The heat-flow problem in silicon: An approach to an analytical solution with application to the calculation of thermal instability in bipolar devices

The experimental data for the temperature dependence of the thermal conductivity of silicon are reviewed. It is proposed that an empirical formula of the form
K = K_{0}/(T-T_{0})
provides a good description of the measurements. The steady-state heat-flow equations are formulated so that the nonlinear heat-flow problem may be solved in terms of an equivalent linear problem. The method is applied in conjunction with an idealized thermal and electrical device model, to calculate the thermal instability boundary (or second breakdown boundary), of a commercial power transistor.