Direct interband light absorption in strongly oblate semiellipsoidal
quantum dots’ ensemble
David B. Hayrapetyan
a,b,1
a
Russian-Armenian State University, 123 Hovsep Emin Str., Yerevan, 0051, Armenia. E-mail;
b
State Engineering University of Armenia,
105 Terian Str., Yerevan, 0009, Armenia.
ABSTRACT
Within the framework of adiabatic approximation the energy levels and direct interband light absorption in
strongly oblate semiellipsoidal quantum dot’s ensemble are studied. Analytical expressions for the particle energy
spectrum and absorption threshold frequency in the regime of strong size quantization are obtained. Selection rules for
quantum transitions are revealed. To facilitate the comparison of obtained results with the probable experimental data,
the small semiaxe size dispersion distribution of quantum dots growing by two experimentally realizing distribution
functions have been taken into account. Distribution functions of Lifshits-Slezov and Gaussian have been considered.
Keywords: Oblate semiellipsoidal quantum dot, interband light absorption, selection rules, quantum dot ensemble
1. INTRODUCTION
Development of the novel growth techniques, such as the Stranski–Krastanov epitaxial method etc., makes
possible to grow semiconductor quantum dots (QDs) of various shapes and sizes
1-3
. As is known, the energy spectrum of
charge carriers (CCs) in QDs is completely quantized and resembles the energy spectrum of atoms (“artificial atoms”). In
a number of papers it has been shown, that small change in external shape of QD strongly influences energy spectrum
and other characteristics of such semiconductor structures
4
. As a result of diffusion, the confining potential, formed
during the growth process, in most cases can be approximated with a high accuracy by a parabolic potential. However,
an effective parabolic potential may arise in a QD in view of features of its external shape
5,6
.
Theoretical investigations of optical properties of QDs remain to be a central concern of physicists because the
results of these investigations can find direct applications in semiconductor devices of new generation
7
. Investigations of
the optical absorption spectrum of various semiconductor structures are a powerful tool for determination of many
characteristics of these systems: forbidden band gaps, effective masses of electrons and holes, their mobilities, dielectric
permittivities, etc. There are many works devoted to the theoretical and experimental study of the optical absorption both
in massive semiconductors and size-quantized systems. The presence of SiQ essentially influences the absorption
mechanism. In fact, the formation of new energy levels of the SQ makes possible new interlevel transitions.
From the theoretical point of view, spherical QDs are easier to investigate taking into account their symmetry,
which allows to obtain analytical solutions for the energy spectrum, coefficient of absorption, charge carriers mobility,
etc.
8,9
. However, modern methods for semiconductor nanostructures growth makes it possible to obtain QDs of different
geometrical shapes and sizes. By now QDs of different geometrical forms and sizes are realized and studied
theoretically: spherical, cylindrical, pyramidal, lens shaped, ellipsoidal, etc.
10-15
. Other examples of the QDs are
semiellipsoidal QDs. The advantage of these ones is the possibility of controlling the energy spectrum with two
geometrical parameters (two semiaxes).
In this paper the electron states and direct interband absorption of light in a strongly oblate semiellipsoidal QD
(SOSQD) is considered. Absorption edge and absorption coefficient are also considered. To facilitate the comparison of
obtained results with the probable experimental data, the small semiaxe size dispersion distribution of quantum dots
growing by two experimentally realizing distribution functions have been taken into account. Distribution function of
Lifshits-Slezov has been considered in the first model and distribution function of Gauss has been considered in the
second case.
1
dhayrap82@gmail.com
Photonics and Micro- and Nano-structured Materials 2011, edited by Rafael Kh. Drampyan,
Proc. of SPIE Vol. 8414, 84140N · © 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.923326
Proc. of SPIE Vol. 8414 84140N-1