Doping dependence of gap state energies

So far it has been assumed that the defect electronic states form a narrow band at E. When there is a broad distribution of energy levels, the defect equilibration favors those with the lowest formation energy, which are the states lowest in the gap (see Eq. (6.40)). The effect of the distribution is particularly significant in comparing the defect states in differently doped materials, because the contribution of the gap state to the formation energy depends on the charge state (Bar- 

The defects which are induced in doped a-Si H reduce the dopant formation energy by providing electronic compensation. Defects are no longer needed to lower the energy when a-Si H is doped with both boron and phosphorus. Instead charged dopant states result from the reaction 

This defect reaction explains the different properties of compensated a-Si H. The law of mass action gives 

The electrical data described in Section 5.2.4 are consistent with this expected behavior. The low defect density and the pinning of p are both observed. The higher doping efficiency explains the wider band tails and the associated reduction in the carrier mobility, because the many extra dopant states directly add localized states to the band tails. In addition, the large Coulomb potential fluctuations due to the high concentration of charged dopants lead to a further broadening of the band tails. 

---