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 L(m) equal to 25 angstrom with a root mean square sigma equal to 5 angstrom for a particular luminescence shape. This model accounts for the wavelength lambda(M) of maximum luminescence and the full width at half maximum (FWHM). Furthermore, a slight variation of the two parameters L(M) and sigma accounts not only for lambda(M) and the FWHM but also for the intensities of the spectra obtained from the same sample with different conditions of preparation.