We consider integrated circuits with semiconductors modeled by modified nodal
analysis and drift-diffusion equations. The drift-diffusion equations are
discretized in space using mixed finite element method. This discretization
yields a high dimensional differential-algebraic equation. We show how proper
orthogonal decomposition (POD) can be used to reduce the dimension of the
model. We compare reduced and fine models and give numerical results for a
basic network with one diode.