el for E~e~tr~t~ermal Simulation A. Ammous, S. Ghedira, B. Allard and H. Morel zyxw CEGELY, NSA-Lyon Build. 40 1, 20 AV Einstein, Villeurbanne F-6962 1, France E-mail: ammous@cegely.insa-lyon.fr zyxw ABSTRACT The literature proposcs some thermal models needed for the electrothermal simulation of power electronic systems. This paper gives a useful analysis about the choice of the thermal model circuit networks, equivalent to a discretisation of the heat equation by the finite difference method and thc finite element method and an analytic model developed by applying an internal approsiination of tlie heat diffusion problem. The efrect of the boundary condition representation and tlie introduced errors on temperature response at the licat source are studied. This study is advantageous particularly for large surges of short time duration. NOMENCLATURE zyxwvutsrq L,S: Effective length and area of the semiconductor device. c: Silicon specific heat. zyxwvutsrq p zyxwvutsrqp : Silicon mass density. zyxwvutsr T: Absolute temperature. Ta: Room temperature, P(0: Dissipated power. K: Thermal conductivity. 1. INTRODUCTION Equivalent electrical circuits as thermal inodeling are largely used because of their easy ~mplciiientatio~i in circuit simulators in whic11 most of the semiconductor device models are implemented This enables a simple coupling between electrical and thermal phenomena. Semiconductor manufactures providc tlic "ef€ective transient therinal impedance ciirvc" [ 11 as the key tool to calculate the peak junction tempcraturc in the device. This curve does not include dissipated power for pulse width in tlie order of few mjcroseconds. This curve is based 011 classical analysis of the temperature evolutioii in the structure, which assumes a semi-finite solid. It is obtained from a convolution method. S. Clement in [2] evokes this problem and proposes a correction of tlie calculated temperature obtained by the analytical formulation developed by the classical method to take in to account tlie finite dimension of the die. This new analysis gives an appropriate correction of the estimated peak junction temperature of seniiconductor devices usefiil in the case of large surges of short time duration. Unfortiinately for a given input power dissipation, the peak junction temperature is given by a convolution model and it does not fit with circuit simulators. On tlie other hand, equivalent electrical circuits and analytical model fit well with circuit simulators. Classical equivalent circuits (Fig. I) are based on a finite difference discrctisation of the heat equation [3-4]. Fig. 1. equivalent thcrnial circuit networks obtained by the FDM A recent paper [5] proposes a11 other equivalent electrical circuit based on the finite element approach (Fig. 2). In 161, the authors proposed an 0-7803-4489-8/98/$10.00 zyxwvutsrqpo 0 1998 IEEE zyxwvutsr 1668