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2.2.5 Temperature dependence of the energy bandgap
Table of Contents -
Glossary -
Study Aids -
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2.2.5 Temperature dependence of the
energy bandgap
The energy bandgap of semiconductors tends to decrease as the
temperature is increased. This behaviour can be better understood
if one considers that the interatomic spacing increases when the
amplitude of the atomic vibrations increases due to the increased
thermal energy. This effect is quantified by the linear expansion
coefficient of a material. An increased interatomic spacing decreases the potential
seen by the electrons in the material, which in turn reduces the size of
the energy bandgap. A direct modulation of the interatomic distance, such
as by applying high compressive (tensile) stress, also causes an
increase (decrease) of the bandgap.
The temperature dependence of the energy bandgap
has been experimentally determined yielding the following
expression for Eg as a function of the temperature T:
(f33)
where Eg(0),
a and
b are the fitting parameters. These
fitting parameters are listed for germanium, silicon and
gallium arsenide in the table below:
| Germanium | Silicon | GaAs |
|---|
| Eg(0) [eV] | 0.7437 | 1.166 | 1.519 |
| a [eV/K] | 4.77 x 10-4 | 4.73 x 10-4 | 5.41 x 10-4 |
| b [K] | 235 | 636 | 204 |
A plot of the
resulting bandgap versus temperature
is shown in the figure below for germanium, silicon and gallium arsenide.
bandgap.xls - eband.gif
Fig.2.2.14 Temperature dependence of the energy
bandgap of germanium (bottom/black curve), silicon (blue curve) and
GaAs (top/red curve).
2.2.4
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2.2.6
© Bart J. Van Zeghbroeck, 1996, 1997
