THE THERMAL-EQUILIBRIUM STATE OF SEMICONDUCTOR-DEVICES

The thermal equilibrium state of two oppositely charged gases confined to a bounded domain Omega subset of R(m), m = 1,2 or m = 3, is entire ly described by the gases' particle densities p, n minimizing the tota l energy epsilon(p, n). It is shown that for given P,N > 0 the energy functional epsilon admits a unique minimizer in {(p, n) epsilon L(2)(O mega) x L(2)(Omega) : p,n greater than or equal to 0, integral(Omega)P = P,integral(Omega)n = N} and that p, n epsilon C(Omega)boolean AND L (infinity)(Omega). The analysis is applied to the hydrodynamic semicon ductor device equations. These equations in general possess more than one thermal equilibrium solution, but only the unique solution of the corresponding variational problem minimizes the total energy. It is eq uivalent to prescribe boundary data for electrostatic potential and pa rticle densities satisfying the usual compatibility relations and to p rescribe V-e and P, N for the variational problem.