Integration of eqns. (2.209) and (2.210) led to the
generation/recombination term which contributes to the carrier continuity equation. The
contributions to the higher order moment equations are obtained by calculating the moments of
the net recombination term in
where an energy independent carrier lifetime has been assumed and the approximation
(2.213) has been used. Since the subsequent integration is carried out in
-space rather than in the energy domain, the effective density of states does not
) due to the normalization of the distribution function,
Using eqns. (2.93) to (2.95) together with
eqn. (2.225) yields
Eqn. (2.228) is written as a net power generation rate
The index must be used since in contrast to the net recombination rate the net energy
generation rate is different for both carrier types.
The contribution to the moment equations of odd order can be neglected since the right hand
sides of eqns. (2.76) to (2.78) are several
orders of magnitude larger than the additional generation term2.13.
Rewriting eqn. (2.228) leads to
Eqn. (2.229) can be manipulated in the same way, so the even moments read
The interpretation of eqn. (2.234) is that a recombining electron on average removes
from the system, while a generated electron introduces an
energy of only
, which means that generated electrons are initially cold.
M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF