Non-exponential decay kinetics: correct assessment and description illustrated by slow luminescence of Si nanostructures

The treatment of time-resolved (TR) photoluminescence (PL) decay kinetics is analysed in details and illustrated by experiments on semiconductor quantum dots, namely silicon nanocrystals (Si NCs). We consider the mono-, stretch- and multi-exponential as well as lognormal (LN) and some complex decay models for continuous and discrete distribution of rates (lifetimes). A particular attention is devoted to the thorough analysis of non-exponential decay kinetics. We explicitly show that a LN distribution of emitter sizes may results in LN distribution of decay rates. On the other hand, the distribution of rates cannot be, strictly speaking, Levy stable distribution (that results in the stretched-exponential decay). We introduce theoretical background and derive expressions to calculate the average decay lifetimes for some common decays with practical examples of their applications. Experimental aspects are discussed with special attention devoted to the major problems of the accurate TR PL data treatment, including background uncertainty, pulse duration, system response function etc. Finally, a thorough literature survey of TR PL in Si NCs is given. The methods and definitions outlined in this systematic review are applicable to various other material systems with slow decay like rare-earth and transition metal-doped materials, amorphous semiconductors, type-II heterostructures, singlet oxygen phosphorescence etc.