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ABSTRACT Micro and nano-structures have opened a new area in materials research since they present interesting phenomena such as efficient luminescence and localization of carriers. An important example of these new materials is porous silicon (PS). It is considered that the quantum confinement is an essential cause of the opto-electronic properties of PS [1], thus microscopic analysis should be performed. We have developed a supercell model to study PS with a tight-binding Hamiltonian, where an sp 3 s* basis set is used. In an otherwise perfect silicon structure empty columns of atoms are produced and passivated with hydrogen atoms [2]. In this work we calculate the dielectric function and compare it against experimental data for bulk c-Si, ultrathin c-Si films and PS. We discuss the importance of considering the relaxation of the electron wavevector (k) conservation in order to include disorder effects in PS.

INTRODUCTION Optical devices from indirect band gap semiconductors, such as crystalline silicon, are not as efficient as direct band gap semiconductors. However, in silicon nanocrystallites the confinement partially breaks the k vector selection rule and allows new radiative transitions even without phonon assistance [3]. Porous silicon (PS) is an example of nanostructured materials, whose fabrication is easy and inexpensive, and with a broad spectrum of applications W4. vhere efficient luminescence is observed. The-. is a great interest in explaining the underlying mechanism of the light emission in PS from a microscopic point of view. In this work we study the optical properties of PS, through the dielectric function, which is related to the absorption coefficient and the refractive index. All the quantum mechanical theoretical works, from the Hamiltonian's point of view, can be classified in two major categories: first principles and semi-empirical frameworks. In spite of the first principle methods success treating small systems, semi-empirical or tight-binding calculations are simple enough to be applied in large supercells with complex morphologies [2]. It would be worth mentioning that the use of phenomenological parameters includes many-body effects, which generally are neglected in a first principles Hamiltonian. In this work we will follow this last approach to calculate the interband transitions between valence and conduction states. On the experimental side, the dielectric function of porous silicon has been measured [5] and it is quite different to that from the bulk crystalline one [6]. Recently a very complete study of the dielectric function of ultrathin crystalline silicon films (6A) has been performed [7]. Our calculations will be compared with all three mentioned measurements. 69 Mat. Res. Soc. Symp. Proc. Vol. 452 0 1997 Materials Research Society

In the next section we describe the microscopic supercell model. Following this we present and discuss the results obtained from the dielectric function. Finally, some conclusions are given.

THEORY We start with a tight-binding Hamiltonian;