Normal distribution of confinement energy from a photoluminescence line shape analysis in oxidized porous silicon

Abstract

Photoluminescence (PL) spectra of oxidized porous silicon (PS) samples plotted against photon energy scale on x-axis would have pure Gaussian form or asymmetric form, depending on the conditions of preparation. At first a pure Gaussian-shape spectrum plotted against photon energy scale on x-axis is analyzed by statistical method on the assumption that the energy of emitted photon would be considered as a random variable simultaneously affected by two independent factors, namely: the statistical spread of wire width and the fluctuation in barrier height of SiOx/Si structures. Comparison of visual plots and statistic characteristic between three spectra plotted against various variables (confinement energy, logarithmic wire width and wire width) scale on x-axis demonstrates the exact description of the spectrum by Gaussian profile using normal distribution of confinement energy. An expression correlating the PL intensity (the number of emitted photons) to the number of wires and quantum efficiency has been developed. Further this expression has been extended to the case of spectrum having asymmetric form, which corresponds to the emission from both wire and dot nano-structures. Thus, our model permits to calculate the structural and spectroscopic parameters such as proportion of wires and dots, integrated intensity, peak energy position, FWHM and standard deviation.