Theoretical studies of atomic-scale processes relevant to crystal growth.

The study of adsorption, diffusion, island formation, and interlayer transport of atoms on a growing surface has been an active field in the past decade, because of both experimental and theoretical advances. Experiments can give detailed images of patterns formed on growing surfaces. An important challenge to the theoretical studies is the identification of dynamical processes controlling the pattern formation and overall surface morphology. This can be achieved by accurate modeling of the atomic interactions, a thorough search for active atomic-scale processes, and simulation of the growth on the experimental timescale to allow for detailed comparison with the experimental measurements. An overview of some of the theoretical methodology used in these studies and results obtained for one of the most extensively studied systems, Pt(111), is given here. A remarkable richness of phenomena has emerged from these studies, where apparently small effects can shift the balance between competing molecular processes and thereby change the morphology of a growing surface. The article concludes with a discussion of possible future directions in this research area.

[1]  Jacobsen,et al.  Thermal Diffusion Processes in Metal-Tip-Surface Interactions: Contact Formation and Adatom Mobility. , 1996, Physical review letters.

[2]  Robert G. Parr,et al.  Density Functional Theory of Electronic Structure , 1996 .

[3]  Daw Model of metallic cohesion: The embedded-atom method. , 1989, Physical review. B, Condensed matter.

[4]  Stechel,et al.  Order-N methods in self-consistent density-functional calculations. , 1994, Physical review. B, Condensed matter.

[5]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[6]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[7]  T. Michely,et al.  The Ice Bilayer on Pt(111): Nucleation, Structure and Melting , 1997 .

[8]  D. W. Bassett,et al.  Diffusion of single adatoms of platinum, iridium and gold on platinum surfaces , 1978 .

[9]  Zhang,et al.  Atomic processes in low temperature Pt-dendrite growth on Pt(111). , 1996, Physical review letters.

[10]  Hernández,et al.  Linear-scaling density-functional-theory technique: The density-matrix approach. , 1996, Physical review. B, Condensed matter.

[11]  H. C. Andersen,et al.  Interatomic potential for silicon clusters, crystals, and surfaces. , 1990, Physical review. B, Condensed matter.

[12]  Kellogg Gl,et al.  Surface diffusion modes for Pt dimers and trimers on Pt(001). , 1991 .

[13]  H. Jónsson,et al.  Diffusion mechanisms relevant to metal crystal growth : Pt/Pt(111) , 1994 .

[14]  Kellogg,et al.  Surface self-diffusion on Pt(001) by an atomic exchange mechanism. , 1990, Physical review letters.

[15]  Karsten Wedel Jacobsen,et al.  Island shapes in homoepitaxial growth of Pt(111) , 1996 .

[16]  Kelly,et al.  Binding and diffusion of a Si adatom on the Si(100) surface. , 1991, Physical review letters.

[17]  Scheffler,et al.  Ab initio calculations of energies and self-diffusion on flat and stepped surfaces of Al and their implications on crystal growth. , 1996, Physical review. B, Condensed matter.

[18]  N. Nagel,et al.  On the shape of the in-phase TEAS oscillations during epitaxial growth of Pt(111) , 1992 .

[19]  T. Michely,et al.  HOW SENSITIVE IS EPITAXIAL GROWTH TO ADSORBATES , 1998 .

[20]  Hannes Jonsson,et al.  Reversible work transition state theory: application to dissociative adsorption of hydrogen , 1995 .

[21]  A. Voter,et al.  Accelerating the dynamics of infrequent events: Combining hyperdynamics and parallel replica dynamics to treat epitaxial layer growth , 1998 .

[22]  Arthur F. Voter,et al.  Accelerating Atomistic Simulations of Defect Dynamics: Hyperdynamics, Parallel Replica Dynamics, and Temperature-Accelerated Dynamics , 1998 .

[23]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[24]  B. C. Garrett,et al.  Current status of transition-state theory , 1983 .

[25]  Jens Nørskov,et al.  The mobility of Pt atoms and small Pt clusters on Pt(111) and its implications for the early stages of epitaxial growth , 1994 .

[26]  H. Jónsson,et al.  Molecular multipole moments of water molecules in ice Ih , 1998 .

[27]  J. Nørskov,et al.  Self-diffusion on copper surfaces , 1991 .

[28]  J. Nørskov,et al.  Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals , 1999 .

[29]  D. E. Sanders,et al.  Metal/metal homo-epitaxy on fcc (001) surfaces: Is there transient mobility of adsorbed atoms? , 1991 .

[30]  M. Lagally,et al.  Surface self-diffusion of Si on Si(001) , 1992 .

[31]  W. Miller,et al.  ON FINDING TRANSITION STATES , 1981 .

[32]  M. Baskes,et al.  Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals , 1984 .

[33]  Yinggang Li,et al.  Potential energy barriers for interlayer mass transport in homoepitaxial growth on fcc(111) surfaces: Pt and Ag , 1994 .

[34]  J. Langer Models of Pattern Formation in First-Order Phase Transitions , 1986 .

[35]  D. R. Hamann,et al.  Pseudopotentials that work: From H to Pu , 1982 .

[36]  J. Tersoff,et al.  New empirical approach for the structure and energy of covalent systems. , 1988, Physical review. B, Condensed matter.

[37]  Ehrlich,et al.  Atom incorporation at surface clusters: An atomic view. , 1991, Physical review letters.

[38]  Arthur F. Voter,et al.  Transition state theory description of surface self-diffusion: Comparison with classical trajectory results , 1984 .

[39]  Petr Nachtigall,et al.  Si adatom binding and diffusion on the Si(100) surface: Comparison of ab initio, semiempirical and empirical potential results , 1995 .

[40]  Yinggang Li,et al.  Nonadiabatic effects in hydrogen diffusion in metals , 1992 .

[41]  H. Jónsson,et al.  Electric fields in ice and near water clusters , 2000 .

[42]  Jackson,et al.  Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. , 1992, Physical review. B, Condensed matter.

[43]  P. Feibelman INTERLAYER SELF-DIFFUSION ON STEPPED PT(111) , 1998 .

[44]  Gerard T. Barkema,et al.  Computer simulation of metal-on-metal epitaxy , 1996 .

[45]  D. Gillespie A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[46]  H. Jónsson,et al.  Atomic exchange processes in sputter deposition of Pt on Pt(111) , 1995 .

[47]  Wheeler,et al.  Phase-field models for anisotropic interfaces. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[48]  Martin Head-Gordon,et al.  Quadratic configuration interaction. A general technique for determining electron correlation energies , 1987 .

[49]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

[50]  P. Jørgensen,et al.  Walking on potential energy surfaces , 1983 .

[51]  W. H. Weinberg,et al.  Theoretical foundations of dynamical Monte Carlo simulations , 1991 .

[52]  Bott,et al.  Inversion of growth speed anisotropy in two dimensions. , 1993, Physical review letters.

[53]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[54]  Arthur F. Voter,et al.  Simulation Of The Layer-Growth Dynamics In Silver Films: Dynamics Of Adatom And Vacancy Clusters On Ag(100) , 1988, Optics & Photonics.

[55]  F. Hudda,et al.  Atomic View of Surface Self‐Diffusion: Tungsten on Tungsten , 1966 .

[56]  Charles T. Campbell,et al.  Ultrathin metal films and particles on oxide surfaces: structural, electronic and chemisorptive properties , 1997 .

[57]  D. E. Sanders,et al.  Metal/metal homoepitaxy on fcc(111) and fcc(001) surfaces : deposition and scattering from small islands , 1992 .

[58]  Kunkel,et al.  Reentrant layer-by-layer growth during molecular-beam epitaxy of metal-on-metal substrates. , 1990, Physical review letters.

[59]  Paul C. Fife,et al.  Thermodynamically consistent models of phase-field type for the kinetics of phase transitions , 1990 .

[60]  Leskovar,et al.  Diffusion of Ge below the Si(100) surface: theory and experiment , 2000, Physical review letters.

[61]  Paul Meakin,et al.  Diffusion-controlled cluster formation in 2—6-dimensional space , 1983 .

[62]  G. Mills,et al.  Simulations of mobility and evaporation rate of adsorbate islands on solid surfaces , 1999 .

[63]  Petr Nachtigall,et al.  Investigation of the reliability of density functional methods: Reaction and activation energies for Si–Si bond cleavage and H2 elimination from silanes , 1996 .

[64]  Smith,et al.  Dimer and String Formation during Low Temperature Silicon Deposition on Si(100). , 1996, Physical review letters.

[65]  J. Simons,et al.  Walking on potential energy surfaces , 1990 .

[66]  Weber,et al.  Computer simulation of local order in condensed phases of silicon. , 1985, Physical review. B, Condensed matter.

[67]  Arthur F. Voter,et al.  Dynamical corrections to transition state theory for multistate systems: Surface self-diffusion in the rare-event regime , 1985 .

[68]  J. Nørskov,et al.  Many-atom interactions in metals , 1993 .

[69]  K. Kern,et al.  Mechanism of the transition from fractal to dendritic growth of surface aggregates , 1994, Nature.

[70]  N. Nagel,et al.  New phenomena in homoepitaxial growth of metals , 1991 .

[71]  Philip I Cohen,et al.  Damped oscillations in reflection high energy electron diffraction during GaAs MBE , 1983 .

[72]  Clarence Zener,et al.  Interstitial Atomic Diffusion Coefficients , 1949 .

[73]  A. Voter A method for accelerating the molecular dynamics simulation of infrequent events , 1997 .

[74]  P. Feibelman Self-diffusion along step bottoms on Pt(111) , 1999 .

[75]  G. Vineyard Frequency factors and isotope effects in solid state rate processes , 1957 .

[76]  B. Poelsema,et al.  Scattering of thermal energy atoms from disordered surfaces , 1989 .

[77]  Stoltze,et al.  Accommodation and diffusion of Cu deposited on flat and stepped Cu(111) surfaces. , 1993, Physical review. B, Condensed matter.

[78]  G. Barkema,et al.  Diffusion mechanism of Cu adatoms on a Cu(001) surface , 1994 .

[79]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

[80]  Hannes Jónsson,et al.  Multipole moments of water molecules in clusters and ice Ih from first principles calculations , 1999 .

[81]  M. Scheffler,et al.  Mechanisms of self-diffusion on flat and stepped Al surfaces , 1994 .

[82]  Yinggang Li,et al.  Predicted growth mode for metal homoepitaxy on the fcc (111) surface , 1996 .

[83]  P. Larsen,et al.  Reflection High-Energy Electron Diffraction and Reflection Electron Imaging of Surfaces , 1989 .

[84]  H. Metiu,et al.  Inter-layer diffusion and motion of adatoms in the vicinity of steps , 1996 .

[85]  Jónsson,et al.  Low-temperature homoepitaxial growth of Pt(111) in simulated vapor deposition. , 1994, Physical review. B, Condensed matter.

[86]  D. Vanderbilt,et al.  Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. , 1990, Physical review. B, Condensed matter.

[87]  Jacobsen,et al.  Island shape-induced transition from 2D to 3D growth for Pt/Pt(111). , 1995, Physical review letters.

[88]  A. Voter Parallel replica method for dynamics of infrequent events , 1998 .

[89]  J. B. Adams,et al.  EAM study of surface self-diffusion of single adatoms of fcc metals Ni, Cu, Al, Ag, Au, Pd, and Pt , 1991 .

[90]  H. Brune Microscopic view of epitaxial metal growth: nucleation and aggregation , 1998 .

[91]  Arthur F. Voter,et al.  Accurate Interatomic Potentials for Ni, Al and Ni3Al , 1986 .

[92]  G. Henkelman,et al.  A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives , 1999 .

[93]  B. D. Kay,et al.  Molecular Beam Studies Of Kinetic Processes In Nanoscale Water Films , 1997 .

[94]  T. Michely,et al.  The homoepitaxial growth of Pt on Pt(111) studied with STM , 1992 .

[95]  Smith,et al.  Experimental and Theoretical Study of the Rotation of Si Ad-dimers on the Si(100) Surface. , 1996, Physical review letters.

[96]  L. Sander,et al.  Diffusion-limited aggregation, a kinetic critical phenomenon , 1981 .

[97]  R. Stanley Williams,et al.  Evolution of Ge islands on Si(001) during annealing , 1999 .

[98]  A. Voter,et al.  Classically exact overlayer dynamics: Diffusion of rhodium clusters on Rh(100). , 1986, Physical review. B, Condensed matter.

[99]  P. Pechukas Statistical Approximations in Collision Theory , 1976 .

[100]  Zhang,et al.  Kinetic mechanism for island shape variations caused by changes in the growth temperature. , 1993, Physical review letters.

[101]  J. Nørskov,et al.  Anisotropic corner diffusion as origin for dendritic growth on hexagonal substrates , 1996 .

[102]  Soler,et al.  Self-consistent order-N density-functional calculations for very large systems. , 1996, Physical review. B, Condensed matter.

[103]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[104]  William H. Miller Dynamics of Molecular Collisions , 1976 .

[105]  G. Gilmer,et al.  Computer Models of Crystal Growth , 1980, Science.

[106]  G. Kellogg,et al.  Field ion microscope studies of single-atom surface diffusion and cluster nucleation on metal surfaces , 1994 .

[107]  P. Feibelman,et al.  Diffusion path for an Al adatom on Al(001). , 1990, Physical review letters.

[108]  D. Wales Finding saddle points for clusters , 1989 .

[109]  Ehrlich,et al.  Atom Movement and Binding on Surface Clusters: Pt on Pt(111) Clusters. , 1996, Physical review letters.

[110]  Daniel T. Gillespie,et al.  Monte Carlo simulation of random walks with residence time dependent transition probability rates , 1978 .

[111]  A. Voter Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events , 1997 .