A Tight-Binding Model for Optical Properties of Porous Silicon
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SCentro de Investigaci6n en Energia, UNAM, A.P. 34, C.P. 62580, Temixco, Mor., M6xico.
ABSTRACT
Semi-empirical tight-binding techniques have been extensively used during the last six decades to study local and extended defects as well as aperiodic systems. In this work we propose a tight-binding model capable of describing optical properties of disordered porous materials in a novel way. Besides discussing the details of this approach, we apply it to study porous silicon (p-Si). For this purpose, we use an sp 3 s* basis set, and supercells, where empty columns are digged in the [001] direction in crystalline silicon (c-Si). The disorder of the pores is considered through a random perturbative potential, which relaxes the wave vector selection rule, resulting in a significant, enlargement of the optically active k-zone. The dielectric function and the light absorption spectra are calculated. The results are compared with experimental data showing a good agreement. INTRODUCTION
From a theoretical point. of view, the study of optical properties starts with the calculation of the electronic band structure. This can be achieved mainly by two possible approaches. First principle methods are very successful in treating small systems. However, semiempirical or tight-binding calculations, less computationally intensive than first. principle calculations, can consequently deal with larger and more complex structures. The use of phenomenological parameters in semi-empirical calculations includes many-body effects, otherwise extremely difficult to consider in first principle methods. Another advantage of the tight-binding approach is the possibility of treating different types of disorder such as local defects, alloys, quasicrystals and amorphous systems. Several well known techniques to treat disorder exist in the literature such as virtual crystal approximation (VCA), average T-matrix approximation (ATA) and coherent potential approximation (CPA). These methods have played an important r6le in the understanding of many new materials though they are mostly appropriate for local disorder and, if self-consistency is included they become extremely computing demanding. We present here a semi-empirical tight-binding supercell model [1] capable to study disordered and nano structured porous media. Our aim is to calculate optical properties from
365 Mat. Res. Soc. Symp. Proc. Vol. 491 01998 Materials Research Society
the electronic band structure. In order to address the disorder, instead of using the conventional procedures, we introduce a new approach which includes a random perturbative potential to simulate the aleatory distribution of pores. This random potential produces a relaxation of the k wavevector selection rule broadening the optically active zone. One of the dominant trends in current research of materials science and solid state physics is the study of nanometric materials and devices. In these nanostructures many new effects take place and it is believed that the quantum confinement plays a mayor rdle in their
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