Ž . Applied Surface Science 142 1999 564–568 Tight-binding description of disordered nanostructures: an application to porous silicon J. Taguena-Martınez a, ) , Yuri G. Rubo a , M. Cruz b , M.R. Beltran c , C. Wang c ¨˜ ´ ´ a Centro de InÕestigacion en Energıa, UNAM, Temixco, Morelos 62580, Mexico ´ ´ b Seccion de estudios de Postgrado e InÕestigacion, ESIME-UC, IPN, 04430 Mexico DF, Mexico ´ ´ ´ c Instituto de InÕestigaciones en Materiales, UNAM, 04510 Mexico DF, Mexico ´ Abstract Ž . Ž . We present the calculations of the coefficient of light photo absorption in porous silicon por-Si using the supercell tight-binding sp 3 s U model, in which the pores are columns digged in crystalline silicon. The disorder in the pore sizes and the undulation of the silicon wires are taken into account by considering nonvertical interband transitions. The results obtained for 8- and 32-atom supercells show a strong dependence on the pore morphology, i.e., the absorption coefficient changes with the shape and size of the silicon wires even at constant porosity. The absorption spectrum of this model for Ž por-Si is defined by the interplay between the decrease in the indirectness of the material connected to the absorption . processes assisted by the scattering on the pores , which effectively reduces the direct gap, and the increase of the gap due to the quantum confinement. q 1999 Elsevier Science B.V. All rights reserved. PACS: 78.65.ys Keywords: Porous silicon; Tight-binding; Absorption 1. Introduction Ž . Porous silicon por-Si thin films have been under intense study since the discovery of efficient visible w x luminescence 1–3 . In spite of the lack of agreement about the detailed microscopic mechanism of the Ž wx. luminescence for a recent review see Ref. 4 , it is generally accepted that quantum confinement in nanometer-sized Si wires plays a key role in the optical properties of this material. One approach to model por-Si is to consider Ž . finite-sized crystalline Si c-Si clusters, as quantum w x w x wires 5,6 and dots 7,8 . This way allows to under- ) Corresponding author stand many effects in por-Si, like the widening of the band gap and the recombination phenomena, but within this approach one misses the fact that the electron states still remain extended. In particular, the energy spectrum of a cluster is discrete while experimentally the absorption exhibits a broad band. Another method to model the electronic structure of wx por-Si 9 is to use a Si supercell periodically re- peated in space. Such calculations are difficult to perform in a first-principles framework, but they become rather feasible in the tight-binding scheme, similar to the sp 3 s U used for crystalline semiconduc- w x tors 10 . The goal of this work is to use such a tight-bind- ing supercell model to calculate the absorption coef- 0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. Ž . PII: S0169-4332 98 00699-0