Electronic Structure of GaN Quantum Dots with an Adjacent Threading Dislocation
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Electronic Structure of GaN Quantum Dots with an Adjacent Threading Dislocation A. D. Andreev (1,3), J.R. Downes(2) and E. P. O’Reilly (3) (1) A.F. Ioffe Institute, St.-Petersburg 194021, Russia, email: [email protected] (2) Queen Mary and Westfield College, London, E1 4NS, UK (3) Department of Physics, University of Surrey, Guildford, GU2 7XH, UK ABSTRACT We present a theoretical analysis of the electronic structure of GaN quantum dots (QD) with an adjacent threading dislocation. The QD carrier spectra and wavefunctions are calculated using a plane-wave expansion method within an 8-band k.p model. The method is very efficient, because the strain and built-in electric fields can be included through their discrete Fourier transforms. The QD structures considered have been analysed experimentally by other groups. The GaN QDs are truncated hexagonal pyramids on a wetting layer with an edge dislocation adjacent to each dot. The built-in piezoelectric potential strongly influences the localisation of the carrier wavefunctions. This potential pushes the electrons to the top of the dot, the holes to the bottom and, additionally, causes strong lateral confinement of the carriers. The effect of the dislocation strain field at the dot edge on the carrier states in each GaN/AlN QD is shown to be insignificant. Results are presented for the confined state energies and optical matrix elements for a range of different sized dots with and without dislocations. The size of the dot influences the energies and overlaps, but the presence of the dislocation has minimal effect. The dependence of the ground state optical transition energy on the size of the dot is in good agreement with experimental data.
INTRODUCTION The wide band gap semiconductors, which form the basis of the blue laser, are increasingly important device materials [1]. Recent publications demonstrate that the light emission from these lasers may in fact originate from dot-like localized states caused by indium composition fluctuations [2]. Stranski-Krastanow GaN quantum dots grown on AlN are now being studied [3-6]. Aside from their wide band gap, the nitrides have several unusual characteristics compared to more common III-V semiconductors; these differences affect the properties of the dots. Device-quality GaN has a very high density of threading dislocations, typically as high as ~108 – 1011 cm-2 [6]. The wurtzite (hexagonal) crystal structure of III-N alloys means that they not only exhibit piezoelectricity but also spontaneous polarization effects. Photoluminescence experiments on a range of differently sized GaN dots has shown that the PL maximum for large dots is red shifted ~ 0.5 eV below the bulk GaN band gap [3-6]. Such a large red shift may arise from built-in piezoelectric and spontaneous polarization effects. Transmission electron microscopy studies of the dots have shown that each dot tends to nucleate adjacent to a threading dislocation [6]. This is probably because the distorted lattice around the dislocation provides a favorable template for the
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