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: 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: 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

2.2.5 2.3

Bart J. Van Zeghbroeck, 1996, 1997