Photonic crystals in biology

Poster Session, Tuesday, June 15
Theme A1 - B702
Size and magnetic field effects on InAs/GaAs self assembled quantum dot nanostructure
1
Imen Saïdi, Karim Sellami 1 *and Kaïs Boujdaria 1
Laboratoire de physique des matériaux, Faculté des Sciences de Bizerte, 7021 Jarzouna, Tunisia
Abstract-In this present work we investigated theoretically, within the effective mass approximation, the electron and hole states in InAs/GaAs
self assembled quantum dots under an external magnetic field. First, using the k.p theory, a theoretical 40x40 model was performed to calculate
the InAs and GaAS semiconductor band structure, and extract the different physical parameters. Then, using an accurate numerical
diagonalization method on Fourrier-Bessel function basis over a large cylinder domain, we calculated numerically the electron and hole eigen
energies and associated wave functions. We considered thereafter the effect of the magnetic field and quantum dot size variation on the charge
carrier energy levels. It is clearly found that the electron and hole energy spectra changes significantly when the quantum size parameters are
modified as well as the magnetic field. Given this striking nanostructure size dependent property, these systems provide the opportunity to
control and tune their optical and electronic properties through t heses parameters.
Self-Assembled Quantum dots, commonly referred to as
self-organized quantum dots, form spontaneously under
certain growth conditions during molecular beam epitaxy or
metal organic chemical vapor deposition, as a consequence of
lattice-mismatch between the semiconductor deposited
material and underlying substrate [1]. The resulting
semiconductor nanostructures consist of three dimensional
islands standing on a two-dimensional wetting layer. Such
islands can be subsequently buried to realize quantum
confinement. In the past 15 years, self assembled quantum
dots have provided vast opportunities for physical research
and technological applications, including quantum
cryptography, quantum computing, optics and optoelectronics.
Consequently, 0Tworldwide efforts in both theory and
experimental investigations have driven the fascinating
aspects of these nanostructures, including growth,
characterization, and applications of quantum dots into an
advanced multidisciplinary field [2].
In the frame work of the effective mass approximation the
electron (hole) hamiltonien is written as:
2
2
P meh ( ) ceh ( )
2 ceh
( )
H Vconf i ge( h)
BB.
2meh
( )
2 2 2
m eh
where is the electron (hole) masse calculated through the
( )
Luttinger parameters extracted from a 40-band k.p model [3].
ceh
is the electron (hole) cyclotron frequency which is
( )
written as function of the magnetic field B as: eB
.
ce( h)
g is the Landé Factor [4], and is the spin operator. meh
( )
V denotes the quantum dot confinement potential that takes
conf
into account the shape of the nanostructure chosen as a
truncated cone as represented below. This potential can be
expressed as V ( r)
V0 (1 D(
z,
))
, where V 0
is the band offset
potential and D is the quantum domain wich is written as:
QD
WL
D( z,
)
D ( z,
)
D ( z,
)
where and D WL stands for
respectively the quantum and wetting layer domains.
Using an accurate numerical diagonalization method on a
Fourrier Bessel basis over a large cylinder domain, the
electron (hole) states can be written as:
n,
n, c
ij
n
ij ,
n ij
n in
e i
j
where: nij reh
i e Jn( e
)sin z, with Z and R are
R Z
n
respectively the height and the radius of large cylinder. is
i
n
the ith root of the n-order Bessel function J , and
n
c
i ,
is the
j
normalization constant.
We calculated numerically the electron and hole eigen
energies and associated wave functions in a truncated cone
shaped InAs/GaAs quantum dot. Our result revealed that this
calculation method provide more accurate results compared to
the commonly used variationnal method.
It is clearly shown that the electron and hole energy spectrum
changes significantly as function of the quantum dot radius.
We notice that from a definite radius R d , the charge carrierstates
begin to appear in the quantum dot, and if R