Influence of donor-pairs on density of states of degenerate N-type semiconductors

A theoretical study to a polarization catastrophe in doped semiconductors

“…In silicon, there are six valleys in HCB at K # 0, and thus the 1s ground state of an isolated donor has sixfold degeneracy in the framework of this effective-mass approximation. Our previous results [ 1,2] reveal good agreement with an optical measurement on Si:P, which show an absorption band from such donor-pairs.…”

“…In our approach these are the states in which one of the electrons is promoted from the donor-pair cluster to the bottom of the HCB. The many-valley character of the HCB is very sensitive in the behavior of the physical properties and has been the subject of many recent investigations [1][2][3][4][5] ; therefore, we have also taken it into account in the calculation [ 1,4,5 1. Such peculiarity does not happen in single valley semiconductors [ 61.…”

“…In the effective mass theory the wave function describing the valley degeneracy, qj, which will appear in Eq. (12), is written as [1,4,10,11] where cpi( r ) is the Bloch function associated with the vth conduction-band minimum (I, = 6 for silicon) and FI( r ) is the 1s hydrogenic envelope function. The factor I is obtained as 1 "…”