Theory of the Gain Characteristics of InGaN/AlGaN QD Lasers
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Cite this article as: MRS Internet J. Nitride Semicond. Res. 4S1, G6.45 (1999) ABSTRACT We present a theoretical analysis of the gain characteristics of InGaN/AlGaN quantum dot (QD) lasers. We calculate the elastic strain distribution caused by the lattice mismatch between the QD and the barrier using an original method which takes into account the hexagonal symmetry of the structure's elastic properties. The method is based on an analytical derivation of the Fourier transform of the strain tensor. The proposed approach is combined with a plane-wave expansion method to calculate the carrier spectrum and wave functions. The many-body gain of a laser containing a periodic array of QDs is calculated using the Pad6 approximation. We show that band gap reduction and the Coulomb enhancement of the interband transition probability can significantly modify the gain spectrum in InGaN/AlGaN QD lasers. INTRODUCTION Wide-band gap semiconductors are attracting considerable attention because of their potential as visible light emitting diodes [1]. At the same time, advances in growth technology has stimulated active investigations in the field of zero dimensional quantum dot (QD) structures. The first GaN-based structures with self-organized QDs have been fabricated recently [2-4]. Lasers based on self-organized QDs have potential advantages over conventional quantum well lasers because of their atomic-like density of states. For wide-band gap heterostructures additional
benefits may arise from using QD structures instead of quantum well ones. Firstly, strain relaxation in QD structures is easier and therefore defect-free fabrication of strongly latticemismatched heterostructures may be possible. Secondly, because of the carrier localization, the role of many-body effects may increase, resulting in a stronger gain enhancement due to Coulomb interactions. Moreover, recent publications [5,6] demonstrate that light emission from InGaN quantum well lasers may originate from dot-like localized states formed because of indium composition fluctuations. It is therefore timely to undertake a theoretical investigation of the gain characteristics of GaN-based QD structures. We present here a theoretical study of the elastic strain distribution, carrier spectrum and many-body gain in structures consisting of a periodic array of InGaN QDs embedded in an AIGaN matrix. Employing the Green's function and Fourier transform techniques we find the 3D strain distribution in the QDs. To calculate the carrier spectrum and wave functions we use the planewave expansion method. This method allows us to take account of the strain-induced modification of the band structure using analytical expressions for the Fourier transform of the strain tensor. We thus avoid explicit calculation of the strain distribution. The calculated carrier spectrum and wave functions are used as input for gain calculations including many-body effects. We demonstrate that band gap reduction and Coulomb enhancement of the interband transition probability significantly modify the
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