In the hydrodynamic transport model,
carrier temperatures are assumed to be different from the lattice temperature.
The basic equations (3.2) through
(3.4) are augmented by energy balance equations which
determine the carrier temperatures. The current relations take the form
Jn = q . . n . grad
+ . . grad
Jp = q . . p . grad
- . . grad
The energy balance equations state conservation
of the average carrier energies. In terms of the carrier temperatures, Tn
and Tp, they can be written as
. Jn - .
+ R . Tn + n .
. Jp - .
+ R . Tp + p .
denote the energy relaxation times, while
Sp are the energy fluxes.
- . grad Tn - . . Jn
- . grad Tp + . . Jp
The thermal conductivities,
, are assumed to obey a generalized Wiedemann-Franz