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Journal of Physical Studies 19(1/2), Article 1601 [8 pages] (2015)
DOI: https://doi.org/10.30970/jps.19.1601 LIGHT ABSORPTION COEFFICIENT CAUSED BY SUB-BAND TRANSITIONS OF ELECTRONS IN SPHERICAL QUANTUM DOT SUPERLATTICESV. I. Boichuk, I. V. Bilynsky, R. I. Pazyuk
Franko Drohobych Pedagogical University, Department of Theoretical Physics, |
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We analyze the electron energy spectrum in three-dimensional arrays of semiconductor quantum dots (QD) as a model of 3D-superlattice and its optical properties. Some numerical simulations have been suggested for the real spherical Al$_x$Ga$_{1-x}$As quantum dot superlattice, where the concentration of Al changes within $x=0.2,\ldots,1.0$. In the tight-binding approximation, the dispersion law of electrons is obtained and analyzed. The dependence of the electron energy on the wave vector for $1s$- and three ($m = 0,\pm1$) $1p$-sub-bands for QDs of different radii and Al concentrations in the matrix of Al$_x$Ga$_{1-x}$As are calculated in details. The dependences of density of electron states on energy in the $1s$- and $1p$-sub-bands are obtained. It is shown that the density of states as a function of energy depends strongly on the QD size, distances between QDs and concentration $x$. Subsequetly, we can control the electronic band structure of this spherical quantum dot superlattice when some parameters of the system are changed. The absorption coefficient of direct sub-band transitions is written in terms of a squared matrix element of the electronic transition and combined density of states. The conducted calculations have shown that in the dipole approximation electronic transitions are allowed between the sub-bands with $m = 0$. The absorption coefficient is characterized by two peaks that correspond to the electron wave vector in the center and at the edge of the Brillouin zone.
PACS number(s): 68.65.Cd, 73.20.At, 78.67.Pt, 79.60.jv