Page 248 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Electron-Phonon
(
function and we have ∂ f ⁄–
F
k
quency 0 ∂E k() = δ E – E ) to give a plasma fre-
2 2 2 2 2 2
4 m
— k
4 
e —
e —
2 2∫
ω 2 pl = ---------------- k δ --------------- E F   dk = ----------------k -----------
–

2 2 F 2
3m π ( 2m∗ ) 3m π — k F
Ω k
(7.28)
2 3 2
e k F ne
= ------------- = --------
3mπ 2 m
where we used the electron density in a degenerate system defined as
3
n = k ⁄ 3π 2 . We conclude that the occurrence of plasma oscillations is
F
due to the long range Coulomb interaction. Typical frequencies are found
for metals at energies —ω ≈ 10eV which, compared to the thermal
pl
energy k T at room temperature, is several orders of magnitude larger.
B
Hence plasma oscillations will not be contained in the thermal density
fluctuations at room temperature.
7.3 Electron-Phonon
Electron-phonon scattering is the major effect in electronic transport at
high temperatures, i.e., in the range of 300 K. There is a dissipation chan-
nel arising that forms the basis for many different transport coefficients
of the electronic system in a semiconductor. The dissipated energy will
change the thermal properties of the lattice system.

The description of electron-phonon interaction on a quantum mechanical
level therefore must include both the electron wavefunction and the lat-
tice wavefunction. The transition of scattering rate between initial and
final states in this interaction will be governed by the Fermi golden rule
(3.82). Suppose that initially the electron occupies a state with wavevec-
tor k. In Figure 7.3 the two possible processes are schematically drawn:
absorption of a phonon with wavevector q and emission of such a
phonon. In both cases the electron wavevector changes by the modulus of
q provided momentum conservation holds. The transition rate reads

Semiconductors for Micro and Nanosystem Technology 245