Density functional calculations of shallow acceptor levels in Si

Abstract

We present a comprehensive study of the binding energies of B, Al, Ga, In, Tl shallow acceptors in bulk Si using density functional theory. Two approaches are used to calculate the binding energies. One is based on the eigenenergy of the single particle Kohn–Sham equation, and another is based on the total energy change during the impurity ionization process. Planewave pseudopotential Hamiltonian under local density approximation is used. A special potential patching method is presented which allows the calculation of 64 000 atom supercells needed for converging the eigenenergies. We found that the calculated impurity eigenenergies reproduce correctly the trend of the element dependence of the binding energy. But the calculated binding energies for In and Tl are much smaller than the experimental values. A linear response formula is derived which relates the total energy difference between the systems with occupied and unoccupied impurity to the impurity state eigenenergy and the impurity state self-interaction. However, the total energy difference gives much worse binding energies when compared to experiment due to the self-interaction error in the local density approximation. We conclude that one must go beyond the usual approximations of the density functional theory in order to predict accurately the binding energies of these shallow impurities.