78 CHAPTER 3. OPTICAL TRANSMITTERS
Figure 3.1: Three fundamental processes occurring between the two energy states of an atom:
(a) absorption; (b) spontaneous emission; and (c) stimulated emission.
The excited atoms eventually return to their normal “ground” state and emit light
in the process. Light emission can occur through two fundamental processes known as
spontaneous emissionandstimulated emission. Both are shown schematically in Fig.
3.1. In the case of spontaneous emission, photons are emitted in random directions with
no phase relationship among them. Stimulated emission, by contrast, is initiated by an
existing photon. The remarkable feature of stimulated emission is that the emitted
photon matches the original photon not only in energy (or in frequency), but also in
its other characteristics, such as the direction of propagation. All lasers, including
semiconductor lasers, emit light through the process of stimulated emission and are
said to emit coherent light. In contrast, LEDs emit light through the incoherent process
of spontaneous emission.
3.1.1 Emission and Absorption Rates
Before discussing the emission and absorption rates in semiconductors, it is instructive
to consider a two-level atomic system interacting with an electromagnetic field through
transitions shown in Fig. 3.1. IfN 1 andN 2 are the atomic densities in the ground and
the excited states, respectively, andρph(ν)is the spectral density of the electromagnetic
energy, the rates of spontaneous emission, stimulated emission, and absorption can be
written as [17]
Rspon=AN 2 , Rstim=BN 2 ρem, Rabs=B′N 1 ρem, (3.1.1)whereA,B, andB′are constants. In thermal equilibrium, the atomic densities are
distributed according to the Boltzmann statistics [18], i.e.,
N 2 /N 1 =exp(−Eg/kBT)≡exp(−hν/kBT), (3.1.2)wherekBis the Boltzmann constant andTis the absolute temperature. SinceN 1 andN 2
do not change with time in thermal equilibrium, the upward and downward transition
rates should be equal, or
AN 2 +BN 2 ρem=B′N 1 ρem. (3.1.3)
By using Eq. (3.1.2) in Eq. (3.1.3), the spectral densityρembecomes
ρem=A/B
(B′/B)exp(hν/kBT)− 1