Size-dependent Electronic and Polarization Properties of Multi-Layer InAs Quantum Dot Molecules - Quantum Dot Molecules - page 153

layer-to-layer separation has been experimentally optimized to obtain uniform QD
layers from the self-assembly growth process [ 26 ]. It should also be noted that the
geometrical parameters for the QDM-2, QDM-3, and QDM-4 are taken directly
from the recent experimental studies [ 4 , 9 , 28 ] where these QDMs have shown
great technological relevance for achieving the isotropic polarization response. For
reference purpose, we also simulate a single QD layer labelled as SQD and shown
in Fig. 5.1 a.
Note that a typical SK growth of a large vertical QDM generally results in an
increase in the size of the upper layer QDs [ 29 ]; however, no such increase in the
QD layer dimensions was reported in the experimental study [ 9 ]. Therefore, we
keep the size of the QD layers uniform in our study. Also, there is no information
available from the experiment on In/Ga intermixing or In-segregation effects during
the growth process. Therefore we assume pure InAs composition profiles in our
study. It should also be noted that we assume circular-base shape for the QD layers
inside the QDMs. However, in Sect. 5.5 , we will examine the impact of geometry
parameters by simulating ellipsoidal shapes and by varying the base diameters and
heights of the QD layers.
The QDMs are embedded inside a sufficiently large GaAs buffer to ensure proper
relaxation of atoms and to accurately accommodate the long-range effects of strain.
The size of the largest GaAs buffer for the QDM-4 containing nine QD layers is
60

106 nm 3 , consisting of

× 60 × ≈ 25 million atoms.

5.2.2 Methodologies

The InAs QDMs embedded in the GaAs matrix are simulated using atomistic
modeling tool NEMO 3-D [ 30 - 32 ]. The NEMO 3-D simulator has previously been
applied to study single [ 33 , 34 ], bilayer [ 5 , 35 ], and multi-layer QD arrays [ 4 , 10 ]and
it has demonstrated quantitative agreement with the available experimental data sets.
The atomistic simulations are performed on a large GaAs matrix surrounding the
QDs to properly account for the long-range impact of the strain and piezoelectric
fields. The size of the GaAs box is selected to be large enough to allow the strain
and piezoelectric fields become zero at the edges of the GaAs box. This ensures
proper relaxation of atoms and therefore correctly models the impact of strain and
piezoelectric potentials in the calculations of electronic structure.
The strain is calculated using atomistic valence force field (VFF) method [ 36 ]
including anharmonic corrections [ 37 ] to the classical Keating potential. Realistic
boundary conditions are chosen for the strain domain [ 38 ]: the substrate is fixed at
the bottom, the GaAs buffer is periodic in the lateral directions, and the capping
layer is free to relax from the top. Linear and quadratic piezoelectric potentials are
computed following the procedure described in references [ 35 , 39 ].
The electronic structure calculations are performed by solving empirical tight
binding Hamiltonian in which each atomic site is represented by twenty bands in
an sp 3 d 5 s ∗ model [ 40 ] including spin. Electronic domain is chosen to be relatively