Ab-initio density function theory electronic structure ...

Web Site: www.ijaiem.org Email: [email protected], [email protected] Volume 2, Issue 4, April 2013 ISSN 2319 - 4847

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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Web Site: www.ijaiem.org Email: [email protected], [email protected] 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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Web Site: www.ijaiem.org Email: [email protected], [email protected] Volume 2, Issue 4, April 2013 ISSN 2319 - 4847 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.

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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

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-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

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-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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Web Site: www.ijaiem.org Email: [email protected], [email protected] Volume 2, Issue 4, April 2013 ISSN 2319 - 4847 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

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Number of core atoms Figure 8 Energy gap variation with the number of core atoms of CdTe nanocrystals

35 30 25 20

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Number of core atoms Figure 9 Valence and conduction bands variation with the number of core atoms of CdTe nanocrystals


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Web Site: www.ijaiem.org Email: [email protected], [email protected] Volume 2, Issue 4, April 2013 ISSN 2319 - 4847 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

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-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

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Energy (ev)


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Web Site: www.ijaiem.org Email: [email protected], [email protected] Volume 2, Issue 4, April 2013 ISSN 2319 - 4847 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

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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

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Te Te -0.4

Te

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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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Web Site: www.ijaiem.org Email: [email protected], [email protected] Volume 2, Issue 4, April 2013 ISSN 2319 - 4847 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. References [1] G. S. Almasi, A. C. Smith, CdTe HgTe Heterostructures, J. Appl. Phys. 39, p. 233, 1968. [2] N. A. Foss, J. Appl. Phys. 39, p. 6029, 1968. [3] N. V. Sochinski, M. D. Serrano, E. Dieguez, F. Agullo-Rueda, U. Pal, J. Piqueras, P. Fernandez, “Effect of thermal annealing on Te precipitates in CdTe wafers studied by Raman scattering and cathodoluminescence,” J. Appl. Phys. 77, p. 2806, 1995. [4] H. Chen, K. Chattopadhyay, K.-T. Chen, A. Burger, M. A. George, J. C. Gregory, P. K. Nag, J. J. Weimer, R. B. James, J. Vac. Sci. Technol. A, 17, p. 97, 1999. [5] T. L. Chu: Current Topics in Photovoltaics, eds. T. J. Coutts and J. D. Meakin, Academic Press, New York, Vol. 3, Chap. 3, pp. 236–281, 1988. [6] K. Zweibel, R. Mithcell, Adv. Solar Energy 6, p. 485, 1991. [7] W.H. Bloss, F. Pfisterer, M. Schubert, T. Walter, “Progress in Photovoltaics: Research and Applications,” 3, 11, pp. 3-24 1995. [8] D. Bonnet, M. Harr, “Manufacturing of CdTe solar cells,” Proc. Int. Conf. Photovolt. Solar Energy Conv. 1, pp. 397-402, 1998. [9] J. Fritsche, S. Gunst, E. Golusda, M. C. Lejard, A. Thien, T. Mayer, A. Klein, R. Wendt, R. Gegenwart, D. Bonnet,W. Jaegermann, Thin Solid Films 387, p. 161, 2001. [10] A. Partovi, J. Millerd, E. M. Garmire, M. Ziari, W. H. Steier, S. B. Trivedi, M. B. Klein, Appl. Phys. Lett. 57, p. 846, 1990. [11] T. L. Chu, S. S. Chu, S.T. Ang, J. Appl. Phys. 58, p. 3206, 1985. [12] F. Wang, A. Schwartzman, A. L. Fahrenbruch, R. Sinclair, R. H. Bube, C. M. Stahle, J. Appl. Phys. 62, p. 1469, 1987. [13] U. Solzbach, H. J. Richter, Surf. Sci. 97, p. 191, 1980. [14] B.J. Kowalski, A. Cricenti, B.A. Orlowski, Surf. Sci. 338, p. 183, 1995. [15] B.J. Kowalski, E. Guziewicz, B.A. Orlowski, A. Cricenti,Appl. Surf. Sci. 142, p. 33, 1999. [16] J. A. Silberman, D. Laser, I. Linday, W. E. Spicer, J. Vac. Sci. Technol. A1, p. 1706, 1983. [17] B. K. Rai, H. D. Bist, R. S. Katiyar, K. T. Chen, A. Burger, J. Appl. Phys. 80, p. 477, 1996. [18] B. Kowalski, A. Cricenti, S. Selci, R. Generosi, B.A.Orlowski, G. Chiarotti, Phys. Rev. B 47, p. 16663, 1993. [19] B. J. Kowalski, B. A. Orlowski, J. Ghijsen, Surf. Sci., pp. 412–413, 544, 1998. [20] J. G. Werthen, J. P. Hearing, R. H. Bube, J. Appl. Phys. 54, p. 1159, 1983. [21] J. A. Silberman, D. Laser, I. Lindau, W. E. Spicer, J. A.Wilson, J. Vac. Sci. Technol. A3, p. 222, 1985. [22] K. T. Chen, D. T. Shi, H. Chen, B. Granderson, M. A. George, W. E. Collins, A. Burger, R. B. James, J. Vac. Sci. Technol. A 15, p. 850, 1997. [23] G. Sh. Shmavonyan, Phys. Stat. Sol. (b) 229, 89, 2002. [24] S. M. Sze and K.K. Ng. "Physics of semiconductor devices", 3rd edition, Wiley, 2007. [25] R. Evarestov, M. Petrashen, and E. Lodovskaya, “The Translational Symmetry in the Molecular Models of Solids,” Physica Status Solidi B, Vol. 68, No. 1, pp. 453-461, 1975. [26] H. M. Abduljalil, M. A. Abdulsattar, S. R. Al-Mansoury, “SiGe Nanocrystals Core and Surface Electronic Structure from ab Initio Large Unit Cell Calculations,” Micro & Nano Letters, Vol. 6, No. 6, p. 386, 2011. [27] M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., “ Gaussian 03, “ Revision B. 01, Gaussian, Inc., Pittsburgh, PA, 2003. [28] M. A. Abdulsattar, “Ab Initio Large Unit Cell Calculations of the Electronic Structure of Diamond Nanocrystals,” Solid State Sciences, Vol. 13, No. 5, pp. 843-849, 2011. [29] J. Perdew, K. Burke and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Letters, Vol. 77, No. 18, pp. 3865-3868, 1996. [30] W. Kohn and I. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects,” Physical Review, Vol. 140, No. 4A, pp. 1133-1138, 1965. [31] R. M. Dreizler and E. K. U. Gross, “Density Functional Theory,” Springer-Verlag, Berlin, 1990.; R. G. Parr and W. Yang, “Density Functional Theory of Atoms and Molecules,” Oxford, New York, 1989. [32] D. C. Langreth and M. J. Mehl, “Beyond the Local – Density Approximation in Calculations of Ground – State Electronic Properties.” Physical Review B, Vol. 28, No. 4, pp. 1809- 1834, 1983.


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Web Site: www.ijaiem.org Email: [email protected], [email protected] Volume 2, Issue 4, April 2013 ISSN 2319 - 4847 [33] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, “Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation,” Physical Review B, Vol. 46, p. 6671, 1992. [34] J. P. Perdew and Y. Wang, Physical Review B, Vol. 45, No.13, p. 244, 1992. 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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