Exciton Fine\nStructure in Axially Symmetric Quantum\nDots and Rods of III–V and II–VI Semiconductors

Both absorption and emission of light in semiconductor\nquantum\ndots occur through excitation or recombination of confined electron–hole\npairs, or excitons, with tunable size-dependent resonant frequencies\nthat are ideal for applications in various fields. Some of these applications\nrequire control over quantum dot shape uniformity, while for others,\ncontrol over energy splittings among exciton states emitting light\nin different polarizations and/or between bright and dark exciton\nstates is of key importance. These splittings, known as exciton fine\nstructure, are very sensitive to the nanocrystal shape. Theoretically,\nnanocrystals of spheroidal shape are often considered, and their nonsphericity\nis treated perturbatively as stemming from a linear uniaxial deformation\nof a sphere. Here, we compare this treatment with a nonperturbative\nmodel of a cylindrical box, free of any restrictions on the cylinder’s\naspect ratio. This comparison allows one to understand the limits\nof validity of the traditional perturbative model and offers insights\ninto the relative importance of various mechanisms controlling the\nexciton fine structure. These insights are relevant to both colloidal\nnanocrystals and epitaxial quantum dots of III–V and II–VI\nsemiconductors.