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Ab-initio density function theory electronic
structure properties of core and surface CdTe
nanocrystals
Mohammed T. Hussein1, Kadhim A. Aadim2, †Qahtan G. Al-zaidi3 and Hamid A. Fayyadh4
1,2,3,4
Department of Physics, College of Science, University of Baghdad, Baghdad, Iraq
†Corresponding author
ABSTRACT
Gaussain 03 code of Ab-initio Density function theory (DFT) coupled with large unit cell method is used to determine the
electronic structure properties of II-VI zinc blende cadmium tellurium (CdTe) nanocrystals at (8,16,54 and 64) for 3D periodic
boundary condition (PBC) core atoms and 2D (PBC) calculation were used to simulate oxygenated (001)-(1x1) surface. The
crystal length was between (1.93-2.54) nm. In the present work, properties including total energy, cohesive energy, energy gap,
valence and conduction band width, ionicity and degeneracy of states for core and surface parts have been investigated. The
obtained results show that the total energy of CdTe nanocrystal increases with increasing the lattice constant, and the lattice
constant for the surface part is smaller than of core part. The ionicity of the core part decreases and its energy gap increases
with increasing number of core atoms. The latter is larger than the energy gap of the surface part. The total energy and
cohesive energy of core part decrease with increasing number of core atoms. The valence and conduction band widths increase
with increasing the number of core atoms, while conduction band width is wider on the surface due to splitting and oxygen
atoms. The results also show that the density of state increase with increase the number of core atoms, and the density of state
of core part is higher than that at the surface part; this is due to the broken bonds and the discontinuity at the surface and
existence of new kind of atoms (oxygen atoms).
Keywords: Electronic Structure, CdTe nanocrystals, Ab – initio Density Function Theory (DFT), Large Unit Cell
(LUC)
1. INTRODUCTION
The potential application of II–VI compounds in the field of photoelectronic devices operating at wavelengths longer
than those possible with the III–V semiconductors was first recognized more than 30 years ago (see for example Refs.
[1], [2]). For this reason, in early review papers and textbooks, the amount of information on II–VI compounds is
comparable to that on Si or III–V semiconductors. However, with the development of the semiconductor science and
technology, the studies of IV–IV and III–V compounds dominated the field, with little space to the study of II–VI
semiconductors. Only in more recent years, with the development of very accurate growing techniques, new projects of
optoelectronic devices based on II– VI directly implanted into the III–V or silicon based electronic circuits have
emerged. CdTe was always considered as a prototype of zinc – blende II–VI crystals and therefore was the subject of
most of the early studies in the field. The interest in this material has recently been increased because of several
– ray and X – ray spectrometers, optical and acoustic-optic
modulators, infrared windows, as substrate material for HgCdTe – based optoelectronic devices, in the epitaxy of other
II–VI compounds for electronic and electro-luminescent application and in the fabrication of polycrystalline thin film
solar cells. It is worth pointing out that CdTe/CdS solar cells have already reached the edge of pilot production [5]–[8]
mainly due to the combination of a reasonable conversion efficiency (CdTe:~ 10%) and low-cost production process
[9]. In addition, CdTe has also been shown to exhibit infrared photorefractivity and hence has acquired additional
significance [10].
For most device applications, the surface of CdTe must be properly passivated. If we consider solid state radiation
detectors, for example, among the factors that affect the performance at room temperature of such devices, surface
leakage current is one of the most detrimental. This limiting factor can be significantly reduced by chemical oxidation
of the CdTe surface, enhancing their performance [4]. Surfaces have no reconstruction and are non-polar structures,
therefore they have been chosen as prototypes for the study of the surface passivation and chemical activity of II–VI
compounds. CdTe and its alloys (especially HgCdTe and ZnCdTe) have been the subject of various studies using
different techniques, including Auger electron spectroscopy (AES) [11], [12], atomic force microscopy (AFM) [4], [9],
high-resolution scanning electron microscopy (HRSEM) [9], low electron energy diffraction (LEED) [13]–[15]
photoelectron emission microscopy (PEEM) [9], photoemission spectroscopy [16], Raman spectroscopy[17], surface
differential reflectivity (SDR) [14], [15], [18], [19] transmission electron microscopy (TEM) [12], X-ray diffraction
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Volume 2, Issue 4, April 2013
ISSN 2319 - 4847
(XRD) [9], X-ray photoelectron spectroscopy (XPS) [4], [9], [11]–[13], [15], [19]–[22] and more recently
photoluminescence (PL), reflectance, electroreflectance (ER) and photocurrent spectra [23].
Although the calculated ternary phase diagram [24] indicates that CdTeO3 and not TeO2 is an equilibrium oxide on
CdTe, some early experimental studies showed that the oxides formed on the CdTe surface exposed to air at room
temperatures were essentially TeO2 with little or undetectable formation of CdO [4], [15], [19], [20]. In contrast, other
works indicate a small amount [22] or even a major formation of CdTeO3 [12], [13], or TeO2/3 [17]. This was later
explained as an indication that the kinetics for the room-temperature reaction towards the more favored CdTeO3 oxide
phase is very slow. In fact, Wang et al. [12] even suggested that TeO2 was, at most, a metastable phase on CdTe
surfaces exposed to air at room temperature. However, a very recent experimental work by Fritsche et al. [9] in which
polycrystalline CdTe films were investigated using a combination of XRD, AFM, PEEM, HRSEM, and XPS after
different pretreatment conditions also suggests the possibility of CdO formation. Their XRD experiments indicate that
the main contributions to the polycrystalline grains spectra belong to and oriented crystallites in roughly equal
amounts, although contributions are also important. They also observed in their XPS spectra that after exposure to air,
the CdTe surface was severely oxidized with the formation of TeO2 and CdO. The existence of a series of experimental
works involving a wide range of techniques could suggest that the oxidation of the CdTe surface is a well – explored
system. However, in sight of the contrasting results inferred from experimental data, it is thought that little is known
about this oxidation process.
In fact, we believe that the oxidation process of the CdTe surface could be dramatically influenced by the surface
preparation and oxidation techniques. Having all these aspects in mind, the aim of this work is to provide an insight in
the early stages of oxygen adsorption on the CdTe surface using the density functional theory coupled with large unit
cell approximation to estimate the electronic properties of CdTe nanocrystals.
2. THEORY
Density functional theory (DFT) and the large unit cell (LUC) were used in the evaluation of the electronic structure of
CdTe nanocrystals using ab-initio method. The Large unit cell (LUC) gives us the profits gained from cyclic boundary
in simulating the solid. The LUC alters the shape and the size of the primitive unit cell so that the symmetry points in
the original Brillouin zone at a wave vector k become equivalent to the central symmetry point in the new reduced zone
[24]. In this method, the number of atoms in the central cell (at k=0) is increased to match the real number of
nanocrystal atoms. The large unit cell method is a super cell method that was suggested and first applied for the
investigation of the electronic band structure of semiconductors. This method differs from other super cell methods.
Instead of adding additional k points to the reciprocal space, the number of atoms in the central cell (k=0) is increased
and a larger central unit cell is formed [25]. k=0 is an essential part of the theory of LUC because it uses only one point
in the reciprocal space that means only one cluster of atoms exist which is the features of quantum dots [26]. The
calculations are carried out by using Gaussian 03 program [27]. The periodic boundary condition (PBC) method
available in Gaussian 03 program is used to perform the present tasks [28]
We shall use the density functional theory at the generalized gradient approximation (GGA) method level [29].
Kohn-Sham density theory [30], [31] is widely used for self-consistent – field electronic structure calculations of the
ground state properties of atoms, molecules, and solids. In this theory, only exchange – correlation energy EXC = EX +
EC as a functional of the electron spin densities n
The local spin density (LSD) approximation:
LSD
E XC
[n , n ]
d 3r n
unif
XC
(n , n )
(1)
Where, and the generalized gradient approximation (GGA) [32], [33]
GGA
E .XC
[n , n ]
d 3 r f (n , n , n , n )
(2)
In comparison with LSD, GGA's tend to improve total energy, atomization energies, energy barriers and structural
energy differences.
To facilitate particle calculations,
unif
XC
and f must be parameterized analytic functions. The exchange-correlation
LSD
energy per particle of a uniform electron gas, E XC ( n , n ) , is well established [34], but the best choice for
f (n , n , n , n ) is still a matter of debate.
3. RESULTS AND DISCUSSION
The nanocrystal core 3D periodic boundary condition (PBC) of CdTe nanocrystalls calculations has been studied
and using 2D (PBC) with particular regard to the oxygenated (001) – (1x1) surface is added to obtain a complete
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electronic structure view. Figures 1 and 2 show the relationship of total energy as a function of the lattice constant
optimization for 8 and 54 – atom core LUC, respectively. The results show that the minimum at the bottom represents
the equilibrium lattice constant of this cell, while the equilibrium lattice constant occurred at a point in which the
attraction forces between the atoms equals to the repulsion forces.
0.59
0.6
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
-47846.92
-47846.94
2
y = 41.295x - 53.52x - 47830
-47846.96
-47846.98
-47847
-47847.02
-47847.04
Lattic constant ( nm )
Figure 1 Total energy versus lattice constant for 8 – atom core (LUC) CdTe nanocrystals
54 CdTe
0.61
-322967.74
-322967.76
0.62
0.63
0.64
0.65
0.66
0.67
2
y = 248.21x - 315.92x - 322867
-322967.78
-322967.8
-322967.82
-322967.84
-322967.86
-322967.88
-322967.9
-322967.92
Lattice constant ( nm )
Figure 2 Optimization of 54 - atom core lattice constant of CdTe nanocrystals
The calculations were carried out for the core geometries as shown in Figures 3 and 4.
Figure 3 Color online: CdTe 8 atoms core LUC
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Figure 4 Color online: CdTe 54 atoms core LUC (parallelepiped shape primitive cell multiple)
Figure 5 shows the total energy variation with lattice constant for 8 atoms of the surface part. These curves and similar
curves for other LUCs are used to obtain equilibrium lattice constants for these cells but the lattice constant is (0.627
nm) less than core part. Figure 6 shows the geometries of oxidized surface for 8 core atoms.
0.623
-95986.8
0.624
0.625
0.626
0.627
0.628
0.629
-95987
-95987.2
-95987.4
-95987.6
-95987.8
-95988
Lattice constant (nm)
Figure 5 Total energy versus lattice constant for 8 – atom oxygenated (001) – (1x1) surface part of CdTe
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Figure 6 Color online: Cd8Te8O4 atoms oxidized surface LUC
Figure 7 shows the relationship between the lattice constant and the number of atoms for all studied LUC sizes of CdTe
(ncs) core. The lattice constants show decreasing values from 0.645 nm to 0.635 nm for 8 atoms and 64 atoms LUC,
respectively. Also shows the optimized core lattice constant of the range of nanocrystals 1.93- 2.54 nm.
Figure 7 Lattice constant as a function of number of core atoms for CdTe nanocrystal
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Figure 8 shows the energy gap for the core part plotted against the number of core atoms in which the energy gap
increases with the increase of the number of core atom. This is attributed to the smaller exciton bohr radius compared
to the quantum confinement. In Figure 9, the valence band width is shown to increases with increasing number of
atoms per LUC, because of the geometry effects on electronic structure of nanocrystals. While we note conduction band
width increases with increasing number of atoms per LUC, reaching to 16 atoms, but at 54 atoms conduction band
width decreases to 6.040 eV and after that it increasing reaching to 64 atoms.
3.6
3.55
3.5
3.45
3.4
3.35
3.3
0
10
20
30
40
50
60
70
Number of core atoms
Figure 8 Energy gap variation with the number of core atoms of CdTe nanocrystals
35
30
25
20
V.B. width
C.B width
15
10
5
0
0
10
20
30
40
50
60
70
Number of core atoms
Figure 9 Valence and conduction bands variation with the number of core atoms of CdTe nanocrystals
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Figure 10 shows the variation of highest – occupied molecular orbital energy (HOMO) and lowest – unoccupied
molecular orbital energy (LUMO) as the core of number of atoms grows up in size and changes its shape. This curve
fluctuates strongly because of the change in size and shape that produces different surfaces that have different
properties.
Figure 10 HOMO & LUMO as a function of number of core atoms for CdTe nanocrystal
In figure 11, the absolute value of the cohesive energy decreases with increasing the number of atoms per LUC. The
atoms on the particle’s surface reconstructed to a more stable structure. The calculated cohesive energy is directly
proportional to the value of the total energy. The correct calculated value of the total energy gives a correct value of the
cohesive energy. Figure 12 shows the atomic iconicity to decrease with increasing the number of atoms for the core
part.
0
10
20
30
40
50
60
70
-43.2
-43.25
-43.3
-43.35
-43.4
-43.45
-43.5
-43.55
Num ber of core atoms
Figure 11 Cohesive energy variation with the number of core atoms of CdTe nanocrystals
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Figure 12 Ionicity relationship with the number of core LUC atoms of InP nanocrystals.
The results of density of states of core 8 atoms LUC and surface 8 atoms as a function of energy levels are shown in
figures 13 and 14, respectively. The results for the core states show larger energy gap and smaller valence and
conduction bands. Owing to perfect symmetry of the core, the core states are more density of states. As we move to the
surface we see low density of states, small energy gap and wider conduction band. This reflects the broken symmetry
and discontinuity at the surface and existence of new kind of atoms (oxygen atoms), and the variation of bond lengths
and angles as well as lattice constant [24], [25]. Figure15 shows the atomic charge of oxidized Cd8Te8 O4 surface as a
function of layer depth using the slap geometry method.
8 CdTe
7
6
5
Eg=3.330eV
4
3
2
1
0
-30
-20
-10
0
10
20
Energy (ev)
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Figure 13 Density of states of 8 Core atoms of CdTe where energy gap of Eg = 3.33 eV is shown between the
conduction band (light lines) and valance band (bold lines)
3.5
Valance band are shown
with blod lines
Conduction band are shown
with ordinary lines
3
2.5
Eg =0.136 eV
2
1.5
1
0.5
0
-25
-20
-15
-10
-5
0
5
10
15
Energy(ev)
Figure 14 Surface density of states of 8 – atom oxygenated (001) – (1x1) for a2. The energy gap Eg of 0.136 eV is
shown between the conduction band (light lines) and valance band (bold lines)
0.6
CdTe-O
Cd
Cd
Cd
0.4
Cd
0.2
O
0
0
2
4
6
8
10
12
-0.2
Te
Te
-0.4
Te
Te
-0.6
O
-0.8
Layer number
Figure 15 Atomic charges as a function of layers depth of oxidized CdTe nanocrystal surface using slap geometry
4. Conclusion
The ab – initio density function theory coupled with large unit cell approach is used to investigate the electronic
properties of core and oxygen adsorption on CdTe surface. The results show that the lattice constant of all sizes CdTe
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nanocrystal core to decrease with increasing the number of core atoms in the LUC. The calculations show that the
energy gap and conduction band increase as CdTe nanocrystal LUC size increases. Moreover, the cohesive energy
(absolute value) for the core part increases with increasing the number of atoms. The energy gap is controlled by the
surface part of the nanocrystals. The surface part has lower symmetry than the core part with smaller energy gap. The
density of states of the core part is higher than that of the surface part. Thus, reflecting the high symmetry and equal
bond lengths and angles in perfect CdTe nanocrystals structure.
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AUTHOR
Dr.Mohammed T.Hussein completed his Ph.D. at the physics department in laser spectroscopy from
Complutense University – Madrid-Spain in 1995. His research interests lie in the field of organic
semiconductor and molecular spectroscopy. He is currently a member of the Nanotechnology &
Optoelectronics Research Group at the Physics department of Baghdad University.
Kadhim A. A. Al-Hamdani received M.Sc. and Ph.D. degrees in thin films physics and plasma physics in
2002 and 2010, respectively from University of Baghdad, College of science, Department of Physics.
Presently, he is assistant professor at the Physics Department and member of plasma research group.
Qahtan G. Al-zaidi received a B. Sc. (1994), M. Sc. (1997), and his Ph. D. (2012) in Optoelectronics
from Baghdad University, Baghdad, Iraq. He was a lecturer at the optics lab of the Physics Department –
College of Science of Baghdad University during the period 1997 –2007. He is currently a researcher at the
department of Physics, Nanotechnology and Optoelectronics Research Group. Dr. Al-zaidi main interests
are the development of chemical sensors based on semiconductor metal oxide nanostructured materials.
Hamid A. Fayyadh received his B. Sc. degree in Physics from Baghdad University, College of Science in
1997. He is currently pursuing his M. Sc. Degree in the field of nanostructured semiconductors materials
and devices within the Nanotechnology & Optoelectronics Research Group at the Physics department.
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