A method, apparatus, device, and medium for transistor heat generation and heat transfer analysis

Abstract

This invention discloses a method, apparatus, device, and medium for analyzing heat generation and heat transfer in transistors. The method includes: dividing the functional simulation region of the transistor to determine multiple sub-simulation regions corresponding to the transistor; determining the non-equilibrium energy density distribution and equilibrium energy density distribution of electrons and phonons in each sub-simulation region at the initial simulation time; constructing a coupled Boltzmann transport model for electrons and phonons corresponding to each sub-simulation region; solving the coupled Boltzmann transport model to determine the non-equilibrium energy density distribution of electrons and phonons in each sub-simulation region at the next simulation time; and iteratively solving the coupled Boltzmann transport model based on the information of each sub-simulation region at the next simulation time until the grid temperature distribution meets a preset convergence condition. This invention improves the accuracy and efficiency in calculating electroacoustic coupling power consumption and heat transfer problems in transistors.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for heat transfer in micro / nano structures and devices, and particularly to a method, apparatus, equipment, and medium for analyzing heat generation and heat transfer in transistors. Background Technology

[0002] With advancements in large-scale integrated circuit technology, the number of transistors integrated on a single chip has reached the tens of billions, and the feature length of a single transistor has drastically decreased to below tens of nanometers. Within these nanoscale transistors, various nanostructures, including nanofilms, nanowires, and nanorods, can significantly reduce the thermal conductivity of the materials. Simultaneously, as the proportion of transistor interfaces and surfaces increases, interfacial thermal resistance and boundary scattering effects hinder the normal transport of hot carriers, slowing down heat transfer. Both of these phenomena lead to extremely high power density distributions within the transistor and severe heat accumulation effects, especially in localized hotspot regions where heat density can reach as high as 10⁻⁶ ohms. 18 W / m 3 The power density and high temperature (60°C to 100°C above room temperature) of electronic devices can directly affect their performance and even disrupt their normal operation.

[0003] Currently, Electronic Design Automation (EDA) software still uses macroscopic constitutive equations to describe the electrothermal transport processes within chips, with heat transfer processes described by methods such as establishing thermal resistance networks. However, these methods struggle to accurately describe thermal transport problems at the nanoscale, and in particular, it is difficult to establish precise thermal resistance network models to capture various nanoscale effects.

[0004] Commonly used heat transfer simulation methods include molecular dynamics simulations, stochastic Monte Carlo simulations, and quantum mechanical ab initio methods. These methods are highly accurate, but they are computationally complex and computationally intensive, and are limited by the size of the simulation system and the simulation time, making them difficult to apply to device and circuit-scale calculations. Summary of the Invention

[0005] This invention provides a method, apparatus, device, and medium for analyzing heat generation and heat transfer in transistors, to solve the problem of accurately describing heat generation and heat transport at the nanoscale and microscale, and to achieve efficient numerical calculations of these processes, thereby improving the accuracy and efficiency in calculating electroacoustic coupling power consumption and heat transfer in transistors.

[0006] According to one aspect of the present invention, a method for analyzing transistor heat generation and heat transfer is provided, the method comprising:

[0007] The functional simulation region of the transistor is divided to determine multiple sub-simulation regions corresponding to the transistor, wherein the feature length of the transistor is at the nano-micro scale;

[0008] Obtain the electron mean free path, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume, and electron heat capacity per unit volume in each of the sub-simulation regions, as well as the electron temperature distribution and phonon temperature distribution at the initial simulation time.

[0009] Based on the doping concentration, the applied voltage of the transistor, the mean free path of the electrons, and the electron saturation drift velocity, the power density distribution of each of the sub-simulation regions is determined, and the electroacoustic coupling coefficient is determined based on the electron unit volume heat capacity and the electron relaxation time.

[0010] Based on the electron temperature distribution and phonon temperature distribution at the initial simulation time, the electron non-equilibrium state energy density distribution, electron equilibrium state energy density distribution, phonon non-equilibrium state energy density distribution, and phonon equilibrium state energy density distribution of each sub-simulation region at the initial simulation time are determined.

[0011] Based on the preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step of electron transport, the simulation time step of phonon transport, the electron relaxation time, the phonon relaxation time, the power density distribution, and the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time, a coupled Boltzmann transport model of electrons and phonons corresponding to each sub-simulation region is constructed.

[0012] The coupled Boltzmann transport model of electrons and phonons is solved to determine the non-equilibrium energy density distribution of electrons and the non-equilibrium energy density distribution of phonons in each sub-simulation region at the next simulation time.

[0013] Based on the phonon unit volume heat capacity, the electron unit volume heat capacity, and the electron non-equilibrium energy density distribution and phonon non-equilibrium energy density distribution at the next simulation time, determine the electron equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, phonon temperature distribution, and grid temperature distribution of each sub-simulation region at the next simulation time.

[0014] Based on the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution of each sub-simulation region at the next simulation time, the coupled Boltzmann transport model is iteratively solved until the calculated grid temperature distribution satisfies the preset convergence condition.

[0015] According to another aspect of the present invention, a transistor heat generation and heat transfer analysis apparatus is provided, the apparatus comprising:

[0016] The sub-simulation region determination module is used to divide the functional simulation region of the transistor and determine multiple sub-simulation regions corresponding to the transistor, wherein the feature length of the transistor is at the nano-micro scale.

[0017] The parameter acquisition module is used to acquire the doping concentration, transistor applied voltage, electron mean free path, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume and electron heat capacity per unit volume in each of the sub-simulation regions, as well as the electron temperature distribution and phonon temperature distribution at the initial simulation time.

[0018] A power density distribution determination module is used to determine the power density distribution of each of the sub-simulation regions based on the doping concentration, the applied voltage of the transistor, the mean free path of the electrons, and the saturation drift velocity of the electrons, and to determine the electroacoustic coupling coefficient based on the electron unit volume heat capacity and the electron relaxation time.

[0019] The energy density distribution determination module is used to determine the non-equilibrium energy density distribution of electrons, the equilibrium energy density distribution of electrons, the non-equilibrium energy density distribution of phonons, and the equilibrium energy density distribution of phonons in each sub-simulation region at the initial simulation time, based on the electron temperature distribution and the phonon temperature distribution at the initial simulation time.

[0020] The coupled Boltzmann transport model construction module is used to construct the coupled Boltzmann transport model of electrons and phonons for each sub-simulation region based on the preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step of electron transport, the simulation time step of phonon transport, the electron relaxation time, the phonon relaxation time, the power density distribution, and the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time.

[0021] The non-equilibrium energy density distribution determination module is used to solve the coupled Boltzmann transport model of electrons and phonons, and determine the non-equilibrium energy density distribution of electrons and phonons in each sub-simulation region at the next simulation time.

[0022] The equilibrium energy density distribution determination module is used to determine the electronic equilibrium energy density distribution, phonon equilibrium energy density distribution, electronic temperature distribution, phonon temperature distribution, and grid temperature distribution of each sub-simulation region at the next simulation time, based on the phonon unit volume heat capacity, the electron unit volume heat capacity, and the electronic non-equilibrium energy density distribution and phonon non-equilibrium energy density distribution at the next simulation time.

[0023] The coupled Boltzmann transport model iterative solution module is used to iteratively solve the coupled Boltzmann transport model based on the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution of each sub-simulation region at the next simulation time, until the calculated grid temperature distribution satisfies the preset convergence condition.

[0024] According to another aspect of the present invention, an electronic device is provided, the electronic device comprising:

[0025] At least one processor; and

[0026] A memory communicatively connected to the at least one processor; wherein,

[0027] The memory stores a computer program that can be executed by the at least one processor, which enables the at least one processor to perform the transistor heat generation and heat transfer analysis method in any embodiment of the present invention.

[0028] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to execute the transistor heat generation and heat transfer analysis method in any embodiment of the present invention.

[0029] The technical solution of this invention involves dividing the functional simulation region of a transistor to determine multiple sub-simulation regions corresponding to the transistor; obtaining the doping concentration, applied transistor voltage, electron mean free path, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume, and electron heat capacity per unit volume, as well as the electron temperature distribution and phonon temperature distribution at the initial simulation time, for each sub-simulation region; and determining the power density distribution of each sub-simulation region based on the doping concentration, applied transistor voltage, electron mean free path, and electron saturation drift velocity, and... The electro-acoustic coupling coefficient is determined based on the electron unit volume heat capacity and the electron relaxation time; the non-equilibrium energy density distribution, equilibrium energy density distribution, phonon non-equilibrium energy density distribution, and phonon equilibrium energy density distribution of each sub-simulation region at the initial simulation time are determined based on the electron temperature distribution and phonon temperature distribution at the initial simulation time; the electro-acoustic coupling coefficient is determined based on the preset collision migration mode, the electron-acoustic coupling coefficient, the simulation time step of electron transport, the simulation time step of phonon transport, the electron relaxation time, the phonon relaxation time, the power density distribution, and the electron temperature distribution at the initial simulation time. Based on the non-equilibrium energy density distributions of electrons, electrons, phonons, and phonons, a coupled Boltzmann transport model for electrons and phonons is constructed for each sub-simulation region. The coupled Boltzmann transport model is solved to determine the non-equilibrium energy density distributions of electrons and phonons in each sub-simulation region at the next simulation time. Based on the phonon heat capacity per unit volume, the electron heat capacity per unit volume, and the non-equilibrium energy density of electrons at the next simulation time, a coupled Boltzmann transport model for electrons and phonons is constructed. The distribution of electron and phonon non-equilibrium energy density is used to determine the electron equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, phonon temperature distribution, and lattice temperature distribution for each sub-simulation region at the next simulation time. Based on these distributions, the coupled Boltzmann transport model is iteratively solved until the calculated lattice temperature distribution meets a preset convergence condition. This invention simulates heat generation and transfer processes by establishing a numerical solution model of electron and phonon coupled terms to optimize the influence of electron-phonon interaction on the heat transport process to a certain extent.By establishing an electron collision probability model, the power density distribution of electrothermal heat generation was calculated. As a source term in the coupled Boltzmann transport model of electrons and phonons, it can completely and effectively describe the physical processes of electrothermal heat generation and heat transport to the outside of the boundary. This solves the problem of accurately describing heat generation and heat transport at the nanoscale and microscale, realizes efficient calculation of numerical heat transfer, and improves the accuracy and efficiency in calculating electroacoustic coupling power consumption and heat transfer in transistors.

[0030] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of a transistor heat generation and heat transfer analysis method provided in Embodiment 1 of the present invention;

[0033] Figure 2 This is a physical schematic diagram of a transistor simulation region according to Embodiment 1 of the present invention;

[0034] Figure 3 This is a schematic diagram of the power density distribution in the x-direction obtained by a power density calculation method according to Embodiment 1 of the present invention;

[0035] Figure 4 This is a schematic diagram illustrating the temperature change over time at a grid point within different sub-simulation regions of a simulation area according to Embodiment 1 of the present invention.

[0036] Figure 5 This is a flowchart of a transistor heat generation and heat transfer analysis method provided in Embodiment 2 of the present invention;

[0037] Figure 6 This is a schematic diagram showing the relationship between relaxation time and material size calculated by a phonon relaxation time correction model of a D2Q9 lattice according to Embodiment 2 of the present invention.

[0038] Figure 7 This is a schematic diagram of the structure of a transistor heat generation and heat transfer analysis device provided in Embodiment 3 of the present invention;

[0039] Figure 8This is a schematic diagram of the structure of an electronic device that implements the transistor heat generation and heat transfer analysis method according to embodiments of the present invention. Detailed Implementation

[0040] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0041] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0042] Example 1

[0043] Figure 1 This invention provides a flowchart of a transistor heat generation and heat transfer analysis method according to Embodiment 1. This embodiment is applicable to simulating the power consumption and heat transfer of transistors at the nanoscale. The method can be executed by a transistor heat generation and heat transfer analysis device, which can be implemented in hardware and / or software and can be configured in an electronic device. Figure 1 As shown, the method includes:

[0044] S110. Divide the functional simulation region of the transistor and determine multiple sub-simulation regions corresponding to the transistor, wherein the characteristic length of the transistor is at the nano-micro scale.

[0045] In this context, a transistor can refer to a solid-state semiconductor device. The characteristic length can refer to a representative length among various lengths of a transistor. For example, the characteristic length can be the length of the transistor's channel. The nanoscale can refer to a scale between micrometers and nanometers. The type of transistor in this embodiment can be, but is not limited to: N-type metal-oxide-semiconductor (NMOS), FinField-Effect Transistor (FINFET), Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET), Gate-all-around Field-Effect Transistor (GAAFET), or Complementary Metal-Oxide Semiconductor (CMOS). For example, a transistor can refer to an NMOS transistor with a characteristic length of 50 nm. The functional analog region can refer to a region within the transistor divided according to function. A transistor can have multiple functional analog regions. For example, a functional simulation region may include regions such as the source region, drain region, channel inversion layer region, substrate, dielectric layer, and gate. A sub-simulation region can refer to a simulation region obtained by dividing the transistor according to a predetermined method. A functional simulation region may correspond to one or more sub-simulation regions.

[0046] Specifically, the transistor feature length is at the nanoscale, and the transistor can be a nanoscale device containing multiple functional regions and both electron and phonon energy carriers. Figure 2 A physical schematic diagram of a transistor simulation region is provided. See also... Figure 2 The functional simulation region of a transistor includes the source region, drain region, gate region, insulating dielectric layer, inversion layer channel region, and silicon substrate. The region to be simulated can be orthogonally divided into nine sub-simulation regions, and a corresponding parallel computing process can be assigned to each sub-simulation region. Each computing process can be responsible for the computational tasks within its corresponding sub-simulation region. By dividing the simulation region into multiple sub-regions for parallel computation, the computation time is reduced, overcoming the shortcomings of quantum mechanical ab initio methods, molecular dynamics simulations, and stochastic Monte Carlo simulations, such as long computation time, high computational cost, and limited computational scale.

[0047] S120. Obtain the mean free path of electrons, doping concentration, transistor applied voltage, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume and electron heat capacity per unit volume, as well as the electron temperature distribution and phonon temperature distribution at the initial simulation time in each sub-simulation region.

[0048] Among these, the electron mean free path, electron saturation drift velocity, electron relaxation time, and electron heat capacity per unit volume can be attribute parameters of the electron. Phonon relaxation time and phonon heat capacity per unit volume can be attribute parameters of the phonon. Attribute parameters can also include angular frequency, intrinsic carrier concentration, relative permittivity, and doping concentration. An electron can refer to a negatively charged subatomic particle. The electron mean free path can refer to the average distance an electron travels between two successive collisions. Generally, the higher the electron concentration, the smaller the electron mean free path. The electron mean free path can be represented by λ. The electron saturation drift velocity can refer to the saturation velocity where the average speed of an electron due to the electric field no longer changes with the action of the electric field. The electron saturation drift velocity can be represented by v. The relaxation time can refer to the time required to reach thermodynamic equilibrium and can be used to represent the time required for a system to tend from an unstable steady state to a certain stable steady state. The electron relaxation time can refer to the relaxation time of the electron. The electron relaxation time can be represented by τ. el Phonons can refer to quasi-particles collectively excited by the crystal structure within a crystal. Phonon relaxation time can refer to the relaxation time corresponding to a phonon. Phonon relaxation time can be represented by τ. ph The terms "heat capacity" and "electronic temperature distribution" refer to the physical quantity used to measure the amount of heat contained in a substance. Phonon heat capacity per unit volume refers to the amount of heat required to raise the temperature of a unit volume of phonons by 1 degree Celsius. Electron heat capacity per unit volume refers to the amount of heat required to raise the temperature of a unit volume of electrons by 1 degree Celsius. "Initial simulation time" refers to the moment before the first simulation calculation begins. Electron temperature distribution refers to the temperature of electrons at various grid points in the simulation region. Phonon temperature distribution refers to the temperature of phonons at various grid points in the simulation region.

[0049] Specifically, each parallel computing process can save the attribute parameters of electrons and phonons within the corresponding sub-simulation region, as well as the electron and phonon temperatures at each grid point at the initial simulation time, into memory. Based on the stored information, the electron mean free path, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume, electron heat capacity per unit volume, and the electron and phonon temperature distributions at the initial simulation time can be obtained for each sub-simulation region. See also Figure 2 T is the equivalent absolute temperature, and the given initial conditions are T = 300 K and boundary conditions. The volumetric heat capacity per unit volume of phonons with different polarization types is calculated using the formula for phonon volumetric heat capacity. The volumetric heat capacity per unit volume of phonons with different polarization types can include the volumetric heat capacity per unit volume of acoustic phonon branches, C.α and the unit volume heat capacity C of the optical phonon branch o The calculation model for the unit volume heat capacity of the acoustic phonon branch is as follows:

[0050]

[0051] Where k is the phonon wave vector, w a The acoustic phonon angular frequency, To reduce Planck's constant, k B denoted by Boltzmann constant, and i represents different branches of the dispersion curve.

[0052] The calculation model for the heat capacity per unit volume of the optical phonon branch is as follows:

[0053]

[0054] Among them, w o Let V be the optical phonon angular frequency, V be the unit cell volume, and V = a. 3 / 4, where a is the lattice constant. The total heat capacity per unit volume of phonons is the sum of the heat capacities of all phonon branches, calculated as follows:

[0055]

[0056] The total heat capacity per unit volume of phonons can also be obtained using experimental measurements. The calculated heat capacity per unit volume of phonons, C... ph Other attribute parameters include group velocity v, relaxation time τ, angular frequency w, and intrinsic carrier concentration n. i The relative permittivity ε of silicon and dielectric layers s and ε ox Different functional regions with different doping concentrations of N β Save it to the computer's memory.

[0057] S130. Based on doping concentration, transistor applied voltage, electron mean free path and electron saturation drift velocity, the power density distribution of each sub-simulation region is determined, and the electroacoustic coupling coefficient is determined based on electron unit volume heat capacity and electron relaxation time.

[0058] Here, power density can refer to the power density of heat generated by electricity. The power density distribution can be represented by Q. The electro-acoustic coupling coefficient can refer to the rate of energy exchange between electrons and phonons. The electro-acoustic coupling coefficient can be represented by G. ep express.

[0059] Specifically, each parallel computing process can determine the power density distribution of each sub-simulation region based on the electron mean free path and electron saturation drift velocity corresponding to each sub-simulation region, and determine the electroacoustic coupling coefficient based on the electron unit volume heat capacity and electron relaxation time corresponding to each sub-simulation region. For example, G ep Represents the electroacoustic coupling coefficient, and the electron heat capacity per unit volume C. el τ is a constant value. el This represents the electron relaxation time. The electroacoustic coupling coefficient can be determined based on the electron's unit volume heat capacity and electron relaxation time. Its physical meaning is the rate at which electrons and phonons exchange energy.

[0060] It should be noted that this invention calculates the power density distribution of electrothermal heat generation by establishing an electron collision probability model, which serves as the source term of the coupled Boltzmann transport model of electrons and phonons, and can completely and effectively describe the physical process of electrothermal heat generation and heat transport to the outside of the boundary.

[0061] For example, S130, "determining the power density distribution of each sub-simulation region based on doping concentration, transistor applied voltage, electron mean free path, and electron saturation drift velocity," may include: for each sub-simulation region, establishing a current density equation and charge conservation relationship based on doping concentration, transistor applied voltage, and electron saturation drift velocity; determining the current density distribution in the sub-simulation region based on the current density equation and charge conservation relationship; determining the potential distribution in the sub-simulation region based on the current density distribution and the differential relationship between current and voltage; constructing an electron collision probability model based on the electron mean free path and channel inversion layer length; and determining the power density distribution in the sub-simulation region based on the potential distribution and the electron collision probability model.

[0062] Here, current density can refer to the current density at each lattice point, describing the current situation at each lattice point. Charge conservation can refer to the fact that the algebraic sum of all charges remains constant. Current density distribution can refer to the current density at each lattice point. Potential distribution can refer to the potential situation at each lattice point. Inversion layer can refer to the thin layer close to the surface where inversion carriers are mainly distributed in the inversion state. Channel inversion layer length can refer to the length of the inversion region of the transistor channel.

[0063] Specifically, for each sub-simulation region, each parallel computing process can determine the current density distribution in that sub-simulation region by calculation based on the current density equation and the charge conservation relationship;

[0064] For example, the equation used to calculate current density is:

[0065] I D (x)=Z|θn (x)|v

[0066] Where Z is the width of the channel inversion layer, θ n denoted by charge concentration, and v is the electron saturation drift velocity.

[0067] For each sub-simulation region, each parallel computing process can determine the potential distribution in that sub-simulation region by calculation based on the current density distribution and the differential relationship between current and voltage; for example, based on the carrier concentration n on the channel inversion layer surface. s and intrinsic carrier concentration n i Calculate the potential difference between the Fermi level and the intrinsic Fermi level within the inversion layer. Based on the relative permittivity ε of the dielectric layer ox Calculate the gate capacitance C gate According to the potential difference Gate capacitance C gate Other property parameters include the relative permittivity ε of silicon. s Inversion layer carrier concentration N c Calculate the threshold voltage V required to produce the inversion layer in the production channel. T :

[0068]

[0069]

[0070] Where, k B ε is Boltzmann's constant, and ε0 is the vacuum permittivity.

[0071] According to the threshold voltage V T Calculate the source-drain current I within the transistor. sd :

[0072]

[0073] Where Z is the width of the channel inversion layer, L is the length of the channel inversion layer, and V is the width of the channel inversion layer. gate E is the applied gate bias voltage. sat μ is the saturation electric field intensity in the inversion layer of the channel. n Let be the electron mobility. Combining the current-voltage relationship in the channel inversion layer, the potential distribution is calculated:

[0074]

[0075]

[0076] Among them I sd This indicates that the current flows from the source to the drain within the channel region. Based on the intrinsic carrier concentration n... iThe donor concentration N in the source and drain regions D and the acceptor concentration N in the channel inversion layer region A Thus, the built-in potential barrier ψ of the pn junction depletion region is calculated. bi :

[0077]

[0078] The source and drain regions are typically heavily doped, while the channel inversion layer region is lightly doped, with a doping concentration difference of more than two orders of magnitude. This is combined with the charge conservation relationship on both sides of the depletion region: qN D W D =qN A W A Then we have the following conclusion W A >>W D This makes the total width of the entire depletion region W = W A +W D ≈W A Calculate the width of the depletion region based on the built-in potential barrier:

[0079]

[0080] Among them, V s The bias applied to the region outside the depletion region.

[0081] According to the built-in potential barrier ψ bi Given the width W of the depletion region, solve the Poisson equation within the depletion region to calculate the built-in potential distribution within the depletion region:

[0082]

[0083] An electron collision probability model is constructed based on the electron mean free path and the channel inversion layer length; for example, the electron collision probability model equation used to calculate the thermal power density is:

[0084]

[0085] Where λ is the mean free path of electrons and L is the length of the inversion layer of the channel.

[0086] For each sub-simulation region, each parallel computing process can determine the power density distribution in that sub-simulation region by calculation based on the potential distribution and the electron collision probability model.

[0087] For example, "determining the power density distribution of the sub-simulation region based on the potential distribution and the electron collision probability model" may include: if the sub-simulation region includes a channel inversion layer sub-simulation region, then the power density distribution of the channel inversion layer sub-simulation region is determined based on the potential distribution, the electron collision probability model, the simulation time step of electron transport, and the carrier concentration in the inversion layer; if the sub-simulation region includes a drain sub-simulation region, then the characteristic decay length is determined based on the maximum potential in the channel inversion layer, the drain region length, and the applied bias voltage to the drain, and the power density distribution of the drain sub-simulation region is determined based on the maximum power density in the channel inversion layer sub-simulation region, the drain region width, the channel inversion layer width, and the characteristic decay length; if the sub-simulation region includes a source sub-simulation region, then the power density distribution of the source sub-simulation region is determined based on the effective electron mass, the electron saturation drift velocity, the carrier concentration in the source, and the electron mean free path.

[0088] Here, the simulation time step can refer to the minimum time interval set in a continuous system simulation. The carrier concentration can refer to the concentration of free electrons and free phonons within the inversion layer of a transistor.

[0089] Specifically, if the sub-simulation region includes the channel inversion layer sub-simulation region, the power density distribution of the channel inversion layer simulation region can be determined based on the potential distribution, electron collision probability model, simulation time step of electron transport, and carrier concentration within the inversion layer, using a calculation model of the power density generated by electrothermal activity in the channel inversion layer sub-simulation region. For example, based on the built-in electric field direction of each pn junction and the electric field direction of the channel inversion layer, if they are in the same direction, the potentials are added; if they are in opposite directions, the potentials are subtracted. Combining the potential distribution and the electron collision probability model equation in the channel inversion layer, the power density distribution generated by electrothermal activity in the channel inversion layer can be calculated.

[0090]

[0091] Δt is the simulated time step for electron transfer, and the power density has a maximum value Q at x = L. max .

[0092] Here, bias voltage can refer to the voltage at a certain point in the overall circuit relative to a certain reference point.

[0093] Specifically, if the sub-simulation region includes a drain (D) sub-simulation region, the characteristic decay length can be determined based on the maximum potential in the channel inversion layer, the drain region length, and the applied bias voltage to the drain, using a calculation model of the characteristic decay length. Furthermore, the power density distribution of the drain sub-simulation region can be determined based on the maximum power density in the channel inversion layer sub-simulation region, the drain region width, the channel inversion layer width, and the characteristic decay length, using a calculation model of the power density generated by electric heating in the drain sub-simulation region. For example, the aforementioned power density has a maximum value Q at x = L. max Based on the maximum power density mentioned above, the power density distribution in the drain region is calculated:

[0094]

[0095]

[0096]

[0097] See Figure 2 x and y represent the horizontal and vertical coordinates of a spatial location, x∈(0,L). d ), y∈(0, H d ). Figure 3 A schematic diagram of the power density distribution in the x-direction obtained from a power density calculation method is provided. (See also...) Figure 3 The peak value of Q max The meaning is the power density Q in the channel. c The maximum value at x = L, which is the power density at the channel-drain junction. H d Z and λ represent the width of the drain region and the width of the channel inversion layer, respectively. d The characteristic attenuation length is calculated using the following model:

[0098]

[0099] Among them, Ψ cmax V is the maximum potential in the inversion layer of the channel. d The bias voltage applied to the drain, L d is the length of the drain region.

[0100] Specifically, if the sub-simulation region includes a source (S) sub-simulation region, the power density distribution of the source sub-simulation region can be determined by calculating the power density generated by electrothermal activity in the source sub-simulation region based on the effective electron mass, electron saturated drift velocity, carrier concentration within the source, and electron mean free path. For example, the calculation model for the power density generated by electrothermal activity in the source sub-simulation region is as follows:

[0101]

[0102] Where m* represents the effective electron mass. Each parallel computing process saves the calculated power density distribution to computer memory.

[0103] S140. Based on the electron temperature distribution and phonon temperature distribution at the initial simulation time, determine the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, and phonon equilibrium energy density distribution for each sub-simulation region at the initial simulation time.

[0104] In this context, the initial condition at the initial simulation time can refer to the initial non-equilibrium energy density distribution being equal to the initial equilibrium energy density distribution.

[0105] Specifically, the initial energy density distribution f of electrons and phonons can be determined by calculation formula based on the electron and phonon temperature distributions at the initial simulation time. i eq (x,t) and f i (x,t), the calculation formula is as follows:

[0106] f i =C v T / N

[0107] Among them, f i For discrete energy density distribution, C v Let f be the heat capacity per unit volume, T be the absolute temperature, and N be the number of discrete directions. The initial energy density distribution f of electrons and phonons. i eq (x,t) and f i (x,t) is stored in the computer's memory.

[0108] S150. Based on the preset collision migration method, electroacoustic coupling coefficient, simulation time step of electron transport, simulation time step of phonon transport, electron relaxation time, phonon relaxation time, power density distribution, and electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time, a coupled Boltzmann transport model of electrons and phonons corresponding to each sub-simulation region is constructed.

[0109] The preset collision migration method can refer to the electron energy density distribution and phonon energy density distribution at the grid point in each sub-simulation region migrating to the neighboring grid point position in the direction of discrete grid point velocity within each simulation time step. After each migration, each grid point position will receive a total of m-1 electron energy density distributions and m-1 phonon energy density distributions from different velocity directions, where m is the number of discrete directions of grid point velocity.

[0110] Specifically, for each sub-simulation region, based on the preset collision migration method, electroacoustic coupling coefficient, simulation time step of electron transport, electron relaxation time, power density distribution, and the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time, a Boltzmann transport model corresponding to the electron in that sub-simulation region is constructed. The constructed Boltzmann transport model corresponding to the electron in that sub-simulation region is as follows:

[0111]

[0112] The subscript i (i = 0, 1, 2, ..., n) represents the discrete direction in the lattice model. The subscript el represents the electron. x is the spatial position of the lattice point. c eli This represents the component of the electron's lattice velocity *c* in the *i* direction. Δt el This represents the simulation time step for electron transport. The simulation time step is equal to the ratio of the spatial step size Δx to the lattice velocity c, i.e., Δt. el =Δx / c. f represents the non-equilibrium energy density distribution of electrons, f eq τ represents the equilibrium energy density distribution of electrons. el G represents the electronic relaxation time. ep denoted by . Q represents the power density distribution of heat generated by electricity.

[0113] For each sub-simulation region, based on the preset collision migration method, electro-acoustic coupling coefficient, simulation time step for phonon transport, phonon relaxation time, and the phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time, a Boltzmann transport model for phonons in that sub-simulation region is constructed. The constructed Boltzmann transport model for phonons in that sub-simulation region is as follows:

[0114]

[0115] The subscript i (i = 0, 1, 2, ..., n) represents the discrete direction in the lattice model. The subscript ph represents the phonon. x is the spatial location of the lattice point. c phi Δt represents the component of the lattice velocity c of the phonon in the i-direction. ph Phonon propagation is carried out using the simulation time step. The simulation time step is equal to the ratio of the spatial step Δx to the grid velocity c, i.e., Δt. ph =Δx / c. f represents the non-equilibrium energy density distribution of phonons, f eq This represents the equilibrium energy density distribution of phonons. ph G represents the phonon relaxation time. ep This represents the electroacoustic coupling coefficient.

[0116] It should be noted that each parallel computing task uses the lattice Boltzmann method to discretize and iteratively calculate the coupled Boltzmann transport model of electrons and phonons. This invention simulates heat generation and transfer processes by establishing a numerical solution of the coupled Boltzmann transport model of electrons and phonons using coupling terms, which can optimize the influence of electron-phonon interactions on the thermal transport process to a certain extent.

[0117] S160. Solve the coupled Boltzmann transport model of electrons and phonons to determine the non-equilibrium energy density distribution of electrons and phonons in each sub-simulation region at the next simulation time.

[0118] The next simulation time can refer to the time of the next simulation after the current simulation ends.

[0119] Specifically, by solving the coupled Boltzmann transport model of electrons and phonons, the non-equilibrium energy density distributions of electrons and phonons in each sub-simulation region at the next simulation time can be determined and stored in computer memory for use as initial information in the next simulation time.

[0120] S170. Based on the phonon unit volume heat capacity, the electron unit volume heat capacity, and the electron non-equilibrium state energy density distribution and phonon non-equilibrium state energy density distribution at the next simulation time, determine the electron equilibrium state energy density distribution, phonon equilibrium state energy density distribution, electron temperature distribution, phonon temperature distribution, and grid temperature distribution of each sub-simulation region at the next simulation time.

[0121] Specifically, Figure 4 A schematic diagram illustrating the time-varying temperature of a grid point within different sub-simulation regions of a simulation domain is presented. The coupled Boltzmann transport model of electrons and phonons can be iteratively calculated using power density distribution, updating the non-equilibrium energy density distributions of electrons and phonons at the grid point. The equilibrium energy density distributions of electrons and phonons at the grid point are then calculated and updated using the law of conservation of energy. Based on the Fermi-Dirac and Bose-Einstein relations, the electron and phonon temperatures at the next time step are calculated and updated. Finally, the weighted temperature at each grid point, i.e., the grid point temperature, is calculated based on the ratio of the individual unit volume heat capacity to the sum of the unit volume heat capacities of the two.

[0122] S180. Based on the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution of each sub-simulation region at the next simulation time, the coupled Boltzmann transport model is iteratively solved until the calculated grid temperature distribution satisfies the preset convergence condition.

[0123] Specifically, the coupled Boltzmann transport model can be iteratively solved based on the non-equilibrium energy density distribution of electrons, the equilibrium energy density distribution of electrons, the non-equilibrium energy density distribution of phonons, the equilibrium energy density distribution of phonons, the electron temperature distribution, and the phonon temperature distribution of each sub-simulation region at the next simulation time. That is, the process returns to steps S150-S170 to calculate the non-equilibrium energy density distribution of electrons, the non-equilibrium energy density distribution of phonons, the equilibrium energy density distribution of electrons, the equilibrium energy density distribution of phonons, the electron temperature distribution, the phonon temperature distribution, and the grid temperature distribution of each sub-simulation region at the next simulation time, until the calculated grid temperature distribution results converge, for example, the change in the grid temperature distribution tends to stabilize.

[0124] The technical solution of this invention divides the functional simulation region of a transistor to determine multiple sub-simulation regions corresponding to the transistor; obtains the doping concentration, applied transistor voltage, electron mean free path, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume, electron heat capacity per unit volume, and electron temperature distribution and phonon temperature distribution in each sub-simulation region at the initial simulation time; determines the power density distribution of each sub-simulation region based on the doping concentration, applied transistor voltage, electron mean free path, and electron saturation drift velocity, and determines the electro-acoustic coupling coefficient based on the electron heat capacity per unit volume and electron relaxation time; determines the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, and phonon equilibrium energy density distribution of each sub-simulation region at the initial simulation time based on the electron temperature distribution and phonon temperature distribution at the initial simulation time; and determines the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, and phonon equilibrium energy density distribution of each sub-simulation region at the initial simulation time based on a preset collision migration mode, electro-acoustic coupling coefficient, simulation time step of electron transport, simulation time step of phonon transport, electron relaxation time, phonon relaxation time, power density distribution, and electron non-equilibrium energy density distribution at the initial simulation time. Based on the energy density distributions of electrons, electrons in equilibrium, phonons in non-equilibrium, and phonons in equilibrium, as well as the electron and phonon temperature distributions, a coupled Boltzmann transport model for electrons and phonons is constructed for each sub-simulation region. The coupled Boltzmann transport model is solved to determine the electron and phonon non-equilibrium energy density distributions for each sub-simulation region at the next simulation time. Based on the phonon and electron heat capacities per unit volume, and the electron and phonon non-equilibrium energy density distributions at the next simulation time, a coupled Boltzmann transport model for electrons and phonons is constructed. The non-equilibrium energy density distribution is determined by analyzing the electron equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, phonon temperature distribution, and grid temperature distribution of each sub-simulation region at the next simulation time. Based on these distributions, the coupled Boltzmann transport model is iteratively solved until the calculated grid temperature distribution meets the preset convergence condition. This invention simulates the heat transfer process by establishing a numerical solution for the coupled Boltzmann transport model of electrons and phonons, which can optimize the influence of electron-phonon interactions on heat generation and heat transport processes to a certain extent.By establishing an electron collision probability model, the power density distribution of electrothermal heat generation was calculated. As a source term in the coupled Boltzmann transport model of electrons and phonons, it can completely and effectively describe the physical processes of electrothermal heat generation and heat transport to the outside of the boundary. This solves the problem of accurately describing heat generation and heat transport at the nanoscale and microscale, realizes efficient calculation of numerical heat transfer, and improves the accuracy and efficiency in calculating electroacoustic coupling power consumption and heat transfer in transistors.

[0125] Example 2

[0126] Figure 5 This is a flowchart of a transistor heat generation and heat transfer analysis method provided in Embodiment 2 of the present invention. Based on the above embodiments, this embodiment provides a detailed description of the effective relaxation time of phonons. Explanations of terms that are the same as or corresponding to those in the above embodiments are not repeated here. Figure 5 As shown, the method includes:

[0127] S210. Divide the functional simulation region of the transistor and determine multiple sub-simulation regions corresponding to the transistor, wherein the characteristic length of the transistor is at the nano-micro scale.

[0128] S220. Obtain the mean free path of electrons, doping concentration, transistor applied voltage, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume and electron heat capacity per unit volume, as well as the electron temperature distribution and phonon temperature distribution at the initial simulation time in each sub-simulation region.

[0129] S230. Based on doping concentration, transistor applied voltage, electron mean free path and electron saturation drift velocity, the power density distribution of each sub-simulation region is determined, and the electroacoustic coupling coefficient is determined based on electron unit volume heat capacity and electron relaxation time.

[0130] S240. Based on the electron temperature distribution and phonon temperature distribution at the initial simulation time, determine the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, and phonon equilibrium energy density distribution for each sub-simulation region at the initial simulation time.

[0131] S250, based on the correction model, doping concentration treatment model, defect treatment model and boundary effect treatment model, processes the phonon relaxation time to determine the effective phonon relaxation time.

[0132] Specifically, based on the calibration model, doping concentration treatment model, defect treatment model, and boundary effect treatment model, the phonon relaxation time is processed to determine the effective phonon relaxation time. This can include: determining the first phonon relaxation time based on the calibration model, the phonon relaxation time, and the ratio of the phonon mean free path to the characteristic length of the simulated region; determining the second phonon relaxation time affected by the doping concentration based on the doping concentration treatment model and the phonon angular frequency; determining the third phonon relaxation time affected by defects based on the defect treatment model, the phonon absolute temperature, and the phonon angular frequency; determining the fourth phonon relaxation time affected by the boundary based on the boundary effect treatment model and the phonon group velocity; and determining the effective phonon relaxation time based on the first, second, third, and fourth phonon relaxation times.

[0133] For example, Figure 6 A schematic diagram illustrating the relationship between relaxation time and material size, calculated using a phonon relaxation time correction model for a D2Q9 lattice, is presented. The functional region corresponding to each parallel computation process is processed; specifically, the phonon relaxation time is effectively corrected based on the correction model, using D2Q9 and D3Q... 15 Taking the calibration model of the lattice configuration LBM as an example:

[0134] D2Q9 LBM:

[0135] D3Q 15 LBM:

[0136] Where Kn is the ratio of the phonon mean free path to the characteristic length of the simulation region, and r represents different functional regions. For example, when the transistor characteristic length reaches the order of the phonon mean free path, the functional region corresponding to the sub-simulation region of each parallel computing process will be processed. The specific processing method is to adjust the phonon relaxation time of the bulk material according to the correction model: τ r =τ bulk / (1+2Kn r Effective correction of relaxation time is performed, and the corrected result is as follows: Figure 6 As shown. The effects of doping concentration, defects, and boundary effects on each sub-simulation region can be addressed by adding collision terms resulting from the corresponding influencing factors to the right-hand side of the Boltzmann transport model of phonons. The computational model for each collision term includes:

[0137] Affected by doping concentration:

[0138]

[0139] Affected by defects:

[0140]

[0141] Affected by boundary effects:

[0142]

[0143] Where A, B, ω0, Γ, and F are model parameters, and v g Let be the phonon group velocity. The effective relaxation time of the coupling is calculated according to the Mathiessen rule, and based on the first phonon relaxation time τ. r The relaxation time τ of the second phonon I The relaxation time τ of the third phonon D and the fourth phonon relaxation time τ B The effective relaxation time of the phonon is determined. The effective relaxation time of the phonon is determined as follows:

[0144] It should be noted that this invention further reduces computation time by dividing the region to be simulated into multiple sub-regions for parallel computation, while overcoming the shortcomings of quantum mechanical ab initio simulation, molecular dynamics simulation, and stochastic Monte Carlo simulation, such as long computation time, high computation cost, and limited computational scale.

[0145] S260. For each sub-simulation region, based on the preset collision migration method, electro-acoustic coupling coefficient, simulation time step of electron transport, electron relaxation time, power density distribution, and electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, electron temperature distribution and phonon temperature distribution at the initial simulation time, construct the Boltzmann transport model corresponding to the electron in the sub-simulation region.

[0146] S270. Based on the preset collision migration method, electro-acoustic coupling coefficient, simulation time step of phonon transport, effective relaxation time of phonons, and the phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution and phonon temperature distribution at the initial simulation time, the Boltzmann transport model corresponding to phonons in this sub-simulation region is constructed.

[0147] The effective phonon relaxation time can be defined as the relaxation time obtained by effectively correcting the phonon relaxation time according to the correction model. eff express.

[0148] Specifically, based on the preset collision migration method, electro-acoustic coupling coefficient, simulation time step of phonon transport, effective relaxation time of phonons, and the phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time, a Boltzmann transport model for phonons in this sub-simulation region is constructed. The constructed Boltzmann transport model for phonons in this sub-simulation region is as follows:

[0149]

[0150] S280. Solve the coupled Boltzmann transport model of electrons and phonons to determine the non-equilibrium energy density distribution of electrons and phonons in each sub-simulation region at the next simulation time.

[0151] S290. Based on the phonon unit volume heat capacity, the electron unit volume heat capacity, and the electron non-equilibrium state energy density distribution and phonon non-equilibrium state energy density distribution at the next simulation time, determine the electron equilibrium state energy density distribution, phonon equilibrium state energy density distribution, electron temperature distribution, phonon temperature distribution, and grid temperature distribution of each sub-simulation region at the next simulation time.

[0152] S291. Based on the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution of each sub-simulation region at the next simulation time, the coupled Boltzmann transport model is iteratively solved until the calculated grid temperature distribution satisfies the preset convergence condition.

[0153] Specifically, the coupled Boltzmann transport model can be iteratively solved based on the non-equilibrium energy density distribution of electrons, the equilibrium energy density distribution of electrons, the non-equilibrium energy density distribution of phonons, the equilibrium energy density distribution of phonons, the electron temperature distribution, and the phonon temperature distribution of each sub-simulation region at the next simulation time. That is, the process returns to steps S260-S290 to calculate the non-equilibrium energy density distribution of electrons, the non-equilibrium energy density distribution of phonons, the equilibrium energy density distribution of electrons, the equilibrium energy density distribution of phonons, the electron temperature distribution, the phonon temperature distribution, and the grid temperature distribution of each sub-simulation region at the next simulation time, until the calculated grid temperature distribution results converge, for example, the change in the grid temperature distribution tends to stabilize.

[0154] The technical solution of this invention obtains the relaxation time by effectively correcting the phonon relaxation time according to the correction model. Based on the effective model, it considers factors such as microscopic size effects, doping, defects and boundary effects, avoiding the inaccuracies caused by macroscopic calculation methods based on Fourier's heat conduction law, and improving the accuracy and efficiency in calculating the electroacoustic coupling power consumption and heat transfer problems in transistors.

[0155] Example 3

[0156] Figure 7 This is a schematic diagram of a transistor heat generation and heat transfer analysis device provided in Embodiment 3 of the present invention. Figure 7As shown, the device includes: a sub-simulation region determination module 310, a parameter acquisition module 320, a power density distribution determination module 330, an energy density distribution determination module 340, a coupled Boltzmann transport model construction module 350, a non-equilibrium energy density distribution determination module 360, an equilibrium energy density distribution determination module 370, and a coupled Boltzmann transport model iterative solution module 380.

[0157] The sub-simulation region determination module 310 is used to divide the functional simulation region of the transistor and determine multiple sub-simulation regions corresponding to the transistor, wherein the characteristic length of the transistor is at the nano-micro scale; the parameter acquisition module 320 is used to acquire the doping concentration, transistor applied voltage, electron mean free path, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume, and electron heat capacity per unit volume, as well as the electron temperature distribution and phonon temperature distribution at the initial simulation time in each sub-simulation region; the power density distribution determination module 330 is used to determine each sub-simulation region based on the doping concentration, transistor applied voltage, electron mean free path, and electron saturation drift velocity. The power density distribution of the domain is determined, and the electro-acoustic coupling coefficient is determined based on the electron unit volume heat capacity and electron relaxation time; the energy density distribution determination module 340 is used to determine the electron non-equilibrium state energy density distribution, electron equilibrium state energy density distribution, phonon non-equilibrium state energy density distribution, and phonon equilibrium state energy density distribution of each sub-simulation region based on the electron temperature distribution and phonon temperature distribution at the initial simulation time; the coupled Boltzmann transport model construction module 350 is used to determine the electron non-equilibrium state energy density distribution, electron equilibrium state energy density distribution, phonon non-equilibrium state energy density distribution, and phonon equilibrium state energy density distribution of each sub-simulation region at the initial simulation time based on the preset collision migration mode, electro-acoustic coupling coefficient, electron transport simulation time step, phonon transport simulation time step, electron relaxation time, phonon relaxation time, power density distribution, and the initial... The simulation process includes calculating the non-equilibrium energy density distribution of electrons, the equilibrium energy density distribution of electrons, the non-equilibrium energy density distribution of phonons, the equilibrium energy density distribution of phonons, the electron temperature distribution, and the phonon temperature distribution at each simulation time. A coupled Boltzmann transport model for electrons and phonons is constructed for each sub-simulation region. A non-equilibrium energy density distribution determination module 360 ​​solves the coupled Boltzmann transport model for electrons and phonons to determine the non-equilibrium energy density distribution of electrons and phonons at the next simulation time. An equilibrium energy density distribution determination module 370 determines the non-equilibrium energy density distribution based on the phonon heat capacity per unit volume, the electron heat capacity per unit volume, and the temperature distribution at the next simulation time. The non-equilibrium energy density distributions of electrons and phonons are used to determine the equilibrium energy density distributions of electrons and phonons, as well as the electron temperature distribution, phonon temperature distribution, and grid temperature distribution for each sub-simulation region at the next simulation time. A coupled Boltzmann transport model iterative solution module 380 is used to iteratively solve the coupled Boltzmann transport model based on these distributions for each sub-simulation region at the next simulation time, until the calculated grid temperature distribution meets the preset convergence conditions.

[0158] The technical solution of this invention divides the functional simulation region of a transistor to determine multiple sub-simulation regions corresponding to the transistor; obtains the doping concentration, applied transistor voltage, electron mean free path, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume, electron heat capacity per unit volume, and electron temperature distribution and phonon temperature distribution in each sub-simulation region at the initial simulation time; determines the power density distribution of each sub-simulation region based on the doping concentration, applied transistor voltage, electron mean free path, and electron saturation drift velocity, and determines the electro-acoustic coupling coefficient based on the electron heat capacity per unit volume and electron relaxation time; determines the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, and phonon equilibrium energy density distribution of each sub-simulation region at the initial simulation time based on the electron temperature distribution and phonon temperature distribution at the initial simulation time; and determines the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, and phonon equilibrium energy density distribution of each sub-simulation region at the initial simulation time based on a preset collision migration mode, electro-acoustic coupling coefficient, simulation time step of electron transport, simulation time step of phonon transport, electron relaxation time, phonon relaxation time, power density distribution, and electron non-equilibrium energy density distribution at the initial simulation time. Based on the energy density distributions of electrons, electrons in equilibrium, phonons in non-equilibrium, and phonons in equilibrium, as well as the electron and phonon temperature distributions, a coupled Boltzmann transport model for electrons and phonons is constructed for each sub-simulation region. The coupled Boltzmann transport model is solved to determine the electron and phonon non-equilibrium energy density distributions for each sub-simulation region at the next simulation time. Based on the phonon and electron heat capacities per unit volume, and the electron and phonon non-equilibrium energy density distributions at the next simulation time, a coupled Boltzmann transport model for electrons and phonons is constructed. The non-equilibrium energy density distribution is determined by analyzing the electron equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, phonon temperature distribution, and grid temperature distribution of each sub-simulation region at the next simulation time. Based on these distributions, the coupled Boltzmann transport model is iteratively solved until the calculated grid temperature distribution meets the preset convergence condition. This invention simulates heat generation and transfer processes by establishing a numerical solution for the coupled Boltzmann transport model of electrons and phonons, which can optimize the influence of electron-phonon interactions on heat generation and transport processes to a certain extent.By establishing an electron collision probability model, the power density distribution of electrothermal heat generation was calculated. As a source term in the coupled Boltzmann transport model of electrons and phonons, it can completely and effectively describe the physical processes of electrothermal heat generation and heat transport to the outside of the boundary. This solves the problem of accurately describing heat generation and heat transport at the nanoscale and microscale, realizes efficient calculation of numerical heat transfer, and improves the accuracy and efficiency in calculating electroacoustic coupling power consumption and heat transfer in transistors.

[0159] Optionally, the power density distribution determination module 330 includes:

[0160] The current density equation establishment submodule is used to establish the current density equation and charge conservation relationship for each sub-simulation region based on the doping concentration, transistor applied voltage and electron saturation drift velocity.

[0161] The current density distribution submodule is used to determine the current density distribution in the sub-simulation region based on the current density equation and the charge conservation relationship;

[0162] The potential distribution determination submodule is used to determine the potential distribution in the sub-simulation region based on the current density distribution and the differential relationship between current and voltage.

[0163] The electron collision probability model construction submodule is used to construct an electron collision probability model based on the electron mean free path and the channel inversion layer length.

[0164] The power density distribution determination submodule is used to determine the power density distribution of the sub-simulation region based on the potential distribution and the electron collision probability model.

[0165] Optionally, the power density distribution determination submodule is specifically used for:

[0166] If the sub-simulation region includes the channel inversion layer sub-simulation region, the power density distribution of the channel inversion layer simulation region is determined based on the potential distribution, electron collision probability model, simulation time step of electron transport, and carrier concentration in the inversion layer.

[0167] If the sub-simulation region includes the drain sub-simulation region, the characteristic decay length is determined based on the maximum potential in the channel inversion layer, the drain region length, and the applied bias voltage to the drain. The power density distribution of the drain sub-simulation region is determined based on the maximum power density in the channel inversion layer sub-simulation region, the drain region width, the channel inversion layer width, and the characteristic decay length.

[0168] If the sub-simulation region includes the source pole simulation region, the power density distribution of the source pole simulation region is determined based on the effective electron mass, electron saturation drift velocity, carrier concentration in the source, and electron mean free path.

[0169] Optionally, the coupled Boltzmann transport model building module 350 includes:

[0170] The electronic Boltzmann transport model construction submodule is used to construct the Boltzmann transport model corresponding to the electron in each sub-simulation region based on the preset collision migration method, electro-acoustic coupling coefficient, simulation time step of electron transport, electron relaxation time, power density distribution, and electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, electron temperature distribution and phonon temperature distribution at the initial simulation time.

[0171] The phonon Boltzmann transport model construction submodule is used to construct the Boltzmann transport model corresponding to the phonons in each sub-simulation region based on the preset collision migration mode, electro-acoustic coupling coefficient, simulation time step of phonon transport, phonon relaxation time, and phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution and phonon temperature distribution at the initial simulation time.

[0172] Optionally, the device may also include:

[0173] The phonon effective relaxation time determination module is used to process the phonon relaxation time based on the correction model, doping concentration processing model, defect processing model and boundary effect processing model to determine the phonon effective relaxation time.

[0174] The phonon Boltzmann transport model construction submodule is specifically used for:

[0175] Based on the preset collision migration method, electro-acoustic coupling coefficient, simulation time step of phonon transport, effective relaxation time of phonons, and the phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution and phonon temperature distribution at the initial simulation time, the Boltzmann transport model corresponding to phonons in this sub-simulation region is constructed.

[0176] Optionally, the phonon effective relaxation time determination module is specifically used for:

[0177] The first phonon relaxation time is determined based on the correction model, phonon relaxation time, and the ratio of phonon mean free path to the characteristic length of the simulated region. The second phonon relaxation time, affected by doping concentration, is determined based on the doping concentration treatment model and phonon angular frequency. The third phonon relaxation time, affected by defects, is determined based on the defect treatment model, phonon absolute temperature, and phonon angular frequency. The fourth phonon relaxation time, affected by boundaries, is determined based on the boundary effect treatment model and phonon group velocity. The effective phonon relaxation time is determined based on the first, second, third, and fourth phonon relaxation times.

[0178] Optionally, the collision migration method is as follows: the electron energy density distribution and phonon energy density distribution at the grid point in each sub-simulation region migrate to the neighboring grid point position in the direction of the discrete grid point velocity within each simulation time step, and after each migration, each grid point position will receive a total of m-1 electron energy density distributions and m-1 phonon energy density distributions from different velocity directions, where m is the number of discrete directions of grid point velocity.

[0179] The transistor heat generation and heat transfer analysis device provided in the embodiments of the present invention can execute the transistor heat generation and heat transfer analysis method provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the method execution.

[0180] Example 4

[0181] Figure 8 A schematic diagram of the structure of an electronic device 10 that can be used to implement embodiments of the present invention is provided. 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 processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0182] like Figure 8 As shown, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 or a random access memory (RAM) 13, communicatively connected to the at least one processor 11. The memory stores computer programs executable by the at least one processor. The processor 11 can perform various appropriate actions and processes based on the computer program stored in the ROM 12 or loaded from storage unit 18 into the RAM 13. The RAM 13 may also store various programs and data required for the operation of the electronic device 10. The processor 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0183] Multiple components in electronic device 10 are connected to I / O interface 15, including: input unit 16, such as keyboard, mouse, etc.; output unit 17, such as various types of displays, speakers, etc.; storage unit 18, such as disk, optical disk, etc.; and communication unit 19, such as network card, modem, wireless transceiver, etc. Communication unit 19 allows electronic device 10 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0184] Processor 11 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. Processor 11 performs the various methods and processes described above, such as transistor heat generation and heat transfer analysis methods.

[0185] In some embodiments, the transistor heat generation and heat transfer analysis method may be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 18. In some embodiments, part or all of the computer program may be loaded and / or installed on electronic device 10 via ROM 12 and / or communication unit 19. When the computer program is loaded into RAM 13 and executed by processor 11, one or more steps of the transistor heat generation and heat transfer analysis method described above may be performed. Alternatively, in other embodiments, processor 11 may be configured to perform the transistor heat generation and heat transfer analysis method by any other suitable means (e.g., by means of firmware).

[0186] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0187] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0188] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0189] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0190] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or computing systems that include middleware components (e.g., application servers), or computing systems that include frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0191] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0192] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0193] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method of transistor heat generation and heat transfer analysis, characterized by, include: The functional simulation region of the transistor is divided to determine multiple sub-simulation regions corresponding to the transistor, wherein the feature length of the transistor is at the nano-micro scale; Obtain the mean free path of electrons, doping concentration, transistor applied voltage, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume and electron heat capacity per unit volume, as well as the electron temperature distribution and phonon temperature distribution at the initial simulation time in each of the sub-simulation regions. Based on the doping concentration, the applied voltage of the transistor, the mean free path of the electrons, and the electron saturation drift velocity, the power density distribution of each of the sub-simulation regions is determined, and the electroacoustic coupling coefficient is determined based on the electron unit volume heat capacity and the electron relaxation time. Based on the electron temperature distribution and phonon temperature distribution at the initial simulation time, the electron non-equilibrium state energy density distribution, electron equilibrium state energy density distribution, phonon non-equilibrium state energy density distribution, and phonon equilibrium state energy density distribution of each sub-simulation region at the initial simulation time are determined. Based on the preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step of electron transport, the simulation time step of phonon transport, the electron relaxation time, the phonon relaxation time, the power density distribution, and the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time, a coupled Boltzmann transport model of electrons and phonons corresponding to each sub-simulation region is constructed. The coupled Boltzmann transport model of electrons and phonons is solved to determine the non-equilibrium energy density distribution of electrons and the non-equilibrium energy density distribution of phonons in each sub-simulation region at the next simulation time. Based on the phonon unit volume heat capacity, the electron unit volume heat capacity, and the electron non-equilibrium energy density distribution and phonon non-equilibrium energy density distribution at the next simulation time, determine the electron equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, phonon temperature distribution, and grid temperature distribution of each sub-simulation region at the next simulation time. Based on the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution of each sub-simulation region at the next simulation time, the coupled Boltzmann transport model is iteratively solved until the calculated grid temperature distribution satisfies the preset convergence condition.

2. The method of claim 1, wherein, The determination of the power density distribution of each sub-simulation region based on the doping concentration, the applied voltage of the transistor, the electron mean free path, and the electron saturation drift velocity includes: For each sub-simulation region, a current density equation and a charge conservation relationship are established based on the doping concentration, the applied voltage of the transistor, and the electron saturation drift velocity; The current density distribution in the sub-simulation region is determined based on the current density equation and the charge conservation relationship. The potential distribution in the sub-simulation region is determined based on the current density distribution and the differential relationship between current and voltage. An electron collision probability model is constructed based on the electron mean free path and the channel inversion layer length. Based on the potential distribution and the electron collision probability model, the power density distribution of the sub-simulation region is determined.

3. The method of claim 2, wherein, Determining the power density distribution of the sub-simulation region based on the potential distribution and the electron collision probability model includes: If the sub-simulation region includes the channel inversion layer sub-simulation region, then the power density distribution of the channel inversion layer simulation region is determined based on the potential distribution, the electron collision probability model, the simulation time step of electron transport, and the carrier concentration in the inversion layer. If the sub-simulation region includes the drain sub-simulation region, the characteristic decay length is determined based on the maximum potential in the channel inversion layer, the drain region length, and the applied bias voltage to the drain. The power density distribution of the drain sub-simulation region is determined based on the maximum power density in the channel inversion layer sub-simulation region, the drain region width, the channel inversion layer width, and the characteristic decay length. If the sub-simulation region includes the source pole simulation region, the power density distribution of the source pole simulation region is determined based on the effective electron mass, electron saturation drift velocity, carrier concentration in the source, and electron mean free path.

4. The method of claim 1, wherein, The method constructs a coupled Boltzmann transport model for electrons and phonons for each sub-simulation region based on a preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step for electron transport, the simulation time step for phonon transport, the electron relaxation time, the phonon relaxation time, the power density distribution, and the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time. For each of the sub-simulation regions, a Boltzmann transport model for electrons in that sub-simulation region is constructed based on a preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step of electron transport, the electron relaxation time, the power density distribution, and the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time. For each sub-simulation region, a Boltzmann transport model for phonons in that sub-simulation region is constructed based on a preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step of phonon transport, the phonon relaxation time, and the phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time.

5. The method of claim 4, wherein, The method further includes: Based on the correction model, doping concentration processing model, defect processing model and boundary effect processing model, the phonon relaxation time is processed to determine the effective phonon relaxation time. The Boltzmann transport model for phonons in the sub-simulation region is constructed based on a preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step of phonon transport, the phonon relaxation time, and the phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time. This includes: Based on the preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step of phonon transport, the effective relaxation time of phonons, and the phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time, a Boltzmann transport model corresponding to phonons in the sub-simulation region is constructed.

6. The method of claim 5, wherein, The process of processing the phonon relaxation time based on the correction model, doping concentration processing model, defect processing model, and boundary effect processing model to determine the effective phonon relaxation time includes: The first phonon relaxation time is determined based on the calibration model, phonon relaxation time, and the ratio of phonon mean free path to the characteristic length of the simulated region. Based on the doping concentration processing model and phonon angular frequency, the relaxation time of the second phonon affected by the doping concentration is determined. Based on the defect handling model, phonon absolute temperature and phonon angular frequency, the relaxation time of the third phonon affected by the defect is determined. Based on the boundary effect processing model and phonon group velocity, the relaxation time of the fourth phonon affected by the boundary is determined. The effective relaxation time of a phonon is determined based on the relaxation time of the first phonon, the relaxation time of the second phonon, the relaxation time of the third phonon, and the relaxation time of the fourth phonon.

7. The method according to any one of claims 1 to 6, characterized in that, The collision migration method is as follows: the electron energy density distribution and phonon energy density distribution at the grid point in each sub-simulation region migrate to the neighboring grid point position in the direction of discrete grid point velocity within each corresponding simulation time step, and after each migration, each grid point position will receive a total of m-1 electron energy density distributions and m-1 phonon energy density distributions from different velocity directions, where m is the number of discrete directions of grid point velocity.

8. A transistor heat generation and heat transfer analysis device, characterized by, include: The sub-simulation region determination module is used to divide the functional simulation region of the transistor and determine multiple sub-simulation regions corresponding to the transistor, wherein the feature length of the transistor is at the nano-micro scale. The parameter acquisition module is used to acquire the doping concentration, transistor applied voltage, electron mean free path, electron saturation drift velocity, electron relaxation time, phonon relaxation time, phonon heat capacity per unit volume and electron heat capacity per unit volume in each of the sub-simulation regions, as well as the electron temperature distribution and phonon temperature distribution at the initial simulation time. A power density distribution determination module is used to determine the power density distribution of each of the sub-simulation regions based on the doping concentration, the applied voltage of the transistor, the mean free path of the electrons, and the saturation drift velocity of the electrons, and to determine the electroacoustic coupling coefficient based on the electron unit volume heat capacity and the electron relaxation time. The energy density distribution determination module is used to determine the non-equilibrium energy density distribution of electrons, the equilibrium energy density distribution of electrons, the non-equilibrium energy density distribution of phonons, and the equilibrium energy density distribution of phonons in each sub-simulation region at the initial simulation time, based on the electron temperature distribution and the phonon temperature distribution at the initial simulation time. The coupled Boltzmann transport model construction module is used to construct the coupled Boltzmann transport model of electrons and phonons for each sub-simulation region based on the preset collision migration method, the electro-acoustic coupling coefficient, the simulation time step of electron transport, the simulation time step of phonon transport, the electron relaxation time, the phonon relaxation time, the power density distribution, and the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution at the initial simulation time. The non-equilibrium energy density distribution determination module is used to solve the coupled Boltzmann transport model of electrons and phonons, and determine the non-equilibrium energy density distribution of electrons and phonons in each sub-simulation region at the next simulation time. The equilibrium energy density distribution determination module is used to determine the electronic equilibrium energy density distribution, phonon equilibrium energy density distribution, electronic temperature distribution, phonon temperature distribution, and grid temperature distribution of each sub-simulation region at the next simulation time, based on the phonon unit volume heat capacity, the electron unit volume heat capacity, and the electronic non-equilibrium energy density distribution and phonon non-equilibrium energy density distribution at the next simulation time. The coupled Boltzmann transport model iterative solution module is used to iteratively solve the coupled Boltzmann transport model based on the electron non-equilibrium energy density distribution, electron equilibrium energy density distribution, phonon non-equilibrium energy density distribution, phonon equilibrium energy density distribution, electron temperature distribution, and phonon temperature distribution of each sub-simulation region at the next simulation time, until the calculated grid temperature distribution satisfies the preset convergence condition.

9. An electronic device, comprising: The electronic device includes: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor to enable the at least one processor to perform the transistor heat generation and heat transfer analysis method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed by a processor, implement the transistor heat generation and heat transfer analysis method according to any one of claims 1-7.

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