Unrelaxed Surface Research Articles

The Pt(110) phase transitions: A study by rutherford backscattering, nuclear microanalysis, LEED and thermal desorption spectroscopy

The adsorbate induced (1×2) (1×1) (2×1)p1g1 phase transitions on Pt(110) have been studied by Rutherford backscattering (RBS), nuclear microanalysis (NMA), LEED and thermal desorption spectroscopy. RBS data indicate that any displacement of the surface atoms from their expected bulk-like lattice sites in the (1×2) phase is ≲ 0.002 nm laterally and ≲ 0.007 nm vertically. This contraint eliminates models for the reconstruction which involve significant lateral displacements (e.g., the paired-atom or hexagonal overlayer models). The RBS data are consistent with both the rumpled model with up/down displacements not exceeding ~0.007 nm and the missing row model with an unrelaxed surface in which the out-of-plane vibrational amplitude is slightly enhanced. A c(8×4) phase, produced by CO (or NO) exposure at T⩽250 K, has also been characterized by RBS which demonstrated that 0.92×10 15 Pt cm −2 move on average by ~0.017 nm laterally out-of-registry with the bulk upon formation of this phase. The values of the saturation adsorbate coverages at T≲200K were determined by NMA to be 0.92 ± 0.05×10 15, 1.0 ± 0.06×10 15 and 1.07 ± 0.10×10 15 CO molecules, NO molecules and D atoms, respectively, per cm 2. The value of the saturation coverage by CO (θ = 1.0) supports recent models of the (2×1)p1g1 overlayer. The isosteric heat of adsorption of CO is 160 ± 15 kJ mol −1 in the range 0.2⩽θ⩽0.5.

Self-consistent pseudopotential calculations for the electronic structure of bulk and (111) surface of α-Sn

Presents a self-consistent local pseudopotential calculation for the electronic structure of bulk alpha -Sn. Calculated band structure and valence charge density are compared with experiment and other theoretical results. The self-consistent pseudopotential method with a slab geometry is applied to the unreconstructed (111) surface of alpha -Sn. The results for the dangling-bond surface states on relaxed and unrelaxed surfaces are presented and compared with the works of Hirabayashi (1969), and Louis and Elices (1975).

Self-consistent electronic structure of the contracted tungsten (001) surface

Self-consistent linearized-augmented-plane-wave energy-band studies using the warped muffin-tin approximation for a seven-layer W(001) single slab with the surface-layer separation contracted by 6% of the bulk interlayer spacing are reported. Surface electronic structure, local densities of states, generalized susceptibility for the surface, work function, and core-level shifts are found to have insignificant differences with corresponding results for the unrelaxed surface. Several differences in surface states between theory and recent angle-resolved photoemission experiments are discussed in the light of new proposed models of the actual unreconstructed surface structure at high temperatures.

The homopolar amorphous surface Structural and electronic properties

Abstract For the first time, the topological dependency of the density of states for the amorphous surface is calculated. The unrelaxed amorphous surface for homopolar semiconductors is briefly defined and described. A model Hamiltonian for computing the configuration-averaged density of surface states is used. A surface from a model with only even-fold rings and a surface from a model with both even-fold and odd-fold rings are investigated. The results are interpreted in terms of the effects of nearest-neighbour surface atoms, the number of unsaturated bonds/surface-atom and the ring structure. The odd-fold rings cause the distribution of the surface density of states to be spread over a larger energy region than for models where the odd-fold rings are absent. It is argued that the amorphous topology must be taken into account when considering models for the gap states. For a tetrahedral solid, the surface states are expected to contribute to the filling of the minima in the bulk valence-band density of states.

Effects of surface relaxation on the electronic structure of ZnO (101̄0)

We have investigated the effect of atomic relaxation on the electronic structure of the nonpolar ZnO (101̄0) surface using the tight binding scattering theoretical method. The bulk material is described by a realistic empirical tight binding Hamiltonian and the relaxation is taken into account by a d−2 scaling of the interaction matrix elements. We find that the ionic surface resonances and the covalent surface states, which we have reported about for the unrelaxed surface previously, are affected very differently by surface relaxation. The covalent surface states strongly shift in energy upon relaxation while the ionic resonances are only marginally affected. This result can easily be interpreted by correlating the changes in the surface electronic structure with the relaxation induced changes of the local binding environment near the surface. Our theoretical results are in good agreement with UPS and EELS data.

Temperature Dependence of Hertzian Indentation Fracture Surface Energy of ThO2

The fracture surface energy, γ, of ThO2 was measured between room temperature and 400°C using the Hertzian indentation technique with cold or preheated steel and alumina indentors. The value of γdecreased strongly with temperature with a suggested saturation at 350°C. This may indicate the change from an unrelaxed fracture surface to a relaxed surface at temperatures where oxygen becomes mobile. The result obtained at 400°C is γ=1.4 J m−2.

Computer renormalization-group calculation of surface states of Si (111)

The computer renormalization-group technique is tested by calculating the surface states of the unreconstructed, unrelaxed, and relaxed (111) surface of Si in the tight-binding approximation. We found a factor of 10 improvement in the speed with the maximum error less than 0.02 eV when compared with conventional calculations. Furthermore, our calculation enables us to deal with much thicker slabs than is otherwise possible.

A model pseudopotential calculation of the electronic structure of Si (111)-1 × 1 surface

We report a model pseudopotential calculation of the electronic structure of Si (111)-1 × 1 unrelaxed, relaxed and expanded surfaces. It is shown that our results for the surface states on these faces are in good agreement with results from other self-consistent pseudopotential and semi-empirical tight-binding calculations.

Madelung and dispersion contributions to the binding energy of an ion on the unrelaxed (100) and (110) faces of the NaCl-type crystal

Very simple formulas have been derived, which make possible the calculation with a high accuracy of the Madelung and dispersion contributions to the binding energy of an ion on the unrelaxed surface of a NaCl-type crystal. The formulas can be applied to practically all possible positions of a surface ion.

Chemisorption of oxygen atoms on aluminum (111): A molecular-orbital cluster study

Self-consistent-field $X\ensuremath{\alpha}$ scattered-wave molecular-orbital calculations have been performed for clusters containing up to 22 aluminum atoms representing the (111) surface of aluminum in interaction with an oxygen atom at various positions above, in, and below the surface. Reasonable agreement with experimental photoemission results for the valence and Al-$2p$ core regions of the spectrum was obtained for two distinct positions of the oxygen atom. The first of these has the oxygen atom between 1 and 2 bohrs above an unrelaxed surface, while the second has the oxygen atom in the first surface layer which has been relaxed by enlarging the threefold site. Both of these models are consistent with available experimental data for some coverage between zero and one monolayer. Additional, as yet unobserved, oxygen-related structure is predicted in the valence region between -5 eV and the Fermi level similar to our previous predictions for Al(100) + 0, which have subsequently been born out experimentally.

Energy-Minimization Approach to the Atomic Geometry of Semiconductor Surfaces

The (110) surface atomic geometries of GaAs and ZnSe and of 2 \ifmmode\times\else\texttimes\fi{} 1 reconstructed (111) surface of Si are calculated by minimizing the total energy of the electron-ion system. The corresponding reductions in total energy between the relaxed and unrelaxed surfaces are calculated to be - 0.51, - 0.30, and - 0.37 eV per surface atom, respectively. Subsurface relaxations are generally found to make a very small (\ensuremath{\le} 0.02 eV) contribution to the reduction in total energy.

The phase problem in LEED

The problem of determining the phases of the diffracted waves when only their intensities can be measured is a question that has received a great deal of attention in the case of X-ray diffraction but has so far been largely ignored in low-energy electron diffraction. By applying a technique similar to the one employed in the Kramers-Kronig analysis of optical reflectivity data it is found that under certain circumstances a good approximation to the phase can be found. The error involved depends on the location of the zeros of the reflectivity in the complex energy plane. In a test calculation for Ni (100) it is found that these zeros are favourably placed for the clean, unrelaxed surface but that any departure from this leads to a serious deterioration in the accuracy of the phase determination.

Electronic states at unrelaxed and relaxed GaAs (110) surfaces

We have shown that, using a general class of Hamiltonians, the transfer-matrix technique may be used to obtain exact solutions for the electronic states at any crystal surface bounded by semi-infinite bulk. This result is formally generalized as a theorem and is used to study the electronic states at a clean GaAs (110) surface. The calculation employs an empirical tight-binding Hamiltonian which realistically models the GaAs surface and allows meaningful comparison with both experiments and self-consistent pseudopotential calculations. Surface states are calculated for the clean (110) surface, and a variety of structural relaxations are studied.

Self-consistent pseudopotential calculations for Ge and diamond (111) surfaces

The self-consistent pseudopotential method with a slab geometry is applied to electronicstructure calculations of the Ge and diamond (111) surfaces. A nonlocal pseudopotential is derived and found to produce an energy band structure of bulk diamond in good agreement with other calculations and experiments. This potential is then used for the diamond surface calculations. The calculations are restricted to unrelaxed unreconstructed surfaces. Various surface states are identified and discussed.

An Effective Pair-Potential Study of the Interaction of a Water Monomer with the Basal-Plane Surface of Ice Ih

AbstractThe central-force effective pair potential of Rahman and others (1975) is used to generate minimal binding-energy surfaces and configurations of a water monomer adsorbed on the unrelaxed basal plane surface of ice Ih. In the initial study H2O molecules arc placed with oxygen atoms fixed at the ice Ih lattice positions and associated hydrogens along the tetrahedral bond directions—restricting the H-O-H bond angles to 109.5°. A rigid-body water monomer adsorbed on the surface interacts with all the H2D molecules in the bulk ice model via the central-force effective pair potential. The center-of-mass height, z, and the dipole orientation of the adsorbed H2O molecule are varied to minimize the total binding energy of the monomer over a particular (x,y) point of the surface. Preliminary results showed that a rigid adsorbed monomer with an H-O-H angle fixed at 104.5° produced only minor deviations in the binding-energy surfaces and that a large bulk-ice model (486 molecules) gave effectively the same results as a smaller ice model (50 molecules). Studies on an infinite ice surface using periodic boundary conditions are in progress and will be used to study surface relaxation and long-range effects on the minimal energy surfaces. Three types of sites on the basal plane were considered: (1) a site with all surface molecule protons pointing out of the surface; (2) a site with all surface molecule protons pointing into the surface; and (3) a site with all rows of surface molecule protons pointing alternately into and out of the surface. A "site" generally refers to a region (about 90 Å2) on the surface over which the minimal binding-energy surface is to be determined.Minimal binding-energy surfaces for the sites have been obtained together with plots showing the surface of the position of the center of mass as a function of x and y. This is a model calculation and is limited by the validity of the potential under close scrutiny. However it gives a qualitative picture of how complex a terrain the real ice Ih surface might present to an adsorbed water molecule and how the water molecule might diffuse from site to site. From these calculations (and in the spirit of this model potential) a value for the mean path length and the mean residence time of the adsorbed water monomer can be estimated.

An Effective Pair-Potential Study of the Interaction of a Water Monomer with the Basal-Plane Surface of Ice Ih

Abstract The central-force effective pair potential of Rahman and others (1975) is used to generate minimal binding-energy surfaces and configurations of a water monomer adsorbed on the unrelaxed basal plane surface of ice Ih. In the initial study H2O molecules arc placed with oxygen atoms fixed at the ice Ih lattice positions and associated hydrogens along the tetrahedral bond directions—restricting the H-O-H bond angles to 109.5°. A rigid-body water monomer adsorbed on the surface interacts with all the H2D molecules in the bulk ice model via the central-force effective pair potential. The center-of-mass height, z, and the dipole orientation of the adsorbed H2O molecule are varied to minimize the total binding energy of the monomer over a particular (x,y) point of the surface. Preliminary results showed that a rigid adsorbed monomer with an H-O-H angle fixed at 104.5° produced only minor deviations in the binding-energy surfaces and that a large bulk-ice model (486 molecules) gave effectively the same results as a smaller ice model (50 molecules). Studies on an infinite ice surface using periodic boundary conditions are in progress and will be used to study surface relaxation and long-range effects on the minimal energy surfaces. Three types of sites on the basal plane were considered: (1) a site with all surface molecule protons pointing out of the surface; (2) a site with all surface molecule protons pointing into the surface; and (3) a site with all rows of surface molecule protons pointing alternately into and out of the surface. A "site" generally refers to a region (about 90 Å2) on the surface over which the minimal binding-energy surface is to be determined. Minimal binding-energy surfaces for the sites have been obtained together with plots showing the surface of the position of the center of mass as a function of x and y. This is a model calculation and is limited by the validity of the potential under close scrutiny. However it gives a qualitative picture of how complex a terrain the real ice Ih surface might present to an adsorbed water molecule and how the water molecule might diffuse from site to site. From these calculations (and in the spirit of this model potential) a value for the mean path length and the mean residence time of the adsorbed water monomer can be estimated.

Studies of vibrational surface modes in ionic crystals: III. Vibrational contributions to the surface thermodynamic functions for the (001) face of LiF, MgO, NaF, NaCl, Nal, RbF, and RbCl

The temperature dependence of the vibrational contributions to surface specific heat, surface entropy, surface energy, and surface Helmholtz free energy have been calculated for the (001) face of seven crystals having the rocksalt structure. The calculations assume a perfect, unrelaxed surface and make use of shell models fitted to bulk phonon spectra determined from inelastic neutron scattering. In terms of the bulk zero-temperature Debye temperature θ 0, the surface specific heat C v s exhibits an effective power law behavior, T α, from at least T = 0.02 θ 0 up to 0.05 θ 0 in most cases (and up to 0.07 θ 0 for NaF), with α ≈ 2.5 in most cases — in contrast with the result of α = 2 in a Debye-like model. (Below 0.02 θ 0, results derived for our 15-layer films depart significantly from intrinsic surface effects because of the finite thickness.) C v s attains a maximum at a temperature T( C max s) ranging from 0.14 θ 0 to 0.20 θ 0, in contrast with the result T( C max s) = 0.21 θ 0 for the Debye-like model. The peak value C max s ranges from 0.34 k B A SUC to 0.41 k B A SUC, where A SUC is the area of the surface unit cell. The shap the peak in C v s differs characteristically between that class of crystals in which there is some overlap of the acoustical and optical bulk bands and that class in which there is an appreciable absolute gap between the acoustical and optical bulk bands; in the latter class the peak is flattened on the low side of the maximum, with the maximum pushed to somewhat higher temperature. On those points of comparison with the rather sparse existing data for surface-excess heat capacity in which the value of specific surface area is not required (e.g., the value of T( C s max)), the agreement ranges from encouraging to equivocal. On those comparisons which require the surface area of the experimental samples (e.g., the magnitude of C s max) the agreement ranges from only fair to bad. Further experimental work is needed, and great care in surface area determinations is necessary.

Self-consistent pseudopotential calculations for Si (111) surfaces: Unreconstructed (1×1) and reconstructed (2×1) model structures

A recently developed method involving self-consistent pseudopotentials has been used to calculate the electronic structure of several Si (111) surface models. The results for (1\ifmmode\times\else\texttimes\fi{}1) unreconstructed, relaxed and unrelaxed surfaces are compared with earlier calculations and discussed in terms of density-of-states curves and charge-density distributions. A fully self-consistent calculation has been carried out for Haneman's (2\ifmmode\times\else\texttimes\fi{}1) reconstructed surface model. It is found that the important experimental results can be understood using this model, and changes in the electronic structure occurring after reconstruction are rationalized on chemical grounds. In particular infrared-absorption measurements, photoemission measurements, and recent angular-dependent photoemission measurements find consistent explanations.

Tight-binding calculations of (111) surface densities of states of Ge and GaAs

Abstract We have used the tight-binding method to calculate the local densities of states of unreconstructed Ge (111) and GaAs (111), ( 111 ) surfaces. In the unrelaxed surface configuration we find two types of states for each surface. The effects of relaxation on Ge surface states are also discussed.

New surface states of an unrelaxed (110) surface

Electronic densities of states are calculated using a simple tight binding model for an unrelaxed (110) surface of Ge and GaAs prototypes. New surface states for Ge and GaAs prototypes are found near the bottom of the valence bands.