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M. Brunk, A. Jüngel:
"Self-heating in a coupled thermo-electric circuit-device model";
in: "ASC Report 36/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8, '?.

The self-heating of a coupled thermo-electric circuit-semiconductor system is modeled
and numerically simulated. The system consists of semiconductor devices, an electric network
with resistors, capacitors, inductors, and voltage sources, and a thermal network. The flow of the
charge carriers is described by the energy-transport equations coupled to a heat equation for the
lattice temperature. The electric circuit is modeled by the network equations from modified nodal
analysis coupled to a thermal network describing the evolution of the temperatures in the lumped
and distributed circuit elements. The three subsystems are coupled through thermo-electric, electric
circuit-device, and thermal network-device interface conditions. The resulting system of nonlinear
partial differential-algebraic equations is discretized in time by the 2-stage backward difference formula
and in space by a mixed finite-element method. Numerical simulations of a one-dimensional
ballistic diode and a frequency multiplier circuit containing a pn-junction diode illustrate the heating
of the semiconductor device and circuit resistors.

Energy-transport equations, lattice heating, thermal network, circuit equations,

http://www.asc.tuwien.ac.at/preprint/2008/asc36x2008.pdf