5.isca RJRS 2012 356
5.isca RJRS 2012 356
5.isca RJRS 2012 356
=
0
2
2
*
2
2
*
2
2 2
h h
*
2
2
2 2
248 . 0 786 . 1
2
) ( ) (
RY g
E
R
e
R
bulk E QD E + =
h
* *
1 1 1
h e
m m
+ =
Figure-4
Variation of effective mass with diameter of nano particles
This equation is a damping one, which increasing of R will
results in moving the eve towards to 21, which is the effective
mass of the bulk substance ZnS. As you can see its obvious that
for bigger dimension (bigger than 2.5nm) the effective mass
changes are very low. This is the cause of obtaining acceptable
results by replacing amounts of bulk substance instead of
smaller ones into the effective mass formula. But for minor
sizes these variation would be huge and highly influence on
obtained results. Through the processed equation the ZnS nano
particle effective mass has obtained and the energy gap
variation reproduced for various amount of size by putting
results from the equation in number 2 equation.
Figure-5
Comparison the mass effective variation with nanoparticle
diameter by applying effective mass variations
By applying effective mass variations, there is no difference
between calculative and experimental results for particles
smaller than 2.5nm.
Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502
Vol. 2(1), 21-24, January (2013) Res. J. Recent Sci.
International Science Congress Association 24
Results and Discussion
We assumed that the ZnS QDs have a wurtzite crystal structure.
The parameters used in this paper are as follows: bulk lattice
constants a=3.83 , c=6.25 ; E
g
=5.7eV. We first calculated
difference energy gap ZnS QDs and its bulk between
experiment effective mass approximation (EMA) shown in
figure -1. Difference energy gap disagree with experimental for
smaller dimensions because effective mass dependence of size
of nano particles, there for the effective mass approximation
method would not predict the ways of how effective mass
variation and its not usable for smaller dimensions. For solving
this problem we have used density functional theory (DFT). for
solving the (kohn-sham) equations the semi-potential
softwarePWscf have been used. For this we built a super-cell
and then we made a vacuum around its 3 dimensions. But it is
one problem and it is dangling band issue, which its the result
of making a vacuum around the particle. To remove the
dangling band we have used the Surface passivation.The surface
of an unpassivated nanocrystal consists of dangling bonds,
which will introduce band gap states. The purpose of a good
passivation is to remove these band gap states. One way to do so
is to pair the unbonded dangling bond electron with other
electrons. If a surface atom has m valence electrons, this atom
will provide m/4 electrons to each of its four bonds in a
tetrahedral crystal. To pair these m/4 electrons in each dangling
bond, a passivating agent should provide (8m( /4 additional
electrons. To keep the system locally neutral, there must be a
positive (8m) /4 nuclear charge nearby. Thus, the simplest
passivation agent can be a hydrogenlike atom with (8m) /4
electrons and a nuclear charge Z= (8m) /4. For III-V and II-VI
systems, the resulting atoms have a noninteger Z, thus a
pseudohydrogen atom. These artificial pseudohydrogen atoms
do describe the essence of a good passivation agent, and thus
can serve as simplified models for the real passivation
situations. This pseudohydrogen model has been used
successfully in our previous studies.
By using density functional theory difference energy gap ZnS
QDs and its bulk agreement with experiment shown in figure-1.
This method not only usable to determine the energy gap
variation but also suitable to calculate the how of effective mass
variations. By applying effective mass variations for effective
mass approximation, there is no difference between calculative
and experimental results for particles smaller than 2.5nm
according figure -5.
Conclusion
In this paper we have shown two methods for measuring the
energy gap of ZnS nano particle and also we shown that the first
method is not usable for smaller sizes (except) we calculated the
effective mass variations. By using the density functional theory
not only we determined the effective mass variation per particle
size, also we showed that by using these variations it is possible
to use the effective mass approximation for smaller sizes.
Acknowledgment
The authors would like to thank the Islamic Azad University,
Mahshahr branch for support in this research.
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