CN111723511A - Electromigration simulation method for three-dimensional packaging interconnection line - Google Patents
Electromigration simulation method for three-dimensional packaging interconnection line Download PDFInfo
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Abstract
The invention discloses a three-dimensional packaging interconnection wire electromigration simulation method. The invention belongs to the technical field of interconnection wire electromigration simulation, and an EM point thermal three-field coupling geometric model is established; determining loading boundary conditions, material parameters and physical field coupling of the geometric model; carrying out meshing on the geometric model, setting step length, and solving the geometric model; and solving according to the geometric model to obtain a temperature field, a current density field and a stress field, substituting the temperature field, the current density field and the stress field into a post-processing equation, and obtaining the diffusion flux divergence of the interconnection wire atoms. The invention applies an atomic diffusion flux analysis model based on physical characteristics, carries out finite element simulation on a common interconnection structure and carries out modeling calculation on the atomic diffusion flux. And the influence of input voltage and lead material on thermal migration, electromigration and stress migration is emphatically discussed by changing model parameters, so that a better interconnection line material and temperature condition are obtained by comparison.
Description
Technical Field
The invention relates to the technical field of interconnection line electromigration simulation, in particular to a three-dimensional packaging interconnection line electromigration simulation method.
Background
With the development of micro-interconnection to deep submicron scale, the problems of high current density, stress concentration, difficult heat dissipation and the like are more prominent, and the atomic migration failure gradually becomes a non-negligible reliability problem of the ultra-large scale integrated circuit. Copper has lower resistivity and better electromigration resistance than aluminum and has become a new generation of interconnect materials.
The phenomenon of electromigration has occurred for over a hundred years, and in 1861, Gerardin, a french scientist, first discovered the phenomenon in liquid alloys, but failure caused by electromigration was not concerned at that time. Researchers find that when the cross-sectional area of the Al wire is small, the on-resistance is too high to meet the requirement of the electron rate, and the miniaturization of electronic devices is difficult to realize. However, under the same cross-sectional area, the on-resistance of the metal Cu wire is only half of that of the metal Al, and the metal Cu is not easy to generate electromigration compared with the Al, so in the late 90 s of the 20 th century, companies such as IBM and Motorola began to use the metal Cu instead of the metal Al in the integrated circuit technology in a large range. Although copper has greater brittleness during the manufacturing process, its superior conductivity and resistance to electromigration failure make Cu wires the first choice in the industry, and the electromigration research of Cu wires is also gradually being carried out. Finite Element Methods (FEM) have become important solution techniques in many fields of engineering and physics. The versatility of finite element simulation is that it can model arbitrarily shaped structures, process complex materials, and apply various types of loads and boundary conditions. This approach can easily be adapted to different sets of formation equations, which makes it particularly attractive in coupled physics simulations.
The Comsol multiprophy software is widely applied to the scientific and industrial fields due to the diversity of interfaces, the convenience of interface interaction and the attention on user requirements as a finite element software. Engineers and researchers can use Comsol Multiphysics software to simulate products and processes involved in various engineering, manufacturing, and research areas.
The existing EM reliability analytical model mainly aims at electromigration analysis under the condition of constant temperature of a single metal wire, the method has simpler calculation but has smaller guiding significance on the practical situation, the main reasons are that temperature gradient exists in a high-density integrated circuit in the practical situation, the three-dimensional structure of an interconnection line has important influence on the temperature and current distribution of the interconnection line, and the parameters closely influence the electromigration of metal atoms.
Disclosure of Invention
The invention carries out theoretical simulation on the established classic interconnection line three-dimensional model, carries out simulation calculation on the diffusion flux of electromigration atoms by simulating the aspects of current density distribution, temperature distribution and the like under the model, and carries out comparative study on the electromigration of different temperature materials, and the invention provides a three-dimensional packaging interconnection line electromigration simulation method, and the invention provides the following technical scheme:
a three-dimensional packaging interconnecting wire electromigration simulation method comprises the following steps:
step 1: establishing an EM point thermal three-field coupling geometric model;
step 2: determining loading boundary conditions, material parameters and physical field coupling of the geometric model;
and step 3: carrying out meshing on the geometric model, setting step length, and solving the geometric model;
and 4, step 4: and solving according to the geometric model to obtain a temperature field, a current density field and a stress field, substituting the temperature field, the current density field and the stress field into a post-processing equation, and obtaining the diffusion flux divergence of the interconnection wire atoms.
Preferably, based on Comsol Multiphsics, an AC/DC module, a solid heat transfer module and a solid mechanics module are adopted to establish an EM point thermal three-field coupling geometric model, and Cu electromigration at different temperatures is simulated.
Preferably, the step 2 specifically comprises:
according to the fact that the initial temperature is 293.15K, the constant temperature is applied to the bottom face, the heat dissipation condition of the surface of the circuit board is simulated by means of heat convection of the top face, the heat insulation boundary conditions are adopted for the vertical faces to represent the heat dissipation condition of a certain position of the circuit board, and the loading boundary conditions of the geometric model are represented by the following formula:
q＝-k▽T
q0＝h·(Text-T)
wherein, CPIs constant voltage heat capacity, k is the coefficient of thermal conductivity, h is the coefficient of heat transfer, T is the temperature, T is the time, u is the voltage, Q is the heat flux, QtedBased on heat flux, q is solid heat transfer heat flux density, q0Heat flux density, T, for heat convectionextIs the outside temperature;
the adopted current is the current conduction in a Cu interconnection line, wherein the input potential of the top surface of the Cu wire is 0.25V and 0.3V, the other end surface of the Cu wire is grounded, and the material parameters are determined by the following formula:
▽·J＝Qj
E＝-▽V
wherein J is current density, QjIs the amount of charge, σ is the conductivity,0in order to have a dielectric constant in a vacuum,rrelative dielectric constant, E electric field strength, JeFor initial test current density, V is potential;
by applying a boundary condition of fixed constraint at the bottom edge, the conducting wire and the substrate are both made of linear elastic materials;
the physical field coupling sets the physical field distribution of the Cu interconnect lines such that the input voltage is 0.25V.
Preferably, the step 3 specifically comprises:
step 3.1: carrying out meshing on the geometric model by adopting a comsol automatic free tetrahedron meshing method, wherein the maximum unit size is 4.4nm, the minimum unit size is 0.32nm, the maximum unit growth rate is 1.4, the curvature factor is 0.4, the resolution of a narrow area is 1.7, the stepping time length is 0.1h, and the total time length is 1 h;
step 3.2: the method comprises the steps of selecting a physical field as electric heating coupling field analysis and solid heat transfer and solid mechanics coupling, calculating electric field, current and potential distribution in a conductor medium through electric field analysis, solving a current conservation equation based on ohm's law, calculating temperature distribution and temperature gradient distribution according to a temperature field, calculating model stress distribution through a solid mechanics module, and finally obtaining the temperature field, a current density field and a stress field.
Preferably, the step 4 specifically includes:
obtaining a temperature field, a current density field and a stress field according to the solution, substituting the temperature field, the current density field and the stress field into a post-processing equation, and obtaining the diffusion flux divergence of the atoms of the interconnection line;
determining an electromigration atomic diffusion flux, the electromigration atomic diffusion flux J is represented byem：
Determining a flux of diffusion of the thermomigrated atom, determining a flux of diffusion of the thermomigrated atom J by the following formulatm：
Determining the stress migration atomic diffusion flux, determining the stress migration atomic diffusion flux J bysm：
Under the comprehensive action of electron wind power, temperature gradient and stress gradient, determining the atomic diffusion flux divergence, and expressing the atomic diffusion flux divergence by the following formula:
div(Jtotal)＝div(Jem)+div(Jtm)+div(Jsm)
wherein N is an Avogastron constant, DoAs diffusion coefficient, EaFor activation energy, Ω is the atomic volume.
The invention has the following beneficial effects:
the invention establishes a three-dimensional classical interconnection line structure through Comsol software. And (4) calculating the diffusion of the atomic diffusion flux by obtaining the temperature, the current density and the stress distribution of the three-dimensional interconnection line through finite element simulation. The invention applies an atomic diffusion flux analysis model based on physical characteristics, carries out finite element simulation on a common interconnection structure and carries out modeling calculation on the atomic diffusion flux. And the influence of input voltage and lead material on thermal migration, electromigration and stress migration is emphatically discussed by changing model parameters, so that a better interconnection line material and temperature condition are obtained by comparison.
Drawings
FIG. 1 is a flow chart of a method for simulating electromigration of a three-dimensional package interconnect;
FIG. 2 is a geometric configuration of an interconnect line;
FIG. 3 is a cross-sectional view of an interconnect grid;
FIG. 4 is a current density distribution graph;
FIG. 5 is a temperature profile;
FIG. 6 is a stress distribution diagram;
FIG. 7 is a graph of current migration distribution;
FIG. 8 is a graph of a thermomigration profile;
fig. 9 is a stress migration profile.
Detailed Description
The present invention will be described in detail with reference to specific examples.
The first embodiment is as follows:
according to fig. 1, the present application provides a method for simulating electromigration of a three-dimensional package interconnection line, comprising the following steps:
step 1: establishing an EM point thermal three-field coupling geometric model;
based on Comsol Multiphsics, an EM point thermal three-field coupling geometric model is established by adopting an AC/DC module, a solid heat transfer module and a solid mechanics module, and Cu electromigration at different temperatures is simulated.
Step 2: determining loading boundary conditions, material parameters and physical field coupling of the geometric model;
the step 2 specifically comprises the following steps:
according to the fact that the initial temperature is 293.15K, the constant temperature is applied to the bottom face, the heat dissipation condition of the surface of the circuit board is simulated by means of heat convection of the top face, the heat insulation boundary conditions are adopted for the vertical faces to represent the heat dissipation condition of a certain position of the circuit board, and the loading boundary conditions of the geometric model are represented by the following formula:
q＝-k▽T
q0＝h·(Text-T)
wherein, CPIs constant voltage heat capacity, k is the coefficient of thermal conductivity, h is the coefficient of heat transfer, T is the temperature, T is the time, u is the voltage, Q is the heat flux, QtedBased on heat flux, q is solid heat transfer heat flux density, q0Heat flux density, T, for heat convectionextIs the outside temperature;
the adopted current is the current conduction in a Cu interconnection line, wherein the input potential of the top surface of the Cu wire is 0.25V and 0.3V, the other end surface of the Cu wire is grounded, and the material parameters are determined by the following formula:
▽·J＝Qj
E＝-▽V
wherein J is current density, QjIs the amount of charge, σ is the conductivity,0in order to have a dielectric constant in a vacuum,rrelative dielectric constant, E electric field strength, JeFor initial test current density, V is potential;
by applying a boundary condition of fixed constraint at the bottom edge, the conducting wire and the substrate are both made of linear elastic materials;
the physical field coupling sets the physical field distribution of the Cu interconnect lines such that the input voltage is 0.25V.
And step 3: carrying out meshing on the geometric model, setting step length, and solving the geometric model;
the step 3 specifically comprises the following steps:
step 3.1: carrying out meshing on the geometric model by adopting a comsol automatic free tetrahedron meshing method, wherein the maximum unit size is 4.4nm, the minimum unit size is 0.32nm, the maximum unit growth rate is 1.4, the curvature factor is 0.4, the resolution of a narrow area is 1.7, the stepping time length is 0.1h, and the total time length is 1 h;
step 3.2: the method comprises the steps of selecting a physical field as electric heating coupling field analysis and solid heat transfer and solid mechanics coupling, calculating electric field, current and potential distribution in a conductor medium through electric field analysis, solving a current conservation equation based on ohm's law, calculating temperature distribution and temperature gradient distribution according to a temperature field, calculating model stress distribution through a solid mechanics module, and finally obtaining the temperature field, a current density field and a stress field.
And 4, step 4: and solving according to the geometric model to obtain a temperature field, a current density field and a stress field, substituting the temperature field, the current density field and the stress field into a post-processing equation, and obtaining the diffusion flux divergence of the interconnection wire atoms.
The step 4 specifically comprises the following steps:
obtaining a temperature field, a current density field and a stress field according to the solution, substituting the temperature field, the current density field and the stress field into a post-processing equation, and obtaining the diffusion flux divergence of the atoms of the interconnection line;
determining an electromigration atomic diffusion flux, the electromigration atomic diffusion flux J is represented byem：
Determining a flux of diffusion of the thermomigrated atom, determining a flux of diffusion of the thermomigrated atom J by the following formulatm：
Determining the stress migration atomic diffusion flux, determining the stress migration atomic diffusion flux J bysm：
Under the comprehensive action of electron wind power, temperature gradient and stress gradient, determining the atomic diffusion flux divergence, and expressing the atomic diffusion flux divergence by the following formula:
div(Jtotal)＝div(Jem)+div(Jtm)+div(Jsm)
wherein N is an Avogastron constant, DoAs diffusion coefficient, EaFor activation energy, Ω is the atomic volume.
As shown in a metal interconnection line graph 2 designed by the invention, as shown in a graph 3, the subsequent calculation can be carried out only by reasonably dividing the grids. And calculating the temperature current density and stress distribution of the interconnection line through voltage, environment temperature and material parameters, inputting 0.25V of voltage and physical field distribution of the Cu interconnection line. As shown in fig. 4 to 6, a current density distribution, a temperature distribution pattern, and a stress distribution can be seen.
The divergence is calculated for research and calculation, the initial temperature is room temperature 293.15K, constant temperature is applied to the bottom surface, the top surface is used for heat convection to simulate the heat dissipation condition of the surface of the circuit board, and the vertical surfaces adopt thermal insulation boundary conditions to represent the heat dissipation condition of a certain position of the circuit board. Convection heat flux equation. Wherein C isPThe constant pressure heat capacity, K the thermal conductivity, h the heat transfer coefficient, 5W/(m 2K), Text the outside temperature 293.15K.
The atomic diffusion flux divergence can effectively characterize electromigration, with the divergence occurring when the atoms are lost and the divergence occurring when the atoms are packed negatively, as shown in fig. 7 to 9, which are distributions of atomic diffusion flux migration divergence under different stresses.
The above description is only a preferred embodiment of the three-dimensional package interconnection line electromigration simulation method, and the protection scope of the three-dimensional package interconnection line electromigration simulation method is not limited to the above embodiments, and all technical solutions belonging to the idea belong to the protection scope of the present invention. It should be noted that modifications and variations which do not depart from the gist of the invention will be those skilled in the art to which the invention pertains and which are intended to be within the scope of the invention.
Claims (5)
1. A three-dimensional packaging interconnecting wire electromigration simulation method is characterized in that: the method comprises the following steps:
step 1: establishing an EM point thermal three-field coupling geometric model;
step 2: determining loading boundary conditions, material parameters and physical field coupling of the geometric model;
and step 3: carrying out meshing on the geometric model, setting step length, and solving the geometric model;
and 4, step 4: and solving according to the geometric model to obtain a temperature field, a current density field and a stress field, substituting the temperature field, the current density field and the stress field into a post-processing equation, and obtaining the diffusion flux divergence of the interconnection wire atoms.
2. The electromigration simulation method of a three-dimensional package Cu interconnect line of claim 1, wherein: the step 1 specifically comprises the following steps: based on Comsol Multiphsics, an EM point thermal three-field coupling geometric model is established by adopting an AC/DC module, a solid heat transfer module and a solid mechanics module, and Cu electromigration at different temperatures is simulated.
3. The electromigration simulation method of a three-dimensional package interconnection line of claim 1, wherein: the step 2 specifically comprises the following steps:
according to the fact that the initial temperature is 293.15K, the constant temperature is applied to the bottom face, the heat dissipation condition of the surface of the circuit board is simulated by means of heat convection of the top face, the heat insulation boundary conditions are adopted for the vertical faces to represent the heat dissipation condition of a certain position of the circuit board, and the loading boundary conditions of the geometric model are represented by the following formula:
q0＝h·(Text-T)
wherein, CPIs constant pressure heat capacity, k is heat conduction systemNumber, h is heat transfer coefficient, T is temperature, T is time, u is voltage, Q is heat flux, QtedBased on heat flux, q is solid heat transfer heat flux density, q0Heat flux density, T, for heat convectionextIs the outside temperature;
the adopted current is the current conduction in a Cu interconnection line, wherein the input potential of the top surface of the Cu wire is 0.25V and 0.3V, the other end surface of the Cu wire is grounded, and the material parameters are determined by the following formula:
E＝-▽V
wherein J is current density, QjIs the amount of charge, σ is the conductivity,0in order to have a dielectric constant in a vacuum,rrelative dielectric constant, E electric field strength, JeFor initial test current density, V is potential;
by applying a boundary condition of fixed constraint at the bottom edge, the conducting wire and the substrate are both made of linear elastic materials;
the physical field coupling sets the physical field distribution of the Cu interconnect lines such that the input voltage is 0.25V.
4. The electromigration simulation method of a three-dimensional package interconnection line of claim 1, wherein: the step 3 specifically comprises the following steps:
step 3.1: carrying out meshing on the geometric model by adopting a comsol automatic free tetrahedron meshing method, wherein the maximum unit size is 4.4nm, the minimum unit size is 0.32nm, the maximum unit growth rate is 1.4, the curvature factor is 0.4, the resolution of a narrow area is 1.7, the stepping time length is 0.1h, and the total time length is 1 h;
step 3.2: the method comprises the steps of selecting a physical field as electric heating coupling field analysis and solid heat transfer and solid mechanics coupling, calculating electric field, current and potential distribution in a conductor medium through electric field analysis, solving a current conservation equation based on ohm's law, calculating temperature distribution and temperature gradient distribution according to a temperature field, calculating model stress distribution through a solid mechanics module, and finally obtaining the temperature field, a current density field and a stress field.
5. The electromigration simulation method of a three-dimensional package interconnection line of claim 1, wherein: the step 4 specifically comprises the following steps:
obtaining a temperature field, a current density field and a stress field according to the solution, substituting the temperature field, the current density field and the stress field into a post-processing equation, and obtaining the diffusion flux divergence of the atoms of the interconnection line;
determining an electromigration atomic diffusion flux, the electromigration atomic diffusion flux J is represented byem：
Determining a flux of diffusion of the thermomigrated atom, determining a flux of diffusion of the thermomigrated atom J by the following formulatm：
Determining the stress migration atomic diffusion flux, determining the stress migration atomic diffusion flux J bysm：
Under the comprehensive action of electron wind power, temperature gradient and stress gradient, determining the atomic diffusion flux divergence, and expressing the atomic diffusion flux divergence by the following formula:
div(Jtotal)＝div(Jem)+div(Jtm)+div(Jsm)
wherein N is an Avogastron constant, DoAs diffusion coefficient, EaFor activation energy, Ω is the atomic volume.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113128097A (en) * | 2021-04-29 | 2021-07-16 | 浙江理工大学 | Method for simulating and predicting heat transfer performance of porous nanofiber medium |
| CN113283085A (en) * | 2021-05-27 | 2021-08-20 | 复旦大学 | Simulation method and system of gate switch |
Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5712510A (en) * | 1995-08-04 | 1998-01-27 | Advanced Micro Devices, Inc. | Reduced electromigration interconnection line |
| US20020107675A1 (en) * | 2000-06-05 | 2002-08-08 | Nec Corporation | Wiring failure analysis method using simulation of electromigration |
| CN102590629A (en) * | 2012-02-10 | 2012-07-18 | 工业和信息化部电子第五研究所 | High-precision electromigration early warning circuit |
| CN102760727A (en) * | 2011-04-27 | 2012-10-31 | 中芯国际集成电路制造(上海)有限公司 | Testing device and method of electromigration of interconnection line |
| CN104252559A (en) * | 2014-08-29 | 2014-12-31 | 浙江中科电声研发中心 | Numerical simulation analysis method for multi-field coupling of loudspeaker |
| CN105592972A (en) * | 2013-08-05 | 2016-05-18 | 千住金属工业株式会社 | Lead-free solder alloy |
| CN106442124A (en) * | 2016-11-30 | 2017-02-22 | 华南理工大学 | Shape-memory alloy material fatigue performance test system in electricity-thermal coupling field |
| CN106485027A (en) * | 2016-10-26 | 2017-03-08 | 东南大学 | A kind of three-dimensional heterogeneous integrated TSV through hole electrothermal forces coupling modeling method and emulation mode |
| CN107153750A (en) * | 2017-06-12 | 2017-09-12 | 北京工业大学 | Supply network electromigration reliability analysis method on a kind of piece based on physical model |
| CN110287639A (en) * | 2019-07-04 | 2019-09-27 | 北京航空航天大学 | A kind of lead-free component interconnection solder joint coupled thermomechanics emulation mode |
| CN110362880A (en) * | 2019-06-25 | 2019-10-22 | 西安交通大学 | Optical fiber attenuation characteristic multiple physical field emulation modelling method in a kind of OPLC cable |
| CN110516378A (en) * | 2019-08-30 | 2019-11-29 | 桂林电子科技大学 | A kind of Finite Element Method that tinbase binary eutectic mutually separates |
-
2020
- 2020-07-02 CN CN202010627520.0A patent/CN111723511B/en active Active
Patent Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5712510A (en) * | 1995-08-04 | 1998-01-27 | Advanced Micro Devices, Inc. | Reduced electromigration interconnection line |
| US20020107675A1 (en) * | 2000-06-05 | 2002-08-08 | Nec Corporation | Wiring failure analysis method using simulation of electromigration |
| CN102760727A (en) * | 2011-04-27 | 2012-10-31 | 中芯国际集成电路制造(上海)有限公司 | Testing device and method of electromigration of interconnection line |
| CN102590629A (en) * | 2012-02-10 | 2012-07-18 | 工业和信息化部电子第五研究所 | High-precision electromigration early warning circuit |
| CN105592972A (en) * | 2013-08-05 | 2016-05-18 | 千住金属工业株式会社 | Lead-free solder alloy |
| CN104252559A (en) * | 2014-08-29 | 2014-12-31 | 浙江中科电声研发中心 | Numerical simulation analysis method for multi-field coupling of loudspeaker |
| CN106485027A (en) * | 2016-10-26 | 2017-03-08 | 东南大学 | A kind of three-dimensional heterogeneous integrated TSV through hole electrothermal forces coupling modeling method and emulation mode |
| CN106442124A (en) * | 2016-11-30 | 2017-02-22 | 华南理工大学 | Shape-memory alloy material fatigue performance test system in electricity-thermal coupling field |
| CN107153750A (en) * | 2017-06-12 | 2017-09-12 | 北京工业大学 | Supply network electromigration reliability analysis method on a kind of piece based on physical model |
| CN110362880A (en) * | 2019-06-25 | 2019-10-22 | 西安交通大学 | Optical fiber attenuation characteristic multiple physical field emulation modelling method in a kind of OPLC cable |
| CN110287639A (en) * | 2019-07-04 | 2019-09-27 | 北京航空航天大学 | A kind of lead-free component interconnection solder joint coupled thermomechanics emulation mode |
| CN110516378A (en) * | 2019-08-30 | 2019-11-29 | 桂林电子科技大学 | A kind of Finite Element Method that tinbase binary eutectic mutually separates |
Non-Patent Citations (5)
| Title |
|---|
| ZHONG GUAN 等: "Atomic flux divergence based current conversion scheme for signal line electromigration reliability assessment", 《IEEE INTERNATIONAL INTERCONNECT TECHNOLOGY CONFERENCE》 * |
| 张元祥: "多物理场下金属微互连结构的电迁移失效及数值模拟研究", 《中国优秀博硕士学位论文全文数据库(博士)信息科技辑》 * |
| 张墅野 等: "三维封装电迁移Cu互连线的多物理场模拟仿真", 《材料导报》 * |
| 杜磊 等: "电迁移物理模型参数统计特性提取新方法", 《电子产品可靠性与环境试验》 * |
| 耿保林: "具有侧面冗余的铜互连线的电迁移效应研究", 《中国优秀博硕士学位论文全文数据库(硕士)信息科技辑》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113128097A (en) * | 2021-04-29 | 2021-07-16 | 浙江理工大学 | Method for simulating and predicting heat transfer performance of porous nanofiber medium |
| CN113128097B (en) * | 2021-04-29 | 2023-11-17 | 浙江理工大学 | Method for simulating and predicting heat transfer performance of porous nanofiber medium |
| CN113283085A (en) * | 2021-05-27 | 2021-08-20 | 复旦大学 | Simulation method and system of gate switch |
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