skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on November 5, 2020

Title: Energy barriers for Pb adatom diffusion on stepped ultrathin Pb(111) quantum nanofilms: First-principles calculations

Abstract

Various properties of Pb(111) nanofilms, prototypical quantum films, have been studied extensively. However, key ab initio-level energy barriers for Pb adatom diffusion on stepped Pb(111) nanofilm surfaces are still not available. Using first-principles density functional theory, we calculate these barriers for films with thicknesses of few monolayers (ML). We find that two-atom exchange is always much more favorable than direct hopping to cross A- or B-type steps. Ehrlich-Schwoebel (ES) barriers for downward transport to a higher-coordination step-edge site depend strongly on the film thickness. For such transport from 2- to 1-ML terraces, or from 4- to 3-ML terraces, there is no an ES barrier, but large ES barriers of more than 100 meV are found from 3- to 2-ML terraces. We also obtain the barriers for diffusion along the step edges and find that these step-edge barriers are significantly larger than terrace diffusion barriers. In addition, we analyze energetics for diffusion on the top flat surface of a nanofilm supported on a vicinal surface, and thus having underlying buried or ghost steps. We quantify the tilted potential energy surface in both ghost A- and B-step regions separating 2- and 3-ML (as well as 3- and 4-ML) terraces. Finally, consequences aremore » discussed for the growth kinetics of supported Pb nanofilms, where the support does not strongly affect electronic states within the film.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [2]
  1. Iowa State Univ., Ames, IA (United States). Dept. of Physics and Astronomy; Ames Lab., and Iowa State Univ., Ames, IA (United States)
  2. Univ. of Utah, Salt Lake City, UT (United States). Dept. of Materials Science and Engineering
Publication Date:
Research Org.:
Ames Laboratory (AMES), Ames, IA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1574814
Report Number(s):
IS-J-10089
Journal ID: ISSN 2469-9950; PRBMDO
Grant/Contract Number:  
CHE-1507223; AC02-07CH11358; FG02-04ER46148
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 100; Journal Issue: 19; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Han, Yong, Evans, James W., and Liu, Feng. Energy barriers for Pb adatom diffusion on stepped ultrathin Pb(111) quantum nanofilms: First-principles calculations. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.100.195405.
Han, Yong, Evans, James W., & Liu, Feng. Energy barriers for Pb adatom diffusion on stepped ultrathin Pb(111) quantum nanofilms: First-principles calculations. United States. doi:10.1103/PhysRevB.100.195405.
Han, Yong, Evans, James W., and Liu, Feng. Tue . "Energy barriers for Pb adatom diffusion on stepped ultrathin Pb(111) quantum nanofilms: First-principles calculations". United States. doi:10.1103/PhysRevB.100.195405.
@article{osti_1574814,
title = {Energy barriers for Pb adatom diffusion on stepped ultrathin Pb(111) quantum nanofilms: First-principles calculations},
author = {Han, Yong and Evans, James W. and Liu, Feng},
abstractNote = {Various properties of Pb(111) nanofilms, prototypical quantum films, have been studied extensively. However, key ab initio-level energy barriers for Pb adatom diffusion on stepped Pb(111) nanofilm surfaces are still not available. Using first-principles density functional theory, we calculate these barriers for films with thicknesses of few monolayers (ML). We find that two-atom exchange is always much more favorable than direct hopping to cross A- or B-type steps. Ehrlich-Schwoebel (ES) barriers for downward transport to a higher-coordination step-edge site depend strongly on the film thickness. For such transport from 2- to 1-ML terraces, or from 4- to 3-ML terraces, there is no an ES barrier, but large ES barriers of more than 100 meV are found from 3- to 2-ML terraces. We also obtain the barriers for diffusion along the step edges and find that these step-edge barriers are significantly larger than terrace diffusion barriers. In addition, we analyze energetics for diffusion on the top flat surface of a nanofilm supported on a vicinal surface, and thus having underlying buried or ghost steps. We quantify the tilted potential energy surface in both ghost A- and B-step regions separating 2- and 3-ML (as well as 3- and 4-ML) terraces. Finally, consequences are discussed for the growth kinetics of supported Pb nanofilms, where the support does not strongly affect electronic states within the film.},
doi = {10.1103/PhysRevB.100.195405},
journal = {Physical Review B},
number = 19,
volume = 100,
place = {United States},
year = {2019},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 5, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Morphological evolution during epitaxial thin film growth: Formation of 2D islands and 3D mounds
journal, April 2006


Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling
journal, October 2018


Atomic View of Surface Self‐Diffusion: Tungsten on Tungsten
journal, February 1966

  • Ehrlich, Gert; Hudda, F. G.
  • The Journal of Chemical Physics, Vol. 44, Issue 3
  • DOI: 10.1063/1.1726787

Step Motion on Crystal Surfaces
journal, September 1966

  • Schwoebel, Richard L.; Shipsey, Edward J.
  • Journal of Applied Physics, Vol. 37, Issue 10
  • DOI: 10.1063/1.1707904

Alternating Layer and Island Growth of Pb on Si by Spontaneous Quantum Phase Separation
journal, February 2003


Thermal Stability and Electronic Structure of Atomically Uniform Pb Films on Si(111)
journal, July 2004


Quantum Beating Patterns Observed in the Energetics of Pb Film Nanostructures
journal, July 2004


Band Structure and Oscillatory Electron-Phonon Coupling of Pb Thin Films Determined by Atomic-Layer-Resolved Quantum-Well States
journal, August 2005


A theory of thin metal films: electron density, potentials and work function
journal, May 1976


Evidence for Quantum Size Effects Observed by Helium Atom Scattering during the Growth of Pb on Cu(111)
journal, October 1989


Phase Relations Associated with One-Dimensional Shell Effects in Thin Metal Films
journal, June 2009


Deeper insight into phase relations in ultrathin Pb films
journal, September 2015


Theory of quantum size effects in thin Pb(111) films
journal, December 2002


Quantum Size Effect on the Diffusion Barriers and Growth Morphology of Pb / Si ( 111 )
journal, June 2006


Thickness-dependent energetics for Pb adatoms on low-index Pb nanofilm surfaces: First-principles calculations
journal, November 2017


Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis
journal, April 2016


Non-classical kinetics processes and morphologies in QSE driven growth in Pb/Si(111)
journal, October 2006


Bilayer-ring second-layer nucleation morphology in Pb Si ( 111 ) 7 × 7
journal, May 2007


Height-dependent barriers and nucleation in quantum size effect growth
journal, October 2008


Controlling nucleation rates in nanostructures with electron confinement
journal, March 2010


Quantum Size Effect on Adatom Surface Diffusion
journal, December 2006


Experimental observation of quantum oscillation of surface chemical reactivities
journal, May 2007

  • Ma, X.; Jiang, P.; Qi, Y.
  • Proceedings of the National Academy of Sciences, Vol. 104, Issue 22
  • DOI: 10.1073/pnas.0611024104

Height-dependent nucleation and ideal layer by layer growth in Pb/Pb(111)/Si(111)
journal, November 2008


Ab initiomolecular dynamics for liquid metals
journal, January 1993


Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


A climbing image nudged elastic band method for finding saddle points and minimum energy paths
journal, December 2000

  • Henkelman, Graeme; Uberuaga, Blas P.; Jónsson, Hannes
  • The Journal of Chemical Physics, Vol. 113, Issue 22, p. 9901-9904
  • DOI: 10.1063/1.1329672

Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points
journal, December 2000

  • Henkelman, Graeme; Jónsson, Hannes
  • The Journal of Chemical Physics, Vol. 113, Issue 22
  • DOI: 10.1063/1.1323224

Quantum size effects in quasi-free-standing Pb layers
journal, April 2007


Level set simulation of directed self-assembly during epitaxial growth
journal, November 2006