Circular and annular constriction resistances within a compound thermal spreader for cooling microelectronic devices

Analytical solutions are obtained for the steady state temperature distributions and one- and two-dimensional resistances of a compound thermal spreader. The spreader has a circular heating device on one face and an annular sink on the other. By means of an analytical expression for the dimensionless total coonstriction (spreading) resistance, a parametric study is performed to demonstrate the influence of various parameters on resistance for typical ranges of conductivity ratio, relative device size, relative sing size, and the relative thicknesses of the chip and substrate. The full results of the parametric study are reproduced in graphic form.