Abstract
A complete four-dimensional solution T( x, y, z, t) to the classical dynamic heat-flow equation, for the case where the power sources lie on the silicon surface, is presented. The solution is found by: (i) applying multiple finite Fourier transforms with respect to x and y; (ii) Laplace-transforming with respect to time; (iii) solving the resulting differential equations for the z variable and determining the Fourier components; (iv) performing the inverse Laplace transforms for all the Fourier terms and summing them. The solution has been used to simulate the thermal behaviour of several different IC power configurations.
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