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We consider a modified time-dependent van Roosbroeck system with saturating velocities and a source term subject to assumptions designed to permit a standard generation term corresponding to impact ionization. This is then a nonlinear parabolic system with a right hand side of the form S = S(., u, Δu, ɛ), coupled with the map L : u ⇔ ɛ defined by the Poisson equation at each t. The analysis leads to existence of solutions for all time as well as uniqueness (and continuous dependence on data) under stronger conditions.

The transient semiconductor problem with generation terms, II