Study Of A Finite Difference Method And A Stable Radial Point Interpolation Method To Simulate Multi-physics Problems

With the development of 5G technology,the chip integration is getting higher and smaller.Correspondingly,the energy density is becoming more and more concentrated.Therefore,Joule heat will cause the temperature of the device to rise continuously.Because the characteristics of many materials will change with the temperature,especially the semiconductor materials,which are commonly used in devices and have a property that the temperature rises rapidly but decreases slowly.Eventually,the temperature will reduce the stability and reliability of the device.In order to solve the above problem,a finite difference method(FDM)are introduced and applied in this dissertation.The mathematic model consists of two parts: static electric field equation and transient temperature field equation.This algorithm can be used to analyse the transient electro-thermal effects of an active circuits and electronic components.In addition,to solve the ill-conditioned problems of the moment matrix of a meshless radial point interpolation method(RPIM),a stable solution based on a truncated singular value decomposition(TSVD)technique is proposed.The electro-thermal coupling process of a thin film resistor,which has a 2-D structure,is simulated and observed.Specifically,the main works of this paper are as follows:1)to analyze the multiphysics process of a circuit or an element of a circuit,such as a resistor,an electro-thermal coupling model is developed based on a three dimensional(3-D)finite difference method by using MATLAB software.2)to study the effect of the temperature on parameters of a circuit,the varieties of the conductivity of a resistor and the thermal conductivity with the temperature is simulated.3)to make the program run faster,the C language is used to code it.4)to solve the ill-conditioning problems in the meshless method,a TSVD method is introduced into the RPIM method to remove the instability.