Effective-mass approximation and statistical description of luminescence line shape in porous silicon

Luminescence spectra obtained in p-type porous silicon are quantitatively explained. After a discussion of the numerical values of the relevant parameters within the framework of the effective-mass approximation used throughout this paper, we take into account the finite potential confining the carriers in silicon crystallites embedded in SiO₂: we find an electron-hole confinement energy proportional to L^-1.64, where L is the diameter of the crystallites, assumed to be spherical. Then using Gaussian statistics for these crystallites and the known data on radiative and nonradiative lifetimes, we obtain a mean diameter Lₘ equal to 25 {} with a root mean square {σ} equal to 5 {} for a particular luminescence shape. This model accounts for the wavelength λM of maximum luminescence and the full width at half maximum (FWHM). Furthermore, a slight variation of the two parameters Lₘ and {σ} accounts not only for λM and the FWHM but also for the intensities of the spectra obtained from the same sample with different conditions of preparation.