3D IC Thermal Simulation Algorithm Using the Finite Difference Method and the Green's Function
Date Issued
2012
Date
2012
Author(s)
Jin, Wilson
Abstract
Nowadays, in the design of many-core processor, it is necessary to make temperature simulation of full die for the design of one core. It is requested to see more than one million mesh grids in a 3D plane in a full chip thermal simulation. For packing more devices per unit volume of modern integrated 3D circuits (ICs), heat conduction has become a big issue of limiting factors. This problem is exacerbated with the emergence of 3D IC where from 2D layers to 3D layer, increasing device density. To develop modern multi-core system on chip architecture, high resolution and full chip thermal simulation with millions of mesh grids, 3D IC thermal simulation becomes an important tool for micro IC design. When facing these performance demands, existing thermal simulation algorithms often requires excessive amount of computation resources to get acceptable results like huge memory, higher performance of CPU, long calculation time, limitation of inserting power source and without inserting TSV.
Accurate and efficient full-chip thermal simulation for a 3D IC is of particular importance. Until now, an analytical thermal simulation method for 3D IC substrates based using the finite difference method, the finite element method and the Green’s function of a Poisson equation has been developed. The Green’s function using discrete cosine transform significantly improved the execution time of thermal simulation compared to the conventional finite difference method. But the Green''s analytical method has a limitation on inserting TSV''s in 3D IC full chip substrate and finite difference method. Finite element methods also have limitation on requiring huge memory resources and high CPU performance.
The specific goal of this research is pursued with developing hybrid method utilized together two or more the analytical thermal simulation methods, aiming to overcome limitation like, uniform layer issue, TSV insertions problem, limitation of mesh size and etc.
First, to improve calculation time of applications at high resolution thermal profile is used a Green''s function method; numerical method of Fast Fourier Transform is proposed. The Green''s thermal simulation is based on the high resolution mesh and uniform material that the thermal resistance between power source and current mesh grid. As such, all uniformed conductivity of mesh grids could be replaced from 2D layer into a Green function based integral equation solution.
Secondly, such as 3D ICs inserting thermal through silicon via’s (TSV) and virtual power source (VPS) of multi-layer, the heterogeneous thermal conductivity is proposed using the conventional finite difference method utilizing spatial domain LUT method together.
TSV’s are high thermal conductivity material of IC to disperse heat from inner layers of a multi-layer 3D IC. The effects of TSV on the chip temperature distribution could make the model as decreasing highest temperature induced by concentrating the power sources. This analytical thermal simulation from faster and better accuracy using hybrid method can be applied to 3D full-chip IC design, offering speed-up computation while delivering accurate temperature profile.
Subjects
3DIC, Thermal Simulation, Finite Difference Method, Green’s Function, Virtual Power Source, Analytical Method, TSV and Via’s, LU Decomposition, Fast Fourier Transform and Discrete cosine transform.
Type
thesis
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