Journal of Nanoparticle Research

, Volume 13, Issue 1, pp 185–191

First principles study of the electronic properties of twinned SiC nanowires

  • Zhiguo Wang
  • Shengjie Wang
  • Chunlai Zhang
  • Jingbo Li
Research Paper

DOI: 10.1007/s11051-010-0017-0

Cite this article as:
Wang, Z., Wang, S., Zhang, C. et al. J Nanopart Res (2011) 13: 185. doi:10.1007/s11051-010-0017-0

Abstract

The electronic properties of saturated and unsaturated twinned SiC nanowires grown along [111] direction and surrounded by {111} facets are investigated using first-principles calculations with density functional theory and generalized gradient approximation. All the nanowires considered, including saturated and unsaturated ones, exhibit semiconducting characteristics. The saturated nanowires have a direct band gap and the band gap decreases with increasing diameters of the nanowires. The hexagonal (2H) stacking inside the cubic (3C) stacking has no effect on electronic properties of the SiC nanowires. The highest occupied molecular orbitals and the lowest unoccupied molecular orbitals are distributed along the nanowire axis uniformly, which indicates that the twinned SiC nanowires are good candidates in realizing nano-optoelectronic devices.

Keywords

Twinned SiC nanowires Electronic properties Ab initio Modeling and simulation 

Introduction

One-dimensional nanomaterials have attracted much attention in recent years owing to their fundamental importance in understanding the concepts about the role of reduced dimensionality and size in optical, electronic, and mechanical properties and their wide range of potential application in novel nanoscale devices (Zhang et al. 1998; Hu et al. 1999). The nano-structures of conventional semiconductor materials of group IV, III–V and, II–VI, such as Si (Cui and Lieber 2001), GaAs (Harmand et al. 2005; Wu et al. 2002), InAs (Jensen et al. 2004; Dick et al. 2005), GaN (Huang et al. 2002; Chen et al. 2001), and ZnSe (Colli et al. 2004, 2005) can all be synthesized experimentally, with their electronic properties that can be easily tailored by controlling their size. Silicon carbide (SiC) is an important wide band gap semiconductor with superior properties, such as high break-down field strength, high thermal conductivity, high saturation drift velocity, and excellent physical and chemical stability. Bulk SiC is not a good candidate for application in optoelectronic integration on account of its indirect band gap. However, SiC nanorods and nanowires have been shown to exhibit more superior properties such as direct band gap (Gali 2007; Yan et al. 2006). Experimental and theoretical results also show that the elasticity and strength of SiC nanorods (nanowires) are considerably greater than those of micrometer-size SiC whiskers and bulk SiC (Wong et al. 1997; Wang et al. 2008a, b; Makeev et al. 2006). One-dimensional nanoscale SiC is more suitable for the fabrication of nanoscale electronic and optoelectronic devices operating at high temperature, high power, and high frequency environments (Fissel et al. 1995). Until now, a variety of one-dimensional and quasi-one-dimensional functional SiC nanostructures have been successfully fabricated, including nanowires, nanotubes, nanocable, and nanospings (Wong et al. 1999; Seong et al. 2004; Pan et al. 2000; Wu et al. 2007; Taguchi et al. 2005; Zhang et al. 2003). Most SiC nanowires are of cubic zinc-blend structured (3C) growth along the [111] direction (Zhang et al. 1998; Sun et al. 2002; Dai et al. 1995; Yang et al. 2007; Shen et al. 2006) with amorphous carbon or SiO2 coating. Recently, twinned SiC nanowires with 〈111〉 axes and {111} surfaces have been observed (Shim and Huang 2007; Wang et al. 2008a, b; Li et al. 2009). The twinned SiC nanowires consist of a mixture of hexagonal (2H) and cubic (3C) stacking of Si–C layers as shown in Fig. 1. The twin formation also occurs in other zinc-blend nanowires such as InP (Moewe et al. 2008; Algra et al. 2008), ZnS (Hao et al. 2006), and ZnSe (Li et al. 2004). Possible explanations for the formation of twins are attributed to minimization of the total energy including contributions from solid surface, liquid surface, solid–liquid interface, twin boundary, and edge at twin boundary (Shim et al. 2008). It is well known that SiC exhibits prominent polytypism resulting in more than 200 crystalline structures with varying stacking sequences (Bechstedt et al. 1997). The electronic properties, such as band structures and band gaps, show great dependence on the polytypes (Choyke et al. 1964; Kächell et al. 1994). The twin fault will affect the mechanical behavior of the SiC nanowires (Wang et al. 2010). Whether a heterostructure can be formed in the twinned SiC nanowires is also essential to understand the electronic properties for practical applications. This study represents an extensive study of the electronic structures of the twinned SiC nanowires using the first-principles density functional theory calculations.
Fig. 1

(Color online) Atomic configurations of the unsaturated (top) and saturated (bottom) twinned SiC nanowires in a cubic crystal structure with non-parallel {111} side facets viewed from a the 〈110〉 direction, b the 〈112〉 direction, and c the 〈111〉 direction

Simulation details

The calculations were performed using the all-electron projector augmented wave method (Kresse and Joubert 1999) encoded in the plane-wave basis Vienna ab initio simulation package (VASP) (Kresse and Furthmüller 1996), using the density functional theory (DFT) with generalized gradient approximations (GGA) (Perdew and Wang 1986) for the exchange-correlation potential. DFT is a theory of electronic structure, based on the electron density distribution, instead of the many-electron wave function (Kohn et al. 1996), which has been widely used in physics and chemistry to investigate the electronic structure (principally the ground state) of many-body systems, in particular—atoms, molecules, and the condensed phases. Convergence with respect to the plane-wave cutoff energy and k-point sampling has been carefully checked. The cutoff energy for the plane-wave basis set is 450 eV. For the Brillouin zone integration, Monkhorst–Pack (Pack and Monkhorst 1977) special k-points, equivalent to the 1×1×5 mesh, are employed. All the atoms are fully relaxed until the Hellmann–Feynman force is less than 0.02 eV/Å.

The optimized lattice constant for 3C-SiC is 4.378 Å, which agrees well with the experimental value of 4.36 Å. For simulating nanowires, periodic boundary conditions were applied along the wire axis (taken as z-axis), and sufficient vacuum space (up to 1.0 nm) was imposed in radical directions to sure that there is no interaction between SiC nanowires. The twinned SiC nanowire with its axis along the [111] direction is surrounded by {111} side facets, which are investigated. The diameters of these nanowiers change from 0.6 to 1.8 nm with segment thickness (t) of 0.5–1.0 nm. The atomic structure and electronic properties of both unsaturated and saturated (with hydrogen) nanowires are investigated.

Results and discussions

The twinned SiC nanowire with its axis along the [111] direction is surrounded by {111}A and {111}B side facets which are tilted in opposite directions (by θ ≈ 19.5°) with respect to the nanowire axis. The A and B side facets are terminated with silicon and carbon atoms, respectively. Along the [111] direction, the {111}A edges move inward and their length increases, while the {111}B edges move outward and their length decreases. The nanowire can be constructed by rotating the twin segment through 60° or 180° and shifting about one twin segment thickness. The twins caused kinks or zigzag appearance of a contoured surface of SiC nanowires as shown in Fig. 1b. The twinned SiC nanowires consist of a mixture of hexagonal and cubic stackings of Si–C layers. Hexagonal (2H) and cubic (3C) stackings are represented by ABAB… and ABCABC…, respectively. The relaxed configurations of the unsaturated nanowires show that the outer and sub-surface layer atoms undergo a bond-length contraction in which Si and C atoms move inward about 0.112–0.327 and 0.031–0.193 Å, respectively. Surface Ga–N bond lengths range from 1.765 to 1.873 Å, which were somewhat smaller than those of bulk 3C-SiC and contracted 1.1–6.9% compared to the bulk value. There is only one dangling bond per surface atom for the twinned nanowires, and one H-atom is required to passivate each surface atom of SiC nanowires. After the passivation of the surface atoms by the H-atoms, the bond length of Si–C bond almost does not change.

The band structures of the saturated twinned SiC nanowires along the ΓX direction (parallel to the growth direction of the nanowires) are shown in Fig. 2a–d. It can be seen that all the nanowires exhibiting a semiconducting character with the bottom of conduction band (CBM) and the top of the valence band (VBM) are all located at the Γ point of the Brillouin zone. In contrast to the indirect band gap character of bulk 3C-SiC, the twinned nanowires have a direct band gaps at Γ point, which are like the perfect [111]-oriented SiC nanowires (Yan et al. 2006). The direct band gap properties of these SiC nanowires make them to be a good candidate for application in optoelectronic nanodevices. Figure 2e–h shows the band structure of unsaturated twinned SiC nanowires. Surface states appear in the fundamental electron energy gap. As the actual band gap without surface states is unknown, we define here an apparent energy gap as the energy difference between the top most filled valence state and the lowest state in the conduction band. It can be seen that the “band gaps” for the unsaturated nanowires are less than those for the saturated ones. This may be due to the existing dangling bonds of edge atoms on the unsaturated surface. These dangling bonds produce edge-induced states (bands) in the band gaps located above the VBM and below the CBM.
Fig. 2

(Color online) Band structures of the saturated (top) and unsaturated (bottom) twinned SiC nanowires. The energy at the Fermi level is set to zero. The diameters of these nanowires are a/e 0.62 nm, b/f 1.24 nm, c/g 1.86 nmm, and d/h 1.24; and the segment thicknesses are a–c/e–g 0.5 nm, and d/h 1.0 nm

Owing to the quantum confinement effects, the band gaps of these saturated SiC nanowires decrease with the increase of the wire size, as shown in Fig. 3. The band gap of the saturated nanowires can be fitted using the following expression: Eg = Egbulk + β/dα, where Egbulk is the band gap value of bulk SiC (the calculated value is 1.36 eV), α and β are fit parameters, and d is the diameter of the nanowires. The fit parameters for these twinned SiC nanowirs are: α = 0.56 and β = 1.96. The α = 0.56 is very close to that of the perfect oriented nanowires (α = 0.6) (Wang et al. 2009).
Fig. 3

(Color online) Band gap as a function of the nanowire diameter

The surface states appear in the band gap and thus narrow the band gaps of the nanowires of twinned SiC nanowires, which can also be clearly evidenced from the projected density of states (PDOS) of surface and core atoms onto Si and C atoms. A similar result is obtained for all the simulated nanowires, and so we show a representative PDOS of nanowire with diameter of 1.86 nm in Fig. 4. We can see that the top most filled valence state and the lowest state in the conduction band arise from the states of the threefold-coordinated atoms on the out facets. After saturation, The VBM and CBM originate mainly from the C and Si atoms inside the nanowires, respectively.The inside atoms have one more neighbor than surface atoms. The difference can be removed by hydrogen saturation, and the surface states within the band gap can be removed. As a result, the band gap of nanowires with diameter of 1.86 nm changed from 0.81 to 2.77 eV. The PDOS is also consistent with the spatial distribution of the the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) states around the atoms, which are responsible for the formation of the VBM and CBM. As shown in Fig. 5, HOMO and LUMO are mainly localized in the central region of the saturated nanowires, whereas they are highly located on the facets of the unsaturated nanowires.
Fig. 4

(Color online) Projected density of states for a unsaturated and b saturated twinned SiC nanowire with a diameter of 1.86 nm and a segment thickness of 0.5 nm

Fig. 5

(Color online) Wave function square contour plots of the HOMO and LUMO states for a unsaturated and b saturated twinned SiC nanowire with a diameter of 1.86 nm and a segment thickness of 0.5 nm

In order to give more insight of whether the twin fault can affect the electronic properties, and to see whether a heterostructure can be formed between the 2H and 3C stacking in the twinned SiC nanowires, we investigate the HOMO and LUMO distribution along the wire axis. If type-II heterostructure is formed, then the electrons and holes will separate from each other, and the nanowires are not good candidates for application in optoelectronic device because the recombination efficiency is reduced. Figure 6 shows the HOMO and LUMO distribution of hydrogen-saturated nanowire with diameter of 1.24 nm and segment thickness of 1.0 nm viewed from 〈110〉, 〈112〉 and 〈111〉 direction. It can be seen that the HOMO and LUMO distribute along the nanowire axis uniformly, indicating that the no heterostructure formed between the different stackings. In this case, electrons and holes stay in the same region (core region of twinned nanowires) after photoexcitation, which is very desirable for the light-emitting devices, where a maximized wavefunction overlap of the electron and hole yields a high radiative recombination rate. The twinned SiC nanowires may exhibit strong electroluminescences, and thus should have high potential for full-color area display applications.
Fig. 6

(Color online) Wave function square contour plots of the HOMO and LUMO states for saturated twinned SiC nanowire with a diameter of 1.24 nm and a segment thickness of 1.0 nm viewed from a the 〈110〉 direction, b the 〈112〉 direction, and c the 〈111〉 direction

Conclusions

In summary, we have performed first-principles calculations on the saturated and unsaturated twinned SiC nanowires grown along by [111] direction and surrounded by {111} side facets. After atomic relaxation, the atoms in the outer and sub-surface layers undergo a bond-length contraction for the unsaturated nanowires. Surface states within the band gap can be removed by hydrogen saturation. The saturated nanowires have a direct band gap at Γ point, and the band gaps of saturated nanowires decrease with increasing diameters of the nanowires due to the quantum confinement. It is of interest to find then the hexagonal (2H) stacking inside the cubic (3C) stacking has no effect on the electronic properties of the SiC nanowires. The highest occupied molecular orbitals and the lowest unoccupied molecular orbitals states distribute along the nanowire axis uniformly, indicating then the twinned SiC nanowires are good candidates in realizing nano-optoelectronic devices.

Acknowledgments

Z. Wang was financially supported by the National Natural Science Foundation of China (10704014) and the Young Scientists Foundation of Sichuan (09ZQ026-029) and UESTC (JX0731). J. Li gratefully acknowledges financial support from the “One-Hundred Talents Plan” of the Chinese Academy of Sciences and National Science Fund for Distinguished Young Scholar (Grants No.60925016).

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Zhiguo Wang
    • 1
    • 2
  • Shengjie Wang
    • 1
  • Chunlai Zhang
    • 1
  • Jingbo Li
    • 2
  1. 1.Department of Applied PhysicsUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  2. 2.State Key Laboratory for Superlattices and Microstructures, Institute of SemiconductorsChinese Academy of SciencesBeijingPeople’s Republic of China

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