Electronic structure calculation of quantum dots using k· p theory

Oliver Stier

Technische Universität Berlin

Hardenbergstraße 36

D-10623 Berlin

*Tel:* (+4930) 31 42 42 63

*Fax:* (+4930) 31 42 25 69

*email:* stier@physik.tu-berlin.de

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 [1]. 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 [1]. 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.

1 O. 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).