Ionization of a P-doped Si(111) nanofilm using two-dimensional periodic boundary conditions

We examine the ionization of a P dopant in a Si(111) nanofilm using first-principles electronic structure calculations with 2D periodic boundary conditions. The electrostatic divergence of a charged periodic system is resolved by defining an electrostatic reference potential along the confined direction. After ionization, there is an overall electrostatic potential drop of the system. A nanofilm with larger periodicity can reduce the potential drop by screening the P ion, and leads to a smaller ionization energy. We compare the ionization energy calculated for the P-doped Si nanofilm with a P-doped Si nanocrystal and a P-doped Si(110) nanowire. As dimensionality decreases, quantum confinement tends to lower the ionization energy by raising the defect level. However, lower dimensionality also reduces screening after P ionization. This leads to a larger electrostatic potential drop and offsets the effect of quantum confinement on the ionization energy.