Geometric and Electronic Structures of Hydrogen-Stabilized Silicon

Oct 16, 2007 - The geometric and electronic structures of hydrogen-stabilized silicon nitride (H−SiN) nanosheets and nanotubes with the stoichiometr...
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J. Phys. Chem. C 2007, 111, 16840-16845

Geometric and Electronic Structures of Hydrogen-Stabilized Silicon Nitride Nanosheets and Nanotubes Tao He, Mingwen Zhao,* Weifeng Li, Chen Song, Xiaohang Lin, Xiangdong Liu, Yueyuan Xia, and Liangmo Mei School of Physics and Microelectronics, Shandong UniVersity, Jinan 250100, China ReceiVed: June 18, 2007; In Final Form: August 16, 2007

The geometric and electronic structures of hydrogen-stabilized silicon nitride (H-SiN) nanosheets and nanotubes with the stoichiometry of HSiN were studied using first-principles calculations within density functional theory. The predicted H-SiN nanosheets present two-dimensional hexagonal characters, while the H-SiN nanotubes are built from rolling up the nanosheet, analogous to the cases of graphene and carbon nanotubes. The stable configurations of the H-SiN nanosheets and nanotubes considered in this work have different hydrogenation modes and surface structures. Their electronic properties are also addressed by performing band-structure calculations and Mulliken population analysis. This work is expected to provide vital information to the future synthesis and utilization of these materials in nanoscience and nanotechnology.

Introduction Silicon nitride is a material of great technological interest because of its superior mechanical and electronic properties that make it suitable for broad applications in numerous industries, such as aerospace, automotive, electronic, metal and mineral processing, machining, petrochemical, and so forth.1-5 Silicon nitride has high strength and hardness, strong resistance to corrosion and thermal shock, high dielectric constant, and strong resistance against radiation. Until now, three crystalline phases of silicon nitride with the stoichiometry of Si3N4 have been found, named as R-, β-, and c-Si3N4.6-13 These crystals possess different electronic properties. R- and β-Si3N4 are indirect bandgap semiconductors,12 whereas c-Si3N4 has a direct band gap at the Γ point.13 The synthesis of one-dimensional Si3N4 nanostructures, such as nanowires,16-19 nanofibers,20 nanobelts,21 nanowhiskers,22 and nanorods23 has been achieved via different approaches. Interestingly, the R-Si3N4 nanotubes with the outer diameter of ∼200 nm were obtained simultaneously in the synthesis of Si3N4 nanowires.16 Thereafter, Q. Wei et al.24 fabricated large-scale R-Si3N4 nanotubes by using a hot-wall chemical-vapor-deposition (CVD) method with the assistance of Ga2O3. F. Wang et al.25 synthesized R-Si3N4 nanotubes from a binary sol-gel route. F. H. Lin et al.26 obtained R-Si3N4 nanotubes at a relatively low temperature using a thermalheating CVD method. Although these nanotubes have crystalline R-Si3N4 tube walls with the thickness of tens of nanometers, which bear no resemblance to either multiwalled or singlewalled carbon nanotubes, they still draw people’s interests because of their potential applications in nanoscale photonics and electrics. Reducing the thickness of the tube wall, especially to a few atomic layers, becomes crucial in the future utility of these materials. It is worth noticing that an ultrathin Si3N4 film with a thickness of less than 3 nm has been grown on a Si(111) surface at low temperatures.27 The growth of a silicon nitride film with a stoichiometry close to SiN and film thickness between 2 and 10 nm has also been achieved using a so-called atomic-layer * Corresponding author. E-mail: [email protected].

controlled deposition technique 28. The realization of ultrathin silicon nitride films containing only a few atomic layers can thus be expected in the near future, probably benefiting from the development of the technique that has been used successfully in the growth of a silica single-atomic layer on a metal substrate.29 Of course, the atomic arrangement of these substratesupported ultrathin films may differ from that of the isolated films because of the structural confinement from the substrate, especially when covalent bonds are formed between the film and the substrate.27 However, if the substrate surface was passivated,28 then the interactions between the deposited film and the substrate are weaken because they arise mainly from van der Walls interactions. Under such conditions, the deposited film may resemble the isolated film in atomic arrangements. These ultrathin films may possess atomic arrangements and stoichiometries different from those of bulk materials and already-synthesized nanostructures of silicon nitrides. Additionally, hydrogen atoms coming from the NH3 or SiH4 source have been revealed to play an important role in the growth of silicon nitride nanomaterials by the CVD method.30,31 The hydrogen atoms passivating the dangling bonds on the surfaces of ultrathin silicon nitride films stabilize these films and thus favor their realization. More interestingly, starting from a silicon nitride single layer, ultrathin silicon nitride nanotubes can be built analogously to the formation of carbon nanotubes from a graphene sheet. The electronic properties of these nanostructures may significantly differ from those of either bulk materials or the already-synthesized nanostructures. To the best of our knowledge, neither experimental nor theoretical work of this issue has been reported to date. The present work is therefore carried out to investigate the geometric and electronic structures of the hydrogen-stabilized silicon nitride (H-SiN) nanosheets and nanotubes using first-principles calculations within density functional theory (DFT). The stable configurations of the H-SiN nanosheets and nanotubes with different hydrogenation modes and surface structures are predicted. The electronic properties of these nanostructures are addressed by performing band-structure calculations combined with partial density of states (PDOS) analysis. This work is expected to provide vital

10.1021/jp074731y CCC: $37.00 © 2007 American Chemical Society Published on Web 10/16/2007

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information to the future synthesis and utility of these materials in nanoscience and nanotechnology. Methods and Computational Details First-principles calculations based on density-functional theory (DFT) were performed with an efficient code known as SIESTA,32-34 which adopted the norm-conserving pseudopotentials35-37 to distinguish the behavior of valence electrons and atomic cores. The valence electron wave functions were expanded by a double-ζ basis set plus polarization functions (DZP). Generalized gradient approximation (GGA) in the form of Perdew, Burke, and Ernzerhof (PBE) was adopted for the exchange-correlation function.38 Numerical integrals were performed on a real space grid with an equivalent cutoff 100 Ry. For the H-SiN nanosheet, two-dimensional (2D) periodic boundary conditions were applied in the sheet plane (taken as x and y directions) and a sufficient vacuum space (up to 20 Å) was kept along the direction perpendicular to the sheet (z direction) to exclude the interaction between adjacent sheets. For the nanotubes, a one-dimensional (1D) periodic boundary condition along the axial direction was employed and a vacuum region of up to 20 Å along the radial direction was specified to ensure that isolated nanotubes were considered. The supercells used in the present work contain two atomic layers for the armchair tubes and four layers of atoms for the zigzag tubes. The Brillouin zone integrations were carried out by using k-point grids of 4 × 4 × 1 for the nanosheets and 1 × 1 × 8 for the tubes according to the Monkhorst-Pack scheme.39 All of the atomic positions along with the lattice vectors were optimized by using a conjugate gradient (CG) algorithm, until each component of the stress tensor was reduced to below 0.5 GPa and the maximum atomic force was less than 0.04 eV/Å. This scheme has been validated in the study of hydrogenated40 and nitrogen-doped silicon carbide nanotubes41 in our previous works. To evaluate the stability and plausibility of these nanostructures, we defined the formation energy (Eform) by the following formula

Eform ) (Etotal - nSi × µSi - nN × µN - nH × µH)/(nSi + n N + n H) where Etotal is the total energy per supercell of the H-SiN nanosheets or nanotubes, nSi (nN or nH) is the number of the Si (N or H) atoms per supercell, µSi, µN, and µH are the chemical potentials of Si, N, and H atoms at 0 K in bulk (diamond) silicon, N2 molecule, and H2 molecule respectively. Obviously, temperature effects are not taken into account in this definition. Results and Discussion We first calculated the equilibrium structure of bulk R-Si3N4 (P31/c) using three-dimensional (3D) periodic boundary conditions and the theoretical scheme described above. The supercell consists of 48 silicon atoms and 64 nitrogen atoms. The optimized lattice constants obtained from the present calculations are a ) 7.91 Å and c ) 5.74 Å, in good agreement with the experimental results: a ) 7.77 Å, c ) 5.62 Å.6 The Si-N bond length and the Si-N-Si bond angle are 1.77 Å and 119.7°, respectively, which also agree well with the experimental values (1.74 Å, 118.8°).7 The Eform value of the bulk R-Si3N4 is -1.26 eV/atom. Considering that the N atom has the tendency to form a graphene-like network, for example, in BN42,43 and BCN44,45 nanostructures as revealed both theoretically and experimentally,

Figure 1. Top and side views of H-SiN nanosheets with different hydrogen modes (a) sheet I and (b) sheet II.

we characterized the geometries of H-SiN nanosheets, in this contribution, by a 2D hexagonal grid consisting of silicon, nitride, and hydrogen atoms with the stoichiometry of HSiN. Silicon and nitrogen atoms are placed alternatively with each Si atom being threefold-coordinated by three N atoms and vice versa. Hydrogen atoms are incorporated into the nanosheet to passivate the dangling bonds on Si atoms. This hypothetic configuration has Si and N atoms being fully coordinated and thus high energetic favorability. The rationality of this configuration can also be evidenced by the experimental results that H atoms have a chemical preference to bind to Si rather than to the N atom in hydrogenated silicon nitride (a-SiNx:H) when the nitrogen content (x) is lower than 1.25.30 In this work, we considered two typical arrangements of the H atoms (hydrogenation mode). One has all of the H atoms located on one side of the nanosheet plane, labeled as the (1 × 1) mode as shown in Figure 1a. In another mode as shown in Figure 1b, the H atoms are placed alternatively on the two sides of the sheet, labeled as the (2 × 2) mode. Both configurations were fully relaxed without any symmetry restrictions using a conjugate gradient (CG) algorithm. A large supercell containing 48 atoms was employed to allow the possible surface relaxations of the sheet. The optimized configurations are presented in Figure 1a and b. The atomic arrangement of the (1 × 1) H-SiN nanosheet

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TABLE 1: Structural Parameters, Formation Energies (Eform), Energy Band Gaps (Eg), and Atomic Charges of the H-SiN Nanosheets, H-SiN Nanotubes, and Bulk r-Si3N4a R-Si3N4 R dSi-N dSi-H N-Si-N Si-N-Si N-Si-H Eform Eg atomic charge

1.77 (1.738b) 107.3 119.7 (118.8b)

(Si) (N)

-1.26 4.41 (5.1c) 0.88 -0.66

sheet I 1.78 1.52 110.7 110.7 108.3 -0.61 4.04e 0.85 -0.68

sheet II

(3,3)

(9,9)

(5,0)

(9,0)

1.77,1.79 1.51 108.5,112.8 112.9,123.3 108.6,109.6 -0.68 4.72d 0.92 -0.76

4.26 1.77,1.79 1.51 108.5,112.9 112.9,123.4 107.3,109.7 -0.68 4.73e 0.92 -0.76

9.00 1.77-1.79 1.50, 1.52 107.8-113.0 112.4-122.9 108.0-109.9 -0.68 4.66e 0.89 -0.74

4.20 1.77, 1.78 1.51 109.3,111.5 114.1,130.7 106.3,113.7 -0.69 4.78d 0.93 -0.78

6.16 1.76-1.79 1.50, 1.51 105.7-111.0 114.4-126.2 107.5-113.1 -0.70 4.86d 0.91 -0.77

a The bond lengths (dSi-N, dSi-H) and tube radii (R) are in angstroms. The bond angles (N-Si-N, Si-N-Si, N-Si-H) are in degrees. The formation energies are in eV/atom, and the band gaps are in eV. The atomic charges are in absolute value of unit charge (|e|). b Experimental result of ref 7. c Experimental result of refs 14 and 15. d Direct band gap. e Indirect band gap.

Figure 2. Stereographs of armchair and zigzag H-SiN nanotubes with different hydrogenation modes (a) (5,5)-OHM, (b) (5,5)-MHM, (c) (5,5)IHM, (d) (9,0)-OHM, (e) (9,0)-MHM, and (f) (9,0)-IHM.

(sheet I) exhibits a graphene-like symmetry. All of the Si (N or H) atoms lie on the same plane parallel to the sheet (Figure 1a). The average values of the Si-N bond lengths and the N-Si-N bond angles are 1.78 Å and 110.7°, respectively, close to those of bulk R-Si3N4 (1.77 Å and 107.3°). The average Si-H bond length and N-Si-H bond angle are 1.52 Å and 108.3°. For the (2 × 2) H-SiN nanosheet (sheet II), however, severe relaxation occurs along the direction perpendicular to the sheet plane, giving rise to rather rough surfaces (Figure 1b). The Si (N or H) atoms are no longer on the same plane. The average values of the Si-N and Si-H bond lengths and the N-Si-N and N-Si-H bond angles are close to those of sheet I, except that the Si-N-Si bond angle (118.1°) is closer to that of the bulk R-Si3N4 (119.7°) as compared to that of sheet I (110.7°) (see Table 1). This may be the reason that sheet II is energetically more favorable than sheet I by about 0.07 eV/ atom. The absolute value of Eform of sheet II is smaller than that of the stable form of silicon nitride (R-Si3N4 crystal) by about 0.58 eV/atom, implying the challenge of realizing the H-SiN nanosheet.46 However, when a H-SiN nanosheet was grown on a substrate, for example, silicon or metal surface, the interaction between the sheet and the substrate, which was

excluded in the present calculations, would facilitate the stability and accordingly the realization of the sheet. Moreover, hydrogen atoms are essential for the stabilization of the SiN nanosheet. Without hydrogen passivation, the SiN nanosheet will undergo severe surface relaxation and exhibit a strong tendency to form an amorphous structure, driven by the dangling bonds on the surfaces. On the basis of the H-SiN nanosheet, H-SiN nanotubes can be built analogously to the formation of carbon nanotubes from a graphene sheet. The as-designed H-SiN nanotubes exhibit chiral characteristics similar to those of carbon nanotubes and are accordingly labeled as armchair (n,n), zigzag (n,0), and chiral nanotubes. We focus on armchair and zigzag tubes in the present work. Three hydrogenation modes, named as outward (OHM), inward (IHM), and mixed hydrogenation modes (MHM), were considered. For the OHM, all of the hydrogen atoms bind to Si atoms from the exterior of the tubes, as shown in Figure 2a and d, whereas for the IHM the hydrogen atoms saturating the Si dangling bonds are placed in the interior of the tubes, as shown in Figure 2c and f. The MHM is the mixture of the OHM and IHM, and the hydrogen atoms locate in the exterior and interior of the tubes, as shown in Figure 2b and e. The optimized

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Figure 3. Top views of the most-stable configurations of (n,n) and (m,0) H-SiN nanotubes for n ) 2-9 and m ) 3-16.

configurations of the (5,5) and (9,0) H-SiN nanotubes with different hydrogenation modes are shown in Figure 2. It is obvious that the surface relaxation is remarkable in MHM, giving rise to rather buckled surfaces with abundant morphologies. We calculated the (n,n) and (m,0) tubes with different hydrogenation modes for n ) 2-9, m ) 3-16. The optimized configurations and the corresponding Eform are plotted in Figures 3 and 4. The Eform value of armchair and zigzag H-SiN nanotubes with IHM decreases with the increase of tube radius and has the tendency to saturate to a value corresponding to the Eform of sheet I. For both the (n,n) and (m,0) tubes, the IHM is energetically more unfavorable than the OHM and MHM, as shown in Figure 4a and b. For the armchair (n,n) tubes, the OHM is more stable than the MHM as n e 5 but becomes less stable as n > 5 (Figure 4a). For the zigzag (m, 0) tubes, the OHM is more stable than the MHM as m e 6 (Figure 4b). It is worth noticing that numerous morphologies of MHM can be

built by changing the ratio of inward hydrogen atoms to the outward hydrogen atoms. Our calculations show that for the armchair tubes the stable forms of MHM have equal numbers of outward and inward hydrogen atoms, which are placed alternatively in the interior and exterior of the tubes, as shown in Figure 3e-h. For the zigzag tubes, however, the ratio of outward to inward hydrogen atoms in the most-stable configurations varies from 5:2 of the (7,0) tube to 21:11 of the (16,0) tube, as shown in Figure 3m-v. The Eform values of the moststable configurations as a function of tube radius are plotted in Figure 4c. Obviously, the zigzag tubes have superior energetic favorability over the armchair tubes. It is interesting to see that there are three extremely energetically more-favorable configurations: (3,3), (5,0), and (9,0) tubes, corresponding to the Eform local minima. The existence of these distinctive configurations is important for the fabrication and utilization of these tubes. The structural parameters, Eform, and band gaps (Eg) of these tubes are listed in Table 1. The relevant

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Figure 5. Electronic band structures of (a) sheet I and (b) sheet II, (c) (3,3), (d) (9,9), (e) (5,0), and (f) (9,0) H-SiN nanotubes. The dashed lines indicate the position of the Fermi levels (EF).

Figure 4. Variation of the formation energies (Eform) of (n,n) and (m,0) H-SiN nanotubes with different hydrogenation modes as a function of (a) n and (b) m. The formation energies of the most-stable configurations vs the tube radius are plotted in Figure 4c. The tube radius was determined by the average distance between the tube axis to the outmost hydrogen atoms

data of bulk R-Si3N4, H-SiN nanosheets, and the (9,9) H-SiN nanotube are also presented for comparison. The average Si-N bond length and Si-N-Si and N-Si-N bond angles of these tubes are close to the values of R-Si3N4. The Si-H distances of these tubes (1.50, 1.52 Å) are also close to that of silicane (1.51 Å) obtained from our calculations. These stable configurations have different hydrogenation modes. For the (3,3) and (5,0) tubes, all of the hydrogen atoms are in the exterior of the tubes (OHM), whereas the (9,9) tube has hydrogen atoms placed alternatively in the interior and exterior of the tube. The ratio of the outward to inward hydrogen atoms for the (9,0) tube is 2:1. The Eform absolute values of these tubes (0.68-0.70 eV/ atom) are comparable to that of sheet II. The (5,0) and (9,0) tubes are even slightly more stable than sheet II by about 0.01 and 0.02 eV/atom, respectively. This indicates that these H-SiN nanotubes may be built easily from rolling up an H-SiN nanosheet, provided that the H-SiN nanosheet can be synthesized. We also checked the thermal stability of these tubes by heating them at 1000 K for 2 ps using a NVT dynamics with a Nose´ thermostat. No collapse tendency toward the formation of silicon nitride nanowires was found at this time scale. This

result implies that these H-SiN nanotubes if synthesized may exist stably at room temperature. We also studied the electronic structures of the H-SiN nanosheets and nanotubes. It was shown that sheet I has an indirect band gap of 4.04 eV with the valence band maxima (VBM) and the conduction band minima (CBM) at 1/7 (K-Γ) and the Γ points, respectively, whereas the energy gap at the Γ point is about 4.1 eV, as shown in Figure 5a, slightly narrower than that of bulk R-Si3N4 (4.41 eV). Sheet II, however, has a direct band gap of 4.72 eV at the Γ point, wider than that of R-Si3N4 by about 0.31 eV. The conduction bands of sheet I near the Fermi level are rather dispersed as compared to those of sheet II. This can be attributed to the closer Si-Si distance in sheet I (2.93 Å) compared to sheet II (2.95, 3.13 Å), which favors the overlap of the wavefunctions between adjacent Si atoms and thus the formation of delocalized states. The atomic charges of the Si and N atoms determined by Mulliken population analysis are 0.85 |e| and -0.68 |e| for sheet I and 0.92 |e| and -0.76 |e| for sheet II, which are close to those of bulk R-Si3N4 (0.88 |e| and -0.66 |e|), indicating the ioniccharacterized Si-N bonds in these materials. This is also consistent with the features of partial electronic density of states (PDOS) obtained by projecting the total density of states onto different atoms. The valence bands and the conduction bands near the Fermi level arise mainly from the states of N and Si atoms, respectively, as shown in Figure 6. However, it should be mentioned that both N and Si states contribute to the VBM and CBM, implying that the Si-N bonds are not purely ionic but have covalent character. The band structures of the armchair H-SiN nanotubes under study exhibit the characteristics of semiconductors with indirect band gaps between 4.32 and 4.91 eV, as shown in Figure 5c and d. All of the zigzag tubes, however, have a direct band gap at the Γ point, as shown in Figure 5e and f. The existence of direct band gap in sheet II and zigzag tubes is quite important for the utilization of these nanostructures in building nanoscale

Geometric and Electronic Structures

Figure 6. Partial density of states (PDOS) of sheet II obtained by projecting the total electronic density of states onto N (top), Si (middle), and H (bottom) atoms.

optoelectronic devices, which is impossible for the bulk R- and β-Si3N4 materials. Finally, we should stress that although the realization of the H-SiN nanosheets and nanotubes is presently challenging, some recent developments in synthesizing ultrathin films28,29 have implied promising synthetic routes toward them. If a H-SiN monolayer sheet can be grown on a dangling-bond-free surface of a substrate, such as a hydrogen-terminated Si surface, then it may resemble the isolated H-SiN nanosheets predicted here in atomic arrangements and electronic properties. H-SiN nanosheets may be formed at the first place because of the energetic favorability arising from the supporting substrate, although in some cases the isolated H-SiN nanotubes have better formation energies than the isolated H-SiN nanosheets. Starting from H-SiN monolayer, H-SiN nanotubes are obtainable, probably via the approaches resembling those to form carbon nanotubes from a graphite sheet. Conclusions We performed first-principles calculations to study the geometric and electronic structures of hydrogen-stabilized silicon nitride nanosheets and nanotubes with the stoichiometry of HSiN. The stable H-SiN nanosheet has a two-dimensional hexagonal grid of Si and N atoms with the Si dangling bonds being passivated by H atoms, which are placed alternatively on the two sides of the sheet, whereas H-SiN nanotubes can be built from rolling up the nanosheet. The hydrogen arrangement strongly affects the energetic favorability of the H-SiN nanotubes and makes some distinctively favorable configurations possible. The stable H-SiN nanosheet and zigzag tubes have a direct band gap at the Γ point. The direct band gaps are crucial for building nanoscale optical and photonic devices. Acknowledgment. This work is supported by the National Natural Science Foundation of China under grant nos. 50402017 and 10374059, the National Basic Research 973 Program of China (grant no. 2005CB623602), and the Program for New Century Excellent Talents in University. References and Notes (1) de Brito Mota, F.; Justo, J. F.; Fazzio, A. Phys. ReV. B 1998, 58, 8323. (2) Vogelgesang, R.; Grimsditch, M.; Wallace, J. S. Appl. Phys. Lett. 2000, 76, 982. (3) Katz, R. N. Science 1980, 208, 841. (4) Choi, S.; Yang, H.; Chang, M.; Baek, S.; Hwanga, H.; Jeon, S.; Kim, J.; Kim, C. Appl. Phys. Lett. 2005, 86, 251901. (5) Powell, M. J.; Easton, B. C.; Hill, O. F. Appl. Phys. Lett. 1981, 38, 794.

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