a storage unit 18, such as a magnetic disk, an optical disk, etc.; and a communication unit 19, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 19 allows the electronic device 10 to exchange information / data with other devices via a computer network such as the Internet and / or various telecommunication networks.

[0095] The processor 11 may be any general-purpose and / or specialized processing component with processing and computing capabilities. Examples of the processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various specialized artificial intelligence (AI) computing chips, various processors for running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The processor 11 executes the various methods and processes described above, such as the iterative initial value determination method for device simulation.

[0096] In some embodiments, the iterative initial value determination method for device simulation can be implemented as a computer program, which is tangibly contained in a computer-readable storage medium, such as the storage unit 18. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 10 via the ROM 12 and / or the communication unit 19. When the computer program is loaded into the RAM 13 and executed by the processor 11, one or more steps of the iterative initial value determination method for device simulation described above can be performed. Alternatively, in other embodiments, the processor 11 can be configured to execute the iterative initial value determination method for device simulation in any other appropriate manner (for example, by means of firmware).

[0097] In the context of the present invention, computer-readable storage media can be tangible media that can contain or store a computer program for use with an instruction execution system, device or equipment or used in combination with an instruction execution system, device or equipment. Computer-readable storage media can include but are not limited to electronic, magnetic, optical, electromagnetic, infrared or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. Alternatively, computer-readable storage media can be machine-readable signal media. More specific examples of machine-readable storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0098] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), a blockchain network, and the Internet.

[0099] A computing system may include clients and servers. The clients and servers are typically remote from each other and typically interact via a communication network. This client-server relationship arises through computer programs running on the respective computers, creating a client-server relationship. The server may be a cloud server, also known as a cloud computing server or cloud host. This server is a hosting product within the cloud computing service ecosystem that addresses the management difficulties and limited scalability of traditional physical hosting and VPS services.

[0100] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present invention can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solution of the present invention can be achieved. This is not limited herein.

[0101] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A method for determining iterative initial values ​​for device simulation, characterized in that: Used to calculate the carrier concentration and potential distribution inside semiconductor devices; The iterative initial value determination method for device simulation includes: An iterative calculation model for device simulation is established based on the Newton iteration algorithm; wherein the iterative calculation model characterizes the relationship between the external voltage and the internal potential and carrier concentration distribution of the semiconductor device; According to the change step of the external voltage, the boundary condition ψ of the i-th simulation is determined i ; Wherein, the boundary condition ψ of the i-th simulation i The external voltage applied to the semiconductor device for the i-th simulation; The initial value y of the iteration of the i-th simulation i and the boundary condition ψ of the i-th simulation i Input the iterative calculation model to perform iterative calculation and determine the iterative optimal solution x of the i-th simulation i ; According to the iterative optimal solution x of the i-th simulation i The quasi-Fermi potential is converted and the optimal solution x for the iterative simulation of the i-th simulation is obtained. i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 ; Repeat the execution to determine the boundary condition ψ of the i-th simulation i Step , and proceed to the next simulation process.

2. The iterative initial value determination method for device simulation according to claim 1, characterized in that: The iterative optimal solution x according to the i-th simulation i The quasi-Fermi potential is converted and the optimal solution x for the iterative simulation of the i-th simulation is obtained. i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 ,include: According to the quasi-Fermi potential and the preset conversion relationship, the iterative optimal solution x i The optimal solution of the carrier concentration in is converted to obtain the carrier quasi-Fermi potential value; wherein the preset conversion relationship represents the relationship between the carrier concentration inside the semiconductor device and the quasi-Fermi potential; According to the carrier quasi-Fermi potential value, converting the iterative optimal solution of the i-th simulation simulation into an iterative conversion solution of the (i+1)-th simulation simulation after Jacobian extrapolation; wherein the iterative conversion solution includes the potential inside the semiconductor device, the electron quasi-Fermi potential conversion expression and the hole quasi-Fermi potential distribution; According to the iterative conversion solution, the initial value y of the iteration of the i+1 simulation is determined after conversion. i+1 .

3. The iterative initial value determination method for device simulation according to claim 2, characterized in that: The preset conversion relationship includes: a conversion relationship between electron concentration and the electron quasi-Fermi potential, and a conversion relationship between hole concentration and the hole quasi-Fermi potential.

4. The iterative initial value determination method for device simulation according to claim 3, characterized in that: The conversion relationship between the electron concentration and the electron quasi-Fermi potential includes: Where n represents the electron concentration, n i represents the intrinsic carrier concentration, ψ represents the potential inside the semiconductor device, represents the electron quasi-Fermi potential, V T It represents the ratio of carrier diffusivity to carrier mobility; The conversion relationship between the hole concentration and the hole quasi-Fermi potential includes: Where p represents the hole concentration, represents the hole quasi-Fermi potential.

5. The iterative initial value determination method for device simulation according to claim 4, characterized in that: The electron quasi-Fermi potential conversion expression includes: Among them, n i represents the optimal solution of electron concentration in the i-th simulation, ψ i represents the optimal solution of the electric potential of the i-th simulation, represents the optimal solution of the electron quasi-Fermi potential of the i-th simulation, represents the electron quasi-Fermi potential conversion expression; The hole quasi-Fermi potential distribution includes: Among them, p i represents the hole concentration of the optimal solution of the i-th simulation, represents the hole quasi-Fermi potential of the optimal solution of the i-th simulation, represents the hole quasi-Fermi potential conversion expression.

6. A device for determining iterative initial values ​​for device simulation, characterized in that: include: A model building module is used to establish an iterative calculation model for device simulation based on the Newton iteration algorithm; wherein the iterative calculation model represents the relationship between the external voltage and the internal potential and carrier concentration distribution of the semiconductor device; The boundary condition determination module is used to determine the boundary condition ψ of the i-th simulation according to the change step of the external voltage i ; Wherein, the boundary condition ψ of the i-th simulation i The external voltage applied to the semiconductor device for the i-th simulation; Iterative calculation module, used to convert the initial value y of the iteration of the i-th simulation i and the boundary condition ψ of the i-th simulation i Input the iterative calculation model to perform iterative calculation to determine the iterative optimal solution x of the i-th simulation i ; Iterative initial value determination module, used for iterative optimal solution x according to the i-th simulation i The quasi-Fermi potential is converted and the optimal solution x for the iterative simulation of the i-th simulation is obtained. i Convert the obtained quasi-Fermi potential to perform Jacobian extrapolation to determine the initial value y of the i+1th simulation iteration i+1 ; A loop calculation module is used to repeatedly determine the boundary value condition ψ of the i-th simulation i Step , and proceed to the next simulation process.

7. An electronic device, characterized in that: The electronic device comprises: at least one processor; and a memory communicatively connected to the at least one processor; wherein, The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to perform the iterative initial value determination method for device simulation according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to implement the iterative initial value determination method for device simulation according to any one of claims 1 to 5 when executed.

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