[Back]

M. Brunk, A. Jüngel:
"Numerical coupling of electric circuit equations and energy-transport models for semiconductors";
in: "ASC Report 12/2007", issued by: Institue for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

A coupled semiconductor-circuit model including thermal effects is proposed. The
charged particle flow in the semiconductor devices is described by the energy-transport equations
for the electrons and the drift-diffusion equations for the holes. The electric circuit is modeled by
the network equations from modified nodal analysis. The coupling is realized by the node potentials
providing the voltages applied to the semiconductor devices and the output device currents for
the network model. The resulting partial differential-algebraic system is discretized in time by the
2-stage backward difference formula and in space by a mixed-hybrid finite-element method using
Marini-Pietra elements. A static condensation procedure is applied to the coupled system reducing
the number of unknowns. Numerical simulations of a one-dimensional pn-junction diode with timedepending
voltage and of a rectifier circuit show the heating of the electrons which allows to identify
hot spots in the devices. Moreover, the choice of the boundary conditions for the electron density
and energy density is numerically discussed.

Energy-transport equations, circuit equations, semiconductor devices, modified

http://www.asc.tuwien.ac.at/preprint/2007/asc12x2007.pdf