Dark and bright excitonic states in nitride quantum dots

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Formation of excitonic states in quantum dots, of nitride based III-V semiconductors GaN and AlN, including Coulombic interaction, exchange interaction, and dielectric effects, are investigated. Dark exciton formation is found to occur for both GaN quantum dots (QD's) with wurtzite structure having positive crystal field splitting and GaN and AlN QD's with zinc-blende structure having zero crystal field splitting. The transition from dark to bright exciton occurs between radii range $20--40\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ depending on the amount of dielectric mismatch between the dot and the surroundings. In wurtzite AlN QD's with negative crystal field splitting, the splitting between the dark and bright excitonic states is very small and vanishes at about $15\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$.