Analysis of a bipolar energy-transport model for a metal-oxide-semiconductor diode

A simplified bipolar energy-transport model for a metal-oxide-semiconductor diode (MOS) with nonconstant lattice temperature is considered. The electron and hole current densities vanish in the diode but the particle temperature may be large. The existence of weak solutions to the system of quasilinear elliptic equations with nonlinear boundary conditions is proved using a Stampacchia trunction technique and maximum principle arguments. Further, an asymptotic analysis for the one-dimensional MOS diode is presented, which shows that only the boundary temperature influences the capacitance-voltage characteristics of the device. The analytical results are underlined by numerical experiments.