Group classification of an energy transport model for semiconductors with crystal heating

We consider an energy transport model for semiconductors describing the electrothermal effects. The unipolar model involves four equations: the continuity and the energy balance equations for the electrons, the thermal diffusion equation for the lattice and the Poisson equation for the electric potential. The model can be derived by moment method from the Boltzmann transport equation for electrons in semiconductors. For this model, we perform a symmetry group classification by the infinitesimal Lie method and exact solutions are found.