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M. Brunk, A. Jüngel:
"Heating of semiconductor devices in electric circuits";
in: "ASC Report 32/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

Thermal effects in a coupled circuit-device system are modeled and numerically
simulated. The circuit equations arise from modified nodal analysis. The
transport in the semiconductor devices is modeled by the energy-transport equations
for the electrons and the drift-diffusion equations for the holes, coupled to the Poisson
equation for the electric potential. The lattice temperature is described by a heat
equation with a heat source including energy relaxation heat, recombination heat,
hole Joule heating, and radiation. The circuit-device model is coupled to a thermal
network. The resulting system of nonlinear partial differential-algebraic equations is
discretized in time using backward difference formulas and in space using (mixed)
finite elements. Heating effects from numerical simulations in a pn-junction diode
and a clipper circuit are presented.

http://www.asc.tuwien.ac.at/preprint/2008/asc32x2008.pdf