On the shifting and broadening of impurity bands and their contribution to the effective electrical bandgap narrowing in moderately doped semiconductors

The role of shifting and broadening of the impurity band in determining the effective bandgap narrowing in moderately doped semiconductors, as obtained from the electrical transport experiments, has been discussed. A model complementary to Lee and Fossum's model (which is based on band tails and many body effects and would hold true at comparatively higher dopant concentrations at which the impurity ionization energy has completely disappeared)has been proposed here. It is shown that Mahan's variational calculations when seen in the right perspective explain the movement of impurity states toward the conduction band. Morgan's formulation has been used for the calculation of the density of states in the impurity band. The model quite satisfactorily explains the electrical bandgap narrowing data for dopant concentrations N < N
2
. For phosphorous-doped silicon, N
2
is found to be 3×10
¹⁹
cm
^-3
.