VACUUM AND NONVACUUM SOLUTIONS OF THE QUASI-HYDRODYNAMIC SEMICONDUCTOR MODEL IN THERMAL-EQUILIBRIUM

The quasi-hydrodynamical model for bipolar semiconductor devices in th ermal equilibrium admits in general solutions for which the non-negati ve electron- or hole-density is not strict positive. In this paper suf ficient conditions depending on the device's data which lead to or pre vent vacuum are presented. The transformation of the model equations t o a single semilinear elliptic mixed boundary value problem for the el ectrostatic potential V reduces the vacuum-non-vacuum discussion to an investigation of the range of V. Monotonicity arguments and the emplo yment of local sub- and supersolutions allow to estimate the size as w ell as the distance from the Dirichlet boundary of the respective vacu um sets. An one-dimensional model is analysed in some detail.