ON THE APPLICATION OF THE KIRCHHOFF TRANSFORMATION TO THE STEADY-STATE THERMAL-ANALYSIS OF SEMICONDUCTOR-DEVICES WITH TEMPERATURE-DEPENDENTAND PIECEWISE INHOMOGENEOUS THERMAL-CONDUCTIVITY

The paper presents a discussion on the application of the Kirchhoff tr ansformation to the thermal analysis of semiconductor devices with tem perature-dependent and piecewise inhomogeneous thermal conductivity. T he Kirchhoff transformation is shown to generally reduce the problem t o the solution of the linear heat equation with nonlinear jump conditi ons on the apparent temperature across subdomains, unless the ratio of the thermal conductivities is temperature independent, in which case the apparent temperature is continuous. In many practical cases, the t emperature dependence of the thermal conductivity can be approximated in all subdomains so as to enforce this condition; one and two-dimensi onal examples are discussed to show that in realistic configurations ( devices with metal heat sinks, multilayered structures made of differe nt semiconductors) the error thereby introduced is acceptably low.