Electronic and Structural Properties of Ultrathin SiO2 Nanowires - The

Article pubs.acs.org/JPCC

Electronic and Structural Properties of Ultrathin SiO2 Nanowires Shin-Pon Ju,* Ken-Huang Lin, and Kuan-Fu Lin Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan ABSTRACT: The simulated annealing basin-hopping (SABH) method incorporating the penalty function was used to predict the lowest-energy structures for SiO 2 nanowires of different sizes. The eight lowest-energy structures for different nanowire sizes were predicted, including two-, three-, four-, and five-membered structures (2MR, 2MR-2O, 3MR-3O, 4MR-4O, and 5MR-5O), 4MR-3facet, 4MR-4facet, and 4MR-5facet (4MR-3f, 4MR-4f, and 4MR-5f). A previous experimental study (Liu et al. ACS Nano 2009, 3 (5), 1160−1166) successfully synthesized silica nanotubes in a confined CNT cylindrical space and found various structures along a range of CNT diameters from 1.2 to 1.4 nm. At diameters larger than 1.7 nm, a disordered structure formed, different from the double-ladder SiO2 structures. This simulation’s predicted structures are in good agreement with this experimental result for 4MR and 5MR structures. In addition, this work predicted 4MR-3f, 4MR-4f, and 4MR-5f structures, which were not found in previous experimental work. Finally, we further investigate the structural and electronic properties of these ultrathin silica nanowires by density functional theory (DFT) calculation.

■

oxidation on Si wafers;4 they compared the influence of catalytic and noncatalytic growth. Their unique bicyclic chain structures appeared as nanowires grown with no catalyst, and in additional growth stages, the nanowire structures revealed a smoother and more uniform morphology. Colorado et al.5 and Lee et al.6 prepared SiO2 nanotubes by using functional singlewalled carbon nanotubes (SWCNTs) as model wafers, and Wang et al.7 based their method on phase separation via the traditional electrospinning technique to fabricate SiO2 nanotube structures. Furthermore, Liu et al.8 synthesized structures formed inside the carbon nanotube by encapsulation of H8Si8O12. A four-membered nanowire was synthesized when they enhanced the diameter of the carbon nanotubes along a range from 1.2 to 1.4 nm, called double ladder structures. A disordered structure was formed when the diameter of carbon nanotubes exceeded 1.7 nm. In addition to experimental studies, many researchers have used simulation techniques to investigate structural and electronic properties. Chernozatonskii et al.9 used density functional theory (DFT) to study SiO2 nanotube junctions as a coating for carbon nanotube and calculated the electronic characteristics. Results show that SiO2 coating does not influence the electronic properties of CNTs around the Fermi level. They concluded that the proposed composite structures offer protection of CNTs from the effects of the ambient environment. Wei et al.10 carried out research on the hydrolysis stabilities of silica molecular chains by DFT calculation. The results demonstrate that hydrolysis for the linear molecular chains first takes place in the middle and

INTRODUCTION Since the carbon nanotube (CNT) was discovered in the 1990s, the preparation and the characteristics of one-dimensional nanomaterials have attracted much research. Onedimensional nanomaterials are used in electronic devices because the material possesses fine electronic and mechanical properties.1 Generally, the most common structure, that of silica including α-quartz, is composed of a fundamental structural unit, the SiO4 tetrahedron. Oxygen atoms are bound to silicon atoms and connect to form the silica tetrahedron, with the O−Si−O angles close to the ideal tetrahedral bond angle of 109.5°. Because the Si−O−Si angles have more variety, bulk SiO2 formed in different crystal phases, such as the Si−O−Si angles in SiO2 bulk form 146° angles in quartz and 181° angles in β-cristobalite. Several-membered rings can be formed by bending the Si−O−Si angles such that the structures such as silica rods, clusters, rings, chains, nanowires, and nanotubes can be constructed. Among all available one-dimensional nanomaterials, SiO2 nanowires find application in high strength light sources and light-emitting diodes (LED) because of their important property of photoluminescence (PL)2−4. Yu et al.2 used the exciter laser ablation method to synthesize amorphous SiO2 nanowires and found that the blue light emission intensity was at an energy around 2.65 and 3 eV. In addition, another method by Li et al. aligned a great number of SiO2 nanotubes and SiO2 nanowires on an anodic alumina slab employing the sol−gel method.3 They used this method to synthesize different long and aligned nanotubes or nanowires by comprising different composition layers and also employed the EDX spectrum to reveal the composition of silicon oxide. Kar et al. synthesized long amorphous silica nanowires on a large-scale by the method employing MgO and graphite powder through thermal © 2012 American Chemical Society

Received: September 30, 2011 Revised: December 7, 2011 Published: January 11, 2012 3918

dx.doi.org/10.1021/jp209436r | J. Phys. Chem. C 2012, 116, 3918−3927

The Journal of Physical Chemistry C

Article

the Buckingham potential with the Coulomb interaction as shown in the following equation:

moves gradually to the ends; however, molecular rings have lower hydrolytic stability than linear molecular chains. In electronic and catalytic studies, Singh et al.11 employed DFT to study ground state structures and electronic properties of SiO and SiO2 nanotubes. They demonstrated that the pentagonal SiO nanotubes are the most stable structures and possess semiconducting properties; however, SiO2 nanotube insulation qualities are quite similar to bulk. Building on experimental results that have shown that new SiO2 structures can be successfully synthesized in confined cylindrical spaces of different sizes, this study predicts possible stable SiO2 nanowire structures of different sizes by the simulated annealing basin-hopping (SABH) method12 with an inclusion of the penalty function. This method offers a limited function that reflects the different confined spaces and simulates the SiO2 nanowires being synthesized. The material properties of SiO2 nanowires can be very different at different sizes. Unlike previous studies, we obtained helical nanowires (4MR-3f, 4MR-4f, and 4MR-5f) as a new predicted structure. These stable SiO2 nanowires obtained by SABH were further investigated by the DFT calculation. Finally, we analyzed their electronic orbitals and deformation density to understand the differences between the SiO2 nanowire and helical nanowire structures.

■

E FB =

⎧ Cij ZiZj ⎫ ⎪ ⎪ rij / ρij ⎨ ⎬ − + ∑ ⎪Aij e 6 ⎪ r r ij ij ⎭ i≠j ⎩

(1)

where rij is the distance between i and j atoms. The partial charges Z of the Coulomb term are +2.4e for the silicon atoms and −1.2e for the oxygen atoms. Aij, ρij, and Cij are the parameters of Buckingham potential, which are all listed in Table 1. Since the coordinates of atoms are randomly assigned Table 1. Parameters of FB and Lennard-Jones Potential i−j

Aij (eV)

Bij (Å)

Cij (Å6 eV)

εij (Å6 eV)

σij (Å)

Si−Si O−O Si−O

79502.113 1428.406 10454.202

0.201 0.358 0.208

446.78 41.374 63.047

0.002 0.002 0.019

2.05 2.05 1.36

during the SABH optimization process, the repulsive energies determined from Buckingham potential are not enough to overcome the stronger attractive energy from Coulomb interaction when the distance of an atomic pair with opposite charges is shorter than 1 Å, which leads to the energy of the structure being unable to converge to a minimum state. As a result, Lennard-Jones (18-6) potential is added in the original interatomic potential to eliminate this situation. The modified potential, therefore, is given by

SIMULATION METHOD

⎡⎛ ⎞18 ⎛ ⎞6⎤ σij ⎥ ⎢ σij FB Eij = Eij + 4εij⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥ ⎝ rij ⎠ ⎥⎦ ⎢⎣⎝ rij ⎠

Density functional theory and molecular statics theory have been employed to investigate the effect of diameter on the structural stability and electronic properties of silica nanowires. Above all, the most important step is to obtain an energetically favorable configuration of the silica nanowire before determining the nanowire properties. Up to now, many global optimization algorithms have been successfully developed to obtain such a favorable configuration, such as genetic algorithms,13 the big-bang method,14 and SABH global optimization algorithm.12 In the traditional BH method, a conjugate gradient method, was used to reach the local minimum, where a new geometry is generated. In our BH method, the conjugate gradient method was replaced by the limited memory BFGS method (LBFGS),15 which can be used to simulate a system consisting of a large number of atoms. Also, using the LBFGS method in the BH method is faster than the conjugate gradient method for a larger system. Furthermore, the simulated annealing (SA) method was also implemented with the BH method to be a SABH method, which includes a wider search domain within the potential energy surface. Therefore, we adopt the LBFGS method in SABH method to converge the system and reach the local minimum. Because the searched configurations are near spherical in geometry in three-dimensional space, we use SABH to combine the penalty function for the one-dimensional nanowire structures. For silica materials, FB potential16 was developed to predict properties of silica nanomaterials, and it has been proven that the predicted properties are more accurate than those by TTAM17 and BKS18 potential, in which potential parameters were fitted from bulk silica materials. FB potential incorporates

(2)

The energy parameter εij and the distance parameter σij can be obtained from ref 19. The adjustment of the parameters εij and σij was done in such a way so as to remain as close as possible to the original potential surface except in the immediate vicinity of the singularities to be eliminated. Furthermore, the penalty function is adopted in the SABH method, which is used to constrain all atoms within a cylindrical space with a specific cross-section radius. The formula of penalty method is shown as follows: ⎧

⎪ EiP = Ei + c × pi ⎨

c = 0,

xi 2 + yi 2 < r02

⎪ c = constant, xi 2 + y 2 ≥ r02 ⎩ i

(3)

where pi = [xi 2 + yi 2 − r02]2

(4)

Ei is the energy of atom i calculated by FB potential, and pi is the penalty potential as shown in eq 4. The pi is applied to atom i only if atom i is located outside the radius of the nanowire (r0). Parameters xi and yi are the coordinates of atom i in the x and y directions; c is defined to discriminate whether the atom is in the wire radius range. The formula of the penalty potential can be defined as any form that provides a constraint condition of the simulation model. In addition, DFT theory was employed to optimize the configurations from the SABH method and obtain the most stable geometries for different sizes of silica nanowires. All DFT calculations reported in this work were carried out with the CASTEP planewave code. The 3919



Article

the Si−O bonding band formed by the hybridization of O 2p, Si 3s, and Si 3p orbitals. The 2p lone-pair electrons of O atoms with a small amount of Si 3p electron form a nonbonding band ranging from 0 to −4 eV. These bonding and nonbonding orbitals can be also seen in the insets of Figure 1b. In terms of the bonding bands, those between −4 and −9.5 eV are dominant because of the contribution of the O atom p orbital and Si atom s orbital, which can be seen in the orbital shown at −5.2 eV. Because the leftmost bands of all nanowires are mainly formed by O 2s orbitals and do not change significantly, only the PDOS changes in the bonding and nonbonding bands of all nanowires are discussed in this study. To investigate the geometrical information of silica nanowires, panels a of Figures 2−9 show the cross-section and side views of seven stable ultrathin silica nanowires of different sizes obtained by the procedure introduced in the simulation method section. The corresponding binding energy, band gap, and diameter of each silica nanowire and the Mulliken charges of Si and O atoms are listed in Table 3. These data are compared

exchange−correlation interaction was treated within the generalized gradient approximation (GGA)20 using the Perdew−Burke−Erzen (PBE) scheme.21 During the geometry optimization process, the convergent conditions were set as 0.001 Ǻ for the atomic displacement, 10−5 eV/atom for the energy change, and 340 eV for the plane-wave cut off energy.

■

RESULTS AND DISCUSSION In order to provide a comparison between quartz and different silica nanowires, the unit cell structure and projected density of states (PDOS) of quartz are displayed in Figure 1a,b,

Table 3. Binding Energy, Diameter, and Mulliken Charge for Different Sizes of Silica Unit Cell Mulliken charge binding energy (eV/ SiO2 unit)

diameter (Å)

Si

OA

OC

−17.236 −17.489

2.363 4.104

2.24 2.21

−1.12 −1.10

−1.12 −1.11

−18.151

5.148

2.30

−1.16

−1.14

−18.084 −18.242

5.335 6.222

2.29 2.33

−1.16 −1.19

−1.13 −1.14

−18.191 −18.250

6.417 7.230

2.32 2.34

−1.19 −1.20

−1.13 −1.14

−18.111 −18.601

7.580

2.30 2.38

−1.18 −1.19

−1.12 −1.19

2MR 2MR2O 3MR3O 4MR-3f 4MR4O 4MR-4f 5MR5O 4MR-5f quartz

with the DFT calculation results of quartz, listed at the bottom of Table 3. In Figure 10, it can be seen that the binding energy displays a significant increase with increasing the wire radius. When the radius is larger than about 5 Å, the binding energy represents a zig−zag variation with increasing radius, in which the binding energies of the helical structures (4MR-3f, 4MR-4f ,and 4MR-5f) are slightly lower than those of the nonhelical structures. Because there are two different types of O atoms for some silica nanowires, these O atoms are labeled with different capital letters to show their Mulliken charge, and the corresponding Si and O atoms can be found in panels a of Figures 2−8. These silica nanowires are designated by different

Figure 1. (a) Quartz. (b) Projected density of states of quartz. (c) Deformation density of quartz.

respectively. The band energy ranges are in agreement with those in previous theoretical studies22−25 and the experimental approach as listed in Table 2.26 The leftmost band stems from the core 2s atomic orbital of the O atom with a small amount of Si 3s and 3p electron . The band between −4.2 and −9.5 eV is

Table 2. Lattice Constants, Band Gap, and Structural Parameters of α Quartz lattice constant (Å) this work

experiment a

a

c

5.027 5.018a 4.815b 4.916i

5.489 5.505a 5.338b 5.405i

band gap (eV) 5.743 5.5a 5.59−6.4b,c,d,e,f 9−9.1g,h

bond length (Å)

bond angle (deg)

Si−O

O−O

Si−Si

Si−O−Si

O−Si−O

1.620 1.60a 1.616−1.631c,d,e 1.609i

2.645−2.650

3.115

2.637e 2.612−2.645i

3.061e 3.058i

147.98 144a 143.03−144.97d,e 143.73i

109.61 109.47a 109.48d,e 108.81−110.52i

Reference 28. bReference 29. cReference 30. dReference 25. eReference 24. fReference 31. gReference 32. hReference 33. iReference 34. 3920



Article

terms according to their geometrical characteristics and will be introduced in the text. The geometrical characteristics of the distances between different atomic pairs and bending angles are summarized in Tables 4 and 5, respectively. The values of SiA−SiB, OA−OB, Table 4. Geometry Characteristics (Distance,Å) 2MR 2MR-2O 3MR-3O 4MR-3f 4MR-4O 4MR-4f 5MR-5O 4MR-5f quartz

SiA−SiB

SiB−SiC

OA−OB

OA−OC

SiA−OA

SiB−OC

2.349 2.353 2.991 3.082 3.191 3.205 3.222 3.249 3.115

2.351 2.794 2.814 2.770 2.812 2.793 2.819 2.790 3.115

2.363 2.365 2.625 2.653 2.652 2.647 2.674 2.656 2.645

2.835 2.749 2.644 2.636 2.630 2.627 2.624 2.650 2.650

1.666 1.668 1.632 1.629 1.620 1.617 1.613 1.629 1.611

1.666 1.649 1.643 1.648 1.646 1.646 1.646 1.664 1.611

Table 5. Bending Angles (deg) 2MR 2MR-2O 3MR-3O 4MR_3f 4MR-4O 4MR_4f 5MR-5O 4MR-5f quartz

SiA−OA−SiB

OA−SiA−OB

SiB−OC−SiC

OC−SiB−OD

89.7 89.7 132.9 142.2 160.1 162.9 178.4 170.7 148.0

90.3 90.3 107.1 109.1 109.9 109.9 109.6 109.1 109.6

89.7 115.9 118.0 114.1 117.4 116.1 117.9 113.8

90.3 115.9 118.0 119.2 117.4 118.1 117.9 118.5

and SiA−OA in the first, third, and fifth columns stand for the distances of Si−Si, O−O, and Si−O pairs within a ring. The values in the other three columns show the distances from a Si atom or an O atom in a ring to the nearest Si or O atoms outside this ring. Bond distances and bending angles listed in Tables 3 and 4 will be used to introduce the geometrical characteristics of different silica nanowires in the following text. The two-membered ring (2MR) silica nanowire with the diameter of 2.363 Å is the thinnest silica nanowire, and its snapshot is shown in Figure 2a. The two-membered rings are connected by the corner-sharing Si atoms to form a 2MR silica nanowire with the normal vector of each two-membered ring plane vertical to those of its two nearest two-membered ring planes. For the bending angles of a two-membered ring, SiA− OA−SiB and OA−SiA−OB are 58.3° and 19.3° smaller than those of quartz, so the SiA−SiB and OA−OB distances within a 2-memembed ring are shorter than those of quartz by 0.77 and 0.28 Å. From the Mulliken charge analysis, lower charge values of Si and O atoms indicate that the 2MR silica nanowire is less ionic than quartz. Since both the bond lengths and bending angles display considerable discrepancies with those of quartz, the 2MR silica nanowire is regarded as a highly strained structure, which leads to the hybridization of bonding and nonbonding bands.22 In the PDOS plot of Figure 2b, one can see that the energy gap between the O−Si bonding band and the O lone-pair nonbonding band for quartz disappears, resulting in a hybridization of bonding and nonbonding bands as shown in the orbital plot at −4 eV, at which the electrons are accumulated between Si and O atoms. This hybrid band mainly comes from the mixture of the p orbitals of the Si and O atoms. The planar 2 MR and a shorter O−O distance

Figure 2. (a) 2MR. (b) Projected density of states of 2MR (SiA−OA). (c) Deformation density of 2MR.

also enhanced the hybridization of the orbitals of lone-pair electrons in quartz.26 The band between the energy ranges higher than that of the hybridization band still remains the nonbonding one, and the PDOS plot for the nonbonding band becomes more pronounced than the nonbonding band in quartz. Past studies demonstrated that the distance of the O−O pair has a considerable influence on the shape of nonbonding bands of silica.24 Since the second nearest distance of O−O pair in 2MR silica nanowire is longer than that of quartz by 0.19 Å, the lone-pair electrons of O atoms tend to be in the atomic orbital as an isolated O atom. Other bonding and nonbonding orbitals are also shown in the insets of Figure 2b. At −5.5 eV, the orbital plot also displays a bonding characteristic, whereas the nonbonding feature can be seen from the orbital at −2.5 eV, where the lone-pair p orbitals are perpendicular to the 2MR. The snapshot of the 2MR-2O silica nanowire is shown in Figure 3a. This nanowire is formed by the connection of twomembered rings at the two Si atoms of each 2MR by two bridging O atoms. This silica nanowire is the second thinnest silica nanowire, with a diameter of 4.104 Å, and the 2MR part is still as square as those of the 2MR silica nanowire. Because the bending angles of SiA−OA−SiB (89.7°) and SiB−OC−SiC (115.9°) are different, there are two different types of O atoms in this 2MR-2O silica nanowire; namely, O atoms within the 2MR and those bridging the two 2MRs. This also leads to different electronic properties for these two O atoms. Figure 3b,c shows the projected density of states (PDOS) for OA and 3921



Article

3c. At −4 eV, the orbital and PDOS plots in Figure 3b indicate that OA atoms contribute more to these nonbonding bands. In terms of the bonding band, those between −6 and −9.1 eV are dominant from the contribution of OC atoms, which can be seen in the orbital shown at −7.2 eV. At −5 eV, both OA and OC atoms contribute to the total DOS. The orbital splitting between OA and OC atoms also indicates that the orbital mixture between the OA and OB atoms is very weak because the OA−OC distance is longer than that of the OA−OB pair both in the two-membered ring and in quartz. Because the SiB−OC bond is slightly shorter than SiA−OA, the electron overlap is stronger between SiB and OC atoms, resulting in a more negative Mulliken charge on OC atoms than on OA atoms. The snapshot of a 3MR-3O nanowire with diameter of 5.148 Å is shown in Figure 4a. This nanowire is composed of threemembered rings (3MR) oriented in parallel, at which each Si atom of a 3MR is linked with the Si atom of the two nearest 3MRs by a bridging O atom. The PDOS plots of two different O atoms as well as the Si atom are shown in Figure 4b,c. The bonding band can be seen in the orbital plot at −4.5 eV. The bonding band is between −4.5 and −8.7 eV, and the nonbonding band is located from 0 to −4.5 eV. One can also see that OA and OC atoms contribute to different parts of the total DOS plot. The 4MR-3facets (4MR-3f) nanowire with diameter of 5.335 Å is formed by the connection of a unit of three helically twisted 4MR facets along the wire axis, where all Si atoms are shared by the four nearest 4MR facets. The diameter of this nanowire is very close to that of the 3MR-3O type. There are two O types in this nanowire, namely, OA (or OB) type and OC (or OD) type. Each OA type atom links two Si atoms along the radial direction, while every OC type atom links two Si atoms along the axial direction. Figure 5b,c shows the PDOS of OA and OC types with the Si atom and total density of states. It is clear that a small energy gap appears between the bonding Si− O band and the nonbonding O lone-pair electron band around −3.2 eV, as can be seen in the case of quartz. This is because the geometrical characteristics of bending angles, SiA−OA−SiB and OA−SiA−OB, of the 4MR-3f nanowire are very close to those of quartz. The OC−SiB−OD angle (119.2°) is larger than the O−Si−O angle (109.6°) of quartz, leading to a slightly distorted SiO4 tetrahedron at the OC−SiB−OD angle, resulting in a reduction in an energy gap between the bonding and nonbonding bands. The bonding orbitals can be seen at −3.8 eV in Figure 5c and at −7.1 eV in Figure 5b. The nonbonding characteristic can also be seen at −0.8 and −2.5 eV for the nonbonding orbitals. From the orbital and PDOS plots, OA and OC atoms contribute to different bands of the total DOS. The 4MR-4O silica nanowire is the predicted structure in this work that is in agreement with experimental results. The structure of 4MR-4O with diameter of 6.222 Å is shown in Figure 6a and is formed by the connection of four-membered rings at the four Si atoms of each 4MR by four bridging O atoms. There are also two O types in this nanowire, OA (or OB) type and OC (or OD) type. Every OC type atom links two Si atoms along the axial direction. We can observe that the combination of OA−SiA−OB angle (109.9°) and the SiA−OA− SiB angle (160.1°) of 4MR-4O type constructs a square geometry. Furthermore, the OC atoms connect each 4MR, making this wire like a “ladder”. Figure 6b,c shows the PDOS of OA and OC types with the Si atom and total density of states. The bonding orbitals can be seen at −4 eV in Figure 6c and at −7 eV in Figure 6b. The nonbonding characteristic can also be

Figure 3. (a) 2MR-2O. (b) Projected density of states of 2MR-2O (SiA−OA). (c) Projected density of states of 2MR-2O (SiB−OC). (d) Deformation density of 2MR-2O.

OC atoms, respectively. The orbitals of different bands can also be seen in the insets of Figure 3b,c. The orbital at −5 eV in Figure 3c shows a bonding characteristic, so the bands at energies higher than −5 eV belong to nonbonding ones and those between −5 and −9.1 eV are bonding bands. From Figure 3b,c, one can see that the contribution to total DOS at different bands from OA and OC are different. For nonbonding bands, OA atoms mainly contribute to the band from 0 to −1.5 eV and a clear build-up of electron density at OA sites can be found in the orbital plot at −1 eV in Figure 3b. From −1.5 to −3.5 eV, OC atoms contribute more to the total DOS, which can be seen in the orbital insets at −2.5 and −3.3 eV in Figure 3922



Article


Figure 5. (a) 4MR-3f. (b) Projected density of states of 4MR-3f (SiA− OA). (c) Projected density of states of 4MR-3f (SiB−OC). (d) Deformation density of 4MR-3f.

seen at −0.5 and −2.5 eV for the nonbonding orbitals. OA and OC atoms contribute to different bands of the total DOS as show in the orbital and PDOS plots. The 4MR-4facets (4MR-4f) silica nanowire with diameter of 6.417 Å is shown in Figure 7a. The difference of diameter between this nanowire and 4MR-4O type is only 0.2 Å. There are also OA (or OB) type and OC (or OD) type in this nanowire. Each OA type atom links two Si atoms along the radial direction, while every OC type atom links two Si atoms along the axial direction. For the bending angles of a four-membered ring, the angles of SiA−OA−SiB, OA−SiA−OB, SiB−OC−SiC, and OC−SiB−OD are 162.9°, 109.9°, 116.1°, and 118.1°, respec-

tively. These angles are very close to the 4MR-4O type. In addition, the distances of SiA−OA and SiB−Oc within a fourmembered ring are also close to the 4MR-4O type. In the PDOS plot of Figure 7b,c, the bonding band is between −3.8 and −9.1 eV, and the nonbonding band is located from 0 eV to −3.8 eV. In addition, the bonding orbitals can be seen at −8 eV in Figure 7b and at −4 eV in Figure 7c. The nonbonding characteristic can also be seen at −0.8 and −1.3 eV for the nonbonding orbitals. Besides, we can observe that the OA and OC atoms contribute to different bands of the total DOS in the orbital and PDOS plots. 3923



Article



Past studies have shown that the geometry of the silica 4MR4O type nanowire is very similar to the double ladder structure that has been synthesized by encapsulation of H8Si8O12.8 According to the experimental outcome, when the diameter of the silica nanowire is increased, disordered and even amorphous structures form. In our simulation, for a nanowire with a radius larger than the 5MR-5O nanowire, the structures were all found to be amorphous by the BH procedure, which is in agreement with experimental results. The structure of 5MR5O silica nanowire with diameter of 7.23 Å is shown in Figure 8a and is formed by the connection of five-membered rings at

the five Si atoms of each 5MR by five bridging O atoms. The ring is pentagonal in configuration from axis view side. The angle of SiA−OA−SiB is near 180°, and SiB−OC−SiC and OC− SiB−OD are both similar. This indicates that the five-membered rings are very symmetric. Figure 8b,c shows the projected density of states (PDOS) for OA and OC atoms, respectively, with the insets showing orbitals of different bands. The orbital at −5.1 eV in Figure 8c shows a bonding character, so the bands at energies higher than −5.1 eV belong to nonbonding ones and those between −5.1 and −9.2 eV are bonding bands. In terms of the bonding bands, those between −6.2 and −9.1 3924



Article



eV are dominant from the contribution of OA atoms, which can be seen in the orbital shown at −6.8 eV. At −5.1 eV, both OA and OC atoms contribute to the total DOS. For the OA atoms, the negative Mulliken charge is more than OC atoms, because the SiA−OA bond is slightly shorter than SiB−OC, and the electron overlap is stronger between SiA and OA atoms. The 4MR-5facets (4MR-5f) silica nanowire is the largest in our calculations, with a diameter of 7.58 Å, and is shown in Figure 9a. The 4MR-5f type is very similar to 4MR-4f, with both OA (or OB) type and OC (or OD) type. Each OA type

atom links two Si atoms along the radial direction, while every OC type atom links two Si atoms along the axial direction. For the bending angles of a four-membered ring, the SiA−OA−SiB, OA−SiA−OB, SiB−OC−SiC, and OC−SiB−OD angles are 170.7°, 109.1°, 113.9°, and 118.5°, respectively. In addition, the distances of OA−Oc within a four-membered ring are the same as quartz. The PDOS for OA and OC atoms are shown in Figure 9b,c, respectively. The bonding band is in the range from −4 to −9.3 eV, and the bands at energies higher than −4 eV belong to the nonbonding band. It can also be seen that OA 3925



Article

research, as well as those found in nature.27−28 We can observe that the relative energy of 2MR and 2MR-2O nanowires have the greatest difference from quartz. Compared with the tetragonal 2D film, the relative energy of 3MR, 4MR, and 5MR types become closer to quartz with an increase in size, namely, diameter.

and OC atoms contribute to different parts of the total DOS plot in every illustration. Further investigation of the structural differences between nanowires of different sizes is shown in Tables 3 and 4, where one can see that the bending angles of OA−SiA−OB, SiB−OC− SiC, and OC−SiB−OD do not change significantly as the diameter of the nanowire is increase from that of 2MR-2O. This also leads to the smaller bond length changes for SiB−SiC, OA−OB, and OA−OC pairs for nanowires larger than 2MR-2O. However, the SiA−OA−SiB angle increases considerably for larger nanowires, leading to a significant increase in the SiA−SiB bond length. Considering the variations of SiA−OA and SiB−OC distances, these two bonds are slightly longer than that of quartz because of the distorted tetrahedron at Si sites in nanowires. Because the OC−SiB−OD angles are larger than 109.6°, the tetrahedron at the OC−SiB−OD angle is relatively more distorted than OA−SiA−OB (about 109°). Consequently, the bond length of SiA−OA is slightly shorter than that of SiB− OC, leading to more negative charge at OA, as shown in Table 2. The charge deformation density is further investigated on the SiA−OA−SiB slice plane, because the SiA−OA−SiB angle changes significantly with the nanowire size. The deformation density of SiO2 nanowire structures for 2MR, 2MR-2O, 3MR-3O, 3MR3f, 4MR-4O, 4MR-4f, 5MR-5O, and 4MR-5f are shown in Figures 1c and 2c and Figures 3−9, panels d (top view). Deformation density is the difference between the electronic distributive density of the SiO2 nanowire and separate silicon and oxygen atoms. The electronic density increases while the equivalent value is positive, with the increase shown as the red region in each illustration. It is clear that after forming the chemical bonds, the electron transfers from Si to O atoms, and the electronic distribution density become more intensive on the O atom. This is supported by analysis of Mulliken charge, where the Si atoms carry the positive charges and the O atoms carry the negative charge. Finally, the plot in Figure 10

■

CONCLUSIONS We have investigated ground-state silica nanowires with different radii using both the SABH method incorporating the penalty method and density functional theory (DFT) calculations to obtain electronic properties of ultrathin silica nanowires. Not only is our simulated 4MR-4O nanowire in agreement with experiment results, but we also predict new structures of 4MR-3f, 4MR-4f, and 4MR-5f. A comparison of relative energies of various silica nanostructures shows that 2MR and 2MR-2O are similar to former research.35 The other structures obtained in this study are more stable than the stishovite and 2D films (Figure 11) found in studies28−34 and

Figure 11. Relative energies of various silica nanostructures.The relative energy of bulk material is given by red dotted lines, and those from simulation studies are given by blue dotted lines. The predicted structure energies relative to quartz in this work are given by black solid lines.

become closer to quartz and cristobalite as the size of the nanowires increases.36 The 4MR-5f nanowire, however, does not follow the size dependence trend, because when the diameter of nanowires is increased to a specific range, the wire will be disordered, a phenomenon also found in experimental results. This is why the 4MR-5f is not as stable as other small size nanowires. Calculations of bonding and nonbonding states connecting rings in each nanowire type demonstrate that the contributions of OA and OC atoms to density of state are different for each energy band. Deformation density shows that the electronic density around Si atoms drops clearly, representing the electron transfer from Si to O atoms. The results are also supported in the calculation of Mulliken charge. The predicted structures in this work are in agreement with experimental results that found SiO2 nanostructures were formed inside CNTs at different radii. In this study, the predicted structures including helical silica nanowires have implications for future experimental research when a cylindrical

Figure 10. The binding energies of various nanowire structures as a function of nanowire diameters.

represents the relative energy of a variety of dimensions, compositions, and geometries both in this work and other 3926



Article

(31) Sun, Q.; Wang, Q.; Kawazoe, Y.; Jena, P. Nanotechnology 2004, 15, 260. (32) Robertson, J. J. Vac. Sci. Technol. B 2000, 18, 1785. (33) Bosio, C.; Czaja, W.; Mertins, H. C. Europhys. Lett. 1992, 18, 319. (34) Levien, L.; Prewitt, C. T.; Weidner, D. J. Am. Mineral. 1980, 65, 920. (35) Xi, Z. X.; Zhao, M. W.; He, T.; Zhang, X. J.; Zhang, H. Y.; Wang, Z. H.; Hou, K. Y.; Fan, Y. C.; Liu, X. D.; Xia, Y. Y. Phys. Lett. A 2009, 373, 4376. (36) Chase, M. W.; Davies, C. A.; Downey, J. R.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. J. Phys. Chem. Ref. Data 1985, 14, 1.

nanoconfined space of any diameter can be produced, within which silica nanowires are synthesized.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

■

ACKNOWLEDGMENTS The authors thank the National Science Council of Taiwan, under Grant Nos. NSC98-2221-E-110-022-MY3, NSC98-2221E-344-001, and NSC99-2911-I-110-512, and National Center for Theoretical Sciences, Taiwan, for supporting this study.

■

REFERENCES

(1) Hirschman, K. D.; Tsybeskov, L.; Duttagupta, S. P.; Fauchet, P. M. Nature 1996, 384, 338. (2) Yu, D. P.; Hang, Q. L.; Ding, Y.; Zhang, H. Z.; Bai, Z. G.; Wang, J. J.; Zou, Y. H.; Qian, W.; Xiong, G. C.; Feng, S. Q. Appl. Phys. Lett. 1998, 73, 3076. (3) Li, S. H.; Zhu, X. F.; Zhao, Y. P. J. Phys. Chem. B 2004, 108, 17032. (4) Kar, S.; Chaudhuri, S. Solid State Commun. 2005, 133, 151. (5) Colorado, R.; Barron, A. R. Chem. Mater. 2004, 16, 2691. (6) Lee, K. G.; Wi, R.; Imran, M.; Park, T. J.; Lee, J.; Lee, S. Y.; Kim do, H. ACS Nano 2010, 4, 3933. (7) Wang, W.; Zhou, J. Y.; Zhang, S. S.; Song, J.; Duan, H. G.; Zhou, M.; Gong, C. S.; Bao, Z.; Lu, B. A.; Li, X. D.; Lan, W.; Xie, E. Q. J. Mater. Chem. 2010, 20, 9068. (8) Liu, Z.; Joung, S. K.; Okazaki, T.; Suenaga, K.; Hagiwara, Y.; Ohsuna, T.; Kuroda, K.; Iijima, S. ACS Nano 2009, 3, 1160. (9) Chernozatonskii, L. A.; Artyukhov, V. I.; Sorokin, P. B. Phys. Rev. B 2006, 74, 6. (10) Wei, X. F.; Zhang, D. J.; Liu, C. B. J. Mol. Struct.: Theochem 2008, 859, 1. (11) Singh, A. K.; Kumar, V.; Kawazoe, Y. Phys. Rev. B 2005, 72, 5. (12) Wales, D. J.; Doye, J. P. K J. Phys. Chem. A 1997, 101, 5111. (13) Woodley, S. M.; Battle, P. D.; Gale, J. D.; Catlow, C. R. A. Phys. Chem. Chem. Phys. 1999, 1, 2535. (14) Jackson, K. A.; Horoi, M.; Chaudhuri, I.; Frauenheim, T.; Shvartsburg, A. A. Phys. Rev. Lett. 2004, 93, 4. (15) Byrd, R. H.; Lu, P. H.; Nocedal, J.; Zhu, C. Y. Siam J. Sci. Comput. 1995, 16, 1190. (16) Flikkema, E.; Bromley, S. T. Chem. Phys. Lett. 2003, 378, 622. (17) Tsuneyuki, S.; Tsukada, M.; Aoki, H.; Matsui, Y. Phys. Rev. Lett. 1988, 61, 869. (18) Vanbeest, B. W. H.; Kramer, G. J.; Vansanten, R. A. Phys. Rev. Lett. 1990, 64, 1955. (19) Yu, J.; Devanathan, R.; Weber, W. J. J. Mater. Chem. 2009, 19, 3923. (20) Perdew, J. P.; Burke, K.; Wang, Y. Phys. Rev. B 1996, 54, 16533. (21) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (22) Binggeli, N.; Troullier, N.; Martins, J. L.; Chelikowsky, J. R. Phys. Rev. B 1991, 44, 4771. (23) Hamann, D. R. Phys. Rev. B 1997, 55, 14784. (24) Tamura, T.; Lu, G. H.; Yamamoto, R.; Kohyama, M. Phys. Rev. B 2004, 69, 10. (25) Tamura, T.; Ishibashi, S.; Tanaka, S.; Kohyama, M.; Lee, M. H. Phys. Rev. B 2008, 77, 8. (26) Fischer, B.; Pollak, R. A.; Distefano, T. H.; Grobman, W. D. Phys. Rev. B 1977, 15, 3193. (27) Hamann, D. R. Phys. Rev. Lett. 1996, 76, 660. (28) Artyukhov, V. I.; Chernozatonskii, L. A. J. Phys. Chem. C 2010, 114, 9678. (29) Luo, X.; Wang, B.; Zheng, Y. J. Appl. Phys. 2009, 106, 4. (30) Zhang, G.; Li, X.; Tung, C. H.; Pey, K. L.; Lo, G. Q. Appl. Phys. Lett. 2008, 93, 3. 3927


Electronic and Structural Properties of Ultrathin SiO2 Nanowires - The

Recommend Documents