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

The paper presents a discussion on the application of the Kirchhoff transformation to the thermal analysis of semiconductor devices with temperature-dependent and piecewise inhomogeneous thermal conductivity. The Kirchhoff transformation is shown to generally reduce the problem to the solution of the linear heat equation with nonlinear jump conditions 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 temperature dependence of the thermal conductivity can be approximated in all subdomains so as to enforce this condition; one and two-dimensional examples are discussed to show that in realistic configurations (devices with metal heat sinks, multilayered structures made of different semiconductors) the error thereby introduced is acceptably low.