Stable numerical simulation method for synergistic effect of total ionization dose and instantaneous dose rate in semiconductor device

Abstract

The invention discloses a stable numerical simulation method for a total ionization dose (TID) and transient dose rate (TDR) synergistic effect in a semiconductor device. According to the method, a control volume finite element tearing interconnection (CV-FETI) method is utilized, discontinuous boundary conditions are included in common numerical properties, a Newton method is adopted to overcome non-convergence caused by nonlinear characteristics of a drift diffusion model, a stable three-dimensional parallel numerical format is adopted, and a non-continuous boundary condition is obtained. Reliable and accurate simulation of radiation of the semiconductor device is realized. Compared with a Gummel iteration method, the method has good numerical stability and precision under the same voltage step. Through comparison with a commercial software calculation result, the effectiveness of the method is verified. The method provided by the invention has the advantages of good stability, precision and applicability, and can be used for high-efficiency and high-precision numerical simulation of the radiation effect of a semiconductor device, thereby improving the performance, robustness and reliability of an integrated circuit.

Description

Technical Field

[0001] The present invention relates to a stable numerical simulation method for the combined effect of total ionizing dose and transient dose rate in a semiconductor device in the field of chips, and more particularly to a numerical simulation method for an integrated circuit designed for FinFET devices. Background Art

[0002] Radiation effects seriously affect the delay, performance, and temperature variation of very large scale integrated circuits. In applications such as outer space, nuclear power plants, and the military, there are harsh radiation conditions, and radiation damage can cause huge cost losses. Especially when the electronic components used in the nuclear power plant control measurement system are damaged by radiation, it will cause serious damage and failures to the measurement system, making it difficult to repair or replace the electronic components inside the nuclear power plant. In space applications, ionizing radiation particles are trapped in the oxide layer, which can damage electronic devices. When using electronic devices under harsh radiation conditions, minimizing the impact of radiation effects is a great challenge, so the research on radiation effects is extremely urgent.

[0003] The numerical simulation method is a widely used method for simulating the radiation effects of semiconductor devices. Although Gummel's method is a general method for semiconductor simulation (D.W. Wang, W.S. Zhao, Z.M. Zhang, Q. Liu, H. Xie, W. Chen, W.Y. Yin, and G. Wang, “A hybrid streamline upwind finite volume-finite element method for semiconductor continuity equations,” IEEE Transactions on Electron Devices, vol. 68, no. 11, pp. 5421–5429, 2021.), during transient simulation, it cannot converge at some challenging points. When using direct fully implicit time discretization, the Gummel iteration is also very slow in numerically solving transient problems. In addition, due to the change in material properties, Si-SiO 2The interface shows a discontinuous distribution of the electric field and carrier concentration, so a discontinuous boundary treatment technique is required. We know that there are different methods to handle discontinuous problems. For example, Michael Harmon et al. adopted a hybrid scheme of the local discontinuous Galerkin method and the mixed finite element method (M. Harmon, I. M. Gamba, and K. Ren, “Numerical algorithms based on galerkin methods for the modeling of reactive interfaces in photoelectrochemical (pec) solar cells,” Journal of Computational Physics, vol. 327, pp. 140–167, 2016.). It is very suitable for solving material changes and strong changes on the interface. Although the discontinuous Galerkin method can naturally handle discontinuous problems, it brings additional degrees of freedom. On this basis, the present invention proposes a control volume finite element tearing and interconnecting CV-FETIM hybrid algorithm that requires fewer degrees of freedom than the DG algorithm. Summary of the Invention

[0004] Aiming at the defects in the prior art, the purpose of the present invention is to provide a stable numerical simulation method for the combined effect of total ionizing dose and instantaneous dose rate in semiconductor devices. The present invention uses the control volume finite element tearing and interconnecting (CV-FETI) method to incorporate discontinuous boundary conditions into the usual numerical properties, overcomes the non-convergence caused by the non-linear characteristics of the drift-diffusion model by using the Newton method, and adopts a stable three-dimensional parallel numerical format to achieve reliable and accurate simulation of semiconductor device radiation.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A stable numerical simulation method for the combined effect of total ionizing dose and instantaneous dose rate in semiconductor devices, comprising the following steps:

[0007] The first step: constructing a geometric model of the semiconductor device and performing mesh generation;

[0008] The second step: determining the mathematical form of the drift-diffusion equations that describe the information of the semiconductor electric potential, electron concentration, and hole concentration fields for the meshed geometric model, where the drift-diffusion equations include the Poisson equation, the current continuity equation, and the carrier drift-diffusion equation;

[0009] The third step: determining the mathematical expression form corresponding to the radiation physical process of the carrier drift-diffusion equations; where N is applied to the silicon dioxide layer in the semiconductor device otImplement the influence of oxidation defects by simulating the total ionizing dose (TID) excitation, by adjusting the instantaneous dose rate R in the silicon layer d Implement the influence of simulating the transient dose rate (TDR) effect;

[0010] Step 4: Discretize the carrier drift-diffusion equations using the control volume finite element tearing and interconnecting (CV-FETI) method, where each point in the silicon-silicon dioxide interface is divided into two points in the silicon layer and in the silicon dioxide layer respectively, so as to incorporate discontinuous boundary conditions into the usual numerical properties;

[0011] Step 5: Use the Newton method to solve the discretized drift-diffusion equations;

[0012] Step 6: Continuously iterate and solve Step 5 until the solution of the drift-diffusion equations obtained reaches the convergence condition, and obtain the potential, electron concentration, and hole concentration field distributions in the semiconductor device.

[0013] In the above technical solution, further, in Step 2, the Poisson equation is:

[0014]

[0015] In the silicon layer,

[0016]

[0017] In the silicon dioxide layer,

[0018] ε = ε ins , Q = N ot

[0019] where ε is the permittivity, Q is the electric charge, ε s is the permittivity of silicon, ε ins is the permittivity of silicon dioxide, φ is the electric potential, q is the unit charge quantity, n and p are the electron concentration and hole concentration respectively, and are the ionized acceptor concentration and ionized donor concentration respectively, N ot is the defect charge concentration applied in the silicon dioxide layer; the current continuity equation is:

[0020]

[0021] The carrier drift-diffusion equation is:

[0022]

[0023] J n and J p are the electron current density and hole current density respectively, t is the time, Gn / R n and G P / R p are the electron generation recombination rate and the hole generation recombination rate respectively, and U r is the carrier generation rate by radiation excitation; E is the electric field, and μ n and μ p are the electron mobility and the hole mobility respectively, and D n and D p are the electron diffusion coefficient and the hole diffusion coefficient respectively.

[0024] Furthermore, in the third step, the influence of the oxidation defects excited by TID can be achieved by applying N ot to the silicon dioxide layer. In addition, the influence of the instantaneous dose rate effect can be achieved by adjusting the instantaneous dose rate R d in the silicon layer.

[0025] The expression form of the generation rate excited by radiation in the radiation physical process is:

[0026] U r = Yg 0 R d f(t)

[0027] where Y is the generation rate coefficient, g 0 is the number of electron-hole pairs generated in the material under a unit radiation dose, R d is the instantaneous dose rate, and f(t) is a square wave pulse function with an amplitude of 1. For silicon material, Y = 1, g 0 = 4×10 13 EHP / rad / cm 3 .

[0028] For the change of the surface carriers of the device caused by TID, the surface recombination caused by the interface traps needs to be considered

[0029]

[0030] where is the outer normal vector of the boundary, n i is the intrinsic carrier concentration, N it is the interface trap, and r is the capture coefficient.

[0031] Furthermore, the fourth step is specifically:

[0032] Due to the discontinuous distribution of the electric field and the source term at the Si-SiO 2 interface, spatial discretization is crucial. To solve this problem, each point in the Si-SiO 2 interface is divided into two points, such as Figure 1As shown. The tearing interconnection method is used to connect Si-SiO 2 Each point in the interface is divided into two points, namely point V in the silicon layer and i and point V in the silicon dioxide layer i ′ , and the finite element hexahedral control volume of the point on the interface is torn into parts C in the silicon layer i and part C in the silicon dioxide layer i ′ , there are: in Si-SiO 2 In the interface, click V i The discontinuous boundary conditions are set as:

[0033]

[0034] in is the normal vector pointing to the silicon dioxide layer, φ i V is the midpoint of the silicon layer i The electric potential, φ i ′ V is the midpoint of the silicon dioxide layer i ′ The potential of the carrier drift-diffusion equations is obtained by using the discontinuous boundary condition, and σ is the interface charge. The Poisson equation and the carrier continuity equation are solved by the controlled volume finite element method.

[0035] Solve the Poisson equation in the silicon layer and the silicon dioxide layer. For Si-SiO 2 V at the interface i The integral equation is:

[0036]

[0037] For the non-Si-SiO 2 Point V at the interface i , the integral equation is expressed as

[0038]

[0039] Among them, C i Point V i The portion of the hexahedron controlling the volume in the silicon layer, C i ′ Point V i The portion of the hexahedron controlling the volume in the silicon dioxide layer, C i the surface, C′ i The surface of Γ IF C i and C′ iThe common surface interface, such as Figure 1 As shown, S is the area integration region and V is the volume integration region;

[0040] Solve the carrier continuity equation in the silicon layer and express it in the conservation form

[0041]

[0042] The Dirichlet boundary condition is:

[0043] q = q D

[0044] The mixed boundary condition is:

[0045]

[0046] Here G is a 2×3 matrix, q, q D , h(q) and s are 2×1 vectors, respectively:

[0047]

[0048] Where J n and J p are 1×3 vectors with current density components in the x, y, and z directions, Integrate over the control volume C i and then apply the divergence theorem to obtain

[0049]

[0050] and The area integral of can be discretized into

[0051]

[0052] denotes the surface; The flux term at the center is approximated as a weighted sum of the edge flux amplitudes, and the Nédélec basis function W j (x, y, z) is used as the weighting factor. The potential gradient and current density flux terms at the grid edges are discretized using the finite difference method and the Scharfetter-Gummel method, respectively.

[0053] Furthermore, the residual equation related to the Poisson equation at the Si-SiO 2 interface can be written as

[0054]

[0055] In other regions, it can be written as

[0056]

[0057] The residual equation corresponding to the carrier transport equation can be written as

[0058] Using the backward difference method that is unconditionally stable for time discretization, the carrier transport residual equation can be transformed into solving the following related problems

[0059]

[0060] Here is a 2×1 vector, and

[0061] Furthermore, in the fifth step, the Newton method is used to iteratively solve the discretized drift-diffusion equation, specifically as follows:

[0062] At the l-step, we use Nb(V i ) to define the neighborhood set of the node V i ={x i ,y i ,z i}, and the Taylor series expansion is used for the residual equation.

[0063] For the point V i in the silicon layer,

[0064]

[0065] For the point V i in the silicon dioxide layer,

[0066]

[0067] Therefore, the related problems solved by the Newton method are:

[0068] JΔU l =-F(U l )

[0069] where

[0070]

[0071] Here J is the 3N s +N ins ×3N s +N ins Jacobian matrix, and F is the 3N s +N ins ×1 vector. N s and N ins are the number of grid points in the silicon layer and the silicon dioxide layer. Ul+1 is obtained through the following formula

[0072] U l+1 = U l + rΔU l

[0073] where r is the damping factor to avoid non - convergence of the solution, taking 1 or 0.

[0074] Furthermore, in the sixth step, the convergence condition is that the absolute error of the electric potential is less than 10 -10 V, and the absolute errors of the electron and hole concentrations are both less than 10 -5 m -3 .

[0075] Compared with the prior art, the remarkable advantages of the present invention are as follows

[0076] (1) For devices such as FinFETs, corresponding physical models are used to solve, and the internal electrical characteristic distribution of the device under the total dose effect can be obtained. (2) The present invention uses the CV - FETIM method to discretize the drift - diffusion equations, and can take into account the discontinuous boundary conditions in the general numerical properties. (3) The Newton iteration method is used to solve the discretized drift - diffusion equations, which improves the convergence speed and maintains good numerical stability. (4) The present invention can simulate the individual transient dose rate and total dose effect, as well as their synergistic effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 is the hexahedral control volume C of vertex V i . i .

[0078] Figure 2 is a schematic diagram of a three - dimensional FinFET structure.

[0079] Figure 3 is the hexahedral grid used in the simulation.

[0080] Figure 4 is the transient drain current of the FinFET when the interface trap N it = 0 cm -2 , N it = 10 12 cm -2 .

[0081] Figure 5 is the transient drain current of the FinFET with interface traps N it = 0 cm -2 and N it = 10 12 cm -2 set on the side.

[0082] Figure 6 are the electron concentration distributions at the moments of (a) 1 ps, (b) 11 ps, (c) 13 ps, and (d) 21 ps.

[0083] Figure 7 are the electron densities along the line at different times. Detailed implementation manners

[0084] The present invention will be further described in detail below with reference to the accompanying drawings. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0085] A stable numerical simulation method for the total ionizing dose and transient dose rate synergistic effect in a semiconductor device of the present invention includes the following steps:

[0086] The first step: Construct a geometric model of the semiconductor device and perform mesh discretization;

[0087] The second step: Determine the mathematical form of the drift-diffusion equations that describe the semiconductor potential, electron concentration, and hole concentration field information for the discretized geometric model. The drift-diffusion equations include the Poisson equation, the current continuity equation, and the carrier drift-diffusion equation;

[0088] The third step: Determine the mathematical expression form corresponding to the radiation physical process of the carrier drift-diffusion equations;

[0089] The fourth step: Use the control volume finite element tearing and interconnecting (CV-FETI) method to perform spatial discretization on the drift-diffusion equations, and include discontinuous boundary conditions in the usual numerical properties;

[0090] The fifth step: Use the Newton method to solve the discretized drift-diffusion equations;

[0091] The sixth step: Continuously iterate and solve the fifth step until the solution of the drift-diffusion equations obtained reaches the convergence condition, and obtain the potential, electron concentration, and hole concentration field distributions in the semiconductor device.

[0092] Specifically, several key technical points are as follows:

[0093] 1. The carrier drift-diffusion model in a semiconductor device can be described by these partial differential equations such as the Poisson equation, the carrier current continuity equation, and the carrier drift-diffusion equation.

[0094] The Poisson equation described is:

[0095]

[0096] In the silicon layer,

[0097]

[0098] In the silicon dioxide layer,

[0099] ε = ε ins , Q = N ot

[0100] The current continuity equation is as follows:

[0101]

[0102] The carrier drift-diffusion equation is as follows:

[0103]

[0104] In the formula, ε s is the dielectric constant of silicon, ε ins is the dielectric constant of silicon dioxide, φ is the electric potential, q is the unit charge quantity, n and p are the electron concentration and hole concentration respectively, and are the ionized acceptor concentration and ionized donor concentration respectively; J n and J p are the electron current density and hole current density respectively, t is the time, G n / R n and G P / R p are the electron generation-recombination rate and hole generation-recombination rate respectively, U r is the carrier generation rate excited by radiation; E is the electric field, μ n and μ p are the electron mobility and hole mobility respectively, D n and D p are the electron diffusion coefficient and hole diffusion coefficient respectively.

[0105] 2. The influence of TID-induced oxidation defects can be achieved by applying N ot in the silicon dioxide layer. In addition, the influence of the transient dose rate effect can be achieved by adjusting the transient dose rate R d in the silicon layer.

[0106] The expression form of the generation rate excited by radiation in the radiation physical process is:

[0107] U r = Yg 0 R d f(t)

[0108] For silicon materials, Y = 1, g 0 = 4×10 13 EHP / rad / cm 3 .

[0109] Regarding the change in the surface carriers of the device caused by TID, the surface recombination caused by interface traps needs to be considered

[0110]

[0111] Among them, is the outer normal vector of the boundary, n i is the intrinsic carrier concentration, N it is the interface trap, and r is the capture coefficient.

[0112] 3. Due to the discontinuous distribution of the electric field and the source term at the Si-SiO 2 interface, spatial discretization is crucial. To solve this problem, the CV-FETIMM method is adopted, that is, each point in the Si-SiO 2 interface is divided into two points, as Figure 1 shown. In the Si-SiO 2 interface, the discontinuous boundary condition of point V i is set as:

[0113] φ i = φ i ′

[0114]

[0115] Among them is the normal vector pointing to the silicon dioxide layer.

[0116] Solve the Poisson equation in the silicon layer and the silicon dioxide layer. For point V 2 at the Si-SiO i interface, the integral equation is:

[0117]

[0118] For points V 2 not at the Si-SiO i interface, the integral equation is expressed as

[0119]

[0120] Solve the carrier continuity equation in the silicon layer and express it in the conservation form

[0121]

[0122] The Dirichlet boundary condition is:

[0123] q = q D

[0124] The mixed boundary condition is:

[0125]

[0126] where G is a 2×3 matrix, and q, q D , h(q), and s are 2×1 vectors.

[0127]

[0128] Integrating over the control volume C i and then applying the divergence theorem, we obtain

[0129]

[0130] and The surface integral of can be discretized into

[0131]

[0132] The flux term at the center is approximated as a weighted sum of the edge flux magnitudes, and the Nédélec basis function W j (x, y, z) is used as the weighting factor. The potential gradient and current density flux terms at the grid edges are discretized using the finite difference method and the Scharfetter - Gummel method respectively.

[0133] The residual equation related to the Poisson equation at the Si - SiO 2 interface can be written as

[0134]

[0135] In other regions, it can be written as

[0136]

[0137] The residual equation corresponding to the carrier transport equation can be written as

[0138]

[0139] Using the backward difference method that is unconditionally stable for time discretization, the carrier transport residual equation can be transformed into solving the following related problem

[0140]

[0141] where is a 2×1 vector, and

[0142] 4. At the l-th step of the Newton iteration method, we use Nb(V i ) to define the neighborhood set of node V i ={x i ,y i ,z i}, and use the Taylor series expansion for the residual equation.

[0143] For the point V i in the silicon layer,

[0144]

[0145] For the point V i in the silicon dioxide layer,

[0146]

[0147] Therefore, the relevant problem solved by the Newton method is:

[0148] JΔU l =-F(U l )

[0149] where

[0150]

[0151] here J is a 3N s +N ins ×3N s +N ins Jacobian matrix, F is a 3N s +N ins ×1 vector. N s and N ins are the number of grid points in the silicon layer and the silicon dioxide layer. U l+1 is obtained through the following formula,

[0152] U l+1 =U l +rΔU l

[0153] where r is a damping factor to avoid non-convergent solutions, taking 1 or 0.

[0154] By using the CV-FETIMM method in the aforementioned 3 and the Newton iteration method in 4, the drift-diffusion equations of carriers in semiconductor devices can be solved, and then the potential, electron concentration, and hole concentration field distributions in the semiconductor devices can be obtained. And through post-processing, the current-voltage curve of the semiconductor device can be obtained. Compared with the Gummel iteration method, the method of the present invention has good numerical stability and accuracy under the same voltage step. By comparing with the calculation results of commercial software, the effectiveness of the proposed method is verified. In addition, the method of the present invention can be effectively applied to the simulation of devices such as MOSFET, STI-LDMOSFET, and FinFET. By adjusting the dose rate, oxidation traps, and interface traps, the synergistic effects of independent TID, independent TDR, and TID-TDR can be simulated. On the picosecond or nanosecond time scale, the duration, amplitude, and decay rate of radiation-induced photocurrent can be simulated. The influence of interface traps on different surfaces can also be studied. The numerical method established by the present invention has the advantages of good stability, accuracy, and applicability, and can be used for high-efficiency and high-precision numerical simulation of the radiation effects of semiconductor devices, thereby improving the performance, robustness, and reliability of integrated circuits.

[0155] Use the simulation software of the synergistic effect between the instantaneous dose rate effect and the total dose effect in the three-dimensional integrated structure designed by the method of the present invention to simulate the synergistic effect characteristics in semiconductor devices. The simulated three-dimensional FinFET structure is as Figure 2 shown. The source, drain, and substrate contacts are all ohmic contacts. The size of the FinFET is 1100×300×200nm 3 , and the gate oxide layer thickness is 3nm. The source and the substrate are both connected to the ground. The hexahedral mesh used in the simulation is as Figure 3 shown. The start time of the transient pulse is 1ps, the end time is 11ps, and the pulse width is 10ps. Figure 4 For the interface trap N it =0cm -2 , N it =10 12 cm -2 The transient drain current of the FinFET. There are two groups of simulation settings with N it =1012cm -2 , and in one group, N it =1012cm -2 is set on the side, and in the other group, N it =1012cm -2 is set on the gate surface. The FinFET is exposed to a dose rate of 1×10 10Under transient ionizing radiation of Rad(Si) / s. When the gate oxide thickness is reduced to less than about 7 nm, the radiation-induced performance degradation related to the gate oxide is basically eliminated, while the field oxide, SOI oxide, and STI oxide usually play a dominant role in radiation-induced degradation. As Figure 4 shown, the interface traps induced by side-surface TID are the main reason for the TID-TDR synergistic effect in FinFETs, and the interface traps induced by gate-surface TID have little effect. Figure 5 To set interface traps N on the side it = 0 cm -2 and N it = 10 12 cm -2 of the FinFET transient drain current. The FinFETs are respectively exposed to transient ionizing radiation with dose rates of 6×10 9 , 8×10 9 and 1×10 10 Rad(Si) / s. On the one hand, as the transient dose rate increases, the amplitude of the photocurrent increases significantly; on the other hand, under each dose rate condition, the increase in interface traps makes the decay rate of the photocurrent larger, the duration shorter, and the amplitude smaller. The electron densities at different times are plotted in Figure 6 , and the electron densities along the line at different times are plotted in Figure 7 , the starting point of the line is (565 nm, 150 nm, 0 nm), and the ending point is (565 nm, 150 nm, 200 nm). R d is fixed at 10 10 Rad(Si) / s. According to the numerical results, the mechanism of transient photocurrent generation is analyzed. There are two PN junctions in the FinFET, one is the source-substrate PN junction, and the other is the drain-substrate PN junction. At 1 ps, the radiation has not yet acted on the FinFET, and the electron and hole densities at this time are the carrier concentrations in the normal state of the device. After 10 ps of irradiation, at 11 ps, a large number of electron-hole pairs are generated in the FinFET device, and at this time, the electron concentration increases significantly from about 10 4 cm -3 to 10 10 cm -3 . The additional electron-hole pairs in the depletion layer are collected under the action of the electric field to form a drift current, resulting in an obvious transient current.

[0156] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention.

Claims

1. A stable numerical simulation method for the synergistic effect of total ionizing dose and instantaneous dose rate in a semiconductor device, characterized in that: The steps include: Step 1: Build a geometric model of the semiconductor device and perform mesh generation; Step 2: Determine the form of a drift-diffusion equation group describing the semiconductor potential, electron concentration and hole concentration field information for the segmented geometric model, wherein the drift-diffusion equation group includes Poisson's equation, current continuity equation and carrier drift-diffusion equation; Step 3: Determine the form of the radiation physics process corresponding to the carrier drift-diffusion equation group; wherein N is applied to the silicon dioxide layer in the semiconductor device ot Simulating the effect of total ionization dose (TID) excitation on oxide defects is achieved by adjusting the instantaneous dose rate R in the silicon layer. d To simulate the impact of transient dose rate TDR effect; Step 4: The carrier drift-diffusion equations are discretized using the controlled volume finite element tearing interconnection method, where each point in the silicon-silicon dioxide interface is split into two points in the silicon layer and in the silicon dioxide layer, respectively, so that the discontinuous boundary conditions are included in the usual numerical properties; Step 5: Use Newton's method to solve the drift-diffusion equations after discretization; Step 6: Continuously iterate step 5 until the solution of the drift-diffusion equations reaches the convergence condition, and obtain the potential, electron concentration and hole concentration field distribution in the semiconductor device.

2. The stable numerical simulation method for the synergistic effect of total ionizing dose and instantaneous dose rate in a semiconductor device according to claim 1, characterized in that: In the second step, the Poisson equation is: In the silicon layer, In the silicon dioxide layer, e=e ins ,Q=N ot In the formula, ε is the dielectric constant, Q is the charge, and ε s is the dielectric constant of silicon, ε ins is the dielectric constant of silicon dioxide, φ is the electric potential, q is the unit charge, n and p are the electron concentration and hole concentration respectively, and are the ionized acceptor concentration and the ionized donor concentration, respectively, N ot is the defect charge concentration applied in the silicon dioxide layer; the current continuity equation is: The carrier drift diffusion equation is: In the formula, J n and J p are the electron current density and the hole current density respectively, t is the time, G n / R n is the electron generation / recombination rate, G P / R p is the hole generation / recombination rate, U r is the carrier generation rate stimulated by radiation; E is the electric field, μ n and μ p are the electron mobility and hole mobility, respectively, and D n and D p are the electron diffusion coefficient and the hole diffusion coefficient, respectively.

3. The stable numerical simulation method for the synergistic effect of total ionizing dose and instantaneous dose rate in a semiconductor device according to claim 1, characterized in that: In the third step, The generation rate of radiation excitation in the radiation physics process is expressed as: U r =Yg0R d f(t) Where Y is the generation rate coefficient, g0 is the number of electron-hole pairs generated in the material under unit radiation dose, and R d is the instantaneous dose rate, f(t) is a square wave pulse function with an amplitude of 1; For the change of device surface carriers due to TID, it is necessary to consider the surface recombination caused by interface traps: in, is the external normal vector of the boundary, n i is the intrinsic carrier concentration, N it is the interface trap and r is the capture coefficient.

4. The stable numerical simulation method for the synergistic effect of total ionizing dose and instantaneous dose rate in a semiconductor device according to claim 3, characterized in that: In the fourth step, the controlled volume finite element tearing interconnection method is used to discretize the carrier drift-diffusion equations, specifically: The tearing interconnection method is used to split each point in the Si-SiO2 interface into two points, namely point V in the silicon layer and point V in the silicon layer. i and point V in the silicon dioxide layer i ′, and tear the finite element hexahedral control volume of the point on the interface into parts C in the silicon layer i and the portion C′ in the silicon dioxide layer i , we have: At the Si-SiO2 interface, point V i The discontinuous boundary conditions are: f i =φ′ i in is the normal vector pointing to the silicon dioxide layer, φ i V is the midpoint of the silicon layer i The electric potential, φ′ i V' is the midpoint of the silicon dioxide layer i The potential of σ is the interface charge. Based on the discontinuous boundary condition, the carrier drift-diffusion equations are discretized. The Poisson equation and carrier continuity equation are discretely solved by the controlled volume finite element method, where the Poisson equation is solved in the silicon layer and the silicon dioxide layer. i The integral equation is: For a point V not at the Si-SiO2 interface i , the integral equation is Among them, C i Point V i The portion of the hexahedral control volume in the silicon layer, C′ i Point V i The portion of the hexahedron controlling the volume in the silicon dioxide layer, C i the surface, C′ i The surface of Γ IF C i and C′ i The common interface of , S is the area sub-region, V is the volume sub-region; Solve the carrier continuity equation in the silicon layer and express it in conservation form The Dirichlet boundary condition is: q=q D The mixed boundary conditions are: Where: G is a 2×3 matrix, q, q D , h(q) and s are all 2×1 vectors, respectively: Among them J n and J p is a 1×3 vector with current density components in the x, y, and z directions. In the control volume C i Integrating over , and applying the divergence theorem, we get and The area separation is express Surface The central flux term is approximated as a weighted sum of the edge flux amplitudes and uses the Nédélec basis function W j (x,y,z) is used as the weighting factor; the potential gradient and current density flux terms at the grid edge are discretized using the finite difference method and the Scharfetter-Gummel method, respectively.

5. The stable numerical simulation method for the synergistic effect of total ionizing dose and instantaneous dose rate in a semiconductor device according to claim 4, characterized in that: The residual equation of Poisson's equation at the Si-SiO2 interface is: In other areas: The residual equation corresponding to the carrier transport equation is: Using the backward difference method which is unconditionally stable to time discretization, the carrier transport residual equation is transformed into solving the following related problems: here is a 2×1 vector, and 6. The stable numerical simulation method for the synergistic effect of total ionizing dose and instantaneous dose rate in a semiconductor device according to claim 5, characterized in that: In the fifth step, the Newton method is used to iteratively solve the discretized drift-diffusion equation, which includes: In step 1, Nb(V i ) Define node V i ={x i ,y i ,z i } and use Taylor series expansion for the residual equation; For point V in the silicon layer i , For point V in the silicon dioxide layer i , Therefore, the relevant problems solved by Newton's method are: JΔU l =-F(U l ) in Here J is 3N s +N ins ×3N s +N ins Jacobian matrix, F is 3N s +N ins ×1 vector; N s and N ins is the number of grid points in the silicon layer and the silicon dioxide layer; U l+1 Obtained by the following formula: U l+1 =U l +rΔU l Where r is the damping factor to avoid non-convergence of the solution, which can be 1 or 0.

7. The stable numerical simulation method for the synergistic effect of total ionizing dose and instantaneous dose rate in a semiconductor device according to claim 1, characterized in that: The convergence condition in the sixth step is that the absolute error of the potential between the solution of the previous iteration step and the solution of the current iteration step is less than 10 -10 The absolute errors of V, electron and hole concentrations are all less than 10 -5 m -3 .

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