- Email: [email protected]
Ring structures of small ZnO clusters
Computational Materials Science 36 (2006) 258–262 www.elsevier.com/locate/commatsci
Ring structures of small ZnO clusters Amit Jain a
a,*
, Vijay Kumar
a,b
, Yoshiyuki Kawazoe
a
Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan b Dr. Vijay Kumar Foundation, 45 Bazaar Street, K.K. Nagar (West), Chennai 600 078, India Received 16 July 2004
Abstract We report results of an ab initio study of the atomic structures of small zinc oxide clusters (ZnO)n n 6 6 using ultrasoft pseudopotential method and the generalized gradient approximation for the exchange-correlation energy. We optimize several isomers for each size in order to obtain the lowest energy structures and to understand the growth behavior. In all cases ring type structures are found to be most favorable. For n = 5 and 6, the ring structures are not planar suggesting that the bonding nature in these cluster has some covalent character. Small clusters are found to have small highest-occupied–lowest unoccupied molecular orbital (HOMO–LUMO) gap in contrast to the typical behavior of large gaps for small clusters that tend to decrease towards the bulk value with an increase in size. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Zinc oxide clusters; Ab initio calculations; Ring structures; Binding energy
1. Introduction Clusters and nanostructures of semiconducting materials are currently attracting a lot of interest as these are expected to play an important role in the development of future nanoscale technologies as well as novel cluster assembled materials with tailor-made properties. One of the major thrusts in the study of clusters is to develop fundamental understanding of materials at the nanoscale as the properties and structures are often quite different from bulk and depend on size and shape as well. While it is becoming possible to measure several properties of clusters, experimental information on structures is often lacking and it is important to understand the structure–property relations from ab initio calculations. II–VI compound semiconductors such as ZnO are tech-
*
Corresponding author. Tel.: +81 22 215 2481; fax: +81 22 215 2052. E-mail address: [email protected] (A. Jain). 0927-0256/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2005.06.008
nologically very important due to the wide band gap. Many of the II–VI compounds are used in photovoltaic solar cells [1–9], optical sensitizers [10], photocatalysts [11,12], quantum devices [13] and so on. Recently zinc oxide (ZnO) has generated tremendous interest due to its unique combination of materials properties as it exhibits interesting LED applications as well as piezoelectric and pyroelectric properties. Several studies have been devoted to understand its structure and properties and the behavior of its nanoparticles and nanowires in recent years [14–25]. However, studies on clusters of ZnO have received little attention. In this paper we report atomic structures of small zinc oxide clusters obtained by using the density function theory. In bulk zinc oxide has wurtzite structure and it is of interest to understand the evolution of structures and properties with an increase in size. Also for applications it is of interest to know competing isomers as well as their properties such as the stability, HOMO–LUMO gaps, bonding nature etc. Here we consider neutral small clusters of ZnO.
A. Jain et al. / Computational Materials Science 36 (2006) 258–262
2. Theoretical method We performed ab initio calculations using ultrasoft pseudopotentials [26] and a plane-wave basis set. A sim˚ edge length in order ple cubic unit cell is used with 18 A to keep the distance between clusters in neighboring cells sufficiently large to make the dispersion effects negligible. In such a big unit cell only the C point is used to represent the Brillouin zone. The exchange-correlation energy is calculated within the generalized gradient approximation (GGA). The structural optimizations are performed using conjugate gradient method. The cutoff energy for the plane wave expansion is taken to be 395 eV. The convergence criteria used for energy ˚ , respectively. and force are 10 5 eV and 10 3 eV/A
259
The structure optimization has been performed without any symmetry constraint.
3. Results and discussion The optimized structures of different isomers are shown in Fig. 1. Isomers marked with ÔaÕ have the lowest energies. The details of the structures and the properties of different isomers are given in Table 1. The binding energy per ZnO molecule is calculated from EB = (nEZn + nEO En(ZnO))/n where n is the number of ZnO molecules in the cluster. The binding energies and HOMO–LUMO gap of the most favourable structures are shown in Figs. 2 and 3. The experimental value for
Fig. 1. Structures of ZnnOn (n = 1–6) clusters. Gray (blue in web version) balls represent zinc and black (red in web version) balls represent oxygen atoms.
260
A. Jain et al. / Computational Materials Science 36 (2006) 258–262
Table 1 ˚ ), O–Zn–O angle, binding energy per ZnO molecule, EB (eV) and HOMO–LUMO gap for (ZnO)n clusters, n = 1–6 Structures, bond lengths (A ˚) HOMO–LUMO gap (eV) Isomer Structure Bond length (Zn–O) (A Angle (O–Zn–O) (°) EB (eV) Linear Rhombus Ring Ring Rhombohedral Ring Capped distorted rhombohedron Ring Double ring Planar fused rings Bent fused rings Double capped distorted cube
Binding energy per ZnO molecule (eV)
1 2a 3a 4a 4b 5a 5b 6a 6b 6c 6d 6e
1.71 1.90 1.83 1.79 2.00 1.78 1.79–2.04 1.77 1.90–2.12 1.79–1.86 1.76–2.18 1.79–2.03
103.94 148.40 168.25 97.80 177.10–178.0 92.11–143.99 176.82–177.56 136.50–137.01 83.80–156.63 85.19–176.82 84.79–140.13
7 6 5 4 3 2 1 0 0
1
2
3
4
5
6
ZnO cluster size
HOMO_LUMO gap (eV)
Fig. 2. Binding energy per ZnO molecule for the most stable ZnO clusters.
3.5 3 2.5 2 1.5 1 0.5 0 0
1
2
3 4 ZnO Cluster size
5
6
Fig. 3. HOMO–LUMO gaps for the most stable ZnO clusters.
the cohesive energy of bulk ZnO is 7.52 eV per formula unit [27] and the band gap is 3.4 eV [22]. ZnO molecule ˚ and quite low binding has a short bond length of 1.71 A energy as well as HOMO–LUMO gap in comparison to other clusters (Table 1). The bond length is elongated to ˚ in the most favorable isomer (2a in Fig. 1) of 1.90 A Zn2O2 which is a rhombus. Also the binding energy and the HOMO–LUMO gap increase significantly, though these values are still much smaller than for larger clusters. We also optimized another structure shown in Fig. 1 2b((i) and (ii) are the side and top views of the
2.31 4.32 5.55 5.97 5.37 6.10 5.66 6.15 6.01 6.00 5.82 5.81
0.63 1.28 2.78 2.85 1.70 2.94 1.60 2.83 2.09 2.54 0.93 1.67
same structure) as initial geometry but it ultimately converged to the structure found in Fig. 1 2a. The O–Zn–O angle in this isomer is much smaller than found in the most favorable structures of larger clusters. The lowest energy structure for Zn3O3 is shown in Fig. 1 3a. This is planar and ring type with each atom having coordination number two. We tried another structure shown in Fig. 1 3b as the initial geometry but this ladder type structure opened up and finally converged to the structure of isomer (3a). The Zn–O bond length in this case is shorter compared with the Zn2O2 cluster and the O–Zn–O angle is much larger (Table 1). This may be due to the release of strain in this structure in comparison to the rhombus structure of Zn2O2 that makes this Zn3O3 structure more stable. This is also clear from the significant increase in the binding energy and also a very large increase in the HOMO–LUMO gap that is more than double the value (Table 1) for Zn2O2. Zn4O4 has two optimized structures (4a and b) but the planar ring structure Zn4O4 (4a) shown in Fig. 1 is significantly more favorable (Table 1). In the case of the isomer (4b) all atoms have coordination number three compared to two in the most favourable ring isomer (4a). It is very interesting scenario because the structure with higher coordination number is usually more stable and it reflects the importance of bond angles. Note that the bond length of the ring structure (4a) decreases in comparison to Zn3O3 but the binding energy and HOMO–LUMO gap increase. Also the O–Zn–O angle becomes larger with the value of 168.25° and it shows the tendency to form near linear O–Zn–O bonds. On the other hand the bond length in the 3-dimensional ˚ and this isomer (4b) increases significantly to 2.0 A structure has strained O–Zn–O angles (97.80°), which might be the reason for the enlargement of the bond lengths and making this isomer unfavorable. The rhombohedral isomer (4b) has 0.60 eV less binding energy than the most favourable planar ring structure and the HOMO–LUMO gap is also much lower (1.70 eV) than the HOMO–LUMO gap for (4a). The initial ladder
A. Jain et al. / Computational Materials Science 36 (2006) 258–262
structure (4c) shown in Fig. 1 converges to the ring structure. The two low-lying optimized structures of Zn5O5 are shown in Fig. 1 5a((i) and (ii) being top and side views) and 5b and their properties are given in Table 1. The ring type structure (5a) has significantly higher binding energy than the 3-dimensional structure shown in (5b). The O–Zn–O angle in the ring isomer also tends to become close to 180°. Therefore, it is more stable and favourable. We also optimized other initial geometries as shown in Fig. 1 5c, 5d and 5e. The initial structures (5c and 5d) open up and converge to the ring isomer while the initial structure (5e) converges to the structure (5b). These results show large basins of attraction for the two isomers. In the ring structure (5a), all atoms have coordination number two whereas in isomer (5b) two atoms have coordination number two and the rest of the atoms have coordination number three. Thus low coordination structures continue to be more favorable. However, the ring isomer is not planar as it can be seen in the side view (5a(ii)). The bond length in isomer (5a) is almost similar to the bond length in isomer (4a) but the O– Zn–O bond angle increases. The small variation in the values of the O–Zn–O bond angles of (5a) is due to the quasiplanar structure in this case. The isomer (5b) can be visualized to be built of a Zn2O2 ring fused with a Zn3O3 isomer such that there are four Zn2O2 rhombi and two bent Zn3O3 ring type ˚ , and units. The bond length varies from 1.79 to 2.04 A is longer than the values in isomer (5a). The O–Zn–O bond angle varies from 92.11° to 143.99° and this causes significant strain in the structure making it unfavorable. It is noteworthy that the binding energy difference between quasiplanar isomer (5a) and the 3-dimensional isomer (5b) is 0.44 eV, which is smaller than the binding energy difference of 0.60 eV between planar (4a) and 3-dimensional (4b) isomers of Zn4O4. This is very much justifiable in the light of the ring type structure (5a) becoming quasiplanar as it indicates the possibility of a trend for most favourable structures going from 2-dimensional to 3-dimensional domain. The difference between the HOMO–LUMO gaps of (5a) and (5b) is still very large, thus making (5a) much more favourable than the (5b) isomer. The optimized low-lying structures of Zn6O6 are shown in Fig. 1 6a ((i) and (ii) being top and side views), 6b ((i) and (ii) being top and side views), 6c, 6d and 6e. Their properties are given in Table 1. The ring type structure shown in (6a) has the highest binding energy and all atoms have coordination number two whereas all other local minimum isomers have at least a few atoms with coordination number three. However, similar to (5a), the ring isomer (6a) is not planar as it can be seen from the side view shown in (6a(ii)). Here it is important to note that both zinc as well as oxygen atoms
261
shift away from the plane whereas in the quasiplanar structure (5a) only oxygen atoms shift away from the plane. This shows that this quasiplanar structure (6a) is more distorted from a planar structure than (5a). The bond length in (6a) is almost similar to the bond length of isomer (5a) but the bond angle O–Zn–O reduces slightly from the values in isomer (5a) though it is still near to linearity with the values of 176.82°– 177.56°. The small variation in O–Zn–O bond angle is due to the quasiplanar structure in this case. The 3-dimensional structure (6b) has all atoms with coordination number three. A similar structure has been found [28] to be lowest in energy for isoelectronic Cd6Se6. Therefore, small ZnO clusters continue to prefer open structures. The structure of this isomer can be visualized to be built of two parallel Zn3O3 ring type units joined by six Zn2O2 ring type units. The bond lengths ˚ and 2.12 A ˚ , which are larger than in the case are 1.90 A of isomer (6a). The bond angle O–Zn–O varies from 136.50° to 137.01° which show still significant strain in the structure that makes it unfavourable. It is very important to note here that the binding energy difference between the quasiplanar (6a) and the 3-dimensional (6b) isomers becomes very small in comparison to those found in the isomers of Zn5O5 and Zn4O4. In the present case it is only 0.14 eV, which indicates very significant increase in the tendency to form stable 3-dimensional structures. The difference between the HOMO–LUMO gap of (6a) and (6b) also reduces significantly in comparison to those found in the isomers of Zn5O5 and Zn4O4, which also strongly support this tendency. The isomer (6c) has four atoms with coordination number three and eight atoms with coordination number two. This local minimum structure is planar with ˚ and bond angle bond length varying from 1.79 to 1.86 A O–Zn–O varying from 83.80° to 156.63°. This structure is very slightly lower in binding energy from (6b) but has significantly higher HOMO–LUMO gap. Therefore this planar structure (6c) is quite competitive with the isomer (6a). The large variation in the O–Zn–O bond angles of isomer (6c) shows significant strain in this structure that make it unfavorable but the small energy difference suggests that the cost of the strain has reduced significantly. The existence of this local minimum structure is very significant to understand that most favourable structure is still quasiplanar similar to (5a), not in a significantly 3-dimensional regime. Both (6b) and (6c) isomers have almost similar binding energies that are only 0.14 and 0.15 eV/atom lower, respectively from (6a) but the significantly higher HOMO–LUMO gap of planar (6c) than the 3-dimensional isomer (6b) shows the preference for quasiplanar structures though there is certainly an incremental trend for relative preference for 3-dimensional regime with an increase in size. These results reflect the subtle difference in the bonding natures in clusters of II–VI compounds.
262
A. Jain et al. / Computational Materials Science 36 (2006) 258–262
The local minimum isomers (6d) and (6e) are both 3-dimensional structures. Their binding energies are significantly lower than the binding energy of (6a) and also have very low values of HOMO–LUMO gaps. Therefore, they are much less stable and not favourable. The HOMO–LUMO gap for n P 3 is nearly the same with the value close to 3 eV within GGA. Therefore, compared with bulk, this is a higher gap as one can expect. Also the binding energy of the clusters is significantly lower than the bulk value as expected.
4. Summary In summary, we have studied the structures and properties of small zinc oxide clusters using ab initio calculations based on ultrasoft pseudopotentials scheme. The most favourable atomic structures of (ZnO)n clusters (n = 1–6) are ring type. For n = 1–4 the ring is planar but for n = 5 and 6 the rings are slightly bent acquire chair shapes. The binding energy difference between the most favourable quasiplanar structure of (ZnO)6 and its nearest 3-dimesional local minimum is small and our results show that there is difference in the bonding nature in clusters of ZnO and other II–VI compound semiconductors. Also our results are indicative for an increasing trend for the relative preference for 3-dimensional structures to be more stable with an increase in size. The HOMO–LUMO gap for n = 1 and 2 is significantly smaller than other clusters which is contrary to the general behavior in elemental semiconductors.
Acknowledgements The authors would like to thank the staff of the Center for Computational Materials Science at the Institute for Materials Research, Tohoku University for making the Hitachi SR8000/64 parallel machines available and for their cooperation. A.J. is grateful for the support of the Japan Society for the Promotion of Science. V. K. thankfully acknowledges the kind hospitality at the Institute for Materials Research.
References [1] A. Kampmann, D. Lincot, J. Electroanal. Chem. 418 (1996) 73. [2] Y.Y. Loginov, K. Durose, H.M. Al-Allak, S.A. Galloway, S. Oktik, A.W. Brinkman, H. Richter, D. Bonnet, J. Cryst. Growth 161 (1996) 159. [3] A. Niemegeers, M. Burgelman, J. Appl. Phys. 81 (1997) 2881. [4] K. Li, A.T.S. Wee, J. Lin, K.L. Tan, L. Zhou, S.F.Y. Li, Z.C. Feng, H.C. Chou, S. Kamra, A. Rohatgi, J. Mater. Sci.: Mater. Electron. 8 (1997) 125. [5] C. Ferekides, J. Britt, Sol. Energy Mater. Sol. Cells 35 (1994) 255. [6] H.C. Chou, A. Rohatgi, N.M. Jokerst, S. Kamra, S.R. Stock, S.L. Lowrie, R.K. Ahrenkiel, D.H. Levi, Mater. Chem. Phys. 43 (1996) 178. [7] S. Naseem, D. Nazir, R. Mumtaz, K. Hussain, J. Mater. Sci. Technol. 12 (1996) 89. [8] J. Touukova, D. Kindl, J. Tousek, Thin Solid Films 293 (1997) 272. [9] T.L. Chu, S.S. Chu, Solid State Electron. 38 (1995) 533. [10] P.J. Sebastian, M. Ocampo, Sol. Energy Mater. Sol. Cells 44 (1996) 1. [11] A.J. Hoffman, G. Mills, H. Yee, M.R. Hoffmann, J. Phys. Chem. 96 (1992) 5546. [12] S. Kuwabata, K. Nishida, R. Tsuda, H. Inoue, H. Yoneyama, J. Electrochem. Soc. 141 (1994) 1498. [13] E. Corcoran, Sci. Am. 263 (11) (1990) 74. [14] P. Schroer, P. Kruger, J. Pollmann, Phys. Rev. B 47 (1993) 6971. [15] D. Vogel, P. Kruger, J. Pollmann, Phys. Rev. B 52 (1995) R14316. [16] M.E. Zandler, E.C. Behrman, M.B. Arrasmith, J.R. Myers, T.V. Smith, J. Mol. Struc. (Theochem) 362 (1996) 215. [17] M. Usuda, N. Hamada, T. Kotani, M.V. Schilfgaarde, Phys. Rev. B 66 (2002) 125101. [18] H. Li, T.M. Briere, K. Shimomura, R. Kadono, K. Nishiyama, K. Nagamine, T.P. Das, Physica B 326 (2003) 133. [19] B. Meyer, D. Marx, Phys. Rev. B 67 (2003) 035403. [20] L.G. Wang, A. Zunger, Phys. Rev. Lett. 90 (2003) 256401. [21] P.X. Gao, Z.L. Wang, Appl. Phys. Lett. 84 (2004) 2883. [22] D.P. Norton, Y.W. Heo, M.P. Ivill, K. Ip, S.J. Pearton, M.F. Chisholm, T. Steiner, Materials Today, June 2004, 34pp. [23] Z.L. Wang, Materials Today, June 2004, 26pp. [24] H. Ohta, H. Hosono, Materials Today, June 2004, 42pp. [25] S.J. Pearton, D.P. Norton, K. Ip, Y.W. Heo, J. Vac. Sci. Technol. B 22 (2004) 932. [26] G. Kresse, J. Hafner, J. Phys.: Condens. Matter. 4 (1994) 8245; G. Kresse, J. Furthmu¨ller, Phys. Rev. B 54 (1996) 11169; D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [27] J.E. Jaffe, J.A. Snyder, Z. Lin, A.C. Hess, Phys. Rev. B 62 (2000) 1660. [28] A. Kasuya, R. Sivamohan, Y. Barnakov, I. Dmitruk, T. Nirasawa, V. Romanyuk, V. Kumar, S. Mamykin, K. Tohji, B. Jeyadevan, K. Shinoda, T. Kudo, O. Terasaki, Z. Liu, R. Belosludov, V. Sundararajan, Y. Kawazoe, Nature Mater. 4 (2004) 99.
Ring structures of small ZnO clusters Amit Jain a
a,*
, Vijay Kumar
a,b
, Yoshiyuki Kawazoe
a
Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan b Dr. Vijay Kumar Foundation, 45 Bazaar Street, K.K. Nagar (West), Chennai 600 078, India Received 16 July 2004
Abstract We report results of an ab initio study of the atomic structures of small zinc oxide clusters (ZnO)n n 6 6 using ultrasoft pseudopotential method and the generalized gradient approximation for the exchange-correlation energy. We optimize several isomers for each size in order to obtain the lowest energy structures and to understand the growth behavior. In all cases ring type structures are found to be most favorable. For n = 5 and 6, the ring structures are not planar suggesting that the bonding nature in these cluster has some covalent character. Small clusters are found to have small highest-occupied–lowest unoccupied molecular orbital (HOMO–LUMO) gap in contrast to the typical behavior of large gaps for small clusters that tend to decrease towards the bulk value with an increase in size. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Zinc oxide clusters; Ab initio calculations; Ring structures; Binding energy
1. Introduction Clusters and nanostructures of semiconducting materials are currently attracting a lot of interest as these are expected to play an important role in the development of future nanoscale technologies as well as novel cluster assembled materials with tailor-made properties. One of the major thrusts in the study of clusters is to develop fundamental understanding of materials at the nanoscale as the properties and structures are often quite different from bulk and depend on size and shape as well. While it is becoming possible to measure several properties of clusters, experimental information on structures is often lacking and it is important to understand the structure–property relations from ab initio calculations. II–VI compound semiconductors such as ZnO are tech-
*
Corresponding author. Tel.: +81 22 215 2481; fax: +81 22 215 2052. E-mail address: [email protected] (A. Jain). 0927-0256/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2005.06.008
nologically very important due to the wide band gap. Many of the II–VI compounds are used in photovoltaic solar cells [1–9], optical sensitizers [10], photocatalysts [11,12], quantum devices [13] and so on. Recently zinc oxide (ZnO) has generated tremendous interest due to its unique combination of materials properties as it exhibits interesting LED applications as well as piezoelectric and pyroelectric properties. Several studies have been devoted to understand its structure and properties and the behavior of its nanoparticles and nanowires in recent years [14–25]. However, studies on clusters of ZnO have received little attention. In this paper we report atomic structures of small zinc oxide clusters obtained by using the density function theory. In bulk zinc oxide has wurtzite structure and it is of interest to understand the evolution of structures and properties with an increase in size. Also for applications it is of interest to know competing isomers as well as their properties such as the stability, HOMO–LUMO gaps, bonding nature etc. Here we consider neutral small clusters of ZnO.
A. Jain et al. / Computational Materials Science 36 (2006) 258–262
2. Theoretical method We performed ab initio calculations using ultrasoft pseudopotentials [26] and a plane-wave basis set. A sim˚ edge length in order ple cubic unit cell is used with 18 A to keep the distance between clusters in neighboring cells sufficiently large to make the dispersion effects negligible. In such a big unit cell only the C point is used to represent the Brillouin zone. The exchange-correlation energy is calculated within the generalized gradient approximation (GGA). The structural optimizations are performed using conjugate gradient method. The cutoff energy for the plane wave expansion is taken to be 395 eV. The convergence criteria used for energy ˚ , respectively. and force are 10 5 eV and 10 3 eV/A
259
The structure optimization has been performed without any symmetry constraint.
3. Results and discussion The optimized structures of different isomers are shown in Fig. 1. Isomers marked with ÔaÕ have the lowest energies. The details of the structures and the properties of different isomers are given in Table 1. The binding energy per ZnO molecule is calculated from EB = (nEZn + nEO En(ZnO))/n where n is the number of ZnO molecules in the cluster. The binding energies and HOMO–LUMO gap of the most favourable structures are shown in Figs. 2 and 3. The experimental value for
Fig. 1. Structures of ZnnOn (n = 1–6) clusters. Gray (blue in web version) balls represent zinc and black (red in web version) balls represent oxygen atoms.
260
A. Jain et al. / Computational Materials Science 36 (2006) 258–262
Table 1 ˚ ), O–Zn–O angle, binding energy per ZnO molecule, EB (eV) and HOMO–LUMO gap for (ZnO)n clusters, n = 1–6 Structures, bond lengths (A ˚) HOMO–LUMO gap (eV) Isomer Structure Bond length (Zn–O) (A Angle (O–Zn–O) (°) EB (eV) Linear Rhombus Ring Ring Rhombohedral Ring Capped distorted rhombohedron Ring Double ring Planar fused rings Bent fused rings Double capped distorted cube
Binding energy per ZnO molecule (eV)
1 2a 3a 4a 4b 5a 5b 6a 6b 6c 6d 6e
1.71 1.90 1.83 1.79 2.00 1.78 1.79–2.04 1.77 1.90–2.12 1.79–1.86 1.76–2.18 1.79–2.03
103.94 148.40 168.25 97.80 177.10–178.0 92.11–143.99 176.82–177.56 136.50–137.01 83.80–156.63 85.19–176.82 84.79–140.13
7 6 5 4 3 2 1 0 0
1
2
3
4
5
6
ZnO cluster size
HOMO_LUMO gap (eV)
Fig. 2. Binding energy per ZnO molecule for the most stable ZnO clusters.
3.5 3 2.5 2 1.5 1 0.5 0 0
1
2
3 4 ZnO Cluster size
5
6
Fig. 3. HOMO–LUMO gaps for the most stable ZnO clusters.
the cohesive energy of bulk ZnO is 7.52 eV per formula unit [27] and the band gap is 3.4 eV [22]. ZnO molecule ˚ and quite low binding has a short bond length of 1.71 A energy as well as HOMO–LUMO gap in comparison to other clusters (Table 1). The bond length is elongated to ˚ in the most favorable isomer (2a in Fig. 1) of 1.90 A Zn2O2 which is a rhombus. Also the binding energy and the HOMO–LUMO gap increase significantly, though these values are still much smaller than for larger clusters. We also optimized another structure shown in Fig. 1 2b((i) and (ii) are the side and top views of the
2.31 4.32 5.55 5.97 5.37 6.10 5.66 6.15 6.01 6.00 5.82 5.81
0.63 1.28 2.78 2.85 1.70 2.94 1.60 2.83 2.09 2.54 0.93 1.67
same structure) as initial geometry but it ultimately converged to the structure found in Fig. 1 2a. The O–Zn–O angle in this isomer is much smaller than found in the most favorable structures of larger clusters. The lowest energy structure for Zn3O3 is shown in Fig. 1 3a. This is planar and ring type with each atom having coordination number two. We tried another structure shown in Fig. 1 3b as the initial geometry but this ladder type structure opened up and finally converged to the structure of isomer (3a). The Zn–O bond length in this case is shorter compared with the Zn2O2 cluster and the O–Zn–O angle is much larger (Table 1). This may be due to the release of strain in this structure in comparison to the rhombus structure of Zn2O2 that makes this Zn3O3 structure more stable. This is also clear from the significant increase in the binding energy and also a very large increase in the HOMO–LUMO gap that is more than double the value (Table 1) for Zn2O2. Zn4O4 has two optimized structures (4a and b) but the planar ring structure Zn4O4 (4a) shown in Fig. 1 is significantly more favorable (Table 1). In the case of the isomer (4b) all atoms have coordination number three compared to two in the most favourable ring isomer (4a). It is very interesting scenario because the structure with higher coordination number is usually more stable and it reflects the importance of bond angles. Note that the bond length of the ring structure (4a) decreases in comparison to Zn3O3 but the binding energy and HOMO–LUMO gap increase. Also the O–Zn–O angle becomes larger with the value of 168.25° and it shows the tendency to form near linear O–Zn–O bonds. On the other hand the bond length in the 3-dimensional ˚ and this isomer (4b) increases significantly to 2.0 A structure has strained O–Zn–O angles (97.80°), which might be the reason for the enlargement of the bond lengths and making this isomer unfavorable. The rhombohedral isomer (4b) has 0.60 eV less binding energy than the most favourable planar ring structure and the HOMO–LUMO gap is also much lower (1.70 eV) than the HOMO–LUMO gap for (4a). The initial ladder
A. Jain et al. / Computational Materials Science 36 (2006) 258–262
structure (4c) shown in Fig. 1 converges to the ring structure. The two low-lying optimized structures of Zn5O5 are shown in Fig. 1 5a((i) and (ii) being top and side views) and 5b and their properties are given in Table 1. The ring type structure (5a) has significantly higher binding energy than the 3-dimensional structure shown in (5b). The O–Zn–O angle in the ring isomer also tends to become close to 180°. Therefore, it is more stable and favourable. We also optimized other initial geometries as shown in Fig. 1 5c, 5d and 5e. The initial structures (5c and 5d) open up and converge to the ring isomer while the initial structure (5e) converges to the structure (5b). These results show large basins of attraction for the two isomers. In the ring structure (5a), all atoms have coordination number two whereas in isomer (5b) two atoms have coordination number two and the rest of the atoms have coordination number three. Thus low coordination structures continue to be more favorable. However, the ring isomer is not planar as it can be seen in the side view (5a(ii)). The bond length in isomer (5a) is almost similar to the bond length in isomer (4a) but the O– Zn–O bond angle increases. The small variation in the values of the O–Zn–O bond angles of (5a) is due to the quasiplanar structure in this case. The isomer (5b) can be visualized to be built of a Zn2O2 ring fused with a Zn3O3 isomer such that there are four Zn2O2 rhombi and two bent Zn3O3 ring type ˚ , and units. The bond length varies from 1.79 to 2.04 A is longer than the values in isomer (5a). The O–Zn–O bond angle varies from 92.11° to 143.99° and this causes significant strain in the structure making it unfavorable. It is noteworthy that the binding energy difference between quasiplanar isomer (5a) and the 3-dimensional isomer (5b) is 0.44 eV, which is smaller than the binding energy difference of 0.60 eV between planar (4a) and 3-dimensional (4b) isomers of Zn4O4. This is very much justifiable in the light of the ring type structure (5a) becoming quasiplanar as it indicates the possibility of a trend for most favourable structures going from 2-dimensional to 3-dimensional domain. The difference between the HOMO–LUMO gaps of (5a) and (5b) is still very large, thus making (5a) much more favourable than the (5b) isomer. The optimized low-lying structures of Zn6O6 are shown in Fig. 1 6a ((i) and (ii) being top and side views), 6b ((i) and (ii) being top and side views), 6c, 6d and 6e. Their properties are given in Table 1. The ring type structure shown in (6a) has the highest binding energy and all atoms have coordination number two whereas all other local minimum isomers have at least a few atoms with coordination number three. However, similar to (5a), the ring isomer (6a) is not planar as it can be seen from the side view shown in (6a(ii)). Here it is important to note that both zinc as well as oxygen atoms
261
shift away from the plane whereas in the quasiplanar structure (5a) only oxygen atoms shift away from the plane. This shows that this quasiplanar structure (6a) is more distorted from a planar structure than (5a). The bond length in (6a) is almost similar to the bond length of isomer (5a) but the bond angle O–Zn–O reduces slightly from the values in isomer (5a) though it is still near to linearity with the values of 176.82°– 177.56°. The small variation in O–Zn–O bond angle is due to the quasiplanar structure in this case. The 3-dimensional structure (6b) has all atoms with coordination number three. A similar structure has been found [28] to be lowest in energy for isoelectronic Cd6Se6. Therefore, small ZnO clusters continue to prefer open structures. The structure of this isomer can be visualized to be built of two parallel Zn3O3 ring type units joined by six Zn2O2 ring type units. The bond lengths ˚ and 2.12 A ˚ , which are larger than in the case are 1.90 A of isomer (6a). The bond angle O–Zn–O varies from 136.50° to 137.01° which show still significant strain in the structure that makes it unfavourable. It is very important to note here that the binding energy difference between the quasiplanar (6a) and the 3-dimensional (6b) isomers becomes very small in comparison to those found in the isomers of Zn5O5 and Zn4O4. In the present case it is only 0.14 eV, which indicates very significant increase in the tendency to form stable 3-dimensional structures. The difference between the HOMO–LUMO gap of (6a) and (6b) also reduces significantly in comparison to those found in the isomers of Zn5O5 and Zn4O4, which also strongly support this tendency. The isomer (6c) has four atoms with coordination number three and eight atoms with coordination number two. This local minimum structure is planar with ˚ and bond angle bond length varying from 1.79 to 1.86 A O–Zn–O varying from 83.80° to 156.63°. This structure is very slightly lower in binding energy from (6b) but has significantly higher HOMO–LUMO gap. Therefore this planar structure (6c) is quite competitive with the isomer (6a). The large variation in the O–Zn–O bond angles of isomer (6c) shows significant strain in this structure that make it unfavorable but the small energy difference suggests that the cost of the strain has reduced significantly. The existence of this local minimum structure is very significant to understand that most favourable structure is still quasiplanar similar to (5a), not in a significantly 3-dimensional regime. Both (6b) and (6c) isomers have almost similar binding energies that are only 0.14 and 0.15 eV/atom lower, respectively from (6a) but the significantly higher HOMO–LUMO gap of planar (6c) than the 3-dimensional isomer (6b) shows the preference for quasiplanar structures though there is certainly an incremental trend for relative preference for 3-dimensional regime with an increase in size. These results reflect the subtle difference in the bonding natures in clusters of II–VI compounds.
262
A. Jain et al. / Computational Materials Science 36 (2006) 258–262
The local minimum isomers (6d) and (6e) are both 3-dimensional structures. Their binding energies are significantly lower than the binding energy of (6a) and also have very low values of HOMO–LUMO gaps. Therefore, they are much less stable and not favourable. The HOMO–LUMO gap for n P 3 is nearly the same with the value close to 3 eV within GGA. Therefore, compared with bulk, this is a higher gap as one can expect. Also the binding energy of the clusters is significantly lower than the bulk value as expected.
4. Summary In summary, we have studied the structures and properties of small zinc oxide clusters using ab initio calculations based on ultrasoft pseudopotentials scheme. The most favourable atomic structures of (ZnO)n clusters (n = 1–6) are ring type. For n = 1–4 the ring is planar but for n = 5 and 6 the rings are slightly bent acquire chair shapes. The binding energy difference between the most favourable quasiplanar structure of (ZnO)6 and its nearest 3-dimesional local minimum is small and our results show that there is difference in the bonding nature in clusters of ZnO and other II–VI compound semiconductors. Also our results are indicative for an increasing trend for the relative preference for 3-dimensional structures to be more stable with an increase in size. The HOMO–LUMO gap for n = 1 and 2 is significantly smaller than other clusters which is contrary to the general behavior in elemental semiconductors.
Acknowledgements The authors would like to thank the staff of the Center for Computational Materials Science at the Institute for Materials Research, Tohoku University for making the Hitachi SR8000/64 parallel machines available and for their cooperation. A.J. is grateful for the support of the Japan Society for the Promotion of Science. V. K. thankfully acknowledges the kind hospitality at the Institute for Materials Research.
References [1] A. Kampmann, D. Lincot, J. Electroanal. Chem. 418 (1996) 73. [2] Y.Y. Loginov, K. Durose, H.M. Al-Allak, S.A. Galloway, S. Oktik, A.W. Brinkman, H. Richter, D. Bonnet, J. Cryst. Growth 161 (1996) 159. [3] A. Niemegeers, M. Burgelman, J. Appl. Phys. 81 (1997) 2881. [4] K. Li, A.T.S. Wee, J. Lin, K.L. Tan, L. Zhou, S.F.Y. Li, Z.C. Feng, H.C. Chou, S. Kamra, A. Rohatgi, J. Mater. Sci.: Mater. Electron. 8 (1997) 125. [5] C. Ferekides, J. Britt, Sol. Energy Mater. Sol. Cells 35 (1994) 255. [6] H.C. Chou, A. Rohatgi, N.M. Jokerst, S. Kamra, S.R. Stock, S.L. Lowrie, R.K. Ahrenkiel, D.H. Levi, Mater. Chem. Phys. 43 (1996) 178. [7] S. Naseem, D. Nazir, R. Mumtaz, K. Hussain, J. Mater. Sci. Technol. 12 (1996) 89. [8] J. Touukova, D. Kindl, J. Tousek, Thin Solid Films 293 (1997) 272. [9] T.L. Chu, S.S. Chu, Solid State Electron. 38 (1995) 533. [10] P.J. Sebastian, M. Ocampo, Sol. Energy Mater. Sol. Cells 44 (1996) 1. [11] A.J. Hoffman, G. Mills, H. Yee, M.R. Hoffmann, J. Phys. Chem. 96 (1992) 5546. [12] S. Kuwabata, K. Nishida, R. Tsuda, H. Inoue, H. Yoneyama, J. Electrochem. Soc. 141 (1994) 1498. [13] E. Corcoran, Sci. Am. 263 (11) (1990) 74. [14] P. Schroer, P. Kruger, J. Pollmann, Phys. Rev. B 47 (1993) 6971. [15] D. Vogel, P. Kruger, J. Pollmann, Phys. Rev. B 52 (1995) R14316. [16] M.E. Zandler, E.C. Behrman, M.B. Arrasmith, J.R. Myers, T.V. Smith, J. Mol. Struc. (Theochem) 362 (1996) 215. [17] M. Usuda, N. Hamada, T. Kotani, M.V. Schilfgaarde, Phys. Rev. B 66 (2002) 125101. [18] H. Li, T.M. Briere, K. Shimomura, R. Kadono, K. Nishiyama, K. Nagamine, T.P. Das, Physica B 326 (2003) 133. [19] B. Meyer, D. Marx, Phys. Rev. B 67 (2003) 035403. [20] L.G. Wang, A. Zunger, Phys. Rev. Lett. 90 (2003) 256401. [21] P.X. Gao, Z.L. Wang, Appl. Phys. Lett. 84 (2004) 2883. [22] D.P. Norton, Y.W. Heo, M.P. Ivill, K. Ip, S.J. Pearton, M.F. Chisholm, T. Steiner, Materials Today, June 2004, 34pp. [23] Z.L. Wang, Materials Today, June 2004, 26pp. [24] H. Ohta, H. Hosono, Materials Today, June 2004, 42pp. [25] S.J. Pearton, D.P. Norton, K. Ip, Y.W. Heo, J. Vac. Sci. Technol. B 22 (2004) 932. [26] G. Kresse, J. Hafner, J. Phys.: Condens. Matter. 4 (1994) 8245; G. Kresse, J. Furthmu¨ller, Phys. Rev. B 54 (1996) 11169; D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [27] J.E. Jaffe, J.A. Snyder, Z. Lin, A.C. Hess, Phys. Rev. B 62 (2000) 1660. [28] A. Kasuya, R. Sivamohan, Y. Barnakov, I. Dmitruk, T. Nirasawa, V. Romanyuk, V. Kumar, S. Mamykin, K. Tohji, B. Jeyadevan, K. Shinoda, T. Kudo, O. Terasaki, Z. Liu, R. Belosludov, V. Sundararajan, Y. Kawazoe, Nature Mater. 4 (2004) 99.