Authors: B Lassen M Willatzen
Publish Date: 2009/01/13
Volume: 96, Issue: 3, Pages: 609-613
Abstract
The possibility of growing complexshaped nanodot structures of various material composition allows optimization of certain physical parameters In the present work we present effective analytical methods for computing conductionband eigenstates in quantumdot structures of complex shape Comparison with detailed finiteelement computations is made The electronic bandstructure model used is a oneband veckcdotvec p model assuming infinite barriers Results based on two semianalytical models are presented The first model employs geometrical perturbation theory to obtain the quantitative effect of quantumdot surface perturbations on electron energy levels Furthermore the method output includes the level of degeneracy and variations with geometry to be assessed The second model allows both energy levels and eigenstates to be easily determined for threedimensional axisymmetrical GaAs structures of varying radius embedded in an AlGaAs matrix by extending a method originally due to Stevenson on electromagnetic waveguide structures Stevenson in J Appl Phys 221447 1951 to account for electron states The latter model simplifies the description of a threedimensional partialdifferential equation problem into a small set of ordinary differential equations For structures with a large aspect ratio the small set reduces to a single ordinary differential equation yet maintaining high accuracy A case study is presented to exemplify the models shown
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