EFFICIENT HEAT-TRANSFER APPROXIMATION FOR THE CHIP-ON-SUBSTRATE PROBLEM

An analytically based approximate solution is presented for the therma l resistance of an axisymmetric heat source mounted on a conductive su bstrate with bottom- and top-side convective cooling of the substrate. The approximation closely matches an exact solution for bottom-side c onvective cooling and reference finite element solutions for top-side and both-side cooling over broad ranges of substrate thickness (10(-4) less than or equal to t less than or equal to 10(4) and 10(-2) less than or equal to t less than or equal to 10(2)), substrate outer radi us (1 less than or equal to b less than or equal to 100) and convecti ve Blot numbers (10(-4) to 10(2)). With bottom-side cooling a minimum in the thermal resistance cart occur over a wide range of substrate th icknesses. The approximate solution possesses simplicity and ease of c omputation as compared to exact or computational solutions for many mi croelectronic applications.