SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

196 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

hv

Substrate

p

n

hv

Substrate

p

n

hv hv

Dislocations

(a) (b)

Figure 4.31: (a)e-hdiffuse to dislocations and recombine. (b) In the presence of energy fluctu-
ations such as in the InGaN the electrons recombine efficiently.

In general, the electron-hole recombination process can occur by radiative and nonradiative
channels. Under the condition of minority carrier recombination or high injection recombination,
as shown in section 3.8.1and section 3.8.2, one can define a lifetime for carrier recombination. If
τrandτnrare the radiative and nonradiative lifetimes, the total recombination time is (for, say,
an electron)
1
τn

=

1

τr

+

1

τnr

(4.9.2)

The internal quantum efficiency for the radiative processes is then defined as

ηQr=

1

τr

1

τr+

1

τnr

=

1

1+ττnrr

(4.9.3)

In high-quality direct gap semiconductors, the internal efficiency is usually close to unity. In
indirect materials the efficiency is of the order of 10 −^2 to 10 −^3.
Before starting the discussion of light emission, let us remind ourselves of some important
definitions and symbols used in this chapter:

Iph: photon current = number of photons passing a cross-section/second.

Jph: photon current density = number of photons passing a unit area/second.

Pop:optical power intensity = energy carried by photons per second per area.