Research Of Electrothermal Coupling Algorithms And Preconditioned Iterators Applied To Integrated Circuit

Due to the continuous development of integrated circuits and their packaging technology,the power density and current density in the circuit are increasing day by day.Therefore,the influence of the increase of power density must be considered in the design of integrated circuits.When the internal power of the circuit increases significantly,the electro-thermal coupling effect is obvious.The electro-thermal coupling effect which obeyed the resistivity law and the Joule law,couple the current density and temperature distribution together,showing the phenomenon of interaction between physical quantities.In general,the size of IR voltage drop affects the performance of integrated circuits,while temperature affects the heat dissipation of integrated circuits.There are many kinds of numerical algorithms could calculate these physical parameters.In this paper,the numerical algorithms for calculating the electro-thermal coupling effect and the models in integrated circuits are studied,the existing numerical algorithms are studied and improved,the advantages and disadvantages of various numerical algorithms are understood,and a numerical algorithm for inhomogeneous media oriented to the electro-thermal coupling effect in integrated circuits is proposed.The main work is as follows:1.In this paper,a single physical process(electrical process and thermal process)is firstly modeled,and finite element algorithm is used as the main method for discrete electrical process and thermal process.Then,the electro-thermal coupling numerical calculation method(ETCM)is proposed to deal with the electro-thermal coupling effect.Since it is impossible to ignore the non-uniform temperature and other inhomogeneous parameters in the calculation process,the vectorized parameter updating method(VUM)is further proposed and applied to ETCM.The two algorithms are combined to obtain the electro-thermal coupling algorithm(ETCM-VUM)to deal with inhomogeneous parameters.VUM treats each physical parameter as a multidimensional vector,and each element within the vector is taken as an independent parameter within the element.The algorithm is verified by the second order partial differential equation with mathematical analytic solution2.In order to speed up the iterative solution of matrix and expand the work of the first step,a generalized minimal residual method(GMRES)with AINV precondition was proposed(PGMRES-AINV).After testing,the AINV precondition can reduce the number of iteration steps and accelerate the convergence of calculation in the four main matrix iterative methods.In addition,the PGMRES-AINV solver can also produce convergence results when the ill-conditioned matrix obtained by other iterative methods for solving the discrete multi-scale model is faced with iteration stagnation,oscillation and non-convergence3.Complete boundary value analysis and electro-thermal coupling effect modeling are carried out for the power transmission network part of integrated circuit,carrier printed circuit board(PCB)and bonding wire in package.In the case of fully considering the iterative coupling relationship between inhomogeneous physical quantity vectors,the ETCM-VUM algorithm and the PGMRES-AINV solver are used to obtain the IR drop and the inhomogeneous temperature and potential distribution in the power transmission network.Since the algorithm is implemented by C programming,the large symmetric sparse matrix adopts the sparse storage method to reduce the memory consumption.,and the PGMRES-AINV solver has a fast convergence speed.Therefore,by comparing the other two commercial software,our algorithm program shows a higher time efficiency.