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The computation of PL spectra is done in the following three steps:

 

•Calculation of the depth-profile of the absorbed radiation in the luminescent layer: This defines where the incident radiation is absorbed. It is assumed that the radiation is re-emitted at the same position. Hence the absorption depth-profile gives also the distribution of emitting light sources.
•Multiplication with the microscopic (internal) efficiency: The so-called internal efficiency is what one would like to get from PL experiments. It gives the spectral  distribution of the emission probability if a photon of the incident radiation is absorbed at a certain point in space. This is the wanted information about the microscopic process.
•Computation of the escape probability for the emitted light: Once a photon is re-emitted it has to find its way through and out of the layer stack in order to be detected. The escape probability depends on reflection coefficients and re-absorption probabilities. These are computed using standard techniques to compute wave propagation effects.

 

The final result of the computation is the expected PL spectrum. The calculation of the absorption profile and the escape probabilities (steps 1 and 3) is straightforward (more or less). The combination of these is called 'external efficiency' in the following. The internal efficiency (i.e. the microscopic process to convert high energy photons to low energy radiation, see step 2) is not known very precisely in most cases. The recommended strategy to proceed is as follows: Compute a guess for the internal efficiency spectrum by a user-defined function (which could be the superposition of several peaks, for example) and vary parameters of the formula (peak positions, widths, strengths) until the simulated PL spectrum matches the measured curve. Examples are discussed in a separate tutorial.

 

To demonstrate the algorithm a simple example of one luminescent layer (porous silicon, 500 nm thickness) on a silicon substrate is considered. The optical constants are taken from the SCOUT database without modification.