The scattering probability can be written, starting from (5.14),
by replacing
with a squared optical coupling constant
[Jacoboni83]. This constant can also include an overlap
factor
. The energy associated with the optical phonon
and the phonon number
can be assumed to be constant. Hence, the resulting
scattering probability is
(5.19)
The scattering rate for optical phonons is a function of the final energy
(5.20)
From the matrix element theorem one can derive that this type of
scattering occurs only in the conduction band valleys along the
directions [Harrison56].