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
![$\displaystyle \{ S_\mathrm{op}^{\tiny\shortstack{abs \\ [-2pt] emi }} \} ^{v}({...
...tbf{k}}}') - E^v({\ensuremath{\mathitbf{k}}}) \mp \hbar\omega_{\mathrm{op}}]\ ,$](img922.png) |
(5.19) |
The scattering rate for optical phonons is a function of the final energy
![$\displaystyle \{ S_\mathrm{op}^{\tiny\shortstack{abs \\ [-2pt] emi }} \} ^v\lef...
... \mp \frac{1}{2} \right ) g^{v}\left(E \pm \hbar \omega_{\mathrm{op}}\right)\ .$](img924.png) |
(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].
E. Ungersboeck: Advanced Modelling Aspects of Modern Strained CMOS Technology