Page 252 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Electron-Phonon
+
, while b c
destroys a phonon with wavevector q
c
k
–
electron with wavevector , creates one with k q + – q k + q k destroys an
and creates a phonon
–
with wavevector q . This is why we call the first term phonon absorption
and the second one phonon emission. Thus the square of the matrix ele-
ment in (7.29) yields according to (7.30) for the emission of a phonon
2 2
—Ξ q
2
1
V kk' q) = -------------------- n +( 1) (7.39)
(
,
;
2MNω q
q
For the absorption matrix element in (7.39) n + 1 has to be replaced by
q
n . The n follow a Bose statistics as described in Section 5.2.2 and thus
q q
we may replace n by
q
1
n = ----------------------------------------------- (7.40)
q
exp ( —ω ⁄ k T) – 1
q B
⁄
which in the high temperature limit yields n = k T —ω . This means
q B q
that the acoustic phonon scattering rate increases linearly with the tem-
perature.
7.3.2 Optical Phonon Scattering
This interaction mechanism occurs in two different ways which both are
due to the optical lattice vibrations in which one sub-lattice moves rela-
tive to a second one.
In silicon this motion creates a shift of the potential field of each ion. The
bond charges follow this motion and slightly accumulate where the two
ions approach increasing the negative charge, while a positive remains
where the ions have moved apart. This is a macroscopic electric field due
to the relative displacement field w of the sub-lattices and thus results in
q
an interaction potential

Non-Polar δE = Dw (7.41)
q
Materials

Semiconductors for Micro and Nanosystem Technology 249