The roughening of metal surfaces

Abstract We address the problem of the departure of a crystal surface from a perfectly ordered crystal plane. We discuss the energetics of the surface defects and their statistical mechanics which lead to the so-called “roughening transition”. The theory of this transition is outlined and a special emphasis is put on the experimental aspects: roughening measurement techniques and critical review of the available data. We pay special attention to the case of vicinal surfaces. Apart from the equilibrium situation there is an increasing interest in the dynamical roughening of crystal surfaces during MBE growth or ion-bombardment etching, or in the reverse problem: the annealing of a non-equilibrium roughness. We review the present state of this field by recalling relevant models which lead to the concept of dynamical scaling and we discuss some recent data. The present review is restricted to the case of metal surfaces; however, most of the concepts which are presented have a much larger generality.

[1]  Conrad,et al.  Roughening of stepped metal surfaces. , 1985, Physical review letters.

[2]  B. Poelsema,et al.  Investigation of a randomly stepped Pt(111) surface using thermal energy atom scattering (TEAS) , 1985 .

[3]  J. Frenken,et al.  On the displacement statistics of an individual step edge in a vicinal surface , 1992 .

[4]  Kern,et al.  Non-Ising behavior of the Pt(110) surface phase transition. , 1989, Physical review letters.

[5]  R. Kariotis Non-equilibrium roughening transitions , 1989 .

[6]  J. Villain,et al.  Surface deconstruction of Au(110) , 1988 .

[7]  Conrad,et al.  Anomalous thermal expansion of Ni(001). , 1990, Physical review letters.

[8]  H. C. Kang,et al.  Scaling analysis of surface roughness and Bragg oscillation decay in models for low-temperature epitaxial growth , 1992 .

[9]  D. Spanjaard,et al.  Concepts in surface physics , 1993 .

[10]  Jürg Fröhlich,et al.  The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas , 1981 .

[11]  Jacobsen,et al.  Interatomic interactions in the effective-medium theory. , 1987, Physical review. B, Condensed matter.

[12]  Zhang,et al.  Dynamic scaling of growing interfaces. , 1986, Physical review letters.

[13]  J. Villain,et al.  Phase transitions on reconstructed (110) surfaces , 1991 .

[14]  J. Weeks,et al.  Monte Carlo Test of Theories for the Planar Model, theFModel, and Related Systems , 1978 .

[15]  Amar,et al.  Monte Carlo study of growth in the two-dimensional spin-exchange kinetic Ising model. , 1988, Physical review. B, Condensed matter.

[16]  Ernst,et al.  Observation of a growth instability during low temperature molecular beam epitaxy. , 1994, Physical review letters.

[17]  S. Stoyanov,et al.  Non-steady state effects in MBE: Oscillations of the step density at the crystal surface , 1988 .

[18]  D. Huse,et al.  Corrections to late-stage behavior in spinodal decomposition: Lifshitz-Slyozov scaling and Monte Carlo simulations. , 1986, Physical review. B, Condensed matter.

[19]  Lai,et al.  Kinetic growth with surface relaxation: Continuum versus atomistic models. , 1991, Physical review letters.

[20]  David,et al.  No thermal roughening on Cu(110) up to 900 K. , 1989, Physical review letters.

[21]  W. Heiland,et al.  Observation of pre-phase transitional phenomena on an Au(110) surface , 1990 .

[22]  R. Lynden-Bell,et al.  A computational study of metal stepped surfaces , 1992 .

[23]  D. L. Blanchard,et al.  Kosterlitz-Thouless roughening at the Ni(113) surface , 1987 .

[24]  Hughes,et al.  Roughening transition of a stepped Cu(113) surface: A synchrotron x-ray-scattering study. , 1987, Physical review letters.

[25]  H. Beijeren,et al.  Exactly solvable model for the roughening transition of a crystal surface , 1977 .

[26]  den Nijs M,et al.  Preroughening transitions in surfaces. , 1987, Physical review letters.

[27]  C. Lent,et al.  Diffraction from stepped surfacesII. Arbitrary terrace distributions , 1985 .

[28]  H. Jagodzinski,et al.  Diffuse LEED intensities of disordered crystal surfaces: III. LEED investigation of the disordered (110) surface of gold , 1978 .

[29]  D. Gorse,et al.  A study of the high temperature stability of low index planes of copper by atomic beam diffraction , 1985 .

[30]  Evans Random-deposition models for thin-film epitaxial growth. , 1989, Physical review. B, Condensed matter.

[31]  Grant,et al.  Dynamics of driven interfaces with a conservation law. , 1989, Physical review. A, General physics.

[32]  C. Jayaprakash,et al.  Simple model for crystal shapes: Step-step interactions and facet edges , 1984 .

[33]  Model diffraction profiles parallel to rough step edges , 1990 .

[34]  G. H. Gilmer,et al.  Simulation of Crystal Growth with Surface Diffusion , 1972 .

[35]  M. Henzler Quantitative evaluation of random distributed steps at interfaces and surfaces , 1978 .

[36]  Joós,et al.  Distribution of terrace widths on a vicinal surface within the one-dimensional free-fermion model. , 1991, Physical review. B, Condensed matter.

[37]  Gibbs,et al.  Thermal roughness of a close-packed metal surface: Pt(001). , 1992, Physical Review Letters.

[38]  M. Lagally,et al.  Diffraction from surfaces with randomly distributed steps , 1982 .

[39]  N. Bartelt,et al.  The role of step collisions on diffraction from vicinal surfaces , 1992 .

[40]  Evans,et al.  Low-temperature epitaxial growth of thin metal films. , 1990, Physical review. B, Condensed matter.

[41]  Ernst,et al.  Observation of dynamical scaling in "spinodal decomposition" in two dimensions. , 1992, Physical review letters.

[42]  J. Weeks,et al.  Phase transition in the two-dimensional Coulomb gas, and the interfacial roughening transition , 1976 .

[43]  N. Bartelt,et al.  Diffraction from stepped surfaces in thermal equilibrium , 1991 .

[44]  Mochrie Thermal roughening of the copper (110) surface: An x-ray diffraction experiment. , 1987, Physical review letters.

[45]  M. Nijs,et al.  Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains. , 1989, Physical review. B, Condensed matter.

[46]  Zangwill,et al.  Morphological instability of a terrace edge during step-flow growth. , 1990, Physical review. B, Condensed matter.

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

[48]  J. Venables,et al.  Nucleation and growth of thin films , 1984 .

[49]  Evans Factors mediating smoothness in epitaxial thin-film growth. , 1991, Physical review. B, Condensed matter.

[50]  Jacob,et al.  Reflection high-energy electron diffraction (RHEED) oscillations at 77 K. , 1989, Physical review letters.

[51]  D. Grempel,et al.  Roughening transition of high-index crystal faces: the case of copper , 1985 .

[52]  Saam Wf Comment on "Universal jump of Gaussian curvature at the facet edge of a crystal , 1989 .

[53]  Wolf,et al.  Kinetic roughening of vicinal surfaces. , 1991, Physical review letters.

[54]  M. Henzler,et al.  Effects of nearest and next-nearest neighbour interaction parameters on atomic correlation functions of stepped surfaces , 1990 .

[55]  C. Jayaprakash,et al.  Thermal evolution of crystal shapes: The fcc crystal , 1984 .

[56]  Sander,et al.  Molecular-beam epitaxial growth and surface diffusion. , 1992, Physical review letters.

[57]  E. Tosatti,et al.  Monte Carlo study of phase transitions and scattering intensities in a model of Au(110) , 1992 .

[58]  E. Tosatti,et al.  Interplay between Ising and six-vertex symmetries in a model for the roughening of reconstructing surfaces , 1990 .

[59]  Yang,et al.  Time-invariant structure factor in an epitaxial growth front. , 1992, Physical review letters.

[60]  B. Salanon,et al.  Scattering of thermal atoms by disordered surfaces. II: Adsorbed defects , 1989 .

[61]  Wolf,et al.  Attractive interaction between steps. , 1991, Physical review letters.

[62]  M. Fisher,et al.  Wall wandering and the dimensionality dependence of the commensurate-incommensurate transition , 1982 .

[63]  Theory of unstable growth. II. Conserved order parameter. , 1991, Physical review. B, Condensed matter.

[64]  K. Kawasaki,et al.  Renormalization Group Theory of the Interfacial Roughening Transition , 1978 .

[65]  R. L. Park,et al.  LEED from statistical step models , 1971 .

[66]  B. E. Sundquist The effect of metallic impurities and temperature on the anisotropy of the surface free energy of solid metals , 1964 .

[67]  E. Kaldis Current Topics in Materials Science , 1980 .

[68]  M. Nijs,et al.  Observation of surface roughening on Ni(115) , 1986 .

[69]  Yang,et al.  High-resolution low-energy electron diffraction study of Pb(110) surface roughening transition. , 1989, Physical review letters.

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

[71]  Puri,et al.  Study of phase-separation dynamics by use of cell dynamical systems. II. Two-dimensional demonstrations. , 1988, Physical review. A, General physics.

[72]  Desai,et al.  Numerical study of the late stages of spinodal decomposition. , 1988, Physical review. B, Condensed matter.

[73]  D. L. Blanchard,et al.  Effects of inelastic scattering on He diffraction lineshapes , 1987 .

[74]  J. Lapujoulade A statistical model for the scattering of atoms from randomly stepped surfaces , 1981 .

[75]  J. Lapujoulade Molecular beam study of surface roughening transition , 1986 .

[76]  Jin Min Kim,et al.  Growth in a restricted solid-on-solid model. , 1989 .

[77]  Conrad,et al.  Approach to thermal roughening of Ni(110): A study by high-resolution low-energy electron diffraction. , 1990, Physical Review Letters.

[78]  Jacques Villain,et al.  Growth with Surface Diffusion , 1990 .

[79]  B. Salanon,et al.  Roughness of Cu (1,1,11): A very anisotropic face , 1987 .

[80]  Willis,et al.  Au(110) (1 x 2)-to-(1 x 1) phase transition: A physical realization of the two-dimensional Ising model. , 1985, Physical review letters.

[81]  W. Kohn,et al.  Elastic interaction of two atoms adsorbed on a solid surface , 1976 .

[82]  J. L. Goldberg,et al.  The equilibration of terrace width distributions on stepped surfaces , 1992 .

[83]  Fabre,et al.  Roughening transition on Cu(113): A quantitative analysis of new experimental results. , 1988, Physical review. B, Condensed matter.

[84]  Gabor A. Somorjai,et al.  The surface reconstructions of the (100) crystal faces of iridium, platinum and gold. I. Experimental observations and possible structural models , 1981 .

[85]  B. Salanon,et al.  Roughening transition and deconstruction transition on Au(110)-(2×1) , 1991 .

[86]  P. I. Tamborenea,et al.  A new universality class for kinetic growth: One-dimensional molecular-beam epitaxy. , 1991, Physical review letters.

[87]  Conrad,et al.  Surface morphology of Ag(110) close to its roughening transition. , 1991, Physical Review Letters.

[88]  Tang,et al.  Kinetic roughening in molecular-beam epitaxy. , 1991, Physical review letters.

[89]  C. Lent,et al.  Diffraction from stepped surfaces: I. Reversible surfaces , 1984 .

[90]  W. Mullins Theory of Thermal Grooving , 1957 .

[91]  Jorge V. José,et al.  Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model , 1977 .

[92]  Grant,et al.  Monte Carlo renormalization-group study of spinodal decomposition: Scaling and growth. , 1989, Physical review. B, Condensed matter.

[93]  M. Hove,et al.  The surface reconstructions of the (100) crystal faces of iridium, platinum and gold: II. Structural determination by LEED intensity analysis , 1981 .

[94]  J. M. Cowley,et al.  Electron diffraction from a statistically rough surface , 1973 .

[95]  E. Tosatti,et al.  Anisotropic roughening theory of the (110) faces of Cu, Ni, Pd, and Ag , 1990 .

[96]  Horn,et al.  X-ray scattering study of the thermal roughening of Ag(110). , 1987, Physical review letters.