Electronic Properties of Porous Silicon
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I.NTRODUCTION Efficient viible luminescence in porous silicon (PS) at room temperature has been reported in samples produced by electrochemical etching in a hydrofluoric solution [1]. This surprising optical property has stimulated a great interest, since it is well known that bulk silicon has an indirect band gap of 1.1 eV, which prevents efficient interband radiative recombination in the visible region. One of the main goals in the optoelectronic industry is to find a cheap material which combines electronic and optical responses. It is believed that PS could be a good candidate to achieve this dream, since silicon is very abundant on earth and its use is supported by three decades of semiconductor technology. The understanding of the electronic properties of PS is also important from the scientific point of view, because this new material presents interesting quantum phenomenon, such as electronic behaviour in low dimensional systems as well as electron localization. There are mainly two different points of view explaining the mechanisms involved in the luminescence process. One of them emphasizes the quantum confinement effect [1] and the other suggests the essential participation of the surface layer [2, 3, 4, 5]. However, the
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morphology and distribution of the pores have not been explored enough. Transmission Electron Michrograph analysis reveals fractality and homogeneity in the distribution of pores at different scales, i.e., a coral-like distribution at a nanometer scale and an homogeneous one at a mesoscopic scale. The columnar diameters range from 20 to 500 A, and its lengths are from 10 - 500 micrometers [6]. On the other hand, it is well known that changes in sample preparation leading to similar porosities but different microstructures can produce very different luminescence lines [7, 8, 9, 10]. In spite of extensive theoretical studies [3, 11, 12, 13, 14, 15, 16], little attention has been paid to the analysis of the PS morphology and the statistics of shapes and distribution of pores, except for simple structures such as squares and circles [17]. However, in real PS samples other types of structure coexist: wire-like, pore-like and grains or dot-like structures, depending on the preparation conditions such as temperature, acid concentration,
and current intensity [1, 19]. In what follows, we present a theoretical model capable of addressing this complex problem.
THE MODEL To model the effects of pores in PS we have to choose a Hamiltonian and a certain geometry. A possible way to study the morphology and the distribution of pores is to use the simplest tight-binding Hamiltonian which allows us to calculate complicated geometries in big supercells. As we are interested in describing the band gap zone, an spas* basis is used, following P. Vogl, H.P. Hjalmarson and J. Dowos work [20, since this is the minimum basis set to obtain an indirect X-like band gap of 1.1eV in bulk crystalline silicon. (010)
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