SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

100 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

Optical mode

Acoustical mode

k

k

16

14

12

10

6

8

4

2

0

0.06

0.05

0.04

0.03

0.02

0.01

0

0 [100] 1.0

TO

LO

GaAs

LA

TA

FREQUENCY

v

(10

12

Hz)

REDUCED WAVE NUMBERk/Kmax

ENERGY

(eV)

(a)

(b)

The two atoms

on the unit cell

vibrate in

opposing motion.

The two atoms

in the unit cell

vibrate along the

same direction.

• –


• –


• –


• –

Figure 3.7: (a) Typical frequency-wavenumber relations of a semiconductor (GaAs in this case).
(b) The displacement of atoms in the optical and acoustic branches of the vibrations is shown.
The motion of the atoms is shown for smallkvibrations.

whereDis called a deformation potential (units are eV) and∂u∂xis the amplitude gradient of the
atomic vibrations.
The optical phonons produce a potential disturbance, which is proportional to the atomic
vibration amplitude, since in the optical vibrations the two atoms in the basis vibrate opposing