Quantum size effects in Pb/Si(111) thin films from density functional calculations

Abstract

The Pb/Si(111) thin films were simulated within the density functional theory (DFT). The wellknown 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 exchangecorrelation 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 spinorbit 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 σ and feeble π 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.

Ab initio prediction of magnetically dead layers in freestanding γ-Ce(111)

“…2, is less than the period of the "abcabc" pattern of the fcc stacking. This can be taken as an indication to the fact that here oscillations of the work function originates more dominantly from the quantum size effects (QSEs) at nanoscale than the period of thin films stacking due to the symmetry of the structure [47]. Our result shows that the work functions of the γ-phase are larger than those of the α-phase, for every number of layers.…”

“…The result shows that the work function oscillate as a function of the number of layers with the period of λ = 2 layers. The oscillation indicates how the quantum size effects (QSEs) [47] can affect the results. The period of oscillation, as shown in Fig.…”

Theoretical study of α-U/W(110) thin films from density functional theory calculations: Structural, magnetic and electronic properties

“…Stojić and coworkers employing the FP-augmented plane waves (FP-APW) method have shown that the α-U compound is a nonmagnetic system in its bulk form, whereas it behaves as a magnetic system with the imposed spin MM of 0.84µ B at its freestanding surfaces 11 . A typical substrate can affect the structure 13 and magnetism 14 of the overlayers that can give rise to a variety of lattice mismatches and as a result to various U-U interlayer (IL) spacings (ILSs). The U-U spacing can change the degree of 5f localizations and thereby electronic structures.…”

Electron-phonon coupling and superconductivity in the (4/3)-monolayer of Pb on Si(111): Role of spin-orbit interaction

“…In fact, in the case of freestanding Pb films [22] or (1 × 1) Pb/Si(111) films of 10-22 ML thickness [39] the first-principles calculations showed a minor influence of spin-orbit coupling on the band dispersion. The DFT calculation of surface formation energies and the density of electronic states for different structures of 1/3 ML of Pb on Si(111) showed that their valence electronic structure is hardly affected by SOC too [44]. However, this is not the case for the dense H 3 phase considered here.…”

“…It is obvious that for a single layer of Pb on Si(111) the effect of substrate should be important [43]. A strong covalent bond between Pb and Si atoms at the interface [3,44] Fig. 2(c).…”