SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

142 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

Thus the average distance an electron can move and then recombine is

<x> =

∫∞

o

xP(x)dx=

∫∞

0

xe−x/Ln

Ln

dx

= Ln (3.9.19)

This average distance(=

√

Dnτn)depends upon the recombination time and the diffusion con-
stant in the material. In the derivations of this section, we used a simple form of recombination
rate

R=

δnp

τn

(3.9.20)

whereτnis given in terms of the radiative and nonradiative rates as

1

τn

=

1

τr

+

1

τnr

(3.9.21)

The simpleδnp/τnform is valid, for example, for minority carrier recombination (pn).
These equations are therefore used widely to discuss minority carrier injection.

3.10 PROBLEMS ....................................

Problem 3.1The electron mobility of Si at 300 K is 1400 cm^2 /V·s. Calculate the mean

free path and the energy gained in a mean free path at an electric field of 1 kV/cm. Assume

that the mean free path =vth·τsc,wherevthis the thermal velocity of the electron (vth∼

2.0× 107 cm/s).

Problem 3.2The mobility of electrons in the material InAs is∼35,000 cm^2 /V·s at 300K

compared to a mobility of 1400 cm^2 /V·s for silicon. Calculate the scattering times in the

two semiconductors. The electron masses are 0.02m 0 and 0.26m 0 for InAs and Si,

respectively.

Problem 3.3Calculate the ionized impurity limited mobility (ND=10^16 cm−^3 ;

1017 cm−^3 ) in GaAs from 77 K to 300 K.

Problem 3.4If the measured room temperature mobility of electrons in GaAs doped

n-type at 5 × 1017 cm−^3 is 3500 cm^2 V−^1 s−^1 calculate the relaxation time for phonon

scattering.

Problem 3.5Calculate the alloy scattering limited mobility in In 0. 53 Ga 0. 47 As as a

function of temperature from 77 K to 400 K. Assume an alloy scattering potential of

1. 0 eV.

Problem 3.6The velocity of electrons in silicon remains∼ 1 × 107 cm s−^1 between

50 kVcm−^1 and 200 kVcm−^1. Estimate the scattering times at these two electric fields.