Electronic structure calculation of quantum dots using k· p theory
Technische Universität Berlin
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The most common approach to calculate confined states in semiconductor quantum dots (QDs) is envelope function theory, in particular, multiband-k· p models. Both single-particle and few-body states, as excitons, trions, or biexcitons, can be modeled in such a framework. However, it is necessary to prove the suitability of those calculations to highly strained, strongly confining QDs since arguments against k· p methods have been raised and controversially discussed.
It will be shown that, indeed, the eight-band k· p model is capable of giving very accurate descriptions of buried QDs, e. g. self-assembled InAs/GaAs QDs . By comparison with empirical pseudopotential calculations available from the literature the possible accuracy of eight-band k· p calculations, as well as their limitations, are examined. Given the chemical composition of the QD, the range of validity of the k· p representation -- as regards the quantization energies and spatial extensions of confined wave functions -- can be determined a priori: It depends on the size of the Brillouin zone region around the G -point in which the true bulk bandstructure of the QD material is well approximated by the k· p bandstructure for bulk.
Based on calculated single electron and holes states, properties of few-particle states can be modeled using the configuration interaction scheme . The presented methods are used to calculate exciton states in InAs/GaAs QDs of different shapes or sizes to examine the impact of a varying dot geometry on the exciton energies, spontaneous recombination life times, and polar exciton-LO-phonon coupling.
1O. Stier, Electronic and Optical Properties of Quantum Dots and Wires, Berlin Studies in Solid State Physics, ed. by C. Thomsen et al. (Wissenschaft & Technik Verlag, Berlin, 2000).