Electronic band structure of the ordered Zn0.5Cd0.5Se alloy calculated by the semi-empirical tight-binding method considering second-nearest neighbor

Electronic band structure of the ordered Zn0.5Cd0.5Se alloy calculated by the semi-empirical tight-binding method considering second-nearest neighbor Estructura electrónica de bandas de la aleación ordenada de Zn0.5Cd0.5Se calculada por el método semi-empírico de enlace fuerte teniendo en cuenta interacción a segundos vecinos Juan Carlos Salcedo-Reyes Thin Films Group, Department of Physics, Faculty of Sciences Pontificia Universidad Javeriana, Cra. 7 No. 40-62, Bogotá, Colombia ; Recibido: 23-07-2007: Aceptado: 14-10-2008: Abstract Usually, semiconductor ternary alloys are studied via a pseudo-binary approach in which the semiconductor is described like a crystalline array were the cation/anion sub-lattice consist of a random distribution of the cationic/anionic atoms. However, in the case of reported III-V and II-VI artificial structures, in which an ordering of either the cations or the anions of the respective fcc sub-lattice is involved, a pseudo-binary approach can no longer be employed, an atomistic point of view, which takes into account the local structure, must be used to study the electronic and optical properties of these artificial semiconductor alloys. In particular, the ordered Zn0.5Cd0.5Se alloy has to be described as a crystal with the simple-tetragonal Bravais lattice with a composition equal to the zincblende random ternary alloy. The change of symmetry properties of the tetragonal alloy, in relation to the cubic alloy, results mainly in two effects: i) reduction of the banned gap, and ii) crystal field cleavage of the valence band maximum. In this work, the electronic band structure of the ordered Zn0.5Cd0.5Se alloy is calculated using a second nearest neighbor semi-empirical tight binding method. Also, it is compared with the electronic band structure obtained by FP-LAPW (fullpotential linearized augmented-plane wave) method. Key words: band gap narrowing; electronic band structure; ordered alloys; Semi-empirical thigh binding method; ZnCdSe alloy. Resumen Aunque la descripción de las aleaciones ternarias semiconductoras se hace tradicionalmente asumiendo la aproximación de compuesto pseudo-binario. Para el caso de aleaciones artificiales de compuestos II-VI y III-V, en las cuales se ha reportado un ordenamiento inducido por el crecimiento, una aproximación de este tipo no es aplicable, de modo que, con el fin de hacer una descripción adecuada de las propiedades ópticas y electrónicas de dichas aleaciones artificiales, se debe asumir una descripción atomística que tenga en cuenta la estructura local. En particular, para la aleación ordenada de Zn0.5Cd0.5Se, el cambio de simetría implica que se debe usar una estructura tetragonal simple, dando lugar, principalmente, a dos efectos: i) disminución de la brecha prohibida del material y ii) un desdoblamiento en el máximo de la banda de valencia. En este trabajo se calcula la estructura de bandas de la aleación ordenada de Zn0.5Cd0.5Se usando la aproximación semi-empírica de enlace fuerte teniendo en cuenta interacción a segundos vecinos y se compara con la estructura de bandas obtenida por el método FP-LAPW (full-potential linearized augmentedplane wave). Se obtiene una buena concordancia de las principales características entre las estructuras de bandas calculadas por el método semi-empírico y el método ab initio. Palabras clave: aleaciones ordenadas; aleaciones de ZnCdSe; Disminución de la brecha de energía; Estructura electrónica de bandas; Modelo de enlace fuerte. INTRODUCTION From the traditional point of view, when two zincblende binary compounds AC and BC are mixed homogeneously obtaining a random ternary alloy A1-xBxC, the ternary II-VI and III-V semiconductors alloys are treated as pseudobinary compounds (Bernard and Zunger, 1987), in which, traveling along the [001] direction, a sequence of cationanion planes can be found. The A and B cations, in a pseudobinary alloy, are randomly distributed in each cation plane. In particular, for the II-VI pseudo-binary zincblende Zn0.5Cd0.5Se alloy, the Se layers are alternating with Zn0.5Cd0.5 layers with a random distribution in average of the same amount of Cd and Zn atoms. However, ordering of isovalent A0.5B0.5C semiconductors alloys has been widely observed and studied (Kuan et al., 1985; Su et al., 1994; Lu et al., 1987; Wei and Zunger, 1991). That is how, at least four ordered structures related to the zincblende structure have been found to date (see Table 1): CuPt (Gomyo et al., 1987), CuAu (Mowgray et al., 1992), femetinite (Wang, 1989), and chalcopyrite (Jen et al., 1986). In particular, in the CuAu ordered structure, a sequence of A-C-B-C-A-C-... planes along the [001] azimuth is found. Sometimes, this structure is described as an (AC)1(BC)1 superlattice. However, it is not a true superlattice. It is a crystal with the simple tetragonal Bravais lattice and the same A0.5B0.5C composition of a zincblende random ternary alloy. Due to changes in symmetry, local ordering, and, in particular, to the change from zincblende unit cell -with space group T2d - to simple tetragonal primitive cell -with space group D52d - predicted and observed changes in material properties such as band gap reduction, valence band splitting, polarization dependence of optical transitions, vibrational spectrum, and others may be expected (Salcedo-Reyes and Hernández-Calderón, 2005). In the case of a pseudo-binary alloy most of the optical, structural and electronic properties are correctly described by the virtual crystal approximation (VCA). However, it is evident that in the case of an ordered alloy, with x=0.5, the VCA approach can no longer be employed to explain the physical properties and a more suitable crystalline structure must be considered. On the other hand, the Semiempirical Tight-Binding (STB) is one example of the so- called simplified quantum mechanical methods, in which a compromise between the computational efficiency and the physical correctness of the approximation is used. The usefulness of these approximated methods comes from the balance between theoretical rigor and pragmatism, speed, and accuracy. That is, despite the generality and transferability of the method is limited, the heavy computational effort of first-principles calculations is avoided by replacing difficult integrals, i.e. the so called two centers (Coulombic) integrals, by empirical parameters to fit experimental results. In general terms, in the STB method the solution to the timeindependent single electron Schrödinger equation is assumed as a linear combination of atomic orbitals centered at each lattice point. The atomic orbitals are assumed to be very small at distances exceeding the lattice constant (this is what is meant by tight-binding), and, therefore, practically all matrix elements are approached by analytical functions of the inter-atomic separation and of the atomic environment. In section 2, the STB method, taking into (...truncated)