The scattering rate due to electron-plasmon interaction can be obtained using Fermi's golden rule (2.95) and the Hamiltonian
(2.130).
Plasmon scattering of electrons represents the long-range part of the electron-electron interaction [39]. Assuming a nonparabolic
and spherical analytical band structure (2.77), the scattering rate is given by:
 |
(2.131) |
The final electron energy is given as:
 |
(2.132) |
where the plasma frequency is (see Appendix B):
 |
(2.133) |
Here the summation over all possible valleys is assumed, and
stands for the contribution from valley
to the electron density.
The cut-off wave vector
is defined as follows:
 |
(2.134) |
and
stand for the boundaries of the momentum transfer:
|
|
 |
(2.135) |
|
|
 |
|
is the final wave vector defined by the equation:
 |
(2.136) |
is the average number of the plasmon excitations defined by the equilibrium Bose-Einstein statistics:
 |
(2.137) |
S. Smirnov: