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The idea is explained and demonstrated in more detail here and in Ref.[15].



We propose a simple and fast yet precise simulation analysis which provides maximum information about a semiconductor laser structure at an on-wafer stage. It is simple because all it requires as input from the experimentalist aside form the nominal structural parameters are luminescence spectra taken at nonlasing excitation intensities. For this no processing of the structures is necessary. Also, the software requires no background knowledge on the physics involved and has a 'self-explaining' graphical interface. It is fast since it is based on a pre-calculated database of gain/absorption and luminescence spectra. The essential comparisons between experimental spectra and theoretical ones can be performed in seconds. Finally, it is precise due to the high quantitative accuracy of the theoretical approach used to calculate the theoretical data base.

From the experimental input, i.e. a set of luminescence spectra for at least two different excitation densities measured under low excitation conditions and the nominal structural parameters, the simulation deduces the inhomogeneous broadening and the actual structural parameters. The former immediately gives information about the quality of the sample. The later quantitatively predicts main characteristics of the structure under operating conditions like gain spectra in the lasing regime, refractive index spectra, differential gain or the linewidth enhancement factor.



1. Experimental Input Requirements
The required experimental input is minimal. The first are the nominal structural parameters. I.e. the width of the well and barrier layers and their material compositions. For these, and if wanted a possible range of parameters around these a database of ideal gain/absorption and luminescence spectra are pre-calculated.

The second is a set of luminescence spectra measured for different moderate excitation intensities. By 'moderate' we mean in the absorptive, non-lasing regime. The intensities should however be not too low. For very weak excitation the luminescence is dominated by light emitted from the usually small number of states at the very low energy side of the spectrum. These states originate from inhomogenities in the structure like well-width fluctuations (local regions where the well is somewhat wider than the nominal value) and impurity- or defect states below the bandgap of the ideal laser. Of course any attempt to compare spectra coming from these states alone with calculated spectra for an ideal structure will fail. At higher excitation (as well as under lasing conditions), the luminescence is dominated by light coming from the actual bandstructure of the quantum-well structure. Here, the inhomogenities lead to an inhomogeneous broadening which results in well defined modifications of the ideal luminescence spectra. To give a feeling for the right ballpark: Typical excitation conditions should excite carrier densities in the order of 10% of the threshold density, but rather wide variations thereof are allowed.

The analysis tool does not require to know the actual intensities or a given ratio between the intensities for the spectra. They just have to be in the reasonable range.


2. Theoretical Analysis Procedure
The analysis works as follows: For the given nominal structural parameters luminescence (spontaneous emission) spectra for a set of carrier densities in the moderate excitation regime is calculated. The carrier densities covering the possible range in the experiments. These spectra are pre-calculated and just looked up. These spectra are 'ideal', meaning they only include homogeneous broadening due to electron-electron and electron-phonon scattering but no inhomogeneous broadening. The luminescence spectra are then inhomogeneously braodened. Comparing the experimental luminescence lineshapes and amplitudes with the theoretical ones for varying inhomogeneous broadening then yields the inhomogeneous broadening present in the experiment. From a possible energetic displacement between the theoretical and experimental spectra the deviations between the nominal and actual structural parameters can be deduced. I.e., deviations from the nominal material compositions like, e.g. the Indium concentration in an InxGa1-xAs quantum well or the nominal well width can be determined. Usually deviations in the concentrations as small as one percent can thus be quantitatively determined.

Finally, using the determined inhomogeneous broadening and actual structural parameters important properties of the structure in the operating/lasing regime are predicted quatitatively. These quantities include the material and modal gain, spontaneous emission, refractive indices, differential gain, linewidth enhancement factor and carrier losses due to radiative and Auger recombination processes. They are again just looked up from a pre-calculated database.

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