SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

3.3. TRANSPORT AND SCATTERING 103

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Polar optical phonon emission

Polar optical phonon absorption

Acoustic phonon scattering

SCATTERING RATE

(10

12

–1s

)

ENERGY (eV)

10.0

9.0

GaAs EXAMPLE

hωop = 36 meV threshold

Figure 3.9: Scattering rates due to acoustic and optical phonons for GaAs electrons at room
temperature.

withnthe free electron density. The scattering rate for an electron with energyEkand momen-
tumkcan be shown to be

W(k)=4πF

(

2 k

λ

) 2 [

1

1+(λ/ 2 k)^2

]

F =

1



(

e^2



) 2

N(Ek)

32 k^4

NI (3.3.21)

whereNIis the ionized impurity density. Note that ionized impurities (and the scattering pro-
cesses discussed here) do not alter the spin of the electron. ThusN(E)is the density of states
withoutcountingthespindegeneracy i.e it is half the usual density of states.