Quantum Size Effects in Pb/Si(111) Thin Films from Density Functional Calculations
The Pb/Si(111) thin films were simulated within the density functional theory (DFT). The well-known Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximation (GGA) and its recent nonempirical successor Wu-Cohen (WC) issue were used to estimate the exchange-correlation functional. Lattice parameters were calculated for Bulk of the Pb and Si compounds to obtain more reliable lattice mismatch at the interface to be consistent with our used full-potential method of calculations. The WC-GGA result predicts the lattice constants of the Pb and Si compounds better than the GGA when compared with experiment. We have found that the spin-orbit coupling (SOC) does not significantly influence the results. Our finding is in agreement with the recent observation of the Rashba-type spin-orbit splitting of quantum well states in ultrathin Pb/Si(111) films. Our result shows, in agreement with experiment, that the top site (T1) is the most stable phase. A combination of tight $\sigma$ and feeble $\pi$ bonds has been found at the interface, which results in a covalent Pb-Si bond. Our calculated electric field gradient (EFG) predicts quantum size effects (QSE) with respect to the number of deposited Pb layers on the Si substrate. The QSE prediction shows that the EFG dramatically drops on going from first to second layer. The EFG calculation shows that this system is not an ideal paradigm to freestanding films.