Page 117 - Photonics Essentials an introduction with experiments

Light-Emitting Diodes

Light-Emitting Diodes 111

er, the energy of the emitted photon is determined primarily by the
energy band gap of the semiconductor. Electrons that are injected into
the conduction band by a bias voltage that exceeds the band gap will
have energy in two forms: kinetic and potential energy. The potential
energy is represented by the band gap. The kinetic energy is the dif-
ference between the energy imparted by the bias voltage, qV B , and the
band gap energy. This kinetic energy is rapidly dissipated in the form
of heat until the electron is sitting at the bottom of the conduction
band, where it waits for a hole to appear in the vicinity so that radia-
tive recombination can take place.
In most cases, the luminescence at room temperature from a real
LED peaks at an energy slightly less than the band gap energy, in-
dicating that the luminescence has its origin in recombination from
electrons and holes lying in impurity levels formed by the p-type and
n-type doping. Further evidence of impurity-based recombination
comes from the extended tail of luminescence at energies well into
the forbidden gap. In addition to the effect of Boltzmann statistics,
the intensity emitted by the LED falls off above the band gap ener-
gy because the emitting material is also a strong absorber of these
higher-energy photons.
The width of the luminescence curve at half maximum value or
FWHM (Full Width at Half Maximum) is slightly less than 3/2 kT at
room temperature from the model. This is about 40 meV. The experi-
mental values for this parameter are invariably larger, on the order of
150 to 300 meV. This result further supports the picture of recombi-
nation from impurity levels that are distributed in energy near the
edges of the conduction and valence bands.
The model behavior predicted in Eq. 6.7 treats only the spectrum
of the light at emission, without considering either the presence of
impurities or the effects of absorption of this light by the surround-
ing material. It is possible to minimize these two effects. For exam-
ple, self absorption, which is responsible for cutting off the high-
energy end of the external emission spectrum, can be nearly elimi-
nated by using a thin active region (that is, less than a wavelength
in thickness) and by surrounding the active region with window lay-
ers having a higher band gap. This is called a heterostructure LED,
and its emission spectrum conforms much more closely to the expec-
tations of the model, as can be seen in Fig. 6.6. Note in particular
that there is now an extended spectral region above the band gap on
the high-energy side, in harmony with the simple model introduced
in Eq. 6.7.
The radiative efficiency of a light-emitting diode can be expressed
as a ratio of the radiative and nonradiative recombination lifetimes:

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.