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CN109543204B - Electric heating integrated analysis method for semiconductor device under human body electrostatic action - Google Patents

Electric heating integrated analysis method for semiconductor device under human body electrostatic action Download PDF

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CN109543204B
CN109543204B CN201710867700.4A CN201710867700A CN109543204B CN 109543204 B CN109543204 B CN 109543204B CN 201710867700 A CN201710867700 A CN 201710867700A CN 109543204 B CN109543204 B CN 109543204B
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丁大志
何云峰
姚猛
籍宇豪
陈如山
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Nanjing University of Science and Technology
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Abstract

The invention discloses an electric-heating integrated analysis method for a semiconductor device under the action of human body static electricity. The method comprises the following steps: 1) establishing a solving model of the semiconductor device, and subdividing the model by adopting a curved hexahedron to obtain structural information of the model; 2) connecting the semiconductor device into a human body electrostatic discharge equivalent model circuit to realize the combined solution of the semiconductor and an external circuit, listing and solving required KVL and KCL equations; 3) analyzing the electric heating characteristics in the semiconductor device to obtain the voltage, current distribution and temperature distribution in the semiconductor device at the current moment; 4) substituting the obtained current value inside the semiconductor device into the equation 2), and if the convergence accuracy of an external circuit is met, outputting the voltage, the current and the temperature value of the semiconductor device at the moment; and if not, continuing to perform iterative solution. The invention connects the semiconductor device with the human body static external circuit model, and can quickly obtain the electric field distribution and the temperature distribution in the device.

Description

Semiconductor device electric heating integrated analysis method under human body electrostatic action
Technical Field
The invention relates to the technical field of transient electrothermal effect analysis of semiconductor devices, in particular to an electrothermal integration analysis method of a semiconductor device under the action of human body static electricity.
Background
Electromagnetic pulses are a transient electromagnetic phenomenon. After the static electricity of human body is injected into the integrated circuit, the electric breakdown or the thermal breakdown of the circuit can be caused, and even the equipment can be completely damaged. Integrated circuits and electronic devices are mainly composed of semiconductor devices, and the integration degree of the circuits is continuously improved and is more and more sensitive to human static electricity. If electrostatic discharge occurs on the electronic component, damage to the electronic component may result; the light breaks down the diode and the heavy damages the integrated circuit. Active components in the circuit, particularly semiconductor devices, are susceptible to absorption of radiated electromagnetic energy and to electrical stress, which can cause severe increases in current and temperature within the device, leading to failure or even damage. In order to take effective measures to prevent electronic equipment or electronic systems from being damaged by human static electricity, the software simulation prediction of semiconductor devices, particularly field effect transistors widely applied, has important theoretical significance and practical value.
The numerical simulation of the physical model of the semiconductor device can accurately simulate the electric field distribution and the heat distribution in the semiconductor device, and provides effective guidance for electromagnetic protection. The simulation of semiconductor devices is divided into models, which mainly include a classical model, a semi-classical model and a quantum model (He, Wei Tong Li. computer simulation method of semiconductor devices [ M ]. Beijing: scientific Press, 1989.12). The classical model is just to solve a drift-diffusion equation set, and in consideration of the characteristics that electrical parameters in electromagnetic pulses are time-varying functions and thermal model time continuity, a time domain method is more suitable, and FDTD and FEM are more commonly used. However, due to the Yee grid characteristic of FDTD, there is a limit in simulating a model having a complicated structure. When the FEM is applied to the time domain, each time step involves the solution of a linear equation set, the calculation amount is huge, and the time is wasted.
Disclosure of Invention
The invention aims to provide a method for analyzing the electric-heating integration of a semiconductor device under the action of human body static electricity, which is a method for analyzing the electric characteristics of the semiconductor device after the semiconductor device is combined with a human body static electricity external circuit so as to quickly obtain the electric field distribution and the temperature distribution in the device.
The technical solution for realizing the purpose of the invention is as follows: a semiconductor device electric heating integration analysis method under human body electrostatic action comprises the following steps:
step one, establishing a solving model of a semiconductor device, and subdividing the model by adopting a curved hexahedron to obtain structural information of the model, wherein the structural information comprises hexahedron unit information and node information;
secondly, connecting the semiconductor device into a human body electrostatic discharge equivalent model circuit to realize the combined solution of the semiconductor and an external circuit, listing required KVL and KCL equations, and solving the equations by using a Newton iteration method;
thirdly, analyzing the electric heating characteristics in the semiconductor device to obtain the voltage, current distribution and temperature distribution in the semiconductor device at the current moment;
and step four, substituting the obtained current value inside the semiconductor device into the equation in the step two, and checking whether the convergence precision of the external circuit solving is met: if yes, outputting the voltage, the current and the temperature value inside the semiconductor device; if not, repeating the second, third and fourth steps until the convergence accuracy is satisfied.
Further, in the first step, the model is subdivided by adopting a curved hexahedron, specifically: and subdividing a physical model of the semiconductor device by adopting ANSYS.
Further, in the third step, the electric heating characteristics inside the semiconductor device are analyzed to obtain the voltage, current distribution and temperature distribution inside the semiconductor device at the present moment, specifically as follows:
(1) starting from a drift-diffusion equation set consisting of a current density equation, a current continuity equation and a Poisson equation, solving to obtain the electric field and current distribution of each node, and obtaining the power density of each node according to the electric field and current distribution;
(2) establishing a heat conduction equation of the semiconductor device, substituting the power density as a heat source item into the heat conduction equation, and solving to obtain the temperature distribution of each node;
(3) according to the obtained temperature, updating parameters related to the temperature in the drift-diffusion equation in the step (1), and calculating the electric field distribution and the current distribution of each node again;
(4) and (4) circulating the steps (1) to (3) until the drift-diffusion equation reaches a convergence condition, wherein the voltage distribution, the current distribution and the temperature distribution at the moment are the electric heating distribution result at the current moment.
Further, in the step (1), an electric field and current distribution of each node are obtained by solving a drift-diffusion equation system composed of a current density equation, a current continuity equation and a poisson equation, and power density of each node is obtained from the electric field and current distribution, specifically as follows:
the current continuity equation and the Poisson equation are normalized by a normalization factor by taking the carrier concentration and the potential as variables, and the normalized equation is as follows:
poisson equation:
Figure BDA0001416484590000021
in the above formula (1), Γ is net doping concentration,
Figure BDA0001416484590000022
is the potential, n is the electron concentration, p is the hole concentration;
electron current density equation:
Figure BDA0001416484590000031
in the above formula (2), J n Is the electron current density, μ n Is the electron mobility;
hole current density equation:
Figure BDA0001416484590000032
in the above formula (3), J p Is the electron current density, μ p Is the electron mobility;
electron current continuity equation:
Figure BDA0001416484590000033
hole current continuity equation:
Figure BDA0001416484590000034
in the formulas (4) and (5), G is an avalanche generation term, an Okuto-Crowell model is adopted, and R is a carrier recombination rate;
performing time difference on the equations (4) and (5) by using a backward Euler method to obtain:
Figure BDA0001416484590000035
Figure BDA0001416484590000036
in the formulae (6) and (7), n m ,p m Is the concentration value of electrons and holes at the present time, n m-1 ,p m-1 The concentration values of electrons and holes at the previous time,
Figure BDA0001416484590000037
for the potential at the present time, the superscript m represents the present time, the superscript m-1 represents the previous time, and Δ t represents the time difference;
performing Galerkin test on the Poisson equation (1), the equation (6) and the equation (7) respectively, shifting terms to enable the right side of the equation to be 0, then performing Taylor expansion to remove nonlinearity and coupling treatment, obtaining an equation form capable of realizing solution by programming through derivation, and obtaining the electron concentration, the hole concentration and the potential at the current moment;
obtaining the electric field intensity of each point in the semiconductor device from the electron concentration, the hole concentration and the electric potential
Figure BDA0001416484590000038
And current density
Figure BDA0001416484590000039
Power density
Figure BDA00014164845900000310
Further, in the step (2), a heat conduction equation of the semiconductor device is established, the power density is substituted into the heat conduction equation as a heat source term, and the temperature distribution of each node is obtained by solving, specifically as follows:
in the solving process of the internal heat distribution of the semiconductor device, the material density, the heat conductivity coefficient and the constant pressure specific heat are set as fixed values, the power density is used as a heat source, and the formula is substituted into the formula:
Figure BDA0001416484590000041
in the formula, T is the temperature of each node;
Figure BDA0001416484590000042
k t is the thermal conductivity of the material, p m Is the density of the material, c m Is the constant specific heat of the material; p d Is the power density of the internal heat source;
solving equation (8) yields the temperature at each point inside the semiconductor device.
Further, in the above (4), the convergence condition of the drift-diffusion equation is that a relative error between the variable carrier concentration and the potential in two iterations is less than 1 × 10 -4 。
Compared with the prior art, the invention has the following remarkable advantages: (1) the semiconductor device is combined with a human body static external circuit, and the electrical characteristics are solved by respectively carrying out a Newton iteration method, so that the method has practical significance; (2) the SETD adopts a curved hexahedron subdivision, the modeling is flexible, the subdivision is convenient, a specific orthogonal polynomial is used as a basis function, and the calculation error is exponentially reduced along with the increase of the polynomial order; (3) the electrical characteristic and the thermal characteristic of the semiconductor device are analyzed integrally, the semiconductor device is not cracked, and the mutual influence among electric heat can be related; (4) the matrix equation formed by the heat conduction equation has good performance, direct inversion is quite convenient, and the temperature distribution in the device can be quickly obtained by using a direct solution method.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a flow chart of the semiconductor and external circuit joint solution.
FIG. 2 is a schematic diagram of an electrostatic equivalent circuit of a human body.
Fig. 3 is a schematic diagram of a PIN tube structure.
FIG. 4 is a graph showing the voltage curve of the semiconductor device at 200V.
Fig. 5 is a graph showing the current curve of the semiconductor device at 200V.
FIG. 6 is a graph showing the change of the maximum temperature with time at 200V.
FIG. 7 is a graph showing the spatial distribution of temperature at 200V when the melting point is reached.
Fig. 8 is a graph showing the voltage curve of the semiconductor device at 500V.
Fig. 9 is a graph showing the current curve of the semiconductor device at 500V.
FIG. 10 is a graph of the maximum temperature with time at 500V.
FIG. 11 is a graph showing the spatial distribution of temperature at 500V when the melting point is reached.
Detailed Description
Referring to fig. 1, the semiconductor device electric heating integration analysis method under human body static electricity of the present invention connects the semiconductor device with a human body static electricity external circuit model, fully understands the physical mechanism of human body static electricity on the semiconductor device, and comprises the following specific steps:
step one, establishing a solving model of a semiconductor device, and subdividing the model by adopting a curved hexahedron to obtain structural information of the model, wherein the structural information comprises hexahedron unit information and node information; the method specifically comprises the following steps: and subdividing a physical model of the semiconductor device by adopting ANSYS.
Secondly, connecting the semiconductor device into a human body electrostatic discharge equivalent model circuit, realizing the combined solution of the semiconductor and an external circuit, listing required KVL and KCL equations, and solving the equations by using a Newton iteration method;
firstly, a semiconductor device is combined with an external circuit of a human body electrostatic model to carry out combined solution (see figure 2), a circuit equation of the combination of the semiconductor device and the external circuit under different human body electrostatic conditions is solved by utilizing a Newton iteration method through analysis of field-circuit integrated coupling, and then analysis of electric-thermal integration of the semiconductor device under the human body electrostatic conditions is obtained, and a circuit schematic diagram is shown in figure 2.
Adding a semiconductor device (taking physical model of PIN tube as an example, see FIG. 3) on the human body electrostatic discharge model, and defining the voltage and current on the semiconductor device as V D And I D According to the above circuit structureKnown as V D ＝U b ，
Figure BDA0001416484590000051
I D ＝f t (V D ). According to kirchhoff's theorem, a circuit equation can be obtained:
Figure BDA0001416484590000052
in the above formula f (V) D ) Representing non-linear relationship of voltage and current in semiconductor
After finishing deformation, the following can be obtained:
Figure BDA0001416484590000061
in the above formula, the superscript t represents the current time, the superscript t-1 represents the previous time, and Δ t represents the time difference.
Solving the six equations by using a Newton iteration method, and continuously updating the voltage and current values at the current moment until convergence. The method comprises the following steps:
Figure BDA0001416484590000062
solving the following formulas by using a Newton iteration method:
Figure BDA0001416484590000071
through the derivation, the form of the equation which is easy to realize solution by programming is obtained:
Figure BDA0001416484590000072
for (18), when f (V) is involved D t ) When deriving (c), the derivative is approximated by a numerical solution of two similar voltages:
Figure BDA0001416484590000073
I D1 ，I D0 for applying a voltage V across the semiconductor device D1 And V D0 The resulting current value is calculated. Therefore, at this time, it is necessary to calculate the electrothermal characteristics inside the semiconductor device, and a specific method is as follows.
Thirdly, analyzing the internal electric heating characteristics of the semiconductor device to obtain the voltage, current distribution and temperature distribution of the semiconductor device at the current moment, wherein the method specifically comprises the following steps:
(1) starting from a drift-diffusion equation set consisting of a current density equation, a current continuity equation and a Poisson equation, solving to obtain the electric field and current distribution of each node, and obtaining the power density of each node according to the electric field and current distribution;
(2) establishing a heat conduction equation of the semiconductor device, substituting the power density as a heat source item into the heat conduction equation, and solving to obtain the temperature distribution of each node;
(3) according to the obtained temperature, updating the parameters related to the temperature in the drift-diffusion equation in the step (1), and calculating the electric field distribution and the current distribution of each node again;
(4) and (4) circulating the steps (1) to (3) until the drift-diffusion equation reaches a convergence condition, wherein the voltage distribution, the current distribution and the temperature distribution at the moment are the electric heating distribution result at the current moment.
In the above step (1), the electric field and the current distribution of each node are obtained by solving from a current density equation, a current continuity equation and a poisson equation, and the power density of each node is obtained from the electric field and the current distribution, which is specifically as follows:
solving the transient drift-shift diffusion equation by a coupling method, namely simultaneously solving a Poisson equation and a current continuity equation by using the carrier concentration n, p and the potential
Figure BDA0001416484590000081
As variables, the current continuity equation and the poisson equation are normalized by a normalization factor, and the normalized equations are as follows:
the transient model equation of the semiconductor device includes:
normalized poisson equation:
Figure BDA0001416484590000082
in the above formula (21), Γ represents net doping concentration,
Figure BDA0001416484590000083
for potential, n is the electron concentration and p is the hole concentration.
Normalized electron current density equation:
Figure BDA0001416484590000084
in the above formula (22), J p Is the electron current density, μ p Is the electron mobility;
normalized hole current density equation:
Figure BDA0001416484590000085
in the above formula (23), J p Is the electron current density, μ p Is the electron mobility;
normalized electron current continuity equation:
Figure BDA0001416484590000091
normalized hole current continuity equation:
Figure BDA0001416484590000092
g is an Avalanche generation term, and an Okuto-Crowell model (Y.Okuto and C.R.Crowell, "Threshold Energy efficiency on Avalanche BreakDown in Semiconductor Junctions", Solid-State Electronics, vol.18, pp.161-168,1975) is adopted, and R is a carrier recombination rate (where, Wei Tong.
Normalized composite rate model:
Figure BDA0001416484590000093
the equations (24) and (25) are time-differentiated by the backward Euler method to obtain:
Figure BDA0001416484590000094
Figure BDA0001416484590000095
in the formula, n m ,p m As the concentration values of electrons and holes at the present time, n m-1 ,p m-1 The concentration values of electrons and holes at the previous time,
Figure BDA0001416484590000096
for the potential at the present time, the superscript m represents the present time, the superscript m-1 represents the previous time, and Δ t represents the time difference;
respectively carrying out Galerkin test on the two formulas obtained by carrying out time difference on the formulas (24) and (25) and the Poisson equation (21), carrying out Taylor expansion to remove nonlinearity and coupling treatment after shifting terms to enable the right side of the equation to be 0, and then carrying out derivation to obtain an equation form capable of realizing solution by programming, and solving to obtain the electron concentration, the hole concentration and the potential at the current moment, wherein the Galerkin test specifically comprises the following steps:
solving a drift diffusion equation by adopting a full-coupling method, and ordering:
Figure BDA0001416484590000097
Figure BDA0001416484590000098
Figure BDA0001416484590000099
the equations after the taylor expansion processing of equation (27), equation (28), and equation (29) are written in the form of equation (30):
Figure BDA0001416484590000101
the final matrix form is obtained by appropriate derivation:
Figure BDA0001416484590000102
in equation (31), each matrix block is as follows:
Figure BDA0001416484590000103
Figure BDA0001416484590000104
Figure BDA0001416484590000105
Figure BDA0001416484590000111
Figure BDA0001416484590000112
Figure BDA0001416484590000113
Figure BDA0001416484590000114
A 32(i,j) ＝-A 31(i,j)
Figure BDA0001416484590000115
Figure BDA0001416484590000116
Figure BDA0001416484590000117
Figure BDA0001416484590000118
for the drift diffusion model, the processing method of the avalanche generation term needs to be particularly pointed out. Its expression is shown as (32):
Figure BDA0001416484590000119
in the above formula (36), the ionization coefficients of electrons and holes are:
Figure BDA0001416484590000121
wherein A is n ,B n And A p ,B p Is a constant.
Because the avalanche term contains current density and electric field intensity, the operation of Galerkin test and the like is very difficult and complicated, and the idea of adopting a non-coupling method of Gummel for the combined solution with the equation (9) is adopted.
As shown in fig. 3, the semiconductor device takes a PIN as an example, and the boundary conditions are as follows:
for the poisson equation, the solution area is the whole semiconductor device, and the boundary conditions are as follows:
drain and source plates are fixed boundary conditions (metal boundary conditions):
Figure BDA0001416484590000122
parallel to the x-coordinate axis is a floating boundary condition
Figure BDA0001416484590000123
For the current continuity equation, the solution region is semiconductor, and the boundary conditions are:
drain and source plates are fixed boundary conditions (metal boundary conditions):
an N region: n- Γ, P-1/Γ P region: n-1/Γ, p- Γ (36)
Parallel to the x-coordinate axis is a floating boundary condition
Figure BDA0001416484590000124
Obtaining the electric field intensity of each point in the semiconductor device from the electron concentration, the hole concentration and the electric potential
Figure BDA0001416484590000125
And current density
Figure BDA0001416484590000126
Power density
Figure BDA0001416484590000127
In the above (2), a heat conduction equation of the semiconductor device is established, the power density is substituted into the heat conduction equation as a heat source term, and the temperature distribution of each node is obtained by solving, specifically as follows:
the Heat Transfer Equation (HTE) is of the form:
Figure BDA0001416484590000128
in the formula, k t [W/(m·℃)]Is the thermal conductivity of the material; ρ is a unit of a gradient m [kg/m 3 ]Is the density of the material; c. C m [J/(kg·℃)]Is the constant specific heat of the material; v S [W/(m 3 ·℃)]Is the heat capacity flow volume of the cooling stream; t is a [℃]Is the temperature of the cooling stream; p d [W/m 3 ]Is the power density of the internal heat source.
In the solving process of the internal heat distribution of the semiconductor device, the material density, the heat conductivity coefficient and the constant pressure specific heat are set as fixed values, the power density is used as a heat source, and the formula is substituted into the formula:
Figure BDA0001416484590000131
in the formula, T is the temperature of each node;
Figure BDA0001416484590000132
k t is the thermal conductivity of the material, p m Is the density of the material, c m Is the constant specific heat of the material; p d Is the power density of the internal heat source;
solving equation (39) yields the temperature at each point inside the semiconductor device.
In the above (4), the convergence condition of the drift-diffusion equation is that the relative error between the two iterations before and after the variable carrier concentration and potential is less than 1 × 10 -4 。
And step four, substituting the obtained current value inside the semiconductor device into the equation in the step two, and checking whether the convergence precision of the external circuit solution is met: if yes, outputting the voltage, the current and the temperature value inside the semiconductor device; if not, repeating the second, third and fourth steps until the convergence accuracy is satisfied.
As shown in fig. 3, when the semiconductor device is exemplified by a PIN tube, a heat conduction equation is solved, and the ambient temperature is set to 300K, the base thereof is set to a first type boundary condition, the temperature is constant to 300K, and the other boundary surfaces are set to a third type boundary condition, that is, a scattering boundary condition.
The compact format of the spectral element method from which the heat transfer equation can be derived, through a similar derivation step as in the first section, is:
Figure BDA0001416484590000133
wherein:
Figure BDA0001416484590000134
[T] ij ＝∫∫∫N i ·N j dv (42)
Figure BDA0001416484590000135
Figure BDA0001416484590000136
Figure BDA0001416484590000137
adopting a forward difference format to obtain:
[T]T n ＝([T]-Δt([S]+[R]))T n-1 +Δt[Rq]+Δt[F] (46)
the matrix T is a quality matrix and is a diagonal matrix or a block diagonal matrix, the inverse of the matrix T can be solved in advance by using a block diagonal matrix inversion method, and an equation to be solved is changed into an explicit equation, so that the calculation amount is reduced, and the calculation efficiency is improved.
The idea of simulating a physical model of a semiconductor device by a numerical method is as follows: first, an initial value is preset at t n Giving initial values of electron concentration, hole concentration and electric potential at different times, substituting into equation (31), solving to obtain values of electron concentration, hole concentration and electric potential at each point in the semiconductor device, and calculating electric field intensity and electric potential at each pointThe current density, the power density, is the product of the electric field strength and the current density. Then, the obtained power density is substituted into the heat conduction equation to obtain the temperature of each point. The temperature-related parameter is updated. The above-mentioned cycle is repeated until convergence is reached, and the distribution of the electric field, temperature, etc. at this time is the result of the current time. The same subdivision grid cells are adopted in the solving process of the thermal field and the electric field.
Examples
The end result of the semiconductor device in combination with the human electrostatic model is as follows:
the semiconductor device and an external circuit are jointly solved (the semiconductor device takes a PIN tube as an example), and from the derivation, two simulation results of different charged amplitudes of human bodies are given, and specific curves are as follows:
(1) when the human body is charged with 200V, the response curve of a semiconductor device (taking a PIN tube as an example) is as follows:
voltage: see figure 4 for details.
Current: see figure 5 for details.
Temperature: see fig. 6, 7 for details.
(2) When the human body is charged with 500V, the response curve of a semiconductor device (taking a PIN tube as an example) is as follows:
voltage: see figure 8 for details.
Current: see figure 9 for details.
Temperature: see fig. 10, 11 for details.
From the above results, it is clear that the distribution of the electric field and temperature inside the device with time change due to the human body static electricity is obtained, and it is very important to study the influence of the semiconductor device such as a semiconductor device on the human body static electricity.

Claims (6)

1. A semiconductor device electric heating integration analysis method under human body electrostatic action is characterized by comprising the following steps:
step one, establishing a solving model of a semiconductor device, and subdividing the model by adopting a curved hexahedron to obtain structural information of the model, wherein the structural information comprises hexahedron unit information and node information;
secondly, connecting the semiconductor device into a human body electrostatic discharge equivalent model circuit to realize the combined solution of the semiconductor and an external circuit, listing the needed KVL and KCL equations, and solving the equations by using a Newton iteration method, wherein the specific steps are as follows:
adding a semiconductor device to the human body electrostatic discharge model, and defining the voltage and current on the semiconductor device as V D And I D Then according to the circuit structure, V D ＝U b ，I D ＝i D ，I D ＝f(V D )；
According to kirchhoff's theorem, a circuit equation is obtained:
Figure FDA0003739727620000011
in the above formula f (V) D ) The nonlinear relation of the voltage and the current in the semiconductor is represented;
obtaining the following through finishing deformation:
Figure FDA0003739727620000012
in the above formula, the superscript t represents the current moment, the superscript t-1 represents the previous moment, and Δ t represents the time difference;
solving the six equations by using a Newton iteration method, continuously updating the voltage and current values at the current moment until convergence, wherein the method comprises the following steps:
Figure FDA0003739727620000021
solving the following formulas by using a Newton iteration method:
Figure FDA0003739727620000022
through the derivation, the form of the equation which is easy to realize solution by programming is obtained:
Figure FDA0003739727620000031
thirdly, analyzing the electric heating characteristics in the semiconductor device to obtain the voltage, current distribution and temperature distribution in the semiconductor device at the current moment;
and step four, substituting the obtained current value inside the semiconductor device into the equation in the step two, and checking whether the convergence precision of the external circuit solution is met: if yes, outputting the voltage, the current and the temperature value inside the semiconductor device; if not, repeating the second, third and fourth steps until the convergence accuracy is satisfied.
2. The method according to claim 1, wherein the semiconductor device is analyzed by electric heating integration under human body electrostatic action, and the method comprises the following steps: in the first step, the model is subdivided by adopting a curved hexahedron, which specifically comprises the following steps: and subdividing a physical model of the semiconductor device by adopting ANSYS.
3. The method according to claim 1, wherein the semiconductor device is analyzed by electric heating integration under human body electrostatic action, and the method comprises the following steps: thirdly, analyzing the electric heating characteristics inside the semiconductor device to obtain the voltage, current distribution and temperature distribution inside the semiconductor device at the current moment, wherein the method specifically comprises the following steps:
(1) solving to obtain the electric field and current distribution of each node from a drift-diffusion equation set consisting of a current density equation, a current continuity equation and a Poisson equation, and obtaining the power density of each node from the electric field and current distribution;
(2) establishing a heat conduction equation of the semiconductor device, substituting the power density as a heat source item into the heat conduction equation, and solving to obtain the temperature distribution of each node;
(3) according to the obtained temperature, updating the parameters related to the temperature in the drift-diffusion equation in the step (1), and calculating the electric field distribution and the current distribution of each node again;
(4) and (4) circulating the steps (1) to (3) until the drift-diffusion equation reaches a convergence condition, wherein the voltage distribution, the current distribution and the temperature distribution at the moment are the electric heating distribution result at the current moment.
4. The method according to claim 3, wherein the semiconductor device is analyzed by electric heating integration under human body electrostatic action, and the method comprises the following steps: in the step (1), electric field and current distribution of each node are obtained by solving a drift-diffusion equation set composed of a current density equation, a current continuity equation and a poisson equation, and power density of each node is obtained by electric field and current distribution, which is specifically as follows:
the current continuity equation and the Poisson equation are normalized by a normalization factor by taking the carrier concentration and the potential as variables, and the normalized equation is as follows:
poisson equation:
Figure FDA0003739727620000041
in the above formula (1), Γ is net doping concentration,
Figure FDA0003739727620000042
is the potential, n is the electron concentration, p is the hole concentration;
electron current density equation:
Figure FDA0003739727620000043
in the above formula (2), J n Is the electron current density, μ n Is the electron mobility;
hole current density equation:
Figure FDA0003739727620000044
in the above formula (3), J p Is electricitySub-current density, μ p Is the electron mobility;
electron current continuity equation:
Figure FDA0003739727620000045
hole current continuity equation:
Figure FDA0003739727620000046
in the formulas (4) and (5), G is an avalanche generation term, an Okuto-Crowell model is adopted, and R is a carrier recombination rate;
performing time difference on the equations (4) and (5) by using a backward Euler method to obtain:
Figure FDA0003739727620000047
Figure FDA0003739727620000048
in the formulae (6) and (7), n m ,p m As the concentration values of electrons and holes at the present time, n m-1 ,p m-1 The concentration values of the electrons and holes at the previous time,
Figure FDA0003739727620000049
for the potential at the present time, the superscript m represents the present time, the superscript m-1 represents the previous time, and Δ t represents the time difference;
performing Galerkin test on the Poisson equation (1), the Poisson equation (6) and the Poisson equation (7) respectively, shifting terms to enable the right side of the equation to be 0, performing Taylor expansion to remove nonlinearity and coupling treatment, deriving to obtain an equation form capable of realizing solution by programming, and solving to obtain the electron concentration, the hole concentration and the potential at the current moment;
obtaining the electric field intensity of each point in the semiconductor device from the electron concentration, the hole concentration and the electric potential
Figure FDA00037397276200000410
And current density
Figure FDA00037397276200000411
Power density
Figure FDA00037397276200000412
5. The method according to claim 3, wherein the semiconductor device is analyzed by electric heating integration under human body electrostatic action, and the method comprises the following steps: in the step (2), a heat conduction equation of the semiconductor device is established, the power density is substituted into the heat conduction equation as a heat source item, and the temperature distribution of each node is obtained by solving, specifically as follows:
in the solving process of the internal heat distribution of the semiconductor device, the material density, the heat conductivity coefficient and the constant pressure specific heat are set as fixed values, the power density is used as a heat source, and the formula is substituted into the formula:
Figure FDA0003739727620000051
in the formula, T is the temperature of each node;
Figure FDA0003739727620000052
k t is the thermal conductivity of the material, p m Is the density of the material, c m Is the constant specific heat of the material; p is d Is the power density of the internal heat source;
solving equation (8) yields the temperature at each point inside the semiconductor device.
6. The method according to claim 3, wherein the semiconductor device is analyzed by electric heating integration under human body electrostatic action, and the method comprises the following steps: in the above (4), the convergence condition of the drift-diffusion equation isThe relative error of two iterations before and after the variable carrier concentration and potential is less than 1 × 10 -4 。
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