In the derivation of the Boltzmann transport equation, several assumptions are inherently
incorporated which result in a limited range of validity. These assumptions
include the items below:
- By the introduction of the distribution function, the original
many-electron problem is replaced by a one-electron problem with an
appropriate potential. According to the Hartree-Fock approximation
[75], the contribution of all surrounding electrons to this
potential is approximated by a surrounding charge density. Thus, the short
range electron-electron interaction can not be described properly. However,
the potential of the surrounding carriers is treated by the electric field
self-consistently.
- The Boltzmann transport equation is a semi-classical equation and thus not compatible with a
quantum mechanical approach, since the carriers are described by Newton's
classic equation set of motion. A particle's position and momentum can never
be determined with arbitrary accuracy because of Heisenberg's uncertainty
relations.
- The collisions are considered to happen instantaneously. The validity of
this approximation is in good agreement with the conception of very long free
flight times compared to the collision times.
M. Wagner: Simulation of Thermoelectric Devices
