Carrier transport simulation method, device, medium, and electronic device

Abstract

The application discloses a carrier transport simulation method and device, a medium and an electronic device. The application determines initial conditions and / or boundary conditions of carrier transport in a semiconductor device, and determines a Poisson equation and a Schrodinger equation corresponding to a closed quantum model. The carrier density in the semiconductor device is determined based on the initial conditions and / or the boundary conditions, the Poisson equation and the Schrodinger equation, so as to realize simulation of the carrier transport in the semiconductor device, and further realize research on the carrier transport in the semiconductor device.

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 and / or boundary conditions for carrier transport in semiconductor devices, and determine the Poisson and Schrödinger equations corresponding to the closed quantum model;

[0006] The carrier density in the semiconductor device is determined based on the initial conditions and / or the boundary conditions, 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 Schrödinger equation is:

[0011]

[0012] Among them, the For containing Laplacian operator of Laplace, the h is the reduced Planck constant, the is the spatial-dependent effective mass, the e i and the are eigenvalues and eigenfunctions of a closed quantum system, respectively; the is the effective potential function, the the is the carrier affinity, the is the exchange correlation function.

[0013] Optionally, the is:

[0014]

[0015] wherein, the f F (e i ) is Fermi function, the V T is carrier thermoelectric voltage, the V T = K B T / q, the is electrochemical potential, the K B is Boltzmann constant, and the T is temperature in Kelvin.

[0016] Optionally, the initial conditions and / or boundary conditions of carrier transport in the semiconductor device are determined, comprising:

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

[0018] gridding the geometric model based on finite volume method to obtain a plurality of first control volumes;

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

[0020] Optionally, the carrier density in the semiconductor device is determined based on the initial conditions and / or the boundary conditions, the Poisson equation and the Schrödinger equation, comprising:

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

[0022] determining the Schrödinger equation corresponding to each of the first control volumes to obtain a second set of analytical equations in numerical matrix form;

[0023] determining initial carrier density;

[0024] solving the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential;

[0025] Optionally, the solving the second set of analytical equations based on the initial carrier density and the first set of analytical equations to obtain the carrier density in the semiconductor device comprises:

[0026] solving the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential;

[0027] determining an estimated carrier density based on the first electrostatic potential;

[0028] solving the second set of analytical equations based on the estimated carrier density to obtain a first eigenfunction;

[0029] determining a target carrier density based on the first eigenfunction;

[0030] if a difference between the target carrier density and the initial carrier density is greater than a preset error, taking the target carrier density as a new initial carrier density, and then performing the solving the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential;

[0031] 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.

[0032] Yet another embodiment of the present application provides a carrier transport simulation device, the device comprising:

[0033] an input determining unit configured to determine initial conditions and / or boundary conditions of carrier transport in a semiconductor device, and determine a Poisson equation and a Schrödinger equation corresponding to a closed quantum model;

[0034] an output determining unit configured to determine a carrier density in the semiconductor device based on the initial conditions and / or the boundary conditions, the Poisson equation and the Schrödinger equation, so as to realize simulation of the carrier transport in the semiconductor device.

[0035] Yet another embodiment of the present application provides a storage medium having a computer program stored therein, wherein the computer program is configured to execute the method described in any one of the above embodiments when running.

[0036] Yet another embodiment of the present application provides an electronic device comprising a memory and a processor, wherein the memory has a computer program stored therein, and the processor is configured to execute the computer program to perform the method described in any one of the above embodiments.

[0037] Compared with existing technologies, the present invention provides a carrier transport simulation method that combines the Poisson equation and Schrödinger equation corresponding to the closed 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

[0038] 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;

[0039] Figure 2 A flowchart illustrating a carrier transport simulation method provided in an embodiment of the present invention;

[0040] Figure 3 This is a schematic diagram of a first control volume provided in an embodiment of the present invention;

[0041] 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

[0042] 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.

[0043] 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.

[0044] 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 1 Only 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.

[0045] The memory 104 can be used to store software programs of application software and modules, such as program instructions / modules corresponding to the carrier transport simulation method in the embodiments of the present application. The processor 102 executes various functional applications and data processing by running the software programs and modules stored in the memory 104, that is, implements the above method. The memory 104 can include a high-speed random access memory, and can also include a non-volatile memory, such as one or more magnetic storage devices, flash memories, or other non-volatile solid-state memories. In some examples, the memory 104 can further include a memory remotely arranged with respect to the processor 102, which can be connected to the computer terminal through a network. Examples of the above network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and a combination thereof.

[0046] The transmission device 106 is used to receive or send data via a network. Specific examples of the above network can include a wireless network provided by a communication provider of a computer terminal. In one example, the transmission device 106 includes a network adapter (Network Interface Controller, NIC), which can be connected to other network devices through a base station so as to communicate with the Internet. In one example, the transmission device 106 can be a radio frequency (Radio Frequency, RF) module, which is used to communicate with the Internet in a wireless manner.

[0047] It should be noted that a real quantum computer is a hybrid structure, which includes two parts: one part is a classical computer responsible for performing classical computation and control; the other part is a quantum device responsible for running a quantum program to implement quantum computation. The quantum program is a sequence of instructions written in a quantum language such as QRunes language that can run on a quantum computer, which supports quantum logic gate operations and ultimately realizes quantum computation. Specifically, the quantum program is a sequence of instructions for operating quantum logic gates in a certain time sequence.

[0048] In practical applications, due to the limitation of the development of quantum device hardware, quantum computation simulation is usually needed to verify quantum algorithms, quantum applications, and the like. Quantum computation simulation is a process of simulating the running of a quantum program corresponding to a specific problem by means of a virtual architecture (i.e., a quantum virtual machine) built by a general-purpose computer. Generally, a quantum program corresponding to a specific problem needs to be constructed. The quantum program referred to in the embodiments of the present application is a program written in a classical language representing quantum bits and their evolution, in which quantum bits, quantum logic gates, and the like related to quantum computation are represented by corresponding classical codes.

[0049] As a way of embodying quantum programs, quantum circuits, also called quantum logic circuits, are the most commonly used general quantum computing model, representing a circuit for operating on qubits in an abstract concept, which consists of qubits, circuits (time lines), and various quantum logic gates, and finally the results are often read out through quantum measurement operations.

[0050] Unlike traditional circuits, which are connected by metal wires to transmit voltage signals or current signals, in quantum circuits, the circuits can be seen as being connected by time, that is, the state of the qubits naturally evolves over time, and in this process, the qubits are operated on according to the instructions of the Hamiltonian operator until they encounter logic gates.

[0051] A quantum program as a whole corresponds to a total quantum circuit, and the quantum program of the present application refers to the total quantum circuit, wherein the total number of qubits in the total quantum circuit is the same as the total number of qubits of the quantum program. It can be understood that a quantum program can be composed of a quantum circuit, a measurement operation for the qubits in the quantum circuit, a register for storing the measurement results, and a control flow node (jump instruction), and a quantum circuit can contain tens, hundreds, or even thousands of quantum logic gate operations. The execution process of a quantum program is the process of executing all quantum logic gates in a certain time sequence. It should be noted that the time sequence refers to the time sequence in which individual quantum logic gates are executed.

[0052] It should be noted that in classical computing, the most basic unit is a bit, and the most basic control mode is a logic gate, which can be combined to achieve the purpose of controlling the circuit. Similarly, the way to handle qubits is quantum logic gates. Using quantum logic gates can make the quantum state evolve, and quantum logic gates are the basis of quantum circuits. Quantum logic gates include single-bit quantum logic gates such as Hadamard gate (H gate), Pauli-X gate (X gate), Pauli-Y gate (Y gate), Pauli-Z gate (Z gate), RX gate, RY gate, RZ gate, etc., and multi-bit quantum logic gates such as CNOT gate, CR gate, iSWAP gate, Toffoli gate, etc. Quantum logic gates are generally represented by unitary matrices, which are not only matrix forms but also operations and transformations. The effect of a general quantum logic gate on a quantum state is calculated by multiplying the quantum state right vector by the unitary matrix on the left.

[0053] Referring to Figure 2 , Figure 2 A flowchart of a carrier transport simulation method provided by an embodiment of the present application can include the following steps:

[0054] Step 201: Determine the initial conditions and / or boundary conditions of carrier transport in a semiconductor device, and determine the Poisson equation and Schrödinger equation corresponding to the closed quantum model.

[0055] Wherein, the carrier is the carrier of current; in the semiconductor device, the carrier includes two types: electron and hole.

[0056] Wherein, for the physical process changing with time, the state at a moment will affect the process after the moment, and the state at the moment is the initial condition; the boundary condition refers to the change rule of the variable or its derivative on the solving region boundary with time and place. The boundary condition includes the first type of boundary condition of given end point value, the second type of boundary condition of given gradient value, and the third type of boundary condition of given end point value and gradient value. The boundary condition in the application can be any one of the above three types of boundary conditions, which is not limited herein.

[0057] Specifically, the Poisson equation is:

[0058]

[0059] Wherein, the is a Laplace operator containing , the is the relative static dielectric constant of the semiconductor device, the is the electrostatic potential to be determined, the is the vacuum dielectric constant, the is the carrier charge quantity, and the

[0060] is the carrier density.

[0061]

[0062] Wherein, the is a Laplace operator containing , the is the reduced Planck constant, the is the spatial-dependent effective mass, the i and the are eigenvalues and eigenfunctions of a closed quantum system respectively; the is an effective potential function, the , the is the carrier affinity, and the is an exchange correlation function.

[0063] Wherein, is:

[0064]

[0065] Wherein, the F (e i ) is a Fermi function, and the T is an exchange correlation function.The carrier thermal voltage, V T =K B T / q, the aforementioned For electrochemical potential, the K B Here, T is the Boltzmann constant, and T is the temperature in Kelvin.

[0066] 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 -23 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.

[0067] 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.

[0068] 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 shown... Figure 3The right side is shown, wherein w, e, n, s, b, t are respectively the center points of the first control volume corresponding to the center P and the interfaces W, E, N, S, B, T, 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 [b, t] × [w, e] × [s, n] P = [b, t] × [w, e] × [s, n], wherein b, t and Δx are not shown.

[0069] It should be noted that the geometric model is divided into a plurality of first control volumes similar to P, and each first control volume can be equal or not equal; generally, only the first control volumes at the end points (or edges) have boundary conditions, and the other first control volumes inside the geometric model do not have boundary conditions.

[0070] As can be seen, the geometric model can be divided into a plurality of control volumes by the finite volume method, so that the discrete equations of the Poisson equation and the Schrödinger equation can be constructed by the integral form of the conservation equation in the subsequent process, thereby realizing the solution of the Poisson equation and the Schrödinger equation.

[0071] Step 202: determining the carrier density in the semiconductor device based on the initial condition and / or the boundary condition, the Poisson equation and the Schrödinger equation, to realize the simulation of carrier transport in the semiconductor device.

[0072] Specifically, in the aspect of determining the carrier density in the semiconductor device based on the initial condition and / or the boundary condition, the Poisson equation and the Schrödinger equation: a first analytical equation group in the form of a numerical matrix can be determined based on the initial condition and the boundary condition of each first control volume and the Poisson equation; the Schrödinger equation corresponding to each first control volume is determined to obtain a second analytical equation group in the form of a numerical matrix; the initial carrier density is determined; the second analytical equation group is iteratively solved based on the initial carrier density and the first analytical equation group, to obtain the carrier density in the semiconductor device.

[0073] For example, after gridding, the discrete Laplacian containing parameters (α x , α y , α z ) is:

[0074]

[0075] For P in the above Figure 3 , by the basic property of definite integral:

[0076]

[0077] Taking the integral average, the above formula is transformed into:

[0078]

[0079] Using the central difference approximation of the first derivative

[0080] Thus, it can be derived that

[0081]

[0082] Where [α x ] b,t , [α y ] w,e , [α z ] s,n Can be calculated by flux conservation.

[0083] Definition

[0084]

[0085]

[0086] Thus, the above formula can be simply recorded as

[0087]

[0088] For Poisson equation:

[0089] α x =-ε x , α y =-ε y , α z =-ε z

[0090] For a plurality of first CVs (Control Volume) meshed, a plurality of the above discrete Poisson equations can be obtained, and the plurality of the above equations are converted into a first analytical equation group in the form of a numerical matrix:

[0091]

[0092] Wherein, the analytical function Is discretized into a column vector Is a fixed vector from the boundary condition. [M1] is a 7-diagonal matrix about β i (Wherein, i=t, b, e, w, n, s ···), Is a nonlinear function of .

[0093] Similarly, for the Schrödinger equation at P, only φ is replaced by the eigenfunction ψ, and the subsequent process is not deduced one by one, see the above derivation process of Poisson equation; wherein:

[0094]

[0095] For the meshed plurality of first CV, a plurality of the above discrete Schrödinger equations can be obtained, and the plurality of discrete equations are converted into a second analytical equation group in the form of a numerical matrix:

[0096]

[0097] Wherein, the eigenfunction is discretized into a column vector is a vector from the fixed boundary condition. [M2] is a 7-diagonal matrix about β i (where i = p, t, b, e, w, n, s).

[0098] It should be noted that the boundary condition may be the same as the boundary condition , or different, which is not limited here.

[0099] It can be seen that [M1] only contains the Laplacian operator term in the Poisson equation, and [M2] not only contains the Laplacian operator term in the Schrödinger equation, but also includes the potential V eff term and the eigenvalue e i term. It can also be seen that the Poisson equation with the boundary condition is a nonlinear equation group, and the Schrödinger equation with the boundary condition is a linear equation group. For the solution of the nonlinear equation group, Newton iteration method can be used; for the solution of the linear equation, Chebyshev-Arnoldi iteration can be used for solution.

[0100] Wherein, the initial carrier density is given in advance.

[0101] Further, a specific implementation of the iterative solving of the second set of analytical equations based on the initial carrier density and the first set of analytical equations is: solving the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential; determining an estimated carrier density based on the first electrostatic potential; solving the second set of analytical equations based on the estimated carrier density to obtain a first eigenfunction; determining a target carrier density based on the first eigenfunction; if a difference between the target carrier density and the initial carrier density is greater than a preset error, taking the target carrier density as a new initial carrier density, and then performing the solving of the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential; 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.

[0102] It should be noted that the initial carrier density is predefined; the estimated carrier density is an estimated value, which can be used to more quickly iteratively solve the target carrier density; and the difference between the target carrier density and the initial carrier density is also predefined.

[0103] Further, after the carrier density in the semiconductor device is determined based on the initial condition and / or the boundary condition, the Poisson equation and the Schrödinger equation, the method can further include:

[0104] determining a target region in which the carrier density in the geometric model is greater than or equal to a preset threshold based on the solved carrier density; meshing the target region based on the finite volume method to obtain a plurality of second control volumes, the second control volumes being smaller than the first control volumes; and determining a new carrier density based on the plurality of second control volumes, and taking the new carrier density as the carrier density in the semiconductor device.

[0105] It should be noted that the manner in which the new carrier density is determined in this embodiment can be, for example, determined by the Poisson equation and the Schrödinger equation corresponding to the closed quantum model, or determined by the Poisson equation corresponding to the semi-classical model, or determined by the Poisson equation and the Schrödinger equation corresponding to the open quantum model. For different physical simulation models, the form of the Schrödinger equation is different, for example, the Schrödinger equation corresponding to the open physical model is different from the form of the Schrödinger equation corresponding to the closed physical model.

[0106] Compared with existing technologies, the present invention provides a carrier transport simulation method that combines the Poisson equation and Schrödinger equation corresponding to the closed 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.

[0107] 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:

[0108] The input determination unit 401 is used to determine the initial conditions and / or boundary conditions for carrier transport in semiconductor devices, as well as to determine the Poisson equation and Schrödinger equation corresponding to the closed quantum model;

[0109] 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 Poisson equation and the Schrödinger equation, so as to realize the simulation of carrier transport in the semiconductor device.

[0110] Specifically, the Poisson equation is:

[0111]

[0112] 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.

[0113] Specifically, the Schrödinger equation is:

[0114]

[0115] Among them, the For containing The Laplace operator, the To reduce Planck's constant, the For space-related directional effective mass, the e i and stated These are the eigenvalues ​​and eigenfunctions of a closed quantum system, respectively; It is the effective potential energy function, the stated The For carrier affinity, the to exchange the relevant functions.

[0116] Specifically, the is:

[0117]

[0118] wherein the f F (e i ) is a Fermi function, the V T is a carrier thermal voltage, the V T = K B T / q, the is an electrochemical potential, the K B is a Boltzmann constant, and the T is a temperature in Kelvin.

[0119] Specifically, the input determining unit 401 is specifically configured to determine the initial condition and / or the boundary condition of carrier transport in the semiconductor device in terms of:

[0120] constructing a geometric model of the semiconductor device;

[0121] griding the geometric model based on a finite volume method to obtain a plurality of first control volumes;

[0122] determining the initial condition and / or the boundary condition of each of the first control volumes.

[0123] Specifically, the output determining unit 402 is specifically configured to determine the carrier density in the semiconductor device based on the initial condition and / or the boundary condition, the Poisson equation and the Schrodinger equation in terms of:

[0124] determining a first analytical equation group in a numerical matrix form based on the initial condition and the boundary condition of each of the first control volumes and the Poisson equation;

[0125] determining the Schrodinger equation corresponding to each of the first control volumes to obtain a second analytical equation group in a numerical matrix form;

[0126] determining an initial carrier density;

[0127] iteratively solving the second analytical equation group based on the initial carrier density and the first analytical equation group to obtain the carrier density in the semiconductor device.

[0128] Specifically, the output determining unit 402 is specifically configured to iteratively solve the second analytical equation group based on the initial carrier density and the first analytical equation group to obtain the carrier density in the semiconductor device in terms of:

[0129] solving the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential;

[0130] determining an estimated carrier density based on the first electrostatic potential;

[0131] solving the second set of analytical equations based on the estimated carrier density to obtain a first eigenfunction;

[0132] determining a target carrier density based on the first eigenfunction;

[0133] if a difference between the target carrier density and the initial carrier density is greater than a preset error, taking the target carrier density as a new initial carrier density, and then performing the solving of the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential;

[0134] 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.

[0135] Compared with the prior art, the carrier transport simulation method provided by the application combines the Poisson equation and the Schrodinger equation corresponding to the closed quantum model with the initial condition and / or the boundary condition of carrier transport in a semiconductor device, so as to determine the carrier density in the semiconductor device, to realize the simulation of carrier transport in the semiconductor device, and to realize the research on carrier transport in the semiconductor device.

[0136] Still another embodiment of the application provides a storage medium having a computer program stored therein, wherein the computer program is configured to perform the steps in the method embodiments in any of the above embodiments when running.

[0137] Specifically, in the embodiment, the above storage medium can be configured to store a computer program for performing the following steps:

[0138] determining the initial condition and / or the boundary condition of carrier transport in the semiconductor device, and determining the Poisson equation and the Schrodinger equation corresponding to the closed quantum model;

[0139] determining the carrier density in the semiconductor device based on the initial condition and / or the boundary condition, the Poisson equation and the Schrodinger equation, to realize the simulation of carrier transport in the semiconductor device.

[0140] Specifically, in the embodiment, the storage medium can include, but is not limited to, a U disk, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk or an optical disk, and various storage media that can store computer programs.

[0141] Another embodiment of the present application also provides an electronic device including a memory and a processor, the memory storing a computer program, and the processor being configured to execute the computer program to perform the steps in the method embodiments of any of the above.

[0142] Specifically, the carrier device can further include a transmission device and an input / output device, wherein the transmission device is connected to the processor, and the input / output device is connected to the processor.

[0143] Specifically, in the embodiment, the processor can be configured to perform the following steps through the computer program:

[0144] determining initial conditions and / or boundary conditions of carrier transport in a semiconductor device, and determining a Poisson equation and a Schrodinger equation corresponding to the closed quantum model;

[0145] determining carrier density in the semiconductor device based on the initial conditions and / or the boundary conditions, the Poisson equation and the Schrodinger equation, to realize simulation of carrier transport in the semiconductor device.

[0146] The above embodiments according to the drawings illustrate the structure, features and effects of the present application, and the above description is only the preferred embodiments of the present application, but the present application is not limited to the embodiments shown in the drawings, any changes or modifications made according to the concept of the present application, or equivalent embodiments with equivalent changes, shall be within the scope of the present application.

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; determining a Poisson equation and a Schrödinger equation corresponding to a closed quantum model; determining a first set of analytical equations 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 the Schrödinger equation corresponding to each of the first control volumes to obtain a second set of analytical equations in a numerical matrix form; and determining an initial carrier density; iteratively solving the second set of analytical equations based on the initial carrier density and the first set of analytical equations to obtain a carrier density 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... 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.

3. The method of claim 2, wherein, The Schrödinger equation is: Among them, the For containing The Laplace operator, the To reduce Planck's constant, the For space-related directional effective mass, the e i and stated These are the eigenvalues ​​and eigenfunctions of a closed quantum system, respectively; 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 f F (e i ) is the Fermi function, the V T is the carrier thermal voltage, the V T = K B T / q, the is the electrochemical potential, the K B is the Boltzmann constant, and the T is the temperature in Kelvin.

5. The method of claim 1, wherein, The iterative solving of the second set of analytical equations based on the initial carrier density and the first set of analytical equations to obtain a carrier density in the semiconductor device comprises: solving the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential; determining an estimated carrier density based on the first electrostatic potential; solving the second set of analytical equations based on the estimated carrier density to obtain a first eigenfunction; determining a target carrier density based on the first eigenfunction; if a difference between the target carrier density and the initial carrier density is greater than a preset error, taking the target carrier density as a new initial carrier density, and then performing the solving of the first set of analytical equations based on the initial carrier density to obtain a first electrostatic potential; 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.

6. 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; determine initial conditions and / or boundary conditions of each of the first control volumes; and determine a Poisson equation and a Schrödinger equation corresponding to a closed quantum model; an output determination unit configured to determine a first set of analytical equations 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; determine the Schrödinger equation corresponding to each of the first control volumes to obtain a second set of analytical equations in a numerical matrix form; determine an initial carrier density; and iteratively solve the second set of analytical equations based on the initial carrier density and the first set of analytical equations to obtain a carrier density in the semiconductor device.

7. A storage medium, characterized by The storage medium has stored therein a computer program, wherein the computer program is configured to execute the method recited in any one of claims 1 to 5 when running.

8. An electronic device comprising a memory and a processor, characterized in that The memory has stored therein a computer program, and the processor is configured to execute the computer program to execute the method recited in any one of claims 1 to 5.

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