Photoluminescence decay of silicon nanocrystals and Lévy stable distributions

Abstract

Recent experiments have shown that photoluminescence decay of silicon nanocrystals can be described by the stretched exponential function. We show here that the associated decay probability rate is the one-sided Levy stable distribution which describes well the experimental data. The relevance of these conclusions to the underlying stochastic processes is discussed in terms of Levy processes.

Improved presentation, references added

References in corpus (5)

• Exact and explicit probability densities for one-sided Levy stable distributions
• Levy stable two-sided distributions: exact and explicit densities for asymmetric case
• Levy stable distributions via associated integral transform
• Operator solutions for fractional Fokker-Planck equations
• The Higher-Order Heat-Type Equations via signed Lévy stable and generalized Airy functions

Cited by in corpus (6)

• On the complete monotonicity of the three parameter generalized Mittag-Leffler function $E_{\alpha ,\beta }^{\gamma }(-x)$
• On the properties of Laplace transform originating from one-sided Lévy stable laws
• Explicit representations for multiscale Lévy processes, and asymptotics of multifractal conservation laws
• On the application of Mittag-Leffler functions to hyperbolic-type decay of luminescence
• Physics and Mathematics of the Photoluminescence of Complex Systems
• The stretched exponential behavior and its underlying dynamics. The phenomenological approach