Theory of the photoluminescence spectra of porous silicon

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Abstract
Porous silicon (PS) with its distribution of crystallite sizes is a highly disordered material. We present a theoretical formulation to explain the photoluminescence (PL) spectra of porous silicon. We base our formalism on the quantum confinement model using methods similar to those of Kane and Lifshitz. A minimal set of parameters is employed whose numerical values are obtained from independent experiments and/or microscopic theories. Our work demonstrates (i) a downshift in the PL peak due to the size distribution, thus facilitating the use of smaller and physically reasonable exciton binding energy; (ii) a PL spectrum with a line-shape asymmetry on the energy scale, having a full width at half maximum of ≃350 eV, in consonance with experiments; (iii) the presence of both columns and dots in PS; (iv) the presence of local inhomogeneities. Modifications of our model and extensions to related experimental phenomena are also discussed.