Page 112 - Photonics Essentials an introduction with experiments

Light-Emitting Diodes

106 Photonic Devices

constant while the nonradiative rate increases. By forming a simple
ratio between the linear extrapolation of the light intensity and the
actual light intensity, it is possible to deduce the ratio of the radiative
and nonradiative recombination rates at a given injection current.
There are only two possibilities for recombination: either it is radia-
tive, that is, a photon is emitted, or it is not. Thus, there are two com-
ponents to the recombination time: a radiative time and a nonradia-
tive time:

1 1 1
= +
total radiative nonradiative
There is a contest between these two recombination channels. If the
radiative recombination time is much shorter than the nonradiative
recombination time, most of the recombination will involve the emis-
sion of photons. This is the case for GaAs, InP, GaN, and other direct
band gap semiconductors. On the other hand, if the radiative recombi-
nation time is much longer than the nonradiative recombination time,
then carrier recombination will produce very little light. This is the
case for Si, Ge, and other indirect band gap semiconductors.

Example 6.1
In Si, radiative ( 10 –3 sec) nonradiative ( 10 –7 sec), and
1 1 1
= + = 10 + 10 = 1.0001 × 10 7
7
3
10 –3 10 –7
total
total = 0.999 × 10 –7 sec
So, most recombination takes place nonradiatively.
Light emission from a light-emitting diodes is the result of radiative
recombination. Radiative recombination requires the following condi-
tions:

1. radiative nonradiative
2. Electrons and holes in the same place [i.e., within a de Broglie
wavelength (~100 Å)] at the same time (i.e., ~ radiative ).
3. Energy is conserved.
4. Momentum is conserved.

When a GaAs p-n diode is forward-biased, the excess minority carri-
ers recombine and emit light. The energy of the emitted light, , sat-
isfies

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