Self-heating effects are accounted for by including the lattice heat flow equation
in the system of partial differential equations.
are the mass density and the specific heat, respectively. The heat
generation term depends on the transport model used.
Due to the assumption that the carrier temperature does not deviate
from the lattice temperature in the DD model, the energy relaxation
times are zero and the heat generation reads:
The last term in (4.23) gives the recombination heat
transferred to the lattice and is proportional to the net
recombination and the band gap eneregy
In the HD transport model, the heat generation is obtained by
substituting the local energy balance equations (here only for electrons):
in the DD heat generation term (4.23). The resulting expression reads:
This solution is obtained from the stationary energy flux balance and
the carrier continuity
equations (4.13), (4.14). The first term
approximates the energy relaxation of the scattering terms of the
Boltzmann equation .
An alternative global self-heating model also
exists . By calculating a spatially constant lattice
temperature it delivers similar results to the standard model, at
greatly reduced computational expenses.
S. Vitanov: Simulation of High Electron Mobility Transistors