2.2.6 Doping dependence of the energy bandgap
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2.2.6 Doping dependence of the
energy bandgap
High doping densities cause the bandgap to shrink. This effect
is explained by
the fact that the wavefunctions of the electrons bound to the impurity atoms
start to overlap as the density of the impurities increase. For instance at
a doping density of 1018 cm-3, the average distance between two impurities
is only 10 nm. This overlap forces the energies to form an energy band
rather than a discreet level. This impurity band reduces the energy band of
the host material by:
(f34)
where N is the doping density, q is the
electronic charge,
es is the dielectric constant of the
semiconductor, k is
Boltzmann's constant and T is the temperature in Kelvin.
For silicon (er = 11.7) this expression further reduces to:
(f35)
From this expression we find that the bandgap shrinkage can typically be
ignored for doping densities less than 1018 cm-3.
A plot of the change in bandgap energy with doping density is shown in the
figure below:
gapdens.xls - gapdens.gif
Fig.2.2.15 Doping dependence of the energy
bandgap of GaAs (top/red curve), germanium (black curve) and
silicon (bottom/blue curve)
2.2.5
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2.3
© Bart J. Van Zeghbroeck, 1996, 1997