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Register a new userQuantum Size Effects in Pb/Si(111) Thin Films from Density Functional Calculations
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Saeid Jalali Asadabadi
Publication date
2009
fields
Physics
and research's language is
English
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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.
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The spatial distribution of the differential conductance for ultrathin Pb films grown on Si(111)7x7 substrate is studied by means of low-temperature scanning tunneling microscopy and spectroscopy. The formation of the quantum--confined states for conduction electrons and, correspondingly, the appearance of local maxima of the differential tunneling conductance are typical for Pb films; the energy of such states is determined mainly by the local thickness of Pb film. We demonstrate that the magnitude of the tunneling conductivity within atomically flat terraces can be spatially nonuniform and the period of the small-scale modulation coincides with the period of Si(111)7x7 reconstruction. For relatively thick Pb films we observe large-scale inhomogeneities of the tunneling conductance, which reveal itself as a gradual shift of the quantized levels at a value of the order of 50 meV at distances of the order of 100 nm. We believe that such large-scale variations of the tunneling conductance and, respectively, local density of states in Pb films can be related to presence of internal defects of crystalline structure, for instance, local electrical potentials and stresses.
Quantum-confined electronic states such as quantum-well states (QWS) inside thin Pb(111) films and modified image-potential states (IPS) above the Pb(111) films grown on Si(111)7$times$7 substrate were studied by means of low-temperature scanning tunnelling microscopy (STM) and spectroscopy (STS) in the regime of constant current $I$. By plotting the position of the $n-$th emission resonances $U^{,}_n$ versus $n^{2/3}$ and extrapolating the linear fit for the dependence $U^{,}_n(n^{2/3})$ in the high-$n$ limit towards $n=0$, we estimate the local work function for the Pb(111) film: $Wsimeq 3.8pm 0.1,$eV. We experimentally demonstrate that modifications of the shape of the STM tip can change the number of the emission peaks associated with the resonant tunnelling via quantized IPS levels for the same Pb terrace; however it does not affect the estimate of the local work function for the flat Pb terraces. We observe that the maxima in the spectra of the differential tunnelling conductance $dI/dU$ related to both the QWS and the modified IPS resonances are less pronounced if the STM tip becomes more blunt.
Spectra of the differential tunneling conductivity for ultrathin lead films grown on Si(111)7x7 single crystals with a thickness from 9 to 50 monolayers have been studied by low-temperature scanning tunneling microscopy and spectroscopy. The presence of local maxima of the tunneling conductivity is typical for such systems. The energies of maxima of the differential conductivity are determined by the spectrum of quantum-confined states of electrons in a metallic layer and, consequently, the local thickness of the layer. It has been shown that features of the microstructure of substrates, such as steps of monatomic height, structural defects, and inclusions of other materials covered with a lead layer, can be visualized by bias-modulation scanning tunneling spectroscopy.
Structural, electronic and magnetic properties were calculated for the optimized $alpha$-U/W(110) thin films (TFs) within the density functional theory. Our optimization for 1U/7W(110) shows that the U-W vertical interlayer spacing (ILS) is expanded by 14.0% compared to our calculated bulk W-W ILS. Spin and orbital magnetic moments (MMs) per U atom were found to be enhanced from zero for the bulk of $alpha$-U to 1.4 $mu_B$ and -0.4 $mu_B$ at the interface of the 1U/7W(110), respectively. Inversely, our result for 3U/7W(110) TFs shows that the surface U-U ILS is contracted by 15.7% compared to our obtained bulk U-U spacing. The enhanced spin and orbital MMs in the 1U/7W(110) were then found to be suppressed in 3U/7W(110) to their ignorable bulk values. The calculated density of states (DOS) corroborates the enhancement and suppression of the MMs and shows that the total DOS, in agreement with experiment, is dominated in the vicinity of Fermi level by the 5f U states. Proximity and mismatch effects of the nonmagnetic W(110) substrate were assessed and found to be important for this system.
We report on total-energy electronic structure calculations in the density-functional theory performed for the ultra-thin atomic layers of Si on Ag(111) surfaces. We find several distinct stable silicene structures: $sqrt{3}timessqrt{3}$, $3times3$, $sqrt{7}timessqrt{7}$ with the thickness of Si increasing from monolayer to quad-layer. The structural bistability and tristability of the multilayer silicene structures on Ag surfaces are obtained, where the calculated transition barriers infer the occurrence of the flip-flop motion at low temperature. The calculated STM images agree well with the experimental observations. We also find the stable existence of $2times1$ $pi$-bonded chain and $7times7$ dimer-adatom-stacking fault Si(111)-surface structures on Ag(111), which clearly shows the crossover of silicene-silicon structures for the multilayer Si on Ag surfaces. We further find the absence of the Dirac states for multilayer silicene on Ag(111) due to the covalent interactions of silicene-Ag interface and Si-Si interlayer. Instead, we find a new state near Fermi level composed of $pi$ orbitals locating on the surface layer of $sqrt{3}timessqrt{3}$ multilayer silicene, which satisfies the hexagonal symmetry and exhibits the linear energy dispersion. By examining the electronic properties of $2times1$ $pi$-bonded chain structures, we find that the surface-related $pi$ states of multilayer Si structures are robust on Ag surfaces.
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