Investigations On Multiphysics Modeling And Simulation Of Integrated Circuits

With the rapid development of 3D ICs technique,the chip achieves higher density,more functionality,smaller size,higher performance,etc.The frequency spectrum of high-speed digital signal reaches a microwave band,which leads to electromagnetic compatibility(EMC)problems.The increasing power density results in serious thermal reliability issues.The high current density can cause electromigration reliability problems of the interconnects.What's more,there exists interaction and coupling effects between Multiphysics,including electromagnetic/electrical field,thermal field and electromigration stress field,which are complex and nonlinear problems.Therefore,Multiphysics co-simulation is particularly significant for the design of 3D ICs.This dissertation focus on solving the Maxwell' equations,heat conduction equation and electromigration Korhonen's equation using numerical and analytical methods.Based on the above methods and connections between Multiphysics,Multiphysics cosimulations of 3D ICs are investigated.The main contributions of the dissertation are shown as follows:1.Based on the gradient model describing conductor surface roughness,an analytical solution for linear conductivity and a semi-analytical solution for arbitrary conductivity are derived to compute magnetic field.By using the proposed semianalytical gradient model(SAGM)model,the impact of surface height distributions with same root-mean-square(RMS)value,such as uniform,normal and Rayleigh distribution,on the coducotor loss of transmission line is studied.It can be seen that conductor surface roughness can not only be described by RMS,but also be charactered by surface height distributions.Therefore,the SAGM model is more reasonable than the gradient model to describe the conductor surface roughness.2.Based on alternating-direction-implicit finite-difference time-domain(ADIFDTD)numerical method,Maxwell's equations with Debye model are solved to analyze the shielding effectiveness of hollow delectric resonator antenna-in-chip(HDRAi P)and EMC problems of its inside circuits.With the electromagnetic pulse(EMP)plane wave,the time domain of electromagnetic field is transformed into its frequency domain using fourier transform.Based on formula of shielding effectiveness,frequency-domain feature of shielding metallic cavity with aperture is studied.The impact of EMP plane wave on the digital signal of the inside circuits is used to demonstrate the time-domain feature of shielding metallic cavity.Electromagnetic simulation is provided to guide the design of shielding metallic cavity with aperture.3.First,an analytical solution is proposed to perform the 1D steady-state thermal analysis of interconnects of power delivery network(PDN).Then,with the half boundary Rao-Wilton-Glisson(HBRWG)basis function,the improved Poisson equation solver can deal with three types of thermal boundary conditions and solve the2 D steady-state heat conduction equation.After that,based on ADI finite difference method(ADI-FDM),the relationship between the meshes of FDM and thermal resistance is estimated to build thermal resistance network to perform 3D transient thermal simulation.Finally,according to the hybrid material theory,the effective resistances of through-silicon via(TSV)array and microchannels array layers are calculated to perform heat transfer simulation in the complex structure and the fluid.The above proposed methods provide effective tools to perform thermal analysis of 3D ICs.4.Separation of variables method is used to solve Korhonen equation describing the electromigration stress and estimate the hydrostatic stress of interconnects of PDN.The determination of eigenvalues is a key step for the solution of separation of variables method.For straight line and star-like simple structures,analytical solutions are derived to estimate the eigenvalues.For complex PDN interconnects,Wittric-Williams(WW)numerical method is used to calculate the eigenvalues.Then,fast Gaussian elimination and secant method are proposed to accelerate the traditional WW method.Based on the characteristic of determinant of matrix,the last diagonal element of upper triangular matrix obtained by Gaussian ellimination is regarded as the determinant of the matrix,which can reduce the multiply operation and avoid numerical overflow.5.The above proposed numerical and analytical methods are employed to investigate the coupling effects of Multiphysics,including electromagnetic/electrical field,thermal field and electromigration stress field.First,SAGM model is proposed to study the impact of conductor surface roughness on the conductor loss and average power handling capacity of transmission lines and investigate the coupling between electromagnetic and thermal fields in frequency domain.Then,ADI numerical method is used to perform the transient electromagnetic-thermal co-simulation of Debye media and investigate the coupling between electromagnetic and thermal fields in time domain.After that,the improved poission equation solver is employed to perform 2D steadystate thermal simulation of Gallium Nitride(Ga N)power devices and investigate selfheating effects caused by electro-thermal coupling.Anderson acceleration method is used to speed up the convergence speed of coupled electro-thermal iterations.Finally,electromigration-thermomigration(EM-TM)equation is developed to carry out the electro-thermal-stress co-simulation of interconnects of PDN.