2.5.2.3 Intravalley Scattering by Optical Phonons

This scattering mechanism is divided into optical deformation potential scattering and polar optical scattering. The latter only takes place in polar semiconductors and is absent in Si, Ge and SiGe. Optical deformation potential scattering can occur in $L$-valleys only due to selection rules, which follow from group theory and depend on the symmetry of initial and final states and also on the symmetry of the perturbation operator [30]. In this case the transition probability for the $L$-valleys is:

$$\lambda(\epsilon_{i})=\frac{\pi D_{o}^{2}}{\rho\omega_{o}}\left(N_{o}+\frac{1}{2}\pm\frac{1}{2}\right)g_{L}(\epsilon_{f}),$$ (2.112)

where $\epsilon_{f}$ is given as:

$$\epsilon_{f}=\epsilon_{i}\mp \hbar\omega_{o}.$$ (2.113)

The upper and lower signs refer to emission and absorption processes, respectively, $D_{o}$ is the optical deformation potential, $\hbar\omega_{o}$ is the respective phonon energy, $\epsilon_{i}$ and $\epsilon_{f}$ are the initial and final electron energies respectively, and $N_{o}$ is the equilibrium phonon distribution function given by the Bose-Einstein statistics:

$$N_{o}=\frac{1}{\exp\bigl(\frac{\hbar\omega_{o}}{k_{B}T_{L}}\bigr)-1}.$$ (2.114)

The numerical values for the parameters [18,20] of the acoustic phonon scattering rate are given in table Table 2.3.

Table 2.3: Numerical values for the intravalley L-L optical deformation potential scattering rate.

Semiconductor	Silicon	Germanium
$D_{opt}$	$2.2\times 10^{8}$ eV/cm	$5.5\times 10^{8}$ eV/cm
$\hbar\omega_{opt}$	$0.0612$ eV	$0.03704$ eV

S. Smirnov: