Journal of Computational Electronics

, Volume 10, Issue 1–2, pp 163–178 | Cite as

Self-heating in a coupled thermo-electric circuit-device model

  • Markus Brunk
  • Ansgar Jüngel


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 Mixed finite-element method Partial differential-algebraic equations 


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© Springer Science+Business Media LLC 2010

Authors and Affiliations

  1. 1.Department C, Institute for MathematicsBergische Universität WuppertalWuppertalGermany
  2. 2.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria

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