Research On Time Domain Analysis Of Nonlinear Semiconductor Devices And Microwave Circuits

With the continuous progress and development of computational electromagnetics,the time-domain numerical methods of electromagnetic field have become more and more stable and efficient.All kinds of complex practical circuit problems can be effectively analyzed by all kinds of time-domain numerical methods in the computational electromagnetics,such as the time-domain integral equation(TDIE)method and the spectral-element time-domain(SETD)method.This dissertation mainly focuses on the electromagnetic coupling problems of semiconductor devices and microwave circuits,for example,electro-thermal coupling problems of micron-scale and nano-scale semiconductor devices,field-circuit coupling problems and field-line-circuit coupling problems of nonlinear semiconductor devices.This dissertation is based on the TDIE method and the SETD method.The time-domain methods of the nonlinear semiconductor devices and microwave circuits are researched in this dissertation.The main research work and achievements of this dissertation are summarized as follows:In the first part of this dissertation,the basic principle of the time-domain surface integral equation method(TD-SIE)and time-domain volume-surface integral equation(TD-VSIE)method based on the marching-on-in-time method are introduced.The established process of the time-domain integral equation,the expression of the time and space basis functions and the solution scheme of the maching-on-in-time method are presented,respectively.The theoretical basis is provided for solving the field-circuit coupling problem and the field-line-circuit coupling problem.Next,the basic principle of the spectral-element time-domain method and the semiconductor equations based on the physical model is given.The concrete form of physical model equations of the micron-scale and nano-scale semiconductor devices is introduced.At the same time,the expression of the basis functions in the SETD method is also given.The theoretical basis is provided for the study on the time domain analysis method of the nonlinear semiconductor devices and microwave circuits.In the second part of this dissertation,the field-circuit coupling algorithm based on the TD-VSIE method is researched at first.The equivalent model of semiconductor devices based on the Modified Node Analysis(MNA)method is given.Then the field-circuit coupling system algorithm based on TD-VSIE method is successfully established and applied to analyze the microwave circuit problem of linear elements based on the equivalent model.Next,a synchronous field-circuit coupling solution technology of the nonlinear semiconductor devices based on the the equivalent model is introduced.Based on this,an improved solution for nonlinear time-domain field-circuit coupled system equations is proposed to accelerate the nonlinear Newton's iteration solution of system matrix equations.It is important that the nonlinear PIN diode limiter circuit is modeled and simulated.Then the nonlinear physical phenomena of spike leakage and flat leakage in the PIN diode limiter are analyzed.In addition to the above field—circuit coupling algorithm,the field-line-circuit coupling algorithm based on the TDIE method is also studied in this dissertation.In order to verify the effectiveness of this algorithm,the calculation results of the TDIE and time-domain finite-difference(FDTD)method are compared.Finally,the transient characteristics of the field-line-circuit coupling structure based on the nonlinear semiconductor devices of the equivalent model are analyzed and the transient port voltage of the sensitive circuit inside the shielded cavity is obtained.In the third part of this dissertation,the time-domain characteristics of the microwave circuits including the micron-scale semiconductor microwave circuit based on physical model is studied at first.A new nonlinear field-circuit coupled system equation based on the TD-VSIE method is established,and then the simulation of the nonlinear microwave circuit including semiconductor based on the physical model is realized.Here the voltage-ampere characteristic of the micro-scale semiconductor devices is obtained by the drift diffusion model,which is solved by the SETD method.Then the discrete Newton iteration solution method is utilized to couple the voltage-ampere characteristics of the physical model semiconductor into the field-circuit system equations.Then the electrical characteristics of PIN diode limiter and MOSFET amplifier are analyzed by the TD-VSIE and SETD method.Next,the time-domain diakoptics method is proposed to effectively analyze he nonlinear microwave circuit,which is the linear response extraction technique with the TD-VSIE field-circuit coupling algorithm.The linear electromagnetic field structure and the nonlinear semiconductor devices can be separately calculated by this method,which can greatly save the overall calculation time.The accuracy and eficiency of the proposed method are verified through the comparison of the simulation results of the microwave amplifier circuit based on the semiconductor equivalent model.As semiconductor devices are analyzed individually by this method,the transient electro-thermal coupling effect of the microwave circuit including semiconductor based on the physical model can be calculated directly.In the fourth part of this dissertation,the transient electro-thermal coupling effect of nano-scale semiconductor devices based on the physical model is studied.The specific derivation process of the nano-semiconductor density gradient model equation and the Dual-Phase-Lag(DPL)heat equation are introduced,which are solved by the spectral-element time-domain method.For the nano-scale ballistic diode model,the simulation results of the drift diffusion model and the density gradient model are compared.The accuracy of the density gradient model for nano-scale semiconductor structures is verified.At the same time,the DPL equations are used to analyze the thermal characteristic of the two-dimensional Si material,the accuracy of the program is verified by the comparison with the literature.Finally,the density gradient model equation is coupled with the DPL heat equation,the electro-thermal characteristics of nano-scale semiconductor devices are given and the temperature distribution of the time-varying law inside the semiconductor device is analyzed.In conclusion,the time-domain analysis process of the electromagnetic coupling of nonlinear semiconductors and microwave circuits is studied in detail in this dissertation.In view of field-circuit coupling problem of the nonlinear semiconductor based on the equivalent model,the field-circuit coupling solution technique based on the TD-VSIE method is established at first.Then the improved solution scheme of the nonlinear field-circuit coupling system equation is proposed.For the field-line-circuit coupling problem of nonlinear semiconductors based on the equivalent model,the solution technology of the line-circuit coupling and the field-line-circuit coupling based on the TDIE method are researched.Aiming at the time-domain simulation technique of semiconductor microwave circuits based on the physical model,the TD-VSIE and SETD hybrid method are proposed.In addition,the time domain diakoptics method is also proposed for effectively analyzing nonlinear microwave circuits,which is the linear impulse response extraction technique with the TD-VSIE field-circuit coupling algorithm.For the electro-thermal coupling problem of the nano-scale semiconductor based on the physical model,the coupling solution technique of density gradient model equations and DPL heat equations is researched,and the transient electro-thermal characteristics of nano-scale semiconductors are successfully analyzed.Through a large number of numerical examples,the correctness and high efficiency of the proposed methods in this dissertation are verified.