SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

134 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

σn[cm-2]

Trap

Figure 3.23: Picture of the capture cross section

Case 1

vth x 0

Case 2 ΔL 2

ΔL 2

ΔL 3

ΔL 3

Path in the

absence of trap

Figure 3.24: Electrons within the “volume” above will be captured by the trap

closer) would have intersected the capture cross section and be captured. Hence all electrons
in the volumeV =σn·vthwill be captured each second by available empty traps. Thus the
number of electrons available to be captured per second is

nσnvth (3.8.25)

and recalling the concentration of available empty traps isNt(1−f), then the rate,racan be
written:
ra=vthσnnNt(1−f) (3.8.26)

OR, the proportionality constant isσnvth(for the rate of electron capture)

vth=

√

2 E

m∗

=

√

2 ·

3 kBT

2 m∗

(3.8.27)