Comment on 'Surface reconstruction on Si(100) studied by the CNDO method'

In a recent paper Ong and Chan (see ibid., vol.1, p.3931 (1989)) examined seven different asymmetric dimer reconstructions for a Si(100) surface using the CNDO (complete neglect of differential overlap) method. The p(4*1) and c(4*2) reconstructions were found to be energetically more favourable, followed by p(2*2) and (2*1). Zandvliet comments only on the results of the four members of the (2*1) family, since experimentally the other asymmetric dimer reconstructions are not observed on the Si(100) and the Ge(100) surfaces

An experimentalists view on the analogy between step edges and quantum mechanical particles

Guided by scanning tunnelling microscopy images of regularly stepped surfaces it will be illustrated that there is a striking similarity between the behaviour of monoatomic step edges and quantum mechanical particles (spinless fermions). The direction along the step edge is equivalent to the time, while the direction perpendicular to the step corresponds to the one-dimensional space along which the quantum mechanical particles are located. The non-crossing condition of the steps, giving rise to entropic repulsion, is related to the boundary condition of the wavefunction of a quantum mechanical particle at an infinitely high barrier. Finally, the step edge stiffness can be related to the mass of the quantum mechanical particle

On the solution, the critical exponents and the transition equation of the simple cubic three-dimensional Ising model

In a recent paper Hoede and Zandvliet introduced the concept of gauging on an equation. This enables the simulation of more complex Ising models by the simple quadratic model. The possibility of simulating the simple cubic model was defended by calculating a sequence of approximations to the transition point from a so-called solution function.\ud In this paper we investigate some aspects of such a simulation, in particular with respect to the solution. It is also shown that taking into account the difference in universality class is possible. It is argued that the critical exponent for the specific heat is 0. The theory then also leads to a choice of the other critical exponents, depending on the validity of the scaling hypothesis of Widom and experimental data. Using the value 3/8 for the critical exponent for the magnetization we establish a relationship between the transition equations of the 2D and the 3D model

On Ising models

For various Ising models two approaches are discussed, one is that of simulating lattices, also called gauging on exact equations, the other is that of calculating analytical expressions for the boundary free energy of Ising lattices. The first approach allows to conjecture a solution for some Ising models, that have sofar not been solved, once some exact partial result for the problem is known. The second approach aims at furnishing such a partial result in the form of a condition for the critical temperature. An example of such a result was recently given for the 2D Ising square lattice with nearest and next-nearest-neighbor interactions. The critical line that separates the ordered (ferromagnetic) phase from the disordered (paramagnetic) phase showed good agreement in the moderate and strong nearest neighbor coupling limit with several results obtained by Monte Carlo, transfer matrix and series expansion results. We extend the discussion of the critical line, finding an excellent fit, now also in other points, like the Padé point, as well as cusp behavior at the Onsager point where the lattice decouples into two 2D square lattices with only nearest-neighbor interaction. Combination of this result with a geometrical argument in the simulation approach leads to a critical exponent $2-\sqrt{2} \approx 0.5858,$ comparable to the exponent $4/7 \approx 0.5714$ found from renormalization arguments.\ud \u

Spontaneous magnetization of the square 2D Ising lattice with nearest- and weak next-nearest-neighbour interactions

We show that the square two-dimensional (2D) Ising lattice with nearest- (J) and weak next-nearest-neighbour interactions (Jd) can be mapped on a square 2D Ising lattice that has only nearest neighbour interactions (J*). For Jd/J << 1 the transformation equation has the simple form GPHT_A_361184_O_XML_IMAGES\GPHT_A_361184_O_ILM0001.gif. This result can be used to derive expressions for several thermodynamic functions of the square 2D Ising lattice with weak next-nearest-neighbour interactions. As an example we consider the spontaneous magnetization and compare it with low-temperature series expansion results

Boundary tension of 2D and 3D Ising models

A simple route to determine the boundary tension of Ising models is proposed. As pointed out by Onsager, the boundary tension is an important quantity since it vanishes at the critical temperature and can thus be used to determine the critical temperature. Here we derive expressions for the boundary tension along various high symmetry directions of the anisotropic square and triangular lattices. The exact results by respectively Onsager (Phys. Rev. 65, 117 (1944)) for the anisotropic square lattice and by Houtappel (Physica 16, 435 (1950)) for the anisotropic triangular lattice are reproduced. Subsequently, we will apply our method to Ising models that have not been exactly solved yet. Valuable results are obtained for the 2D square Ising lattice with nearest and weak next‐nearest neighbour interactions as well as for the strongly anisotropic 3D Ising lattice

Antiphase boundaries on low-energy ion bombarded Ge(001)

Surface vacancy and adatom clusters have been created on Ge(001) by bombarding the surface with 800 eV argon ions at various substrate temperatures ranging from room temperature to 600 K. The vacancies preferentially annihilate at the ends rather than at the sides of the dimer rows, resulting in monolayer deep vacancy islands which are elongated in a direction of the dimer rows of the upper terrace. As vacancy islands nucleate and expand, the dimer rows in neighbouring vacancy islands need not, in general, align with each other. An antiphase boundary will develop if two growing vacancy islands meet, but their internal dimer rows are not in the same registry. In contrast to Si(001), where only one type of antiphase boundary is found, we have found three different types of antiphase boundaries on Ge(001). Higher dose (> several monolayers) room temperature ion bombardment followed by annealing at temperatures in the range 400¿500 K results in a surface which contains a high density of valleys. In addition to the preference for the annihilation of dimer vacancies at descending versus ascending steps we also suggest that the development of antiphase boundaries drives the roughening of this surface. Finally, several atomic rearrangement events, which might be induced by the tunneling process, are observed after low-dose ion bombardment at room temperature

Bistability in the Shape Transition of Strained Islands

The equilibrium shape of a monatomic strained island on a substrate depends on the step free energies and the difference in surface stress between the island and the substrate. For small island sizes the step free energies dominate, resulting in compact islands. Beyond a critical island size, however, the strain energy becomes dominant and the island maximizes its perimeter, resulting in elongated islands. Here we show that for strained islands with force monopoles pointing in opposing directions at neighboring steps, a regime exists near the critical island size where both compact and elongated shapes can coexist

The optical and the electronic response of the Ge(111)-c(2 × 8) surface to O2 exposure

This Communication describes a study concerning the interaction of molecular oxygen with a clean Ge(111)-c(2 × 8) surface. This reaction has been studied by in situ monitoring the ellipsometric reflection and the surface conductance. In order to explain the experimental results a model is proposed assuming a gradual disappearance of donor and acceptor surface states. The final stage in the adsorption process is characterized by the saturation of an acceptor surface state related to an optical transition at hv = 1.9 eV

Order-disorder phase transition of the Ge(001) surface

The order-disorder phase transition of the Ge(001) surface can be described by taking into account only electrostatic interactions between the asymmetric dimers. The transition fits approximately the two-dimensional Ising universality class and accordingly the critical exponent of the order parameter, β, has a value near 1/8 and is observable from an analysis of diffraction intensities. The charge transfer between the up and down atom of the asymmetric dimer consistent with the observed phase transition temperature is about 0.08e