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Capped ZnO (3, 0) nanotubes as building blocks of bare and H passivated wurtzite ZnO nanocrystals
Superlattices and Microstructures 85 (2015) 813–819
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Capped ZnO (3, 0) nanotubes as building blocks of bare and H passivated wurtzite ZnO nanocrystals Mudar Ahmed Abdulsattar Ministry of Science and Technology, Baghdad, Iraq
a r t i c l e
i n f o
Article history: Received 4 July 2015 Accepted 6 July 2015 Available online 6 July 2015 Keywords: Diamondoids DFT Nanocrystals
a b s t r a c t In the present work we propose building blocks of hexagonal type crystals and nanocrystals of zinc oxide including wurtzite structure that are called wurtzoids. These molecules are ZnO (3, 0) nanotubes capped at their two terminals with Zn or O atoms. Hexagonal part of these molecules is included in the central part of these molecules. This part can be repeated to increase hexagonal structure ratio. Hydrogen passivated and bare ZnO wurtzoids are investigated. Results show bare wurtzoids have shorter and stronger surface sp2 bonds than H passivated sp3 bonded wurtzoids. The calculated energy gap of these molecules shows the expected trend of gaps. Calculated binding energy per atom shows that wurtzoids are tight and stable structures which are not the case of ZnO diamondoids. Vibrational frequencies manifest the expected trends of hexagonal type structures. Reduced mass and force constant of these vibrations are investigated to illustrate the sp2 and sp3 bonding effects of bare and H passivated ZnO nanocrystals respectively. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Current research in materials science is focused on ZnO and other materials such as GaN and InN as promising future semiconductor materials. Zinc oxide has many industrial applications that include electronics, sensors, additives, etc. [1,2]. The molecular and nanoscale new technologies add other dimensions to the already diverse applications of zinc oxide. ZnO can be prepared in several polymorphs that include wurtzite (B4), zincblende (B3) and rock salt (B1) phases [3–6]. The wurtzite phase is the most stable phase at normal conditions. The zincblende phase can be stabilized by growing ZnO on a cubic substrate while the rock salt is stable only at relatively high pressures. At the nanoscale, surface conditions strongly affect the properties of ZnO nanoparticles [3]. As an example, ZnO bare and passivated nanocrystals can have a range of energy gap values that expands on going to the molecular limit as we shall see below. In order to work at molecular and nanoscale ranges we have to discover the exact molecular species that can be formed in such scales. One of these structures is diamondoids used to investigate molecular and nanoscale limits of cubic diamond and zincblende structure materials [7–9]. These structures are not applicable to ZnO since ZnO zincblende structure cannot exist unless it is grown on a cubic substrate. In the present work we shall suggest building blocks for ZnO wurtzite structure. These building blocks are ZnO (3, 0) nanotubes. (3, 0) nanotubes are the smallest nanotubes in their diameter. As we can see from Fig. 1a and b these nanotubes have the same wurtzite hexagonal interlocking rings of atoms in boat conformation [10]. On the contrary chair conformation of cubic diamondoids is the building block of diamond and zincblende structures [7–9]. As a
E-mail address: [email protected] http://dx.doi.org/10.1016/j.spmi.2015.07.015 0749-6036/Ó 2015 Elsevier Ltd. All rights reserved.
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(a) Bare wurtzoid
(b) Part of ZnO (3,0) nanotube
(c) Bare triwurtzoid (lateral view)
(d) Bare triwurtzoid (upper view)
(e) H passivated wurtzoid
(f) H passivated triwurtzoid
Fig. 1. A comparison between the structure of: (a) bare wurtzoid, (b) part of ZnO (3, 0) nanotube, (c) bare triwurtzoid (lateral view), (d) bare triwurtzoid (upper view), (e) H passivated wurtzoid and (f) H passivated triwurtzoid. Blue, red and white balls are Zn, O and H atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
result wurtzite structure can be viewed as a bundle of ZnO (3, 0) nanotubes. These building blocks can be also applied to other materials that have hexagonal structures including wurtzite structure. 2. Theory All-electron density functional theory (DFT) at the level of B3LYP (Becke, three-parameter, Lee–Yang–Parr) with valence double-zeta 6-31G(d) basis including polarization functions is used to optimize ZnO bare and H passivated (HP) clusters that are the seeds of wurtzite structure. Calculations include bare clusters ZnO, Zn3O3, Zn7O7, Zn13O13, Zn21O21 and Zn39O39. These same clusters are also investigated after complete hydrogen passivation at their surface. Passivated clusters are ZnOH2, Zn3O3H6, Zn7O7H14, Zn13O13H26, Zn21O21H30 and Zn39O39H54. Partial hydrogen passivation is not considered in the present work. These molecular-nano species are not chosen arbitrarily. ZnO is the smallest molecule of zinc oxide. Zn3O3 is the hexagonal ring shaped molecule that is the building block of zincblende and wurtzite structures. Zn7O7 (Fig. 1a) is a (3, 0) nanotube (Fig. 1b) that is capped by Zn and O atoms at its terminating ends. This molecule proved to be stable for other Zn chalcogens such as ZnSe [11] for bare and partial H charges. This molecule has the wurtzite structure signature [10]. This signature is manifested by the interlocking rings of atoms in boat conformation at the center of Zn7O7 molecule. The dimensions of the central part of this molecules (excluding the upper and lower capping atoms) are 3.25 and 5.2 Å which are the (a) and (c) lattice parameters of wurtzite ZnO structure in the hexagonal crystal convention [1]. For this reason this
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molecule is termed as the building block of wurtzite structure and as a consequence named as ‘‘wurtzoid’’ in the present work. Note that the capping atoms are essential for the stabilization of this molecule. These capping atoms make the coordination number of all surface atoms 3 and 4 for bare and H passivated clusters respectively. The molecule Zn13O13 is an elongated wurtzoid in which the central part is equal to 2c (c is the hexagonal lattice parameter) as in Fig. 2a. This molecule is termed wurtzoid2c. Zn21O21 molecule is a three wurtzoids connected together from their lateral sides as in Fig. 1c and d. This molecule is termed as triwurtzoid. The last molecule Zn39O39 is an elongated triwurtzoid in which the length of the central part is equal to 2c. This molecule is terminated triwurtzoid2c as in Fig. 2b. Passivated clusters are the same clusters mentioned above with full hydrogen passivation at their surface such as HP wurtzoid (Fig. 1e) and HP triwurtzoid (Fig. 1f). The number in the prefix of the name of these wurtzoids refers to the lateral expansion of these wurtzoids while the number in the suffix refers to the expansion in horizontal direction along c lattice parameter. The largest molecule triwurtzoid2c dimensions are 1.4 1.22 1.26 nm in the standard molecular xyz orientation and can be considered as a small nanocrystals. Note that in the present work we discuss the relation between (3, 0) nanotubes and wurtzite structure which is termed as 2H polymorph. 4H, 6H and other polymorphs can also be constructed using the present wurtzoids but will not be discussed here. Vibrational reduced masses and force constants of IR and Raman spectra of the present bare and HP wurtzoid molecules and nanocrystals are calculated. The frequencies of vibrations are corrected using 0.96 scale factor that is usually used with the present theory and basis (B3LYP/6-31G(d)) [12]. All the calculations are performed using Gaussian 09 program [13].
3. Results and discussion One can see from the stoichiometry of bare wurtzoids mentioned above in the previous section that the surface Zn or O atoms have dangling bonds that lead to graphite-like sp2 hybridization. HP wurtzoids on the other hand have sp3 bonding hybridization that is common in bulk diamond, zincblende and wurtzite structures. This fact leads to many differences in the structural and electronic properties of these molecules as we will see in the following figures. Fig. 3 shows Energy gap of bare and HP wurtzoids as a function of total number of Zn and O atoms. It can be seen that HP wurtzoids follow quantum confinement effect of descending gap as a function of total number of atoms. Experimental bulk ZnO wurtzite hexagonal structure gap is 3.37 eV [14]. This limit is shown in Fig. 3. Fig. 3 also shows that bare wurtzoids have oscillatory gap that ends at slightly lower gap than bulk experimental value. The two curves should unite in one value as the size of a nanocluster becomes large enough so that surface effects are neglected. Highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the bare and HP cases are shown. It can be seen that HOMO levels are less sensitive than LUMO for surface effects. This is manifested by the large differences between LUMO levels in the two cases of bare and HP clusters especially for small clusters. This is expected since LUMO levels are rough estimation of electron affinity obtained by adding electrons that passivate surface dangling bonds. The present result of energy gap can be considered as a good match with experiment. The present result is better than many previous recorded calculations that generally underestimate the gap [14,1].
(a) Wurtzoid2c
(b) triwurtzoid2c
Fig. 2. ZnO bare wurtzoid2c (Zn13O13) and triwurtzoid2c (Zn39O39) atomic positions as calculated by present theory and basis (B3LYP/6-31G(d)). Blue, red and white balls are Zn, O and H atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Energy gap passivated HOMO passivated LUMO passivated Experimental wurtzite Energy gap bare LUMO bare HOMO bare
8 6
Energy (eV)
4 2 0 -2
0
10
20
30
40
50
60
70
80
90
-4 -6 -8 -10
Total number of Zn and O atoms Fig. 3. Energy gap of bare and H passivated wurtzoids as a function of total number of Zn and O atoms. HOMO, LUMO and experimental bulk wurtzite gap [14] are shown.
8
Cohesive Energy (eV)
7 6 5 4 3
Hydrogenated wurtzoids Bare wurtzoids
2
Experimental cohesive energy
1 0 0
10
20
30
40
50
60
70
80
90
Total number of Zn and O atoms Fig. 4. Binding energy per atom of ZnO wurtzoids. The results are compared with the experimental binding energy of bulk wurtzite ZnO at 7.55 eV [14].
Fig. 4 shows binding energy per atom of ZnO bare and HP wurtzoids. The results are compared with the binding energy of bulk ZnO wurtzite structure at 7.52 eV [14]. The present method underestimates the value of the cohesive energy. The highest investigated clusters of bare and HP triwurtzoid2c have the cohesive energies of 3.72 and 5.6 eV respectively that averages at 4.66 eV. Better results can be obtained using local spin density approximation (LSDA) within the present basis states. The highest investigated clusters of bare and HP triwurtzoid2c cohesive energies in LSDA/6-31G(d) method and basis have the values of 6.54 and 8.58 eV respectively in which the experimental value are approximately at the mid point between these two values. However, the LSDA method under estimate the energy gap by nearly 2 eV. As nanoclusters increase in size surface effects diminish and the bare and passivated cohesive energies converge to one value. Fig. 5 shows a comparison between the distribution of bond lengths of bare and HP wurtzoids. The highest two peaks are at 1.94 and 2.05 Å for Zn–O bond length in bare and HP wurtzoids respectively. The experimental value of Zn–O bond length is at 1.97 Å between the upper two mentioned values. This is in agreement with the general understanding of sp2 bonds being shorter and stronger than sp3 bonds. Small two peaks are located at 1.86 and 2.02 Å for bare and HP wurtzoids respectively. These two peaks belong to the nearly horizontal bonds at the center of bare and passivated wurtzoid in Fig. 1a and e respectively. These are the ultimate strongest and shortest Zn–O bonds in wurtzoids. H related bonds also appear in the case of passivated wurtzoid at 0.97 and 1.54 Å. These correspond to O–H and Zn–H bond lengths respectively. They are in good agreement with the average of O–H and Zn–H bond lengths derived from experiments at 0.964 and 1.565 respectively [12]. Figs. 6 and 7 show a comparison of vibration reduced mass and force constant of bare and HP wurtzoids. For a material composed of two atoms with high difference in their masses, vibration frequencies at Brillion zone boundary are approximately given by [15]:
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20 H passivated Bare Experimental
18
Zn-O
Number of bonds
16 14 12 10 8 O-H
6 Zn-H
4 2 0 0.9
1.1
1.3
1.5
1.7
1.9
2.1
Bond length (Å) Fig. 5. A comparison between the distribution of bond lengths of bare and H passivated ZnO wurtzoid. Experimental value of Zn–O bond length at 1.97 Å is shown [12,14].
60 EXP LO
Reduced mass (amu)
50
40 HP-HRMM
30
Bare H passivated Experimental LO Bare HRMM HP HRMM
B-HRMM
20
10
0 0
200
400
600
800
1000
Frequenct (cm-1) Fig. 6. A comparison of vibrational reduced masses (in amu) of bare and H passivated wurtzoid. The highest reduced mass mode (HRMM) in both cases is shown. Experimental longitudinal optical mode (LO) is shown [14].
m1
1 2p
sffiffiffiffiffiffiffi k1 ðAcoustical BranchÞ; m1
m2
1 2p
sffiffiffiffiffiffiffi k2 ðOptical BranchÞ: m2
ð1Þ
ð2Þ
m1 and m2 are the heavy (Zn) and light (O) atoms respectively in present wurtzoids. k is the force constant. The highest longitudinal optical mode (LO) should coincide with highest reduced mass mode (HRMM) or highest force constant mode (HFCM) in their regions [16,17]. From Figs. 6 and 7 the value at 626.7 cm1 is the value that correspond to this limit for bare wurtzoid. The value 505.8 cm1 corresponds to this limit for HP-wurtzoid. The experimental LO mode is in the range 587– 591 cm1 in Raman spectroscopy and the range 588–592 cm1 for IR spectroscopy for bulk ZnO [14]. As we can see this value is in between that of bare and HP wurtzoids. It was proved previously that LO vibrations for hydrogen passivated C and Si nanocrystals are red shifted with respect to bulk [16,17]. This result is in agreement with the present finding in which the
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5
Force constant (mDyne/Å)
EXP LO
H passivated Bare Experimental LO B-HFCM HP-HFCM
4
B-HFCM
3
HP-HFCM
2
1
0 0
200
400
600
800
1000
Frequency (cm-1) Fig. 7. A comparison of vibrational force constants (mDyne/Å) of bare and H passivated wurtzoid. The highest force constant mode (HFCM) in both cases is shown. Experimental longitudinal optical mode (LO) is shown [14].
HP-wurtzite HRMM at 505.8 cm1 is red shifted with respect to the average experimental 590 cm1 for bulk ZnO. A new finding which is proved for the first time in this work is that the bare cluster of atoms LO mode is blue shifted with respect to bulk as in the present 626.7 cm1 for bare wurtzoid with respect to the experimental bulk LO mode at 590 cm1. Previous theoretical estimation of this mode is at 628 cm1 [18] that shows the accuracy of the present method. For HP wurtzoid more than two kind of atoms exist (Zn, O and H) so that a third region for H vibrations exist. This region that starts from 688 to 3648 cm1 (most of this region is not shown in Figs. 6 and 7) is characterized by reduced mass that is very close to 1 atomic mass units (amu). Fig. 6 shows vibrations of bare wurtzite in the region 89–247 cm1 has reduced masses that reach more than 50 amu. According to Eq. (1) a collection of Zn atoms are responsible for these vibrations. The same is true for the region 333–627 cm1 that has reduced masses around 18 amu for the vibration of a collection of O atoms. For the HP-wurtzoid the Zn and O vibration ranges are 56–219 cm1 and 232–506 cm1 respectively. The reduced masses are very much smaller because of partial coupling with H atoms. From Eqs. (1), (2) the force constant can be written:
k ¼ 4p2 lm2 :
ð3Þ
In the above equation the force constant should take the shape of a parabola as a function of frequency for a constant reduced mass l. This is approximately true for the regions mentioned above with the exception of O vibrations of HP-wurtzoid in which the reduced mass fluctuates strongly. 4. Conclusions Molecules that can be used as building blocks of hexagonal wurtzite structure are proposed in the present work. These building blocks are capped ZnO (3, 0) nanotubes with varying lengths. When these nanotubes are elongated and made as a bundle the exact bulk ZnO wurtzite structure is obtained. To check the validity of our assumptions we tested several properties and compared with experiment. The energy gap size variation is acceptable since the experimental gap is confined between the bare and HP limits. The same is true for bond lengths and LO vibrational frequency. The binding energy is underestimated using the present method and basis (B3LYP/6-31G(d)) although good results cab be obtained using (LSDA/6-31G(d)). References [1] Yong-Sung Kim, Eun-Cheol Lee, K.J. Chang, Stability of wurtzite and rocksalt MgxZn1xO alloys, J. Korean Phys. Soc. 39 (2001) S92–S96. [2] Jason Kyle Cooper, Synthesis, characterization, and exciton dynamics of II–VI semiconducting nanomaterials and ab initio studies for applications in explosives sensing, Ph.D. thesis in Chemistry, University of California, Santa Cruz, 2013. [3] Csaba E. Szakacs, Erika F. Merschrod S., Kristin M. Poduska, Structural features that stabilize ZnO clusters: an electronic structure approach, Computation 1 (2013) 16–26. [4] J. Serrano, A.H. Romero, F.J. Manjon, R. Lauck, M. Cardona, A. Rubio, Pressure dependence of the lattice dynamics of ZnO: an ab initio approach, Phys. Rev. B 69 (2004) 094306. [5] J. Pellicer-Porres, A. Segura, V. Panchal, A. Polian, F. Decremps, P. Dumas, High-pressure study of the infrared active modes in wurtzite and rocksalt ZnO, Phys. Rev. B 84 (2011) 125202. [6] Ekaterina Badaeva, Yong Feng, Daniel R. Gamelin, Xiaosong Li, Investigation of pure and Co2+-doped ZnO quantum dot electronic structures using the density functional theory: choosing the right functional, New J. Phys. 10 (2008) 055013.
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[7] G. Ramachandran, S. Manogaran, Vibrational spectra of triamantane X18H24, iso-tetramantane X22H28 and cyclohexamantane X26H30 (X = C, Si, Ge, Sn) – a theoretical study, THEOCHEM 816 (2007) 31–41. [8] M.A. Abdulsattar, Diamondoids approach to electronic, structural and vibrational properties of GeSi superlattice nanocrystals: a first-principles study, Struct. Chem. 25 (2014) 1811–1818. [9] J. Fischer, J. Baumgartner, C. Marschner, Synthesis and structure of sila-adamantane, Science 310 (2005). 825-825. [10] G. Banfalvi, C12: the building block of hexagonal diamond, Cent. Eur. J. Chem. 10 (2012) 1676–1680. [11] Sachin P. Nanavati, V. Sundararajan, Shailaja Mahamuni, Vijay Kumar, S.V. Ghaisas, Optical properties of zinc selenide clusters from first-principles calculations, Phys. Rev. B 80 (2009) 245417. [12] NIST Computational chemistry comparison and benchmark database, release 15b, 2011,
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Capped ZnO (3, 0) nanotubes as building blocks of bare and H passivated wurtzite ZnO nanocrystals Mudar Ahmed Abdulsattar Ministry of Science and Technology, Baghdad, Iraq
a r t i c l e
i n f o
Article history: Received 4 July 2015 Accepted 6 July 2015 Available online 6 July 2015 Keywords: Diamondoids DFT Nanocrystals
a b s t r a c t In the present work we propose building blocks of hexagonal type crystals and nanocrystals of zinc oxide including wurtzite structure that are called wurtzoids. These molecules are ZnO (3, 0) nanotubes capped at their two terminals with Zn or O atoms. Hexagonal part of these molecules is included in the central part of these molecules. This part can be repeated to increase hexagonal structure ratio. Hydrogen passivated and bare ZnO wurtzoids are investigated. Results show bare wurtzoids have shorter and stronger surface sp2 bonds than H passivated sp3 bonded wurtzoids. The calculated energy gap of these molecules shows the expected trend of gaps. Calculated binding energy per atom shows that wurtzoids are tight and stable structures which are not the case of ZnO diamondoids. Vibrational frequencies manifest the expected trends of hexagonal type structures. Reduced mass and force constant of these vibrations are investigated to illustrate the sp2 and sp3 bonding effects of bare and H passivated ZnO nanocrystals respectively. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Current research in materials science is focused on ZnO and other materials such as GaN and InN as promising future semiconductor materials. Zinc oxide has many industrial applications that include electronics, sensors, additives, etc. [1,2]. The molecular and nanoscale new technologies add other dimensions to the already diverse applications of zinc oxide. ZnO can be prepared in several polymorphs that include wurtzite (B4), zincblende (B3) and rock salt (B1) phases [3–6]. The wurtzite phase is the most stable phase at normal conditions. The zincblende phase can be stabilized by growing ZnO on a cubic substrate while the rock salt is stable only at relatively high pressures. At the nanoscale, surface conditions strongly affect the properties of ZnO nanoparticles [3]. As an example, ZnO bare and passivated nanocrystals can have a range of energy gap values that expands on going to the molecular limit as we shall see below. In order to work at molecular and nanoscale ranges we have to discover the exact molecular species that can be formed in such scales. One of these structures is diamondoids used to investigate molecular and nanoscale limits of cubic diamond and zincblende structure materials [7–9]. These structures are not applicable to ZnO since ZnO zincblende structure cannot exist unless it is grown on a cubic substrate. In the present work we shall suggest building blocks for ZnO wurtzite structure. These building blocks are ZnO (3, 0) nanotubes. (3, 0) nanotubes are the smallest nanotubes in their diameter. As we can see from Fig. 1a and b these nanotubes have the same wurtzite hexagonal interlocking rings of atoms in boat conformation [10]. On the contrary chair conformation of cubic diamondoids is the building block of diamond and zincblende structures [7–9]. As a
E-mail address: [email protected] http://dx.doi.org/10.1016/j.spmi.2015.07.015 0749-6036/Ó 2015 Elsevier Ltd. All rights reserved.
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(a) Bare wurtzoid
(b) Part of ZnO (3,0) nanotube
(c) Bare triwurtzoid (lateral view)
(d) Bare triwurtzoid (upper view)
(e) H passivated wurtzoid
(f) H passivated triwurtzoid
Fig. 1. A comparison between the structure of: (a) bare wurtzoid, (b) part of ZnO (3, 0) nanotube, (c) bare triwurtzoid (lateral view), (d) bare triwurtzoid (upper view), (e) H passivated wurtzoid and (f) H passivated triwurtzoid. Blue, red and white balls are Zn, O and H atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
result wurtzite structure can be viewed as a bundle of ZnO (3, 0) nanotubes. These building blocks can be also applied to other materials that have hexagonal structures including wurtzite structure. 2. Theory All-electron density functional theory (DFT) at the level of B3LYP (Becke, three-parameter, Lee–Yang–Parr) with valence double-zeta 6-31G(d) basis including polarization functions is used to optimize ZnO bare and H passivated (HP) clusters that are the seeds of wurtzite structure. Calculations include bare clusters ZnO, Zn3O3, Zn7O7, Zn13O13, Zn21O21 and Zn39O39. These same clusters are also investigated after complete hydrogen passivation at their surface. Passivated clusters are ZnOH2, Zn3O3H6, Zn7O7H14, Zn13O13H26, Zn21O21H30 and Zn39O39H54. Partial hydrogen passivation is not considered in the present work. These molecular-nano species are not chosen arbitrarily. ZnO is the smallest molecule of zinc oxide. Zn3O3 is the hexagonal ring shaped molecule that is the building block of zincblende and wurtzite structures. Zn7O7 (Fig. 1a) is a (3, 0) nanotube (Fig. 1b) that is capped by Zn and O atoms at its terminating ends. This molecule proved to be stable for other Zn chalcogens such as ZnSe [11] for bare and partial H charges. This molecule has the wurtzite structure signature [10]. This signature is manifested by the interlocking rings of atoms in boat conformation at the center of Zn7O7 molecule. The dimensions of the central part of this molecules (excluding the upper and lower capping atoms) are 3.25 and 5.2 Å which are the (a) and (c) lattice parameters of wurtzite ZnO structure in the hexagonal crystal convention [1]. For this reason this
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molecule is termed as the building block of wurtzite structure and as a consequence named as ‘‘wurtzoid’’ in the present work. Note that the capping atoms are essential for the stabilization of this molecule. These capping atoms make the coordination number of all surface atoms 3 and 4 for bare and H passivated clusters respectively. The molecule Zn13O13 is an elongated wurtzoid in which the central part is equal to 2c (c is the hexagonal lattice parameter) as in Fig. 2a. This molecule is termed wurtzoid2c. Zn21O21 molecule is a three wurtzoids connected together from their lateral sides as in Fig. 1c and d. This molecule is termed as triwurtzoid. The last molecule Zn39O39 is an elongated triwurtzoid in which the length of the central part is equal to 2c. This molecule is terminated triwurtzoid2c as in Fig. 2b. Passivated clusters are the same clusters mentioned above with full hydrogen passivation at their surface such as HP wurtzoid (Fig. 1e) and HP triwurtzoid (Fig. 1f). The number in the prefix of the name of these wurtzoids refers to the lateral expansion of these wurtzoids while the number in the suffix refers to the expansion in horizontal direction along c lattice parameter. The largest molecule triwurtzoid2c dimensions are 1.4 1.22 1.26 nm in the standard molecular xyz orientation and can be considered as a small nanocrystals. Note that in the present work we discuss the relation between (3, 0) nanotubes and wurtzite structure which is termed as 2H polymorph. 4H, 6H and other polymorphs can also be constructed using the present wurtzoids but will not be discussed here. Vibrational reduced masses and force constants of IR and Raman spectra of the present bare and HP wurtzoid molecules and nanocrystals are calculated. The frequencies of vibrations are corrected using 0.96 scale factor that is usually used with the present theory and basis (B3LYP/6-31G(d)) [12]. All the calculations are performed using Gaussian 09 program [13].
3. Results and discussion One can see from the stoichiometry of bare wurtzoids mentioned above in the previous section that the surface Zn or O atoms have dangling bonds that lead to graphite-like sp2 hybridization. HP wurtzoids on the other hand have sp3 bonding hybridization that is common in bulk diamond, zincblende and wurtzite structures. This fact leads to many differences in the structural and electronic properties of these molecules as we will see in the following figures. Fig. 3 shows Energy gap of bare and HP wurtzoids as a function of total number of Zn and O atoms. It can be seen that HP wurtzoids follow quantum confinement effect of descending gap as a function of total number of atoms. Experimental bulk ZnO wurtzite hexagonal structure gap is 3.37 eV [14]. This limit is shown in Fig. 3. Fig. 3 also shows that bare wurtzoids have oscillatory gap that ends at slightly lower gap than bulk experimental value. The two curves should unite in one value as the size of a nanocluster becomes large enough so that surface effects are neglected. Highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the bare and HP cases are shown. It can be seen that HOMO levels are less sensitive than LUMO for surface effects. This is manifested by the large differences between LUMO levels in the two cases of bare and HP clusters especially for small clusters. This is expected since LUMO levels are rough estimation of electron affinity obtained by adding electrons that passivate surface dangling bonds. The present result of energy gap can be considered as a good match with experiment. The present result is better than many previous recorded calculations that generally underestimate the gap [14,1].
(a) Wurtzoid2c
(b) triwurtzoid2c
Fig. 2. ZnO bare wurtzoid2c (Zn13O13) and triwurtzoid2c (Zn39O39) atomic positions as calculated by present theory and basis (B3LYP/6-31G(d)). Blue, red and white balls are Zn, O and H atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Energy gap passivated HOMO passivated LUMO passivated Experimental wurtzite Energy gap bare LUMO bare HOMO bare
8 6
Energy (eV)
4 2 0 -2
0
10
20
30
40
50
60
70
80
90
-4 -6 -8 -10
Total number of Zn and O atoms Fig. 3. Energy gap of bare and H passivated wurtzoids as a function of total number of Zn and O atoms. HOMO, LUMO and experimental bulk wurtzite gap [14] are shown.
8
Cohesive Energy (eV)
7 6 5 4 3
Hydrogenated wurtzoids Bare wurtzoids
2
Experimental cohesive energy
1 0 0
10
20
30
40
50
60
70
80
90
Total number of Zn and O atoms Fig. 4. Binding energy per atom of ZnO wurtzoids. The results are compared with the experimental binding energy of bulk wurtzite ZnO at 7.55 eV [14].
Fig. 4 shows binding energy per atom of ZnO bare and HP wurtzoids. The results are compared with the binding energy of bulk ZnO wurtzite structure at 7.52 eV [14]. The present method underestimates the value of the cohesive energy. The highest investigated clusters of bare and HP triwurtzoid2c have the cohesive energies of 3.72 and 5.6 eV respectively that averages at 4.66 eV. Better results can be obtained using local spin density approximation (LSDA) within the present basis states. The highest investigated clusters of bare and HP triwurtzoid2c cohesive energies in LSDA/6-31G(d) method and basis have the values of 6.54 and 8.58 eV respectively in which the experimental value are approximately at the mid point between these two values. However, the LSDA method under estimate the energy gap by nearly 2 eV. As nanoclusters increase in size surface effects diminish and the bare and passivated cohesive energies converge to one value. Fig. 5 shows a comparison between the distribution of bond lengths of bare and HP wurtzoids. The highest two peaks are at 1.94 and 2.05 Å for Zn–O bond length in bare and HP wurtzoids respectively. The experimental value of Zn–O bond length is at 1.97 Å between the upper two mentioned values. This is in agreement with the general understanding of sp2 bonds being shorter and stronger than sp3 bonds. Small two peaks are located at 1.86 and 2.02 Å for bare and HP wurtzoids respectively. These two peaks belong to the nearly horizontal bonds at the center of bare and passivated wurtzoid in Fig. 1a and e respectively. These are the ultimate strongest and shortest Zn–O bonds in wurtzoids. H related bonds also appear in the case of passivated wurtzoid at 0.97 and 1.54 Å. These correspond to O–H and Zn–H bond lengths respectively. They are in good agreement with the average of O–H and Zn–H bond lengths derived from experiments at 0.964 and 1.565 respectively [12]. Figs. 6 and 7 show a comparison of vibration reduced mass and force constant of bare and HP wurtzoids. For a material composed of two atoms with high difference in their masses, vibration frequencies at Brillion zone boundary are approximately given by [15]:
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20 H passivated Bare Experimental
18
Zn-O
Number of bonds
16 14 12 10 8 O-H
6 Zn-H
4 2 0 0.9
1.1
1.3
1.5
1.7
1.9
2.1
Bond length (Å) Fig. 5. A comparison between the distribution of bond lengths of bare and H passivated ZnO wurtzoid. Experimental value of Zn–O bond length at 1.97 Å is shown [12,14].
60 EXP LO
Reduced mass (amu)
50
40 HP-HRMM
30
Bare H passivated Experimental LO Bare HRMM HP HRMM
B-HRMM
20
10
0 0
200
400
600
800
1000
Frequenct (cm-1) Fig. 6. A comparison of vibrational reduced masses (in amu) of bare and H passivated wurtzoid. The highest reduced mass mode (HRMM) in both cases is shown. Experimental longitudinal optical mode (LO) is shown [14].
m1
1 2p
sffiffiffiffiffiffiffi k1 ðAcoustical BranchÞ; m1
m2
1 2p
sffiffiffiffiffiffiffi k2 ðOptical BranchÞ: m2
ð1Þ
ð2Þ
m1 and m2 are the heavy (Zn) and light (O) atoms respectively in present wurtzoids. k is the force constant. The highest longitudinal optical mode (LO) should coincide with highest reduced mass mode (HRMM) or highest force constant mode (HFCM) in their regions [16,17]. From Figs. 6 and 7 the value at 626.7 cm1 is the value that correspond to this limit for bare wurtzoid. The value 505.8 cm1 corresponds to this limit for HP-wurtzoid. The experimental LO mode is in the range 587– 591 cm1 in Raman spectroscopy and the range 588–592 cm1 for IR spectroscopy for bulk ZnO [14]. As we can see this value is in between that of bare and HP wurtzoids. It was proved previously that LO vibrations for hydrogen passivated C and Si nanocrystals are red shifted with respect to bulk [16,17]. This result is in agreement with the present finding in which the
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5
Force constant (mDyne/Å)
EXP LO
H passivated Bare Experimental LO B-HFCM HP-HFCM
4
B-HFCM
3
HP-HFCM
2
1
0 0
200
400
600
800
1000
Frequency (cm-1) Fig. 7. A comparison of vibrational force constants (mDyne/Å) of bare and H passivated wurtzoid. The highest force constant mode (HFCM) in both cases is shown. Experimental longitudinal optical mode (LO) is shown [14].
HP-wurtzite HRMM at 505.8 cm1 is red shifted with respect to the average experimental 590 cm1 for bulk ZnO. A new finding which is proved for the first time in this work is that the bare cluster of atoms LO mode is blue shifted with respect to bulk as in the present 626.7 cm1 for bare wurtzoid with respect to the experimental bulk LO mode at 590 cm1. Previous theoretical estimation of this mode is at 628 cm1 [18] that shows the accuracy of the present method. For HP wurtzoid more than two kind of atoms exist (Zn, O and H) so that a third region for H vibrations exist. This region that starts from 688 to 3648 cm1 (most of this region is not shown in Figs. 6 and 7) is characterized by reduced mass that is very close to 1 atomic mass units (amu). Fig. 6 shows vibrations of bare wurtzite in the region 89–247 cm1 has reduced masses that reach more than 50 amu. According to Eq. (1) a collection of Zn atoms are responsible for these vibrations. The same is true for the region 333–627 cm1 that has reduced masses around 18 amu for the vibration of a collection of O atoms. For the HP-wurtzoid the Zn and O vibration ranges are 56–219 cm1 and 232–506 cm1 respectively. The reduced masses are very much smaller because of partial coupling with H atoms. From Eqs. (1), (2) the force constant can be written:
k ¼ 4p2 lm2 :
ð3Þ
In the above equation the force constant should take the shape of a parabola as a function of frequency for a constant reduced mass l. This is approximately true for the regions mentioned above with the exception of O vibrations of HP-wurtzoid in which the reduced mass fluctuates strongly. 4. Conclusions Molecules that can be used as building blocks of hexagonal wurtzite structure are proposed in the present work. These building blocks are capped ZnO (3, 0) nanotubes with varying lengths. When these nanotubes are elongated and made as a bundle the exact bulk ZnO wurtzite structure is obtained. To check the validity of our assumptions we tested several properties and compared with experiment. The energy gap size variation is acceptable since the experimental gap is confined between the bare and HP limits. The same is true for bond lengths and LO vibrational frequency. The binding energy is underestimated using the present method and basis (B3LYP/6-31G(d)) although good results cab be obtained using (LSDA/6-31G(d)). References [1] Yong-Sung Kim, Eun-Cheol Lee, K.J. Chang, Stability of wurtzite and rocksalt MgxZn1xO alloys, J. Korean Phys. Soc. 39 (2001) S92–S96. [2] Jason Kyle Cooper, Synthesis, characterization, and exciton dynamics of II–VI semiconducting nanomaterials and ab initio studies for applications in explosives sensing, Ph.D. thesis in Chemistry, University of California, Santa Cruz, 2013. [3] Csaba E. Szakacs, Erika F. Merschrod S., Kristin M. Poduska, Structural features that stabilize ZnO clusters: an electronic structure approach, Computation 1 (2013) 16–26. [4] J. Serrano, A.H. Romero, F.J. Manjon, R. Lauck, M. Cardona, A. Rubio, Pressure dependence of the lattice dynamics of ZnO: an ab initio approach, Phys. Rev. B 69 (2004) 094306. [5] J. Pellicer-Porres, A. Segura, V. Panchal, A. Polian, F. Decremps, P. Dumas, High-pressure study of the infrared active modes in wurtzite and rocksalt ZnO, Phys. Rev. B 84 (2011) 125202. [6] Ekaterina Badaeva, Yong Feng, Daniel R. Gamelin, Xiaosong Li, Investigation of pure and Co2+-doped ZnO quantum dot electronic structures using the density functional theory: choosing the right functional, New J. Phys. 10 (2008) 055013.
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[7] G. Ramachandran, S. Manogaran, Vibrational spectra of triamantane X18H24, iso-tetramantane X22H28 and cyclohexamantane X26H30 (X = C, Si, Ge, Sn) – a theoretical study, THEOCHEM 816 (2007) 31–41. [8] M.A. Abdulsattar, Diamondoids approach to electronic, structural and vibrational properties of GeSi superlattice nanocrystals: a first-principles study, Struct. Chem. 25 (2014) 1811–1818. [9] J. Fischer, J. Baumgartner, C. Marschner, Synthesis and structure of sila-adamantane, Science 310 (2005). 825-825. [10] G. Banfalvi, C12: the building block of hexagonal diamond, Cent. Eur. J. Chem. 10 (2012) 1676–1680. [11] Sachin P. Nanavati, V. Sundararajan, Shailaja Mahamuni, Vijay Kumar, S.V. Ghaisas, Optical properties of zinc selenide clusters from first-principles calculations, Phys. Rev. B 80 (2009) 245417. [12] NIST Computational chemistry comparison and benchmark database, release 15b, 2011,