The impact of energy band diagram and inhomogeneous broadening on the optical differential gain in nanostructure lasers

We present a general theoretical model for the optical differential gain in semiconductor lasers. The model describes self assembly quantum dots (QDs), self assembly quantum wires (QWRs) and single quantum-well lasers. We have introduced the inhomogeneous broadening due to size fluctuations in the assembly cases. At each dimensionality, we have considered the carrier populations in the excited states and in the reservoirs, where conduction and valence bands are treated separately. We show that for room temperature operation the differential gain reduction due to increased size inhomogeneity is more pronounced in QDs than in QWRs. We show this reduction to be smaller than the one-order reduction attributed to state filling in conventional dot and wire assemblies operating at room temperature. The integration prefactor coefficient of the differential gain in zero-dimensional cases exceed one- and two-dimensional coefficients only for low temperatures where the homogenous broadening is considerably smaller than the thermal energy. The differential gain of QDs, QWRs, and compressively strained single quantum-well lasers operating at room temperature and close to equilibrium is nearly the same.