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Carrier Localization in InGaN/GaN Quantum Wells

Watson-Parris, Duncan Thomas Stephens

[Thesis]. Manchester, UK: The University of Manchester; 2011.

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Abstract

Presented in this thesis are extensive theoretical investigations into the causes and effects of carrier localization in InGaN/GaN quantum wells. The results of the calculations agree well with experimental data, where it is available, and provide additional insights into the mechanisms that lead to some of the experimentally observed effects of localization.Firstly, the wave functions of the electrons and holes in InGaN/GaN quantum wells have been calculated by numerical solution of the effective-mass Schrödinger equation. In our calculations we have assumed a random distribution of indium atoms, as suggested by the results of atom probe tomography: this allows us to find the contributions to the carriers' potential energy that arise from band gap fluctuations, the deformation potential and the spontaneous and piezoelectric fields. We show that the fluctuations in alloy composition can be sufficient to localize the carriers; our results are in good agreement with the results of experiment and more detailed ab-initio calculations, but we also obtain information about the distribution of localized states which those methods cannot yet provide. We find that the holes are localized on a short scale in randomly-occurring regions of high indium content, whereas the electrons are localized on a longer length scale. We consider the effect of well width fluctuations and find that these contribute to electron localization, but not to hole localization. We also simulate the low-temperature photoluminescence spectrum and find good agreement with experiment for the energy, width and shape of the photoluminescence peak.Secondly, we have used first-order time-dependent perturbation theory to study the diffusion of the carriers between their localized states at non-zero temperatures. The rates for scattering via the interaction with acoustic phonons are calculated using the carrier wave functions, and the resulting master equation for the distribution of the carriers is solved by a Monte Carlo method. We find that, even towards room temperature, the carriers are localized to a small number of states, and that their diffusion lengths are proportional to a combination of the density of localized states and the localization length. The experimentally-observed `S-shape' of the photoluminescence peak energy as a function of temperature is reproduced in our results and is explained by the thermal redistribution of holes among the localized states. A reduction of the depth of this S-shape is found as the excitation power is increased, as has been observed experimentally, and which we attribute to the saturation of the localized states.