Inverse problem for the luminescence

The analysis of the luminescence response is one of the easiest tools for studying the physical properties of materials. In particular, much information can be obtained by deconvoluting the time curve of the luminescence decay. The deconvolution is nontrivial, except the case of the multi-exponential decay, since the numerical inverse-Laplace transformation is mathematically incorrect problem.


In my PhD Thesis I derive the inversion formulas for the power-law decay (see demonstration), observed for example in some conjugated polymers and nanostructured silicon as an after-glow or phosphorescence. This method applied for porous silicon is consistent with the measurements of the thermally stimulated luminescence complementing the latter at small activation energies.