Intervalley Scattering

Both acoustic and optical phonons can cause electron transitions between states in different conduction band valleys. This scattering can be formally treated in the same way as intravalley scattering by optical phonons[Harrison56,Conwell67].

The scattering rate for intervalley scattering out of a valley $v$ for a phonon mode $\eta$ is given by

$$\{ S_\eta^{\tiny\shortstack{abs \\ [-2pt] emi }} \} ^{v}\left(E\r... ...2} \right ) g^{v'}\left(E^{v'} \pm \hbar \omega_\eta - \Delta E^{v'v}\right)\ ,$$ (5.21)

where a summation over the final valleys is performed. The allowed final valleys $v'$ are determined by the selection rules for a phonon mode $\eta$: $g$-type phonons can induce transitions between valleys which are located on the same axis in the three dimensional $\mathitbf{k}$ space, whereas transitions among orthogonal axes are labeled $f$-type. The squared coupling constants $\{D_tK_\eta^{v'v}\}^2$ depend upon the initial and final valley and the phonon branch $\eta$ involved in the transition. $Z^{v'}$ denotes the number of possible final equivalent valleys, $N_\eta$ is the phonon number, and $\Delta E^{v'v}$ is the difference between the energies of the minima of the final and initial valley. Since strain is able to change $\Delta E^{v'v}$, the intervalley scattering rate can be efficiently reduced through strain.

The numerical values entering the bulk phonon scattering rates are summarized in Table 5.1.

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