Carrier transport simulation methods, devices, media and electronic equipment

Abstract

This invention discloses a carrier transport simulation method, apparatus, medium, and electronic device. The invention determines the initial and / or boundary conditions of carrier transport in a semiconductor device, and the Green's function equations corresponding to the Poisson and Schrödinger equations in the open quantum model. Based on the initial and / or boundary conditions, and the Green's function equations corresponding to the Poisson and Schrödinger equations, the carrier density in the semiconductor device is determined, thereby simulating carrier transport in the semiconductor device and enabling the study of carrier transport in semiconductor devices.

Description

Technical Field

[0001] This invention belongs to the field of quantum simulation computing technology, and in particular to carrier transport simulation methods, devices, media and electronic equipment. Background Technology

[0002] Modern integrated circuits, as the core of electronic information equipment, have achieved widespread application, and their stability has always been a focus of attention. With the continuous shrinking of feature sizes in modern integrated circuit processes, quantum effects are having an increasingly significant impact on the electrical performance of the semiconductor devices included in integrated circuits. Electrical performance is determined by the transport of charge carriers (in physics, electrons and holes are collectively referred to as charge carriers) in semiconductor devices, and the level of understanding of charge carrier transport in semiconductor devices will determine the future development of integrated circuits. Currently, there is a lack of effective methods for studying charge carrier transport in semiconductor devices. Summary of the Invention

[0003] The purpose of this invention is to provide a carrier transport simulation method, apparatus, medium, and carrier device, aiming to enhance the research on carrier transport in semiconductor devices.

[0004] One embodiment of this application provides a carrier transport simulation method, the method comprising:

[0005] Determine the initial conditions and / or boundary conditions for carrier transport in semiconductor devices, and determine the Green's function equations corresponding to the Poisson equation and the Schrödinger equation for the open quantum model;

[0006] The carrier density in the semiconductor device is determined based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation, so as to realize the simulation of carrier transport in the semiconductor device.

[0007] Optionally, the Poisson equation is:

[0008]

[0009] Among them, the For containing The Laplace operator, the The relative static dielectric constant of the semiconductor device is... The electrostatic potential to be determined is given by ε0, where ε0 is the vacuum permittivity and q is the charge carrier quantity. denoted as carrier density.

[0010] Optionally, the Green's function equation corresponding to the Schrödinger equation is:

[0011]

[0012] Wherein, (E+iη) represents energy, and the For containing The Laplace operator, the To reduce Planck's constant, the For space-related directional effective mass, the The single-particle Green's function corresponding to the energy, the The Dirac function; It is the effective potential energy function, the stated The For carrier affinity, the To exchange related functions.

[0013] Optionally, the for:

[0014]

[0015] Wherein, the f We (μ We E), the f Ea (μ Ea E) are the Fermi functions at the We port and Ea port of the geometric model, respectively, and μ We The above The electrochemical potentials of the We port and the Ea port are respectively, and the Γ We, (E), the Γ Ea (E) are the expansion functions for the We port and the Ea port, respectively.

[0016] Optionally, determining the initial conditions and / or boundary conditions for carrier transport in the semiconductor device includes:

[0017] Construct a geometric model of the semiconductor device;

[0018] The geometric model is meshed based on the finite volume method to obtain multiple first control volumes;

[0019] Determine the initial conditions and / or boundary conditions for each of the first control volumes.

[0020] Optionally, determining the carrier density in the semiconductor device based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation includes:

[0021] Based on the initial and boundary conditions of each of the first control volumes, the Poisson equation determines a first set of analytical equations in numerical matrix form;

[0022] The Green's function equation corresponding to the Schrödinger equation for each of the first control volumes is determined to obtain the second set of analytical equations in numerical matrix form;

[0023] Determine the initial electrostatic potential;

[0024] The carrier density in the semiconductor device is obtained by iteratively solving the second set of analytical equations based on the initial electrostatic potential and the first set of analytical equations.

[0025] Optionally, the step of iteratively solving the second analytical equation set based on the initial electrostatic potential and the first analytical equation set to obtain the carrier density in the semiconductor device includes:

[0026] Based on the initial electrostatic potential, the second set of analytical equations is solved to obtain the first characteristic function;

[0027] The initial carrier density is determined based on the first characteristic function;

[0028] The target electrostatic potential is obtained by solving the first set of analytical equations based on the initial carrier density.

[0029] Based on the target electrostatic potential, the second set of analytical equations is solved to obtain the second characteristic function;

[0030] The target carrier density is determined based on the second characteristic function;

[0031] If the difference between the target carrier density and the initial carrier density is greater than a preset error, then the target electrostatic potential is used as the new initial electrostatic potential, and then the second analytical equation set is solved based on the initial electrostatic potential to obtain the first characteristic function.

[0032] If the difference between the target carrier density and the initial carrier density is less than or equal to the preset error, then the target carrier density is taken as the carrier density in the semiconductor device.

[0033] Another embodiment of this application provides a carrier transport simulation device, the device comprising:

[0034] The input determination unit is used to determine the initial conditions and / or boundary conditions for carrier transport in semiconductor devices, as well as the Green's function equations corresponding to the Poisson equation and the Schrödinger equation in the open quantum model.

[0035] The output determination unit is used to determine the carrier density in the semiconductor device based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation, so as to realize the simulation of carrier transport in the semiconductor device.

[0036] Another embodiment of this application provides a storage medium storing a computer program, wherein the computer program is configured to execute the method described in any of the preceding claims when running.

[0037] Another embodiment of this application provides an electronic device including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the method described in any of the preceding claims.

[0038] Compared with existing technologies, the present invention provides a carrier transport simulation method that combines the Poisson equation and the Green's function equation corresponding to the Schrödinger equation of the open quantum model with the initial conditions and / or boundary conditions of carrier transport in semiconductor devices, thereby determining the carrier density in the semiconductor device, realizing the simulation of carrier transport in semiconductor devices, and thus realizing the study of carrier transport in semiconductor devices. Attached Figure Description

[0039] Figure 1 A hardware structure block diagram of a computer terminal for a carrier transport simulation method provided in an embodiment of the present invention;

[0040] Figure 2 A flowchart illustrating a carrier transport simulation method provided in an embodiment of the present invention;

[0041] Figure 3 This is a schematic diagram of a first control volume provided in an embodiment of the present invention;

[0042] Figure 4 This is a schematic diagram of the structure of a carrier transport simulation device provided in an embodiment of the present invention. Detailed Implementation

[0043] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0044] The present invention first provides a carrier transport simulation method, which can be applied to electronic devices, such as computer terminals, specifically ordinary computers, quantum computers, etc.

[0045] The following detailed explanation uses a computer terminal as an example. Figure 1 This is a hardware structure block diagram of a computer terminal for a carrier transport simulation method provided in an embodiment of the present invention. Figure 1 As shown, a computer terminal may include one or more ( Figure 1Only one is shown in the diagram. A processor 102 (which may include, but is not limited to, a microprocessor MCU or a programmable logic device FPGA, etc.) and a memory 104 for storing data based on carrier transport simulation methods are also shown. Optionally, the computer terminal may further include a transmission device 106 for communication functions and an input / output device 108. Those skilled in the art will understand that... Figure 1 The structure shown is for illustrative purposes only and does not limit the structure of the computer terminal described above. For example, the computer terminal may also include components that are more complex than those described above. Figure 1 The more or fewer components shown, or having the same Figure 1 The different configurations shown.

[0046] The memory 104 can be used to store software programs and modules for application software, such as the program instructions / modules corresponding to the molecule parameter configuration method in this embodiment. The processor 102 executes various functional applications and data processing by running the software programs and modules stored in the memory 104, thereby implementing the above-described method. The memory 104 may include high-speed random access memory and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory 104 may further include memory remotely located relative to the processor 102, and these remote memories can be connected to a computer terminal via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0047] The transmission device 106 is used to receive or send data via a network. Specific examples of the network described above may include a wireless network provided by a communication provider for the computer terminal. In one example, the transmission device 106 includes a Network Interface Controller (NIC), which can connect to other network devices via a base station to communicate with the Internet. In another example, the transmission device 106 may be a Radio Frequency (RF) module, used for wireless communication with the Internet.

[0048] It's important to note that a true quantum computer has a hybrid structure, comprising two main parts: a classical computer responsible for performing classical computations and control, and a quantum device responsible for running quantum programs to achieve quantum computation. A quantum program is a sequence of instructions written in a quantum language such as QRunes that can run on a quantum computer, supporting operations on quantum logic gates and ultimately enabling quantum computing. Specifically, a quantum program is a sequence of instructions that operates on quantum logic gates according to a specific timing order.

[0049] In practical applications, due to limitations in the development of quantum device hardware, quantum computing simulations are often required to verify quantum algorithms, quantum applications, and so on. Quantum computing simulation is the process of simulating the execution of a quantum program corresponding to a specific problem using a virtual architecture (i.e., a quantum virtual machine) built with the resources of a regular computer. Typically, it is necessary to construct a quantum program corresponding to a specific problem. The quantum program referred to in this embodiment of the invention is a program written in a classical language that represents qubits and their evolution, wherein qubits, quantum logic gates, etc., related to quantum computing all have corresponding classical code representations.

[0050] Quantum circuits, also known as quantum logic circuits, are a manifestation of quantum programming and are the most commonly used general-purpose quantum computing model. They represent circuits that operate on qubits under an abstract concept. They consist of qubits, circuits (timelines), and various quantum logic gates. Finally, the results are often read out through quantum measurement operations.

[0051] Unlike traditional circuits that use metal wires to transmit voltage or current signals, in quantum circuits, the circuits can be seen as being connected by time. That is, the state of a quantum bit evolves naturally over time, following the instructions of the Hamiltonian operator until it encounters a logic gate and is operated on.

[0052] A quantum program corresponds to a single quantum circuit. The quantum program described in this invention refers to this single quantum circuit, where the total number of qubits in the single quantum circuit is the same as the total number of qubits in the quantum program. This can be understood as follows: a quantum program can consist of a quantum circuit, measurement operations on the qubits within the quantum circuit, registers storing the measurement results, and control flow nodes (jump instructions). A single quantum circuit can contain dozens, hundreds, or even thousands of quantum logic gate operations. The execution of a quantum program is the process of executing all the quantum logic gates in a specific timing order. It should be noted that the timing order refers to the chronological sequence in which individual quantum logic gates are executed.

[0053] It's important to note that in classical computing, the most basic unit is the bit, and the most fundamental control mode is the logic gate. Circuit control can be achieved through combinations of logic gates. Similarly, the way to process qubits is through quantum logic gates. Quantum logic gates enable the evolution of quantum states and are the foundation of quantum circuits. Quantum logic gates include single-qubit gates, such as Hadamard gates (H-gates), Pauli-X gates (X-gates), Pauli-Y gates (Y-gates), Pauli-Z gates (Z-gates), RX gates, RY gates, RZ gates, etc.; and multi-qubit gates, such as CNOT gates, CR gates, iSWAP gates, Tofoli gates, etc. Quantum logic gates are generally represented using unitary matrices, which are not only matrix forms but also operations and transformations. Generally, the effect of a quantum logic gate on a quantum state is calculated by left-multiplying the unitary matrix by the matrix corresponding to the right vector of the quantum state.

[0054] See Figure 2 , Figure 2 A flowchart illustrating a carrier transport simulation method provided in this embodiment of the invention may include the following steps:

[0055] Step 201: Determine the initial conditions and / or boundary conditions for carrier transport in the semiconductor device, and determine the Green's function equations corresponding to the Poisson equation and the Schrödinger equation for the open quantum model.

[0056] Among them, charge carriers are the carriers of electric current; in semiconductor devices, charge carriers include two types: electrons and holes.

[0057] In this context, for a physical process that evolves over time, the state at a certain moment will influence the process after that moment; the state at that moment is the initial condition. Boundary conditions refer to the variation of the variable or its derivative at the boundary of the solution domain with time and location. Boundary conditions include the first type of boundary conditions given endpoint values, the second type of boundary conditions given gradient values, and the third type of boundary conditions given both endpoint values ​​and gradient values. The boundary conditions described in this invention can be any one of the above three types, and are not limited thereto.

[0058] Specifically, the Poisson equation is:

[0059]

[0060] Among them, the For containing The Laplace operator, the The relative static dielectric constant of the semiconductor device is... The electrostatic potential to be determined is given by ε0, where ε0 is the vacuum permittivity and q is the charge carrier quantity. denoted as carrier density.

[0061] Specifically, the Green's function equation corresponding to the Schrödinger equation is:

[0062]

[0063] Wherein, (E+iη) represents energy, and the For containing The Laplace operator, the To reduce Planck's constant, the For space-related directional effective mass, the The single-particle Green's function corresponding to the energy, the The Dirac function; It is the effective potential energy function, the stated The For carrier affinity, the To exchange related functions.

[0064] Specifically, the aforementioned for:

[0065]

[0066] Wherein, the f We (μ We E), the f Ea (μ Ea E) are the Fermi functions at the We port and Ea port of the geometric model, respectively, and μ We The above The electrochemical potentials of the We port and the Ea port are respectively, and the Γ We, (E), the Γ Ea (E) are the expansion functions for the We port and the Ea port, respectively.

[0067] in, ε0 and q are both known parameters. With position The properties of the semiconductor device material are related; for example, if the same material is isotropic, then the ε of Si is... r The ε of GaAs is 11.8. r The ε of 4H-SiC is 12.8. r The ε of GaN is 9.7. r It is 9; ε0 = 8.854187817 × 10 -12 F / m, q=1.6×10 -19 C, K B =1.380649×10 -13 J / K, The energy eV, composed of the electron e and the voltage V, is related to the input excitation voltage V and the position; for isotropic semiconductor devices, the oriented effective mass is equal in all spatial directions. For anisotropic semiconductor devices, the directional effective mass is related to the physical material properties at its location.

[0068] Specifically, regarding the determination of the initial conditions and / or boundary conditions for carrier transport in the semiconductor device: a geometric model of the semiconductor device can be constructed; the geometric model can be meshed based on the finite volume method to obtain multiple first control volumes; and the initial conditions and / or boundary conditions for each of the first control volumes can be determined.

[0069] For example, such as Figure 3 As shown, Figure 3 This is a schematic diagram of a first control volume provided in an embodiment of the present invention. Figure 3 The left side is a three-dimensional perspective view of a first control volume provided in an embodiment of the present invention. Figure 3 The right side is a two-dimensional plan view of a first control volume provided in an embodiment of the present invention. For example... Figure 3 As shown on the left, the centers of the first control volume to the west, east, back, south, bottom, and top of the center P (not shown in the figure) of the first control volume correspond to W, E, N, S, B, and T, respectively; as Figure 3 As shown on the right, w, e, n, s, b, and t are the center points corresponding to the interfaces between the center P of the first control volume and W, E, N, S, B, and T, respectively. The length Δx of P is [b, t], the width Δy of P is [w, e], the height Δz of P is [s, n], and the volume D of P is... P = [b,t]×[w,e]×[s,n], where b, t and Δx are not shown.

[0070] It should be noted that the geometric model is divided into multiple first control volumes similar to P. Each first control volume may be equal or unequal. Generally speaking, only the first control volumes at the endpoints (or edges) have boundary conditions, while the other first control volumes inside the geometric model do not have boundary conditions.

[0071] It can be seen that the geometric model can be divided into multiple control volumes using the finite volume method, which facilitates the subsequent construction of discrete equations for the Green's functions corresponding to the Poisson and Schrödinger equations using integral conservation equations, thereby enabling the solution of the Green's functions corresponding to the Poisson and Schrödinger equations.

[0072] Step 202: Determine the carrier density in the semiconductor device based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation, so as to realize the simulation of carrier transport in the semiconductor device.

[0073] Specifically, regarding the determination of the carrier density in the semiconductor device based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation: a first set of analytical equations in numerical matrix form can be determined based on the initial conditions and boundary conditions of each first control volume and the Poisson equation; the Green's function equation corresponding to the Schrödinger equation for each first control volume can be determined to obtain a second set of analytical equations in numerical matrix form; an initial electrostatic potential can be determined; and the second set of analytical equations can be iteratively solved based on the initial electrostatic potential and the first set of analytical equations to obtain the carrier density in the semiconductor device.

[0074] For example, after meshing, it includes the parameter (α) x α y α z The discrete Laplace operator for ) is:

[0075]

[0076] Regarding the above Figure 3 P in the equation is determined by the fundamental property of definite integrals:

[0077]

[0078] Taking the average of the integrals, the above expression becomes:

[0079]

[0080] Using the central difference approximation of the first derivative

[0081]

[0082] Therefore, we can conclude

[0083]

[0084] [α] x ] b,t 、[α y ] w,e 、[α z ] s,n It can be calculated from flux conservation.

[0085] definition

[0086]

[0087]

[0088] Therefore, the above formula can be simplified as follows:

[0089]

[0090] For the Poisson equation:

[0091] α x =-ε x α y =-ε y α z =-ε z

[0092] For multiple first CVs (control volumes) in a gridded manner, multiple discretized Poisson equations can be obtained. These equations can then be transformed into a first set of analytical equations in numerical matrix form:

[0093]

[0094] Among them, analytic function Discretize into column vectors Let [M] be a vector derived from a fixed boundary condition. [M] represents the vector with respect to β. i A 7-diagonal matrix (where i = p, t, b, e, w, n, s) for Nonlinear functions.

[0095] Similarly, for the Green's function equation at P, we only need to replace φ with the Green's function G. The subsequent derivations are omitted here; please refer to the derivation of the Poisson equation above. Where:

[0096]

[0097] For multiple first CVs in a gridded manner, multiple discretized Green's function equations as described above can be obtained. These multiple discretized Green's function equations can then be transformed into a second set of analytical equations in numerical matrix form:

[0098]

[0099] in, It is the numerical matrix of the Hamiltonian in the finite device domain, Σ We,Ea These are the self-energy matrices for the west and east surfaces (terminals). Since an infinite system is being simplified to a finite system, these two matrices are additional external matrices. Both boarding functions are calculated by...

[0100] Γ We,Ea (E)=i[∑We,Ea (E)-∑ + we,Ea (E)]

[0101] The obtained size of the Broadening function and They are all the same size. However, only one block of these matrices contains non-zero elements.

[0102] Among them, g ww,ee These are called surface green's functions, and they can be calculated using various methods, including analytical methods. Here, the Sancho-Rubio numerical method is considered [see MPL Sancho, JML Rubio, L. Rubio, J. Phys. FMet. Phys. 15(4), 851–858 (1985)]. Cw I wC The Hamiltonian originates from the interaction between the transport channel and the surface terminal.

[0103]

[0104] It can be seen that [M] only contains the Laplace operator terms from the Poisson equation. It includes not only the Laplace operator term, but also the energy term (E+iη) and the potential energy term. In the open quantum model, the "adiabatic" method can be used to solve [Armagnat P, Lacerda A, Rossignol B, et al. The self-consistent quantum-electrostatic problem in strongly non-linear regime[J]. arXiv preprint arXiv:1905.01271,2019.]. The Schrödinger equation can be transformed into a Green's function using the non-equilibrium Green's function method, and the Green's function can be discretized using the finite volume method to obtain a linear system. Then, the recursive Green's function can be used to calculate the huge G(E) part as needed by outputting parameters, thereby further calculating the electron density in the open quantum model.

[0105] Specifically, in obtaining the carrier density in the semiconductor device by iteratively solving the second analytical equation set based on the initial electrostatic potential and the first analytical equation set, the method includes:

[0106] Based on the initial electrostatic potential, the second set of analytical equations is solved to obtain the first characteristic function;

[0107] The initial carrier density is determined based on the first characteristic function;

[0108] The target electrostatic potential is obtained by solving the first set of analytical equations based on the initial carrier density.

[0109] Based on the target electrostatic potential, the second set of analytical equations is solved to obtain the second characteristic function;

[0110] The target carrier density is determined based on the second characteristic function;

[0111] If the difference between the target carrier density and the initial carrier density is greater than a preset error, then the target electrostatic potential is used as the new initial electrostatic potential, and then the second analytical equation set is solved based on the initial electrostatic potential to obtain the first characteristic function.

[0112] If the difference between the target carrier density and the initial carrier density is less than or equal to the preset error, then the target carrier density is taken as the carrier density in the semiconductor device.

[0113] It should be noted that the initial electrostatic potential is predetermined; the preset error between the target carrier density and the initial carrier density is also predetermined.

[0114] Compared with existing technologies, the present invention provides a carrier transport simulation method that combines the Poisson equation and the Green's function equation corresponding to the Schrödinger equation of the open quantum model with the initial conditions and / or boundary conditions of carrier transport in semiconductor devices, thereby determining the carrier density in the semiconductor device, realizing the simulation of carrier transport in semiconductor devices, and thus realizing the study of carrier transport in semiconductor devices.

[0115] See Figure 4 , Figure 4 This is a schematic diagram of the structure of a carrier transport simulation device provided in an embodiment of the present invention. Figure 2 Corresponding to the aforementioned process, the apparatus includes:

[0116] The input determination unit 401 is used to determine the initial conditions and / or boundary conditions for carrier transport in the semiconductor device, and to determine the Green function equations corresponding to the Poisson equation and the Schrödinger equation for the open quantum model.

[0117] The output determination unit 402 is used to determine the carrier density in the semiconductor device based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation, so as to realize the simulation of carrier transport in the semiconductor device.

[0118] Specifically, the Poisson equation is:

[0119]

[0120] Among them, the For containing The Laplace operator, the The relative static dielectric constant of the semiconductor device is... The electrostatic potential to be determined is given by ε0, where ε0 is the vacuum permittivity and q is the charge carrier quantity. denoted as carrier density.

[0121] Specifically, the Green's function equation corresponding to the Schrödinger equation is:

[0122]

[0123] Wherein, (E+iη) represents energy, and the For containing The Laplace operator, the To reduce Planck's constant, the For space-related directional effective mass, the The single Green's function corresponding to energy, the The Dirac function; It is the effective potential energy function, the stated The For carrier affinity, the To exchange related functions.

[0124] Specifically, the aforementioned for:

[0125]

[0126] Wherein, the f We (μ We E), the f Ea (μ Ea E) are the Fermi functions at the We port and Ea port of the geometric model, respectively, and μ We The above The electrochemical potentials of the We port and the Ea port are respectively, and the Γ We, (E), the Γ Ea (E) are the expansion functions for the We port and the Ea port, respectively.

[0127] Specifically, regarding the determination of the initial conditions and / or boundary conditions for carrier transport in the semiconductor device, the input determination unit 401 is specifically used for:

[0128] Construct a geometric model of the semiconductor device;

[0129] The geometric model is meshed based on the finite volume method to obtain multiple first control volumes;

[0130] Determine the initial conditions and / or boundary conditions for each of the first control volumes.

[0131] Specifically, in determining the carrier density in the semiconductor device based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation, the output determination unit 402 is specifically used for:

[0132] Based on the initial and boundary conditions of each of the first control volumes, the Poisson equation determines a first set of analytical equations in numerical matrix form;

[0133] The Green's function equation corresponding to the Schrödinger equation for each of the first control volumes is determined to obtain the second set of analytical equations in numerical matrix form;

[0134] Determine the initial electrostatic potential;

[0135] The carrier density in the semiconductor device is obtained by iteratively solving the second set of analytical equations based on the initial electrostatic potential and the first set of analytical equations.

[0136] Specifically, in the process of iteratively solving the second analytical equation set based on the initial electrostatic potential and the first analytical equation set to obtain the carrier density in the semiconductor device, the output determination unit 402 is specifically used for:

[0137] Based on the initial electrostatic potential, the second set of analytical equations is solved to obtain the first characteristic function;

[0138] The initial carrier density is determined based on the first characteristic function;

[0139] The target electrostatic potential is obtained by solving the first set of analytical equations based on the initial carrier density.

[0140] Based on the target electrostatic potential, the second set of analytical equations is solved to obtain the second characteristic function;

[0141] The target carrier density is determined based on the second characteristic function;

[0142] If the difference between the target carrier density and the initial carrier density is greater than a preset error, then the target electrostatic potential is used as the new initial electrostatic potential, and then the second analytical equation set is solved based on the initial electrostatic potential to obtain the first characteristic function.

[0143] If the difference between the target carrier density and the initial carrier density is less than or equal to the preset error, then the target carrier density is taken as the carrier density in the semiconductor device.

[0144] Compared with existing technologies, the present invention provides a carrier transport simulation method that combines the Poisson equation and the Green's function equation corresponding to the Schrödinger equation of the open quantum model with the initial conditions and / or boundary conditions of carrier transport in semiconductor devices, thereby determining the carrier density in the semiconductor device, realizing the simulation of carrier transport in semiconductor devices, and thus realizing the study of carrier transport in semiconductor devices.

[0145] Another embodiment of the present invention provides a storage medium storing a computer program, wherein the computer program is configured to execute the steps in any of the method embodiments above when running.

[0146] Specifically, in this embodiment, the storage medium can be configured to store a computer program for performing the following steps:

[0147] Determine the initial conditions and / or boundary conditions for carrier transport in semiconductor devices, and determine the Green's function equations corresponding to the Poisson equation and the Schrödinger equation for the open quantum model;

[0148] The carrier density in the semiconductor device is determined based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation, so as to realize the simulation of carrier transport in the semiconductor device.

[0149] Specifically, in this embodiment, the storage medium may include, but is not limited to, USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks, and other media capable of storing computer programs.

[0150] Another embodiment of the present invention provides a charge carrier device including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the steps in any of the method embodiments described above.

[0151] Specifically, the aforementioned charge carrier device may further include a transmission device and an input / output device, wherein the transmission device is connected to the aforementioned processor, and the input / output device is connected to the aforementioned processor.

[0152] Specifically, in this embodiment, the processor can be configured to perform the following steps via a computer program:

[0153] Determine the initial conditions and / or boundary conditions for carrier transport in semiconductor devices, and determine the Green's function equations corresponding to the Poisson equation and the Schrödinger equation for the open quantum model;

[0154] The carrier density in the semiconductor device is determined based on the initial conditions and / or the boundary conditions, the Green's function equation corresponding to the Poisson equation and the Schrödinger equation, so as to realize the simulation of carrier transport in the semiconductor device.

[0155] The above description, based on the embodiments shown in the figures, details the structure, features, and effects of the present invention. The above description is only a preferred embodiment of the present invention, but the present invention is not limited to the scope of implementation shown in the figures. Any changes made in accordance with the concept of the present invention, or equivalent embodiments modified to have equivalent changes, that do not exceed the spirit covered by the specification and figures, should be within the protection scope of the present invention.

Claims

1. A carrier transport simulation method characterized by, The method comprises: constructing a geometric model of a semiconductor device; meshing the geometric model based on a finite volume method to obtain a plurality of first control volumes; determining initial conditions and / or boundary conditions of each of the first control volumes, and determining a Green function equation corresponding to a Poisson equation and a Schrodinger equation of an open quantum model; determining a first analytical equation group in a numerical matrix form based on the initial conditions and the boundary conditions of each of the first control volumes and the Poisson equation; determining a Green function equation corresponding to the Schrodinger equation corresponding to each of the first control volumes to obtain a second analytical equation group in a numerical matrix form; determining an initial electrostatic potential; solving the second analytical equation group based on the initial electrostatic potential to obtain a first characteristic function; and determining an initial carrier density based on the first characteristic function; solving the first analytical equation group based on the initial carrier density to obtain a target electrostatic potential; solving the second analytical equation group based on the target electrostatic potential to obtain a second characteristic function; determining a target carrier density based on the second characteristic function; if the difference between the target carrier density and the initial carrier density is greater than a preset error, taking the target electrostatic potential as a new initial electrostatic potential, and then performing the solving of the second analytical equation group based on the initial electrostatic potential to obtain a first characteristic function; if the difference between the target carrier density and the initial carrier density is less than or equal to the preset error, taking the target carrier density as the carrier density in the semiconductor device to realize the simulation of carrier transport in the semiconductor device.

2. The method of claim 1, wherein, The Poisson equation is: Among them, the For containing The Laplace operator, the The relative static dielectric constant of the semiconductor device is... For the electrostatic potential to be determined, the The vacuum permittivity is denoted as . The carrier charge quantity, the denoted as carrier density.

3. The method of claim 2, wherein, The Green function equation corresponding to the Schrodinger equation is: Among them, the For energy, the For containing The Laplace operator, the To reduce Planck's constant, the For space-related directional effective mass, the The single Green's function corresponding to energy, the The Dirac function; It is the effective potential energy function, the stated The For carrier affinity, the To exchange related functions.

4. The method according to claim 2 or 3, characterized in that, The is: wherein the , the are Fermi functions of the port, port, the , the are electrochemical potentials of the port, the port, the , the are broadening functions of the port, the port.

5. A carrier transport simulation apparatus characterized by comprising: The device comprises: an input determination unit configured to construct a geometric model of a semiconductor device; mesh the geometric model based on a finite volume method to obtain a plurality of first control volumes; and determine initial conditions and / or boundary conditions of each of the first control volumes, and determine a Green function equation corresponding to a Poisson equation and a Schrodinger equation of an open quantum model; The output determining unit is configured to determine a first analytic equation group in a numerical matrix form based on initial conditions and boundary conditions of each first control volume and the Poisson equation; determine a Green function equation corresponding to the Schrodinger equation corresponding to each first control volume to obtain a second analytic equation group in a numerical matrix form; determine an initial electrostatic potential; solve the second analytic equation group based on the initial electrostatic potential to obtain a first characteristic function; determine an initial carrier density based on the first characteristic function; solve the first analytic equation group based on the initial carrier density to obtain a target electrostatic potential; solve the second analytic equation group based on the target electrostatic potential to obtain a second characteristic function; determine a target carrier density based on the second characteristic function; if a difference between the target carrier density and the initial carrier density is greater than a preset error, take the target electrostatic potential as a new initial electrostatic potential, and then perform the solving of the second analytic equation group based on the initial electrostatic potential to obtain a first characteristic function; if the difference between the target carrier density and the initial carrier density is less than or equal to the preset error, take the target carrier density as a carrier density in the semiconductor device to realize the simulation of the carrier transport in the semiconductor device.

6. A storage medium, characterized by The storage medium has a computer program stored therein, wherein the computer program is configured to execute the method in any one of claims 1 to 4 when running.

7. An electronic device comprising a memory and a processor, characterized in that The memory has a computer program stored therein, and the processor is configured to execute the computer program to execute the method in any one of claims 1 to 4.

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