Electrothermal Simulation and Optimal Design of Thermoelectric Cooler Using Analytical Approach

Abstract

In this article, electrothermal modeling and simulation of thermoelectric cooling (TEC) in the package design of VLSI systems are performed by solving coupled heat conduction and current continuity equations. We propose a new analytical solution to the coupled partial differential equations (PDEs) which describe temperature and voltage with the reduction from 3-D to 1-D. In addition to this, we derive new analytic expressions for two key performance metrics for TEC devices: 1) the maximum temperature difference and 2) the maximum heat-flux pumping capability, which can be guided for the optimal design of thermoelectric cooler to achieve the maximum cooling performance. Furthermore, for the first time, we observe that when the dimensionless figure of merit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ZT_{0}$ </tex-math></inline-formula> value is larger than 1, there is no maximum heat-flux value, which means the heat dissipation due to the Peltier and Fourier transfer effects is larger than the heat generation caused by the Joule heating effect, which can lead to more efficient TEC cooling design. The accuracy of the proposed 1-D formulas is verified by a 3-D finite element method using COMSOL software. The compact model delivers many orders of magnitude speedup and memory saving compared to COMSOL with marginal accuracy loss. Compared with the conventional simplified 1-D energy equilibrium model, the proposed analytical coupled multiphysics model is more robust and accurate.