Transient Thermal Analysis And Electromagnetic-thermal Cosimulation Using Discontinuous Galerkin Time-domain Method

With continuously increasing integration density and shrinking features of high speed integrated circuits,it may induce serious power dissipation problem and temperature rise in the 3D system package.And these thermal issues would not only degrade the electrical performance,but also lead to serious reliability issue of the overall system.Therefore,effective thermal analysis,thermal management and electrothermal interaction co-simulation are essential at the design of electronic devices.In this thesis,a discontinuous Galerkin time-domain(DGTD)algorithm is proposed to solve thermal conduction equation and provide numerical solver tools for the thermal analysis of some complicated 3D integrated circuits system packages.The transient electromagnetic–thermal co-simulation of dispersive media is also implemented in an iterative scheme based the framework of DGTD algorithm.The DGTD method is proposed to conduct the transient thermal analysis for complicated integrated circuits in this dissertation.The DGTD method is capable of modeling arbitrary shapes and simultaneously can achieve high-order accuracy by adopting hierarchical basis functions.Since the thermal equation as a parabolic partial differential equation(PDE)is thus unable to be directly solved by the DGTD algorithm.To handle this problem,an auxiliary variable named heat flux is introduced and the thermal equation is transformed to be a hyperbolic PDE that can be written into a conservative form.Together with the auxiliary differential equation(ADE)governing the auxiliary variable,the newly constructed thermal equation can be solved by the DGTD method.All operators in the DGTD analysis are local,and the information exchange between the neighboring mesh elements is implemented by a term called numerical flux.Specifically,the coefficients of numerical flux are redefined to consider the convection boundary condition.Then,to verify and validate the accuracy of the proposed algorithm,the thermal characteristics of some complicated 3D integrated circuits system packages are analyzed.The Joule heating effects of on-chip multilayer interconnects in the presence of electrostatic discharge(ESD)pulses is carried out with the DGTD thermal analysis.Instead of directly considering the physical presence of through silicon-vias(TSV)and ball grid array,the thermal effects of TSVs in the interposer and ball grid array in the micro-bump layer are replaced by equivalent thermal models,which are from extraction based on the thermal theory.The temperature distribution and thermal analysis of integrated package are studied.To further demonstrate the capability of the proposed algorithm for analyzing complicated multiscale systems,a 3-D integrated circuit package with vertically stacked-up chips connected by TSVs is also studied and all the mesh elements in this package structure are modeled rigorously with practical geometrical size.In this thesis,the transient electromagnetic–thermal simulation is performed for dispersive media using the DGTD method.In practice,since some electrical parameters of dispersive media may be temperature-dependent(e.g.,the permittivity).The thermal distribution in the media due to self-heating effects will change their values and in turn impact the electromagnetic performance.Thus,the electrical and thermal co-simulation requires a coupled mechanism in an iterative way.Instead of executing the complex convolution in the time domain,the ADE method is employed to manipulate dispersive media,where the polarization current density is introduced as an auxiliary variable.As the heat source in electromagnetic–thermal simulation,the transient power loss density for three typical dispersive media(Debye,Lorentz,and Drude model)is derived by the electrodynamic approach and also explained with equivalent circuit models.And several numerical examples of dispersive media are studied by the proposed transient electromagnetic–thermal simulation scheme based on the DGTD approach.Both the frequency-dependent and temperature-dependent properties of dispersive media are considered in the modeling.