Photonic crystals in biology

Poster Session, Tuesday, June 15
Theme A1 - B702
Observation of the ground and excited states in a zero-dimensional semiconductor nanostructure
under the magnetic field
Saban Aktas, 1* Figen Karaca Boz 1 , Abdullah Bilekkaya 2 and Sevket Erol Okan 1
1 Department of Physics, Trakya University, Edirne 22030, Turkey
2 Department of Electronics, Trakya University Edirne Vocational College of Technical Sciences, Edirne 22100, Turkey
Abstract— The ground and excited states in a zero–dimensional semiconductor nanostructure (quantum dot) have observed as
a function of the dot radius under a magnetic field. The energies of the 1s, 1p, 1d and 1f states of a spherical quantum dot have
been calculated using the fourth order Runge-Kutta method without magnetic field and the variational method with magnetic
field within the effective mass approximation. It is shown that the energies in quantum dot with a small radius very small
change with magnetic field, whereas energy changes with large radius are affected by the magnetic field.
The experimental progress has made possible the
fabrication of zero-dimensional semiconductor nanostructure
(quantum dot) which impose quantum confinement in three
directions to a charge carrier [1].The 1s-1s transition energies
in spherically layered semiconductor quantum dots (QDs)
were compared with the experimental results [2] and it was
found that thick CdS outer layers prevent the charge carriers
from escaping from the particles. Recently, the energies of
electronic levels of the spherical QD has been presented by
Özmen et al. [3,4]. Wenfang Xie found that the linear and
nonlinear optical absorption coefficients are strongly affected
by the confinement strength of QDs, and the external magnetic
field [5,6].
In this work, we will focus on studying the energies of
ground (1s), first (1p), second (1d), and third (1f) excited
states of the spherical QD. The Hamiltonian of the QD in the
effect of a magnetic field can be written in reduced units,
2 2b
1 2 2 2
H i r sin v(
r)
. (1)
r
4
The above equation has been solved using the Runge–Kutta
numerical method without the magnetic field (B=0). The
Hamiltonian in the presence of the magnetic field has been
calculated using the variational approach. The binding energy
E B of the hydrogenic impurity is defined as the difference
between the energies with and without the impurity. Namely,
E n 0( b 0)
and E ni ( b 1) are obtained from Eq.1. Thus, the
impurity binding energy in the QD is
E B
E ( b
.
n0
0) E ni
( b 1)
Fig. 1 shown the binding energies of 1s, 1p, 1d, and 1f
states as a function of the magnetic field for R Dot = 2a* value.
The barrier height is given as V=Q c 1.247x for the Al
concentration x=0.25 in the unit of eV., where Q c is the
conduction band offset parameter taken to be Q c =0.60. As
seen from the figure, the binding energies increase with
increasing the magnetic field. The character of the binding
energy for 1s state is different than other states.
E B
(R*)
3,2
2,7
2,2
1,7
1,2
0 5 10 15 20
B(T)
Figure 1: The binding energies of 1s, 1p, 1d, and 1f states as a function
of the magnetic field for R Dot = 2a* value.
In summary, we showed that the energies of the ground and
excited states in zero-dimensional semiconductor
nanostructure as a function of magnetic field for various the
dot radius. For small dot radii, the contribution of the
magnetic field is very small. The contribution to the energy of
the magnetic field becomes dominant for large dot radii. These
results are a good agreement with the results of our previous
studies [6,7]. Our results might be useful for some devices in
the future. This work was partially supported by Trakya
University under Grant No. TUBAP 739-754-759-886-929-
2008(58).
.
*Corresponding author: sabana@trakya.edu.tr
[1] M. A. Reed et al., Phys. Rev. Lett. 60, 535 (1988)
[2] D. Schooss, A. Mews, A. Eychmüller, H. Weller, Phys. Rev B 49 17072
(1994). ( and references therein)
[3] A. Özmen et al., Optics Comm., 282 3999 (2009).
[4] B. Çakır et al., Superlattices and Microstructures, (In Press)
[5] Wenfang Xie, Commun. Theor. Phys. 51, 923 (2009)
[6] F. K. Boz et al. Appl. Surf. Sci. 255, 6561 (2009)
[7] F. K. Boz et al. Appl. Surf. Sci. 256, 3832 (2010)
1s
1p
1d
1f
6th Nanoscience and Nanotechnology Conference, zmir, 2010 266