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Band gap tuning of defective silicon carbide nanotubes under external electric field: Density functional theory
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Band gap tuning of defective silicon carbide nanotubes under external electric field: Density functional theory
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Department of Physics, Al al-Bayt University, Al-Mafraq – 130040, Jordan
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Jamal A. Talla
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Article history: Received 7 November 2018 Received in revised form 25 January 2019 Accepted 28 March 2019 Available online xxxx Communicated by R. Wu Keywords: Silicon carbide nanotube Stone Wales defects Electrical properties Longitudinal electric field Transverse electric field Partial density of state Density functional theory
We have theoretically investigated the effect of applying longitudinal and transverse electric field on silicon carbide nanotubes with different orientations of Stone Wales defects. We found that each type of Stone Wales defects maintained different formation energy. We have also successfully proved that the orientation of Stone Wales defects in silicon carbide nanotubes response quite differently upon applying external electric field, whereas, two important and interesting phenomena were observed. First, the semiconductor-metal phase transition occurred in silicon carbide nanotubes as well as the three types of Stone Wales defects. However, clear band gap variations were observed in all silicon carbide nanotubes under study. Second, the band gap variations in pristine silicon carbide nanotubes and nanotubes with different orientations of Stone Wales defects have the same trend, even though all silicon carbide nanotubes have clear band gap values under different strengths of the applied external electric field. However, band gap tuning under longitudinal electric field is less significant compared to band gap tuning under the transverse electric field. © 2019 Published by Elsevier B.V.
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1. Introduction
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The success in synthesizing carbon nanotubes has sparked significant theoretical and experimental research on nanomaterials of other elements such as; BN, AlN, and GaN [1,2]. Besides, several other nanotubes have been synthesized as well, including; TiO2 , NiCl, H2 Ti3 O3 [1]. Like carbon nanotubes, silicon carbide nanotubes possess unusual physical properties [3,4], including; high thermal conductivity, high hardness and a superior radiation resistance [5–8]. These unusual properties could be attributed to large bond length in silicon carbide nanotubes compared to bond length in carbon nanotubes [8,9]. Furthermore, compared to carbon nanotubes, silicon carbide nanotubes are expected to possess not only higher reactivity of exterior surface but also stability at high temperature [10–12]. For the above reasons, silicon carbide nanotubes are considered as a good candidate for electronic and optical applications that require operating in harsh environments [7,13–15]. In addition, silicon carbide nanotubes have been widely employed in wide range of technological applications that require high frequency, high breakdown field strength high temperature, high thermal conductivity and radiation resistance [1,16,17]. Previous theoretical investigations have shown that silicon carbide nanotubes that consisting of alternating carbon and silicon
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E-mail address: [email protected]. https://doi.org/10.1016/j.physleta.2019.03.040 0375-9601/© 2019 Published by Elsevier B.V.
atoms are energetically favorable structure [8,18]. Whereas, it has theoretically proved that the most stable silicon carbide nanotubes have the ratio of carbon to silicon of “1: 1” [8,18]. However, unlike carbon nanotube, silicon carbide nanotubes are not only semiconducting materials with large band gap but also do not depend on the tube chirality as in carbon nanotubes [7]. Therefore, the electrical properties of silicon carbide nanotubes make them suitable for wide range of gas sensor application [8]. Certainly, future possibilities and promises for different applications of silicon carbide nanotubes like nano-devices and nano-sensors are tremendous. Except carbon, group IV elements have significant energy variations between sp2 and sp3 bonds [1,19]. As a matter of fact, silicon carbide nanotubes have also a huge energy difference between the sp2 and sp3 orbitals. Regardless these facts, silicon carbide nanotubes have been successfully produced by different researchers. For example, Sun et al. have produced silicon carbide nanotubes by substituting half of the carbon atoms from a multi-walled carbon nanotube with silicon atoms [16]. Although the produced silicon carbide nanotubes were multi-walled with inter-planar spacing higher than that in multi-walled carbon nanotubes, the higher inter-spacing is a good indication that separating tubes from each other will be much easier because of the weak coupling between inner and outer tubes [16]. Mechanical deformation on silicon carbide nanotubes has a strong impact on the optical, electrical, structural, and surface reactivity [8]. Wang et al. pointed out that structural transformation
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Fig. 1. Different orientations of the Stone Wales defect. a) Pristine silicon carbide nanotube. b) Type I of Stone Wales defect (χ = 19.11o ). c) Type II of Stone Wales defect (χ = 40.89o ). d) Type III of Stone Wales defect (χ = 79.11o ). While Az represents the direction for longitudinal electric field (axial direction), Rx, represent the directions of transverse electric field (radial direction).
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occurs in the ultrathin silicon carbide nanotubes under uniaxial stress [8,20]. The results show that the tubes transform into semiconducting tubes with an indirect band gap [11,21]. Meanwhile, the effect of structural deformations and adsorption of transition metal atoms on the electronic properties of nanotubes have also been experimentally studied [8]. However, Gali et al. reported that the electronic properties of doped zigzag and armchair silicon carbide nanotubes with boron atom have no significant difference [22]. Unintentional defects such as Stone Wales defects may also play a crucial rule in modifying the electronic properties of silicon carbide nanotubes [3,23]. Stone Wales defects may occur randomly at any of the three sets of nonequivalent Si-C bonds. As a matter of fact, Stone Wales defects form when Si-C bond rotate by 90o and as a consequence the four adjacent hexagonal rings convert into two pentagons and two heptagons [3,23]. Therefore, three possible orientations may occur, refer to Fig. 1. In this study, we implemented density functional theory to study the impacts of three orientations of Stone Wales defects on the chiral (8, 4) silicon carbide nanotubes under longitudinal and transverse electric field. We hope in this study to give some insight how to predict the existence and orientation of Stone Wales defects and how to tune the electronic properties of silicon carbide nanotubes via applying external electric field for possible future applications.
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2. Computational details
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Our ultimate goal in this study is to tune the electronic properties of silicon carbide nanotubes that contain different orientations of Stone Wales defects via applying longitudinal and transverse electric field. Since the structure is symmetric, it makes no difference in the results whether the field is in the direction Rx or R y as long as it is transverse. In order to perform the calculations, a chiral (8, 4) silicon carbide nanotube with three different orientations
of Stone Wales defects was separately modeled. For clarity pur-
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poses, we identify the orientation of the Stone Wales defect with
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an angle (θ ) in such a way −π /2 ≤ θ ≤ π /2. By identifying the
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chiral angle (χ ), 0 ≤ χ ≤ π /6, three different possible orientations
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π /3 − χ , χ , and π /3 + χ . By calculating the chiral angle for (8, 4) silicon carbide nanotube (χ = 19.11o ), the three
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possible angles of Stone Wales defects are 19.11 (type I), 40.89
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comparison, pristine silicon carbide nanotubes were also modeled.
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The lattice constant “a and “b for all simulated structures were
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set to be very large to avoid any possible interaction between nan-
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otube and its image [25–27]. To maintain the tube periodicity, “c
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was set to be exactly the same as the nanotube lattice parameter [28]. Density functional calculations were performed with “Cam-
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bridge Serial Total Energy Package” (CASTEP) code. To relax the
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nanotubes, we first performed geometry optimization using gener-
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alized gradient approximation (GGA). In addition to pristine silicon
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carbide nanotubes, three different possible orientations of Stone
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Wales defects were modeled in the nanotubes surface, namely (Type I, Type II, and Type III). All four structures were fully optimized without applying electric field, until the force on each atom was less than 0.03 eV Å−1 . Besides, SCF tolerance, maximum dis-
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placement and maximum stress were set as 1 × 10−5 eV/atom,
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0.001 Å and 0.05 GPa. While Monkhorst-Pack grid was generated
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using 1 × 1 × 8 k-point, ultra soft pseudo-potentials were used to
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represent core electrons. Additionally, cut off energy was set to 400 eV with k points along the tube axis to ensure calculations con-
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vergence. The optimized structures have bonds lengths vary in the
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range from 1.770 Å to 1.800 Å. Finally, an external constant electric
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Fig. 2. Band structure for all nanotube under study without applying electric field: a) pristine silicon carbide nanotubes, b) silicon carbide nanotubes with type I of Stone Wales defects, c) silicon carbide nanotubes with type II of Stone Wales defects, d) silicon carbide nanotubes with type III of Stone Wales defects. The red dashed line represents the Fermi energy. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.) Table 1 The total energy and the formation energies for the three types of Stone Wales defects.
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3. Results and discussion
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We have investigated the effect of longitudinal and transverse electric fields on (8, 4) chiral silicon carbide nanotubes with three different orientations of Stone Wales defects. The required energy to form Stone Wales defects on silicon carbide nanotube surface is known as the formation energy which can be calculated as follows [10,29]:
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E F ormation = E De f ects − E P ristine
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E De f ects and E P ristine are the total energies for the silicon carbide nanotube containing a Stone Wales defect and the pristine nanotube, respectively. Our calculations revealed that the formation energies for the three types of Stone Wales defects are 5.76 eV, 2.50 eV, and 2.93 eV for type I, type II and type III of Stone Wales defects respectively, refer to Table 1. As we can see, the formation energy of Stone Wales defects is very sensitive to the Stone Wales defects orientations. The highest formation energy in type I could be attributed to a highest rolling-up strain of Stone Wales defect.
This finding is Similar to previous studies on the formation energies of Stone Wales defects in carbon nanotubes [29]. Compared to pristine silicon carbide nanotubes and close to the fusion of the two heptagons in the defective region, the Si–C bonds lengths significantly increased, which a good indication of a higher reactivity in these sites [11,30]. Such results were observed in all types of Stone Wales defect under study. From the above, introducing Stone Wales defect to silicon carbide nanotubes can significantly increase their sensitivity toward hazardous molecules, like CO, N2 H2 and HCHO [11]. Fig. 2 represent the band structure for pristine silicon carbide nanotubes as well as the band structure for silicon carbide nanotubes with different orientations of Stone Wales defects before applying any electric field. Upon introducing Stone Wales defects to silicon carbide nanotubes, the band gap in the three defective structures is significantly decreased. Whereas, the most significant influence of the Stone Wales defects observed in Type III, refer to Table 2. A clear influence of Stone Wales defect on Silicon carbide nanotube is the defects formation energy levels close to Fermi energy. The defects level evolved from Stone Wales defects of type I is close to the band gap center and the energy difference between the top of the valence band and the bottom of the conduction band. The band gap of pristine silicon carbide nanotubes is 1.884 eV. However, upon introducing Stone Wales defects, the band gap significantly decrease to 1.223 eV, 1.131 eV and 1.028 eV for type I, type II and type III of Stone Wales defects, respectively, refer to Fig. 2. While, the bottom of the conduction band in silicon carbide nanotube consists of silicon 3p states, the top of the valence band consist of both carbon 2p states as well as silicon
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Table 2 Band structure variations upon applying longitudinal electric field for all nanotubes under study.
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Longitudinal Electric field eV/Å/e
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Type II (θ = 40.89o ) (eV)
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Fig. 4. A comparison between pristine silicon carbide nanotubes and silicon carbide nanotubes with different orientations of Stone Wales defects upon applying transverse electric field.
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Table 3 Band structure variations upon applying transverse electric field for all nanotubes under study.
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Fig. 3. A comparison between pristine silicon carbide nanotubes and silicon carbide nanotubes with different orientations of Stone Wales defects upon applying longitudinal electric field.
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3p states. In other words, the bottom of the conduction band and the top of the valence band were occupied by silicon 3p states and carbon 2p states. These findings prove the sensitivity of the orientation of Stone Wales defects in tuning the band gap of silicon carbide nanotubes [1,7]. To further tune the electronic properties of silicon carbide nanotubes with different orientations of Stone Wales defects, we gradually introduced longitudinal ( Az) and transverse (Rx) electric field from 0.0 eV/Å/e to 2.0 eV/Å/e. The band gap of silicon carbide nanotubes under longitudinal electric field is shown in Fig. 3 and Table 2. It can be seen from Fig. 3 that the band gap decreases with the increasing the external longitudinal electric field. This could be attributed to asymmetry of electrostatic potential under the applied electric field. Whereas, the decrease in the band gaps with increasing the longitudinal electric field is an indication that the semiconductor metals phase transition occurs for silicon carbide nanotube under longitudinal electric field. Yet it needs a strong electric field to mix neighboring sub-bands and considerably tune the band structure. However very strong electric field will create undesirable surface deformation, especially when the structure has topological defects such as Stone Wales defects. In addition, since we are dealing with periodic structure, the finite space effect at different external longitudinal electric field values is not negligible. Fig. 4 and Table 3 represent how the applied transverse electric field tunes the energy gap for all silicon carbide nanotubes under study. The band gap in all four silicon carbide nanotubes were decrease quadratically with increasing the transverse electric field, refer to Fig. 4 and Table 3. This might be correlated to a local charge separation induced by applying transverse electric field on the silicon carbide nanotube. While, the charge density of conduction band lowest state is moved to the opposite direction of the applied field, the charge density of the valence band highest state
Transverse Electric field eV/Å/e
Pristine (eV)
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Type I
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(θ = 79.11o )
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1.131 1.088 0.979 0.830 0.668 0.504 0.337 0.116 0.008 0.000 0.000
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(θ = 19.11o )
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is moved with the same direction of the applied electric field. On one hand, the energy of conduction band minimum state shifts down as a result of the accumulated charge in regions of higher electric potential. On the other hand, the energy of valence band maximum state shifts up as a result of the accumulated charge in low electrical potential zone. Based on Stark effect, the relation between small electric fields and the band gap energy is quadratic as the top of valence band and the bottom of conduction band are non-degenerate [3]. However, when the field becomes larger, potentials, within the valence and conduction sub-band complexes, will be produced. This perturbation will cause huge mixing among sub-band states. In this regime, the external electric field will control the wavefunction of the band edge states. With no doubt, this charge density is an indication that the bottom of the conduction band state is moved away from the external electric field, which eventually localized on one side of the silicon carbide nanotube. Whereas, the top of the valence band state is moved toward the electric field, which eventually localized on the other side of the silicon carbide nanotube. However, some kinetic energy will be consumed as a consequence of localizing the wavefunction on both sides of the tube. While the edge of the conduction band minimizes its energy because of the applied electric field, the charge is piled up in greater electric potential regions. Similarly, the valence band edge increases its accumulated charge in low electric potential. Consequently, the decrease in the conduction band energy and increase in the valence band energy will directly reduces the band gap. As seen in Fig. 3 and Fig. 4, the band gap reduced upon applying external electric field. This reduction in the band gap is largest
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Fig. 5. Partial density of states for all nanotube under study without applying electric field: a) pristine silicon carbide nanotubes, b) silicon carbide nanotubes with type I of Stone Wales defects, c) silicon carbide nanotubes with type II of Stone Wales defects, d) silicon carbide nanotubes with type III of Stone Wales defects. The red dashed line represents the Fermi energy.
for silicon carbide nanotubes with type III of Stone Wales defects. While, the degenerate states at zero electric field clearly split with increasing the strength of the applied field, the degree of tuning the band gap under longitudinal electric field is less significant compared to tuning the band gap under transverse electric field. Whereas, applying transverse electric field will further separate the charge densities of the lowest unoccupied molecular orbital and highest occupied molecular orbital states. Furthermore, upon applying transverse electric field, the band gap energy monotonically reduced because of the rapid decrease of the nearly free electron band which moves to one side of the unit cell. Therefore, applying transverse electric field will smoothly redistribute the charge density and consequently the nearly free electron band will rapidly decrease and eventually the gap closed. In order to neglect finite space effect at different external transverse electric field values, a very large unit cell dimensions were set. While applying different values of transverse electric field on the pristine silicon carbide nanotubes and silicon carbide nanotubes with different orientations of Stone Wales defects, we observed two main interesting phenomena. First of all, the semiconductor-metal phase transition existed in all samples regardless the existence of Stone Wales defects or not. However, some variations were observed in the band-gap between pristine silicon carbide nanotubes and silicon carbide nanotubes with different orientations of Stone Wales defects. These variations in the band gap indicate a strong effect resulted by introducing different orientations of Stone Wales defects to silicon carbide nanotube surface. Second, the band-gap variations for silicon carbide nanotubes with three types of Stone Wales defects have the same trend; even
though each orientation of Stone Wales defects has clear band gap values under different values of external transverse electric field (Table 2). The differences in the electron transition of the defective silicon carbide nanotubes are significantly improved upon introducing transverse electric fields. Like pristine silicon carbide nanotube, a phase transition from semiconductor to metal occurs in silicon carbide nanotubes with different types of Stone Wales defects when electric field strength reach around 0.4 eV/Å/e. However, applying transverse electric field induces discrepancies in the band gaps and in the partial density of states; refer to Fig. 4. The mechanism behind closing the band gap could be attributed to the valence band maximum state which contributed by both P x and P y orbitals for all silicon carbide nanotubes under investigation. Furthermore, the conduction band minimum state of silicon carbide nanotubes with different orientations of Stone Wales defects consisted of P z orbitals which ruled by pentagon and heptagon rings in the defective site. In addition, these P z orbital state in the minimum conduction π states move toward each other and consequently, the band gap starts to close. This exactly will happen when sub-band mixing becomes more declared as the field strength reached 0.4 eV/Å/e and beyond, refer to Fig. 3. This might explain why the band gaps of silicon carbide nanotubes with different orientations of Stone Wales defects are smaller than the band gap of pristine silicon carbide nanotubes. We also studied the partial density of states for all four Si-C tubes. From Fig. 5, the partial density of states of pristine silicon carbide nanotubes at the Fermi level is wide, (∼1.884), which consistent with the obtained value from the band structure at Fermi level. Significant peaks close to the Fermi level were observed. However; the s elec-
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trons have no observed peaks whatsoever which means that the only contribution in the DOS of silicon carbide nanotubes is mainly from 2p electrons, refer to Fig. 5.
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Based on our results, it is more likely to tune the band gap of silicon carbide nanotubes with Stone Wales defects within a certain range by controlling the strength of the applied electric field for specific applications. Besides, it is possible to predict the existence and orientation of Stone Wales defects in silicon carbide nanotubes by applying a transverse electric field while rotating the silicon carbide nanotube that contains Stone Wales defects. As soon as we maintained the maximum values of the band gap, we can predict the position as well as the orientation of Stone Wales defects. Finally, our results demonstrate that applying external electric field to silicon carbide nanotubes that contain different orientations of Stone Wales defects play a critical rule on manipulating the electrical properties of silicon carbide nanotubes, yet no deformation noticed in the silicon carbide structures.
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References
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[1] K.M. Alam, A.K. Ray, Phys. Rev. B 77 (2008) 035436. [2] B. Xiao, H. Hu, J.-x. Zhao, Y.-h. Ding, Physica E, Low-Dimens. Syst. Nanostruct. 56 (2014) 377–385. [3] J.A. Talla, Comput. Condens. Matter 15 (2018) 25–30. [4] Jamal Talla, Majid Abusini, Khaled Khazaeleh, Rami Omari, Mohammed Serhan, H. El-Nasser, Mater. Express 7 (2017) 516–522. [5] K. Adhikari, A.K. Ray, Solid State Commun. 151 (2011) 430–435.
[6] R. Ansari, M. Mirnezhad, H. Rouhi, NANO 09 (2014) 1450043. [7] R.J. Baierle, P. Piquini, L.P. Neves, R.H. Miwa, Phys. Rev. B 74 (2006) 155425. [8] H.-L. Chen, S.-P. Ju, J.-S. Lin, J. Zhao, H.-T. Chen, J.-G. Chang, M.H. Weng, S.-C. Lee, W.-J. Lee, J. Nanopart. Res. 12 (2010) 2919–2928. [9] M. Khodadad, S.M. Baizaee, M. Yuonesi, H. Kahnouji, Physica E, Low-Dimens. Syst. Nanostruct. 59 (2014) 139–143. [10] X. Wang, K.M. Liew, J. Phys. Chem. C 116 (2012) 26888–26897. [11] X. Zhou, W.Q. Tian, J. Phys. Chem. C 115 (2011) 11493–11499. [12] S. Behzad, R. Chegel, R. Moradian, M. Shahrokhi, Superlattices Microstruct. 73 (2014) 185–192. [13] R.-L. Liang, Y. Zhang, J.-M. Zhang, V. Ji, Physica B, Condens. Matter 405 (2010) 2673–2679. [14] R.J. Baierle, R.H. Miwa, Phys. Rev. B 76 (2007) 205410. [15] S.-J. Wang, C.-L. Zhang, Z.-G. Wang, Chin. Phys. Lett. 27 (2010) 106101. [16] X.-H. Sun, C.-P. Li, W.-K. Wong, N.-B. Wong, C.-S. Lee, S.-T. Lee, B.-K. Teo, J. Am. Chem. Soc. 124 (2002) 14464–14471. [17] Z. Wang, F. Gao, J. Li, X. Zu, W.J. Weber, J. Appl. Phys. 106 (2009) 084305. [18] A. Wu, Q. Song, L. Yang, Q. Hao, Theor. Comput. Chem. 977 (2011) 92–96. [19] G. Alfieri, T. Kimoto, Nanotechnology 20 (2009) 285703. [20] X. Wang, K.M. Liew, J. Phys. Chem. C 116 (2012) 1702–1708. [21] D. Huilong, G. Zhenyu, G. Keith, D. Chunmiao, H. Tingjun, L. Shuit-Tong, L. Youyong, Nanotechnology 26 (2015) 275201. [22] A. Gali, Phys. Rev. B 73 (2006) 245415. [23] S.A. Curran, J.A. Talla, D. Zhang, D.L. Carroll, J. Mater. Res. 20 (2005) 3368–3373. [24] L.G. Zhoua, S.-Q. Shib, Appl. Phys. Lett. 83 (2003) 3. [25] J.A. Talla, S.A. Salman, Nanosci. Nanotechnol. Lett. 7 (2015) 1–6. [26] S.A. Salman, J.A. Talla, A. Abuzir, E. Yasin, J. Comput. Theor. Nanosci. 12 (2015) 8. [27] Jamal A. Talla, Saed A. Salman, Nanosci. Nanotechnol. Lett. 7 (2015) 6. [28] J.A. Talla, A.A. Ghozlan, Chin. J. Phys. (2018). [29] L.G. Zhou, S.-Q. Shi, Appl. Phys. Lett. 83 (2003) 1222–1224. [30] S.H. Yang, W.H. Shin, J.K. Kang, J. Chem. Phys. 125 (2006) 084705.
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Band gap tuning of defective silicon carbide nanotubes under external electric field: Density functional theory
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Department of Physics, Al al-Bayt University, Al-Mafraq – 130040, Jordan
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Jamal A. Talla
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Article history: Received 7 November 2018 Received in revised form 25 January 2019 Accepted 28 March 2019 Available online xxxx Communicated by R. Wu Keywords: Silicon carbide nanotube Stone Wales defects Electrical properties Longitudinal electric field Transverse electric field Partial density of state Density functional theory
We have theoretically investigated the effect of applying longitudinal and transverse electric field on silicon carbide nanotubes with different orientations of Stone Wales defects. We found that each type of Stone Wales defects maintained different formation energy. We have also successfully proved that the orientation of Stone Wales defects in silicon carbide nanotubes response quite differently upon applying external electric field, whereas, two important and interesting phenomena were observed. First, the semiconductor-metal phase transition occurred in silicon carbide nanotubes as well as the three types of Stone Wales defects. However, clear band gap variations were observed in all silicon carbide nanotubes under study. Second, the band gap variations in pristine silicon carbide nanotubes and nanotubes with different orientations of Stone Wales defects have the same trend, even though all silicon carbide nanotubes have clear band gap values under different strengths of the applied external electric field. However, band gap tuning under longitudinal electric field is less significant compared to band gap tuning under the transverse electric field. © 2019 Published by Elsevier B.V.
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1. Introduction
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The success in synthesizing carbon nanotubes has sparked significant theoretical and experimental research on nanomaterials of other elements such as; BN, AlN, and GaN [1,2]. Besides, several other nanotubes have been synthesized as well, including; TiO2 , NiCl, H2 Ti3 O3 [1]. Like carbon nanotubes, silicon carbide nanotubes possess unusual physical properties [3,4], including; high thermal conductivity, high hardness and a superior radiation resistance [5–8]. These unusual properties could be attributed to large bond length in silicon carbide nanotubes compared to bond length in carbon nanotubes [8,9]. Furthermore, compared to carbon nanotubes, silicon carbide nanotubes are expected to possess not only higher reactivity of exterior surface but also stability at high temperature [10–12]. For the above reasons, silicon carbide nanotubes are considered as a good candidate for electronic and optical applications that require operating in harsh environments [7,13–15]. In addition, silicon carbide nanotubes have been widely employed in wide range of technological applications that require high frequency, high breakdown field strength high temperature, high thermal conductivity and radiation resistance [1,16,17]. Previous theoretical investigations have shown that silicon carbide nanotubes that consisting of alternating carbon and silicon
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E-mail address: [email protected]. https://doi.org/10.1016/j.physleta.2019.03.040 0375-9601/© 2019 Published by Elsevier B.V.
atoms are energetically favorable structure [8,18]. Whereas, it has theoretically proved that the most stable silicon carbide nanotubes have the ratio of carbon to silicon of “1: 1” [8,18]. However, unlike carbon nanotube, silicon carbide nanotubes are not only semiconducting materials with large band gap but also do not depend on the tube chirality as in carbon nanotubes [7]. Therefore, the electrical properties of silicon carbide nanotubes make them suitable for wide range of gas sensor application [8]. Certainly, future possibilities and promises for different applications of silicon carbide nanotubes like nano-devices and nano-sensors are tremendous. Except carbon, group IV elements have significant energy variations between sp2 and sp3 bonds [1,19]. As a matter of fact, silicon carbide nanotubes have also a huge energy difference between the sp2 and sp3 orbitals. Regardless these facts, silicon carbide nanotubes have been successfully produced by different researchers. For example, Sun et al. have produced silicon carbide nanotubes by substituting half of the carbon atoms from a multi-walled carbon nanotube with silicon atoms [16]. Although the produced silicon carbide nanotubes were multi-walled with inter-planar spacing higher than that in multi-walled carbon nanotubes, the higher inter-spacing is a good indication that separating tubes from each other will be much easier because of the weak coupling between inner and outer tubes [16]. Mechanical deformation on silicon carbide nanotubes has a strong impact on the optical, electrical, structural, and surface reactivity [8]. Wang et al. pointed out that structural transformation
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Fig. 1. Different orientations of the Stone Wales defect. a) Pristine silicon carbide nanotube. b) Type I of Stone Wales defect (χ = 19.11o ). c) Type II of Stone Wales defect (χ = 40.89o ). d) Type III of Stone Wales defect (χ = 79.11o ). While Az represents the direction for longitudinal electric field (axial direction), Rx, represent the directions of transverse electric field (radial direction).
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occurs in the ultrathin silicon carbide nanotubes under uniaxial stress [8,20]. The results show that the tubes transform into semiconducting tubes with an indirect band gap [11,21]. Meanwhile, the effect of structural deformations and adsorption of transition metal atoms on the electronic properties of nanotubes have also been experimentally studied [8]. However, Gali et al. reported that the electronic properties of doped zigzag and armchair silicon carbide nanotubes with boron atom have no significant difference [22]. Unintentional defects such as Stone Wales defects may also play a crucial rule in modifying the electronic properties of silicon carbide nanotubes [3,23]. Stone Wales defects may occur randomly at any of the three sets of nonequivalent Si-C bonds. As a matter of fact, Stone Wales defects form when Si-C bond rotate by 90o and as a consequence the four adjacent hexagonal rings convert into two pentagons and two heptagons [3,23]. Therefore, three possible orientations may occur, refer to Fig. 1. In this study, we implemented density functional theory to study the impacts of three orientations of Stone Wales defects on the chiral (8, 4) silicon carbide nanotubes under longitudinal and transverse electric field. We hope in this study to give some insight how to predict the existence and orientation of Stone Wales defects and how to tune the electronic properties of silicon carbide nanotubes via applying external electric field for possible future applications.
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2. Computational details
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Our ultimate goal in this study is to tune the electronic properties of silicon carbide nanotubes that contain different orientations of Stone Wales defects via applying longitudinal and transverse electric field. Since the structure is symmetric, it makes no difference in the results whether the field is in the direction Rx or R y as long as it is transverse. In order to perform the calculations, a chiral (8, 4) silicon carbide nanotube with three different orientations
of Stone Wales defects was separately modeled. For clarity pur-
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poses, we identify the orientation of the Stone Wales defect with
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an angle (θ ) in such a way −π /2 ≤ θ ≤ π /2. By identifying the
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chiral angle (χ ), 0 ≤ χ ≤ π /6, three different possible orientations
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π /3 − χ , χ , and π /3 + χ . By calculating the chiral angle for (8, 4) silicon carbide nanotube (χ = 19.11o ), the three
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comparison, pristine silicon carbide nanotubes were also modeled.
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The lattice constant “a and “b for all simulated structures were
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otube and its image [25–27]. To maintain the tube periodicity, “c
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was set to be exactly the same as the nanotube lattice parameter [28]. Density functional calculations were performed with “Cam-
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bridge Serial Total Energy Package” (CASTEP) code. To relax the
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alized gradient approximation (GGA). In addition to pristine silicon
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carbide nanotubes, three different possible orientations of Stone
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Wales defects were modeled in the nanotubes surface, namely (Type I, Type II, and Type III). All four structures were fully optimized without applying electric field, until the force on each atom was less than 0.03 eV Å−1 . Besides, SCF tolerance, maximum dis-
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placement and maximum stress were set as 1 × 10−5 eV/atom,
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vergence. The optimized structures have bonds lengths vary in the
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Fig. 2. Band structure for all nanotube under study without applying electric field: a) pristine silicon carbide nanotubes, b) silicon carbide nanotubes with type I of Stone Wales defects, c) silicon carbide nanotubes with type II of Stone Wales defects, d) silicon carbide nanotubes with type III of Stone Wales defects. The red dashed line represents the Fermi energy. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.) Table 1 The total energy and the formation energies for the three types of Stone Wales defects.
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3. Results and discussion
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We have investigated the effect of longitudinal and transverse electric fields on (8, 4) chiral silicon carbide nanotubes with three different orientations of Stone Wales defects. The required energy to form Stone Wales defects on silicon carbide nanotube surface is known as the formation energy which can be calculated as follows [10,29]:
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E F ormation = E De f ects − E P ristine
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E De f ects and E P ristine are the total energies for the silicon carbide nanotube containing a Stone Wales defect and the pristine nanotube, respectively. Our calculations revealed that the formation energies for the three types of Stone Wales defects are 5.76 eV, 2.50 eV, and 2.93 eV for type I, type II and type III of Stone Wales defects respectively, refer to Table 1. As we can see, the formation energy of Stone Wales defects is very sensitive to the Stone Wales defects orientations. The highest formation energy in type I could be attributed to a highest rolling-up strain of Stone Wales defect.
This finding is Similar to previous studies on the formation energies of Stone Wales defects in carbon nanotubes [29]. Compared to pristine silicon carbide nanotubes and close to the fusion of the two heptagons in the defective region, the Si–C bonds lengths significantly increased, which a good indication of a higher reactivity in these sites [11,30]. Such results were observed in all types of Stone Wales defect under study. From the above, introducing Stone Wales defect to silicon carbide nanotubes can significantly increase their sensitivity toward hazardous molecules, like CO, N2 H2 and HCHO [11]. Fig. 2 represent the band structure for pristine silicon carbide nanotubes as well as the band structure for silicon carbide nanotubes with different orientations of Stone Wales defects before applying any electric field. Upon introducing Stone Wales defects to silicon carbide nanotubes, the band gap in the three defective structures is significantly decreased. Whereas, the most significant influence of the Stone Wales defects observed in Type III, refer to Table 2. A clear influence of Stone Wales defect on Silicon carbide nanotube is the defects formation energy levels close to Fermi energy. The defects level evolved from Stone Wales defects of type I is close to the band gap center and the energy difference between the top of the valence band and the bottom of the conduction band. The band gap of pristine silicon carbide nanotubes is 1.884 eV. However, upon introducing Stone Wales defects, the band gap significantly decrease to 1.223 eV, 1.131 eV and 1.028 eV for type I, type II and type III of Stone Wales defects, respectively, refer to Fig. 2. While, the bottom of the conduction band in silicon carbide nanotube consists of silicon 3p states, the top of the valence band consist of both carbon 2p states as well as silicon
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Table 2 Band structure variations upon applying longitudinal electric field for all nanotubes under study.
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Longitudinal Electric field eV/Å/e
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Fig. 4. A comparison between pristine silicon carbide nanotubes and silicon carbide nanotubes with different orientations of Stone Wales defects upon applying transverse electric field.
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Table 3 Band structure variations upon applying transverse electric field for all nanotubes under study.
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Fig. 3. A comparison between pristine silicon carbide nanotubes and silicon carbide nanotubes with different orientations of Stone Wales defects upon applying longitudinal electric field.
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3p states. In other words, the bottom of the conduction band and the top of the valence band were occupied by silicon 3p states and carbon 2p states. These findings prove the sensitivity of the orientation of Stone Wales defects in tuning the band gap of silicon carbide nanotubes [1,7]. To further tune the electronic properties of silicon carbide nanotubes with different orientations of Stone Wales defects, we gradually introduced longitudinal ( Az) and transverse (Rx) electric field from 0.0 eV/Å/e to 2.0 eV/Å/e. The band gap of silicon carbide nanotubes under longitudinal electric field is shown in Fig. 3 and Table 2. It can be seen from Fig. 3 that the band gap decreases with the increasing the external longitudinal electric field. This could be attributed to asymmetry of electrostatic potential under the applied electric field. Whereas, the decrease in the band gaps with increasing the longitudinal electric field is an indication that the semiconductor metals phase transition occurs for silicon carbide nanotube under longitudinal electric field. Yet it needs a strong electric field to mix neighboring sub-bands and considerably tune the band structure. However very strong electric field will create undesirable surface deformation, especially when the structure has topological defects such as Stone Wales defects. In addition, since we are dealing with periodic structure, the finite space effect at different external longitudinal electric field values is not negligible. Fig. 4 and Table 3 represent how the applied transverse electric field tunes the energy gap for all silicon carbide nanotubes under study. The band gap in all four silicon carbide nanotubes were decrease quadratically with increasing the transverse electric field, refer to Fig. 4 and Table 3. This might be correlated to a local charge separation induced by applying transverse electric field on the silicon carbide nanotube. While, the charge density of conduction band lowest state is moved to the opposite direction of the applied field, the charge density of the valence band highest state
Transverse Electric field eV/Å/e
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is moved with the same direction of the applied electric field. On one hand, the energy of conduction band minimum state shifts down as a result of the accumulated charge in regions of higher electric potential. On the other hand, the energy of valence band maximum state shifts up as a result of the accumulated charge in low electrical potential zone. Based on Stark effect, the relation between small electric fields and the band gap energy is quadratic as the top of valence band and the bottom of conduction band are non-degenerate [3]. However, when the field becomes larger, potentials, within the valence and conduction sub-band complexes, will be produced. This perturbation will cause huge mixing among sub-band states. In this regime, the external electric field will control the wavefunction of the band edge states. With no doubt, this charge density is an indication that the bottom of the conduction band state is moved away from the external electric field, which eventually localized on one side of the silicon carbide nanotube. Whereas, the top of the valence band state is moved toward the electric field, which eventually localized on the other side of the silicon carbide nanotube. However, some kinetic energy will be consumed as a consequence of localizing the wavefunction on both sides of the tube. While the edge of the conduction band minimizes its energy because of the applied electric field, the charge is piled up in greater electric potential regions. Similarly, the valence band edge increases its accumulated charge in low electric potential. Consequently, the decrease in the conduction band energy and increase in the valence band energy will directly reduces the band gap. As seen in Fig. 3 and Fig. 4, the band gap reduced upon applying external electric field. This reduction in the band gap is largest
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Fig. 5. Partial density of states for all nanotube under study without applying electric field: a) pristine silicon carbide nanotubes, b) silicon carbide nanotubes with type I of Stone Wales defects, c) silicon carbide nanotubes with type II of Stone Wales defects, d) silicon carbide nanotubes with type III of Stone Wales defects. The red dashed line represents the Fermi energy.
for silicon carbide nanotubes with type III of Stone Wales defects. While, the degenerate states at zero electric field clearly split with increasing the strength of the applied field, the degree of tuning the band gap under longitudinal electric field is less significant compared to tuning the band gap under transverse electric field. Whereas, applying transverse electric field will further separate the charge densities of the lowest unoccupied molecular orbital and highest occupied molecular orbital states. Furthermore, upon applying transverse electric field, the band gap energy monotonically reduced because of the rapid decrease of the nearly free electron band which moves to one side of the unit cell. Therefore, applying transverse electric field will smoothly redistribute the charge density and consequently the nearly free electron band will rapidly decrease and eventually the gap closed. In order to neglect finite space effect at different external transverse electric field values, a very large unit cell dimensions were set. While applying different values of transverse electric field on the pristine silicon carbide nanotubes and silicon carbide nanotubes with different orientations of Stone Wales defects, we observed two main interesting phenomena. First of all, the semiconductor-metal phase transition existed in all samples regardless the existence of Stone Wales defects or not. However, some variations were observed in the band-gap between pristine silicon carbide nanotubes and silicon carbide nanotubes with different orientations of Stone Wales defects. These variations in the band gap indicate a strong effect resulted by introducing different orientations of Stone Wales defects to silicon carbide nanotube surface. Second, the band-gap variations for silicon carbide nanotubes with three types of Stone Wales defects have the same trend; even
though each orientation of Stone Wales defects has clear band gap values under different values of external transverse electric field (Table 2). The differences in the electron transition of the defective silicon carbide nanotubes are significantly improved upon introducing transverse electric fields. Like pristine silicon carbide nanotube, a phase transition from semiconductor to metal occurs in silicon carbide nanotubes with different types of Stone Wales defects when electric field strength reach around 0.4 eV/Å/e. However, applying transverse electric field induces discrepancies in the band gaps and in the partial density of states; refer to Fig. 4. The mechanism behind closing the band gap could be attributed to the valence band maximum state which contributed by both P x and P y orbitals for all silicon carbide nanotubes under investigation. Furthermore, the conduction band minimum state of silicon carbide nanotubes with different orientations of Stone Wales defects consisted of P z orbitals which ruled by pentagon and heptagon rings in the defective site. In addition, these P z orbital state in the minimum conduction π states move toward each other and consequently, the band gap starts to close. This exactly will happen when sub-band mixing becomes more declared as the field strength reached 0.4 eV/Å/e and beyond, refer to Fig. 3. This might explain why the band gaps of silicon carbide nanotubes with different orientations of Stone Wales defects are smaller than the band gap of pristine silicon carbide nanotubes. We also studied the partial density of states for all four Si-C tubes. From Fig. 5, the partial density of states of pristine silicon carbide nanotubes at the Fermi level is wide, (∼1.884), which consistent with the obtained value from the band structure at Fermi level. Significant peaks close to the Fermi level were observed. However; the s elec-
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trons have no observed peaks whatsoever which means that the only contribution in the DOS of silicon carbide nanotubes is mainly from 2p electrons, refer to Fig. 5.
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Based on our results, it is more likely to tune the band gap of silicon carbide nanotubes with Stone Wales defects within a certain range by controlling the strength of the applied electric field for specific applications. Besides, it is possible to predict the existence and orientation of Stone Wales defects in silicon carbide nanotubes by applying a transverse electric field while rotating the silicon carbide nanotube that contains Stone Wales defects. As soon as we maintained the maximum values of the band gap, we can predict the position as well as the orientation of Stone Wales defects. Finally, our results demonstrate that applying external electric field to silicon carbide nanotubes that contain different orientations of Stone Wales defects play a critical rule on manipulating the electrical properties of silicon carbide nanotubes, yet no deformation noticed in the silicon carbide structures.
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References
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[1] K.M. Alam, A.K. Ray, Phys. Rev. B 77 (2008) 035436. [2] B. Xiao, H. Hu, J.-x. Zhao, Y.-h. Ding, Physica E, Low-Dimens. Syst. Nanostruct. 56 (2014) 377–385. [3] J.A. Talla, Comput. Condens. Matter 15 (2018) 25–30. [4] Jamal Talla, Majid Abusini, Khaled Khazaeleh, Rami Omari, Mohammed Serhan, H. El-Nasser, Mater. Express 7 (2017) 516–522. [5] K. Adhikari, A.K. Ray, Solid State Commun. 151 (2011) 430–435.
[6] R. Ansari, M. Mirnezhad, H. Rouhi, NANO 09 (2014) 1450043. [7] R.J. Baierle, P. Piquini, L.P. Neves, R.H. Miwa, Phys. Rev. B 74 (2006) 155425. [8] H.-L. Chen, S.-P. Ju, J.-S. Lin, J. Zhao, H.-T. Chen, J.-G. Chang, M.H. Weng, S.-C. Lee, W.-J. Lee, J. Nanopart. Res. 12 (2010) 2919–2928. [9] M. Khodadad, S.M. Baizaee, M. Yuonesi, H. Kahnouji, Physica E, Low-Dimens. Syst. Nanostruct. 59 (2014) 139–143. [10] X. Wang, K.M. Liew, J. Phys. Chem. C 116 (2012) 26888–26897. [11] X. Zhou, W.Q. Tian, J. Phys. Chem. C 115 (2011) 11493–11499. [12] S. Behzad, R. Chegel, R. Moradian, M. Shahrokhi, Superlattices Microstruct. 73 (2014) 185–192. [13] R.-L. Liang, Y. Zhang, J.-M. Zhang, V. Ji, Physica B, Condens. Matter 405 (2010) 2673–2679. [14] R.J. Baierle, R.H. Miwa, Phys. Rev. B 76 (2007) 205410. [15] S.-J. Wang, C.-L. Zhang, Z.-G. Wang, Chin. Phys. Lett. 27 (2010) 106101. [16] X.-H. Sun, C.-P. Li, W.-K. Wong, N.-B. Wong, C.-S. Lee, S.-T. Lee, B.-K. Teo, J. Am. Chem. Soc. 124 (2002) 14464–14471. [17] Z. Wang, F. Gao, J. Li, X. Zu, W.J. Weber, J. Appl. Phys. 106 (2009) 084305. [18] A. Wu, Q. Song, L. Yang, Q. Hao, Theor. Comput. Chem. 977 (2011) 92–96. [19] G. Alfieri, T. Kimoto, Nanotechnology 20 (2009) 285703. [20] X. Wang, K.M. Liew, J. Phys. Chem. C 116 (2012) 1702–1708. [21] D. Huilong, G. Zhenyu, G. Keith, D. Chunmiao, H. Tingjun, L. Shuit-Tong, L. Youyong, Nanotechnology 26 (2015) 275201. [22] A. Gali, Phys. Rev. B 73 (2006) 245415. [23] S.A. Curran, J.A. Talla, D. Zhang, D.L. Carroll, J. Mater. Res. 20 (2005) 3368–3373. [24] L.G. Zhoua, S.-Q. Shib, Appl. Phys. Lett. 83 (2003) 3. [25] J.A. Talla, S.A. Salman, Nanosci. Nanotechnol. Lett. 7 (2015) 1–6. [26] S.A. Salman, J.A. Talla, A. Abuzir, E. Yasin, J. Comput. Theor. Nanosci. 12 (2015) 8. [27] Jamal A. Talla, Saed A. Salman, Nanosci. Nanotechnol. Lett. 7 (2015) 6. [28] J.A. Talla, A.A. Ghozlan, Chin. J. Phys. (2018). [29] L.G. Zhou, S.-Q. Shi, Appl. Phys. Lett. 83 (2003) 1222–1224. [30] S.H. Yang, W.H. Shin, J.K. Kang, J. Chem. Phys. 125 (2006) 084705.
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