Page 113 - Photonics Essentials an introduction with experiments

Light-Emitting Diodes

Light-Emitting Diodes 107

= E c – E v ,
where E c is the energy of the electron in the conduction band and E v is
the energy of the hole in the valence band. At room temperature, the
momentum change of the electron in radiative transition is negligible.
The three most important performance characteristics of a light-
emitting diode are:

1. Spectral lineshape
What is the wavelength/energy of the emission peak?
What is the width of the emission spectrum in energy at one-half
the maximum emission?
2. Quantum efficiency
What is the internal quantum efficiency?
What is the external quantum efficiency?
3. Modulation bandwidth
What is the frequency at which the direct current modulation of
the output is half its low frequency (<1 kHz) value?

6.3 The Energy Spectrum of Light
The intensity of the emitted light is proportional to the number of
states in the conduction band that are occupied by an electron multi-
plied by the number of empty states in the valence band with the
same momentum. This can be expressed as an integral over all possi-
ble transition energies:
I( ) = (energy density of states at E = ) ×
(probability that a conduction band state is occupied) ×
(probability that a valence band state is unoccupied) ×
(probability that a rediative transition will occur)dE (6.3)
The energy density of states is the total number of states between E
and E + E. The form of the density of states can be directly deter-
mined from the electronic bandstructure. There are two electron
states for each value of momentum, k. The energy of an electron near
the edge of the conduction band can be expressed as

2 2
k
E(k) = + E G (6.4)
2m
In three dimensions, the number of k-states having energy less
than E(k) is the volume of k-space. That is, one electron spin-up plus
one electron spin-down equals two electrons times the volume in k-

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