Page 249 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Interacting Subsystems
k
k+q
absorption

q

k-q

k
emission

Figure 7.3. Schematic representa-
q
tion of phonon absorption and
phonon emission processes.

2π 2
(
,
;
W kk' q) = ------ V kk' q;,( ) δ E –( k E ± —ω ) (7.29)
q
k'
—
where the transition matrix element is given by
,
,
|
ˆ
(
,
V kk' q) = 〈 k' n ± 1|V kk' q,, k n 〉 (7.30)
;
q
q
k n , | q 〉 indicates the Dirac notation of a product of two wavefunctions
one from the electronic system and one from the lattice vibrational sys-
ˆ
tem. We must further specify the interaction potential operator V kk' q,, .
This operator characterizes the nature of the different electron-phonon
interactions given in the following sections.
7.3.1 Acoustic Phonons and Deformation Potential Scattering
The description of a periodic potential structure as given in Section 3.3 is
appropriate for situations where the ions forming the potential are not
subject to displacement. From Sections 2.3 and 2.4 we know that this

246 Semiconductors for Micro and Nanosystem Technology