Felix Yndurain

Model calculation of the electronic structure of a (111) surface in a diamond-structure solid

The authors present exact results for a model calculation of the surface electronic structure of a (111) face of a diamond-type solid. The model contains only one s-state per atom, but allows for surface rearrangement both at the outer layer and at the outer bounds. Two kinds of surface states are found. The first kind are localized at the outer bounds and split off the bulk bands as the bond potential increases beyond a critical value. The second kind are intrinsic surface states and exist independently of the surface rearrangement but only in a restricted domain in the Brillouin zone where structure factors are smaller than 1. These intrinsic states have not been discussed before; they exist also in more realistic hybrid models of diamond-structure solids.

New theoretical method to study densities of states of tetrahedrally coordinated solids

Abstract A new simple method is proposed to calculate local densities of states of arbitrary tetrahedrally coordinated solids. It involves the selection of a finite cluster of atoms connected to an infinite Bethe lattice of coordination four. The method is accurate, is easily handled numerically, and converges fast. Low-order approximations yield sufficient information which is susceptible to consistent physical interpretation. This has been made for the diamond, BC-8 and ST-12 structures in terms of the ring topology around a given atom. Comparison with exact calculations is very good and the ring interpretation is physical and conceptually appealing.

Electronic density of states of group-IV semiconductors: A cluster-Bethe lattice approach for realistic Hamiltonians

Abstract We have extended the cluster-Bethe lattice method to study realistic tight-binding Hamiltonians. The numerical solution of the transfer matrix in the Bethe lattice is very stable and requires about 50 steps of our iterative procedure to reach convergency. We apply this method to study the density of states of group-IV semiconductors (C, Si, Ge) using a five-parameter sp 3 Hamiltonian, which takes into account all possible interactions between sp 3 hybrids in nearest-neighbor atoms. Our results show clearly that the main features of the density of states are due to short-range order. Clusters of about 30 atoms reproduce very well the crystalline density of states. Based on our results we propose a model for the density of states in the gap region of an amorphous semiconductor.

Electronic surface structure of a tetrahedrally coordinated covalent solid with a simple four-state Hamiltonian

It is shown that for electronic surface problems in a tetrahedrally coordinated solid it is possible to reduce a four-orbital sp3 tight-binding model to an equivalent one-orbital s model. This is the surface analogue of the Weaire-Thorpe transformation (1971) for the bulk. One example of the transformation, which is a reasonably good representation of (111) surface of silicon, is carried out in detail. It exhibits four bands of surface states-two of them almost totally overlapping-in the valence-band region and one band of dangling-bond surface states in the optical gap. The calculation is for the whole two-dimensional Brillouin zone and compares satisfactorily with other calculations.

New theory of binary alloys with short-range order properties

Abstract A new method for treating the electronic structure of binary alloys is presented. It is based on the study of a finite size cluster connected at its edges to a Bethe-lattice of the same coordination number. An illustrative example is presented. It includes concentration sequences which are (i) random, (ii) with a tendency to segregation and (iii) with a tendancy to form binary compounds. Energy gaps and localized states appear naturally in the method.

Electronic surface structure of a tetrahedrally coordinated binary compound

The electronic surface structure has been studied of a binary compound in the zincblende structure with GaAs as a prototype. Two models are presented: (i) a one-orbital s-like model and (ii) a three-parameter four-orbital sp3 model. Various kinds of surface states are found and analysed: dangling bonds, back bonds and intrinsic atomic-like states. Both surfaces, the (111)-ga and the (1?1?1?)-as, are discussed and their similarities and differences emphasized. Comparison with experiment yields good qualitative agreement.

Effects of the local configuration on the lattice dynamics of group IV semiconductors

In order to investigate the relative importance of short‐range order and local topology in determining the vibrational properties of group IV semiconductors, we introduce a cluster Bethe lattice method. A cluster of atoms with any desired configuration is treated exactly. The rest of the system is treated within the Bethe Peierls Approximation, which retains the short‐range tetrahedral order. Main features of perfect crystaol density of states are already present in small clusters. A few cases of effects of disorder are studied.

Electronic surface properties of group V semimetals

Abstract We have studied the electronic surface properties of the (111) surface of group V semimetals (As, Sb, Bi) using a Greens function formalism in the tight-binding representation. We find that no surface states appear unless the surface layer relaxes, but any relaxation is enough to produce bona fide surface states.

Characterization of Amorphous Systems Using Local Configurations

We present a new method to study the electronic density of states of an amorphous system of atoms with four‐fold coordination in terms of the local density of states of an atom in a small cluster of this system. Our results show unequivocally that the number and type of rings of bonds in the vicinity of and passing through a certain atom are intimately related to the position and number of peaks in the local density of states of this atom. The method involves choosing a small cluster of atoms and using the Bethe lattice as a boundary condition.

A rigorous proof of the existence of band tails in disordered magnetic insulators

Abstract From the knowledge of the first moments of the density of states and, using a Lagrangian formalism, exact upper and lower bounds to the density of states of a simple hole in a magnetic insulator are calculated within the Hubbard model. These bounds provide a rigorous proof of the existence of band tails in the case of an antiferromagnetic spin arrangement in a simple cubic lattice. When the spin arrangement is random, the results suggest very strongly the existence of band tails.