Optical Intravalley Scattering

The scattering probability can be written, starting from (5.14), by replacing $\Xi^2q^2\xi^2$ with a squared optical coupling constant $\{D_tK^{v}\}^2$ [Jacoboni83]. This constant can also include an overlap factor $\mathscr{O}$. The energy associated with the optical phonon $\hbar\omega_{\mathrm{op}}$ and the phonon number $N_q=N_{\mathrm{op}}$ can be assumed to be constant. Hence, the resulting scattering probability is

$$\{ S_\mathrm{op}^{\tiny\shortstack{abs \\ [-2pt] emi }} \} ^{v}({... ...tbf{k}}}') - E^v({\ensuremath{\mathitbf{k}}}) \mp \hbar\omega_{\mathrm{op}}]\ ,$$ (5.19)

The scattering rate for optical phonons is a function of the final energy $E\pm\hbar \omega_{\mathrm{op}}$

$$\{ S_\mathrm{op}^{\tiny\shortstack{abs \\ [-2pt] emi }} \} ^v\lef... ... \mp \frac{1}{2} \right ) g^{v}\left(E \pm \hbar \omega_{\mathrm{op}}\right)\ .$$ (5.20)

From the matrix element theorem one can derive that this type of scattering occurs only in the conduction band valleys along the $\langle111\rangle$ directions [Harrison56].

E. Ungersboeck: Advanced Modelling Aspects of Modern Strained CMOS Technology