Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học
Structures and electronic properties of Si nanowires grown along the [110] direction: Role of surface reconstruction Toru Akiyama * , Kohji Nakamura, Tomonori Ito Department of Physics Engineering, Mie University, 1577 Kurima-Machiya, Tsu 514-8507, Japan article info Article history: Received 30 May 2008 Accepted for publication 4 August 2008 Available online 9 August 2008 Keywords: Density functional calculation Surface energy Silicon Nanostructures abstract The atomic and electronic structures of silicon nanowires grown along the [110] direction are systemat- ically investigated using first-principles pseudopotential method. For nanowires whose diameters are $4 nm, the calculations taking account of various surface reconstructions both with and without hydro- gen atoms on nanowire facets demonstrate that the reconstruction on nanowire facets is strongly depen- dent on hydrogen chemical potential l H . The nanowire terminated by H atoms is stabilized for high l H whereas the pristine nanowire is favorable for low l H . The nanowires with partially hydrogenated facets also appear within a certain l H range. Peculiar features in the electronic structure caused by facet edges are found in both pristine and partially hydrogenated nanowires. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Semiconductor nanowires (NWs) are recently paid much atten- tion as potential building blocks for nanoelectronic and photonic devices. Silicon NWs (Si NWs) are in particular attracting great interest due to their compatibility with conventional Si-based technology. Furthermore, they are scientifically of interest and importance for a prototype of nanoscale materials to study effects of quantum confinement, dimensionality, and orientation. So far, Si NWs of diameters below 10 nm have been synthesized by solution techniques [1], oxide-assisted catalyst-free method [2–4], and me- tal-catalytic vapor–liquid–solid (VLS) method [5–8]. More recently, Si NWs fabricated by means of Au nanocluster- catalyzed VLS method using the chemical vapor deposition (CVD) have been shown to be the controlled growth of molecular-scale Si NWs [7]: the high-resolution transmission electron microscopy (HRTEM) has shown that Si NWs are single crystal with little or no visible amorphous oxide down to diameters as small as 4 nm. Furthermore, it have been shown that, importantly, the smallest- diameter NWs are grown primarily along the [110] direction while the NWs with large diameter are grown along the [111] direction. The HRTEM has also observed the hexagonal nanowire shape which consists of {001} and {111} facets. On the other hand, re- cent theoretical investigations have investigated the effect of the nanowire size on the electronic properties for Si NWs terminated with hydrogen in an idealized symmetric dihydride structure [9– 11]. Zhao et al. investigated the size and orientation dependence on the structural, electronic, and optical properties of hydrogen- passivated Si NWs with diameter up to 4.2 nm and found that quantum confinement becomes significant for diameter less than 2 nm, where the dielectric function exhibits strong anisotropy and new low-energy absorption peaks start to appear in the imag- inary part of the dielectric function for polarization along the wire axis [9]. Vo et al. also clarified the effects of surface reconstruction on the opto-electronic properties for dihydride and monohydride cases on the {0 0 1} facets [10]. In spite of these findings, there still remain matters to debate about effects of surface reconstruction both on {001} and {111} facets of Si NWs: since the reconstruction could depends on temperature and pressure of hydrogen ambient during and after the fabrication process in the CVD, it is expected that various surface reconstructions including those in clean sur- faces exhibit on the nanowire facets. Due to higher surface–volume ratio in thin NWs compared to those in thick or bulk phase, effect of surface reconstruction could be crucial on the electronic proper- ties of thin NWs. In this paper, effects of surface reconstruction on structural and electronic properties of Si NWs grown along the [110] direction are systematically investigated based on total energy electronic structure calculations. In particular, we focus on the surface recon- struction of nanowire facets in Si NWs with diameter of $4nm, which have been successfully fabricated by the CVD. The relative stability among NWs with various surface reconstructions is deter- mined based on the calculated formation energy depending on hydrogen chemical potential which represents temperature and pressure effects of hydrogen ambient. Furthermore, effects of sur- face reconstruction of nanowire facets on the electronic structures are examined from the calculated band structures and wave func- tion characters. We find that the reconstruction on nanowire facets is strongly dependent on hydrogen chemical potential l H and Si 0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2008.08.002 * Corresponding author. Tel.: +81 59 232 1211x3978; fax: +81 59 231 9726. E-mail address: akiyama@phen.mie-u.ac.jp (T. Akiyama). Surface Science 602 (2008) 3033–3037 Contents lists available at ScienceDirect Surface Science journal homepage: www.elsevier.com/locate/susc NWs with partially hydrogenated facets appear within a certain l H range. We further propose that peculiar features in the electronic structure caused by facet edges could be realized in both pristine and partially hydrogenated nanowires. 2. Calculation procedure All calculations have been performed within the generalized gradient approximation in density functional theory (DFT) [12]. We use norm-conserving pseudopotentials [13] and the conju- gate-gradient technique [14,15] both for the electronic structure calculation and for the geometry optimization. In the optimized geometries the remaining forces acting on the atoms are less than 5.0  10 À2 Ry/Å. The valence wave functions are expanded by the plane-wave basis set with a cutoff energy of 10 Ry which gives an enough convergence of total energy to discuss the relative sta- bility. We employ a supercell in which a nanowire is placed with its facets being separated by $7 Å from those of adjacent NWs. 1 Two atomic-layers are employed to simulate the periodicity along the [110] direction. 2 Eight k-points are used in the integration over one-dimensional Brillouin zone. We construct hexagonal nanowire models whose diameters are $3.7 nm according to the following procedure: First, we have con- firmed a possible nanowire shape using Wulff’s theorem [16] in which the ratio of surface energy to the distance from the centre of crystal to the surface is constant. Assuming that nanowire facets during the growth consist of clean surface, we have obtained that the ratio of the distance for {0 01} facet to that for {111} facet is 1.03 [17]. This value can be satisfied by taking hexagonal shape considered in this study. Next, we have determined the nanowire size which reproduces the diameter fabricated by the CVD [7]. The diameter of nanowire model is 3.7 nm, which is comparable to the experimental value of 4 nm. Therefore, it is expected that clean surface will appear on the nanowire facets during the growth condition. However, surface Si atoms can be terminated with H atoms after the growth by changing hydrogenation conditions. Considering such situations, we here consider both pristine and hydrogen terminated NWs. We adopt asymmetric dimers with p(2  1)-type structure for pristine {00 1} facets, and monohydride and dihydride configuration for H-terminated {001} facets [18]. For pristine {111} facets, we take account of two types of (2  1) surface, such as buckling structure [19] and p -bonded chain [20] configurations, because recent calculations for flat Si(111) surfaces have shown that the p -bonded structure is unstable compared to the buckling structure when the width of dangling bonds is less than three top-layer atoms in the ½11 2 direction [21]. These calcu- lated results indicate a plausibility of the buckling structure as a relevant surface reconstruction on {111} facets with finite flat sur- face area. The dimers, adatoms, and stacking faults (DAS) model [22] for the (7  7) structure is excluded in the present study be- cause such reconstruction requires more surface areas. For H-ter- minated {111} facets, the (1  1) structure is considered. The relative stability of Si NWs is determined using the forma- tion energy E f [18] written as E f ¼ E tot À n Si l Si À n H l H þ n H e z ; ð1Þ where E tot is the total energy of nanowire in the supercell, l Si ( l H )is the chemical potential of an Si (H) atom, n Si (n H ) is the number of Si (H) atoms, and e z is the zero-point energy of Si–H vibrations. The value of l Si is equal to that in bulk Si and the zero of l H is taken to be the chemical potential at which the formation energy of SiH 4 is equal to zero. The value of e z is taken to be 0.21 eV which corresponds to the zero-point energy per H atom in SiH 4 . We also estimate the temperature at 1 atom of partial pressure of H 2 from the standard partition function, within the harmonic approxima- tion, including both rotational and zero-point vibrational energies [23]. 3. Results and discussion Fig. 1a shows the calculated formation energy per Si–H unit as a function of H-chemical potential for various structures. The calcu- lated formation energy indicates that the energetically lowest structure depends on l H . For l H lower than À0.81 eV, the pristine nanowire with p -bonded chain on {111} facets and p(2  1) sur- face on {001} facets, shown in Fig. 2a, is the most favorable struc- ture. This structure is found to be stable compared to the pristine nanowire with buckling structure (pristine: {111}-(2  1) buckling in Fig. 1) by 0.12 eV/Si–H pair, which is comparable to the energy difference between the buckling and p -bonded chain structures on flat Si(111) surface (0.13 eV/1  1 cell). The appearance of p - bonded chain implies that the stability of {111} facets is similar to that in clean Si(111) surface. 3 In contrast, for l H higher than À0.75 eV, H-terminated nanowire on both {00 1} and {111} facets is stabilized. As shown in Fig. 2d, this completely H-terminated nanowire consists of monohydride configuration on {0 0 1} facets and (1  1) H-terminated surfaces on {111} facets: the NWs with dihydride facets are not found as stable configurations over entire l H range considered in this study, although recent calculations have shown that Si NWs with canted dihydride NWs could appear for high l H [10]. Since in flat Si(001) surface monohydride configuration is stable over wide H-chemical potential range and dihydride structure is favorable in the limit range [18], it is reasonable to conclude that dihydride {001} facets might appear in the limited condition. In addition to these structures, we found that partially H-termi- nated structures are stabilized in the narrow l H range. Fig. 1b shows the formation energy between low and high l H where pris- tine and completely H-terminated NWs are stabilized, respectively. Only {001} facets are hydrogenated for À0.81 < l H < À0.78 eV (Fig. 2b) and {1 1 1} facets are hydrogenated for À0.78 < l H < À0.75 eV (Fig. 2c). Since the number of adsorbed hydrogen atoms in the former structure (12 atoms in the unit cell) is smaller than the number in that in the latter one (24 atoms in the unit cell), these partially hydrogenated structures can be interpreted as inter- mediate structures between pristine and completely hydrogenated structures. The estimated temperature range for partially hydroge- nated NWs is 530–570 K, implying that partially hydrogenated NWs can be formed in such narrow temperature range. However, due to the very small energy difference, it can be expected that these NWs coexist in this temperature range. The analysis of the electronic structure for stable NWs clarifies that the surface reconstruction on nanowire facets crucially affects the electronic structure. Fig. 3 shows the Kohn-Sham band struc- ture of stable NWs. In the case of NWs which possess nanowire fac- ets without H atom, as shown in Fig. 3a–c, surface related 1 For the flat Si(111) surfaces, the validity of surface separation has been checked by using slab geometry with 7–12 Å thick vacuum region. We found that the surface energy and positions of surface atoms of Si(111)-(2  1) p -bonded chain surface are identical within 0.01 eV and 0.01 Å, respectively. 2 Although the size of unit cell along the [110] direction is insufficient to obtain the most stable c(4  2) reconstruction on Si(001) surfaces, the energy difference between p(2  1) and c(4  2) is found to be negligible compared with the energy differences discussed in the paper (the calculated energy difference is within 0.01 eV/ 1  1 cell). Therefore, the relative stability depending on hydrogen chemical potential could be the same as those using larger supercells. 3 The result is different from the relative stability between the buckling and p - bonded chain structures in Ref. [21]. This is because the geometry of top-layer Si atoms on nanowire facets are different from that in Ref. [21]. There are boundaries between the (2  1) with p -bonded chain and (1  1) structure along the ½ 1 10 direction in the nanometer-scale Si(1 11) surface while no boundary exists on top- layer Si atoms of p -bonded chain-like structure on {111} facets of Si NWs. 3034 T. Akiyama et al. / Surface Science 602 (2008) 3033–3037 electronic states appear around the band gap. In the pristine nano- wire, as shown in Fig. 3a, both localized electronic states caused by p -bonded chains on {111} facets (arrows in Fig. 3b) and dangling bonds of p(2  1) surface on {001} facets (arrows in Fig. 3c) are formed. In addition, the electronic states originating from the nanowire edges between adjacent {111} facets are formed near the Fermi level at the zone boundary (arrowheads in Fig. 3b). Due to these electronic states, it is expected that pristine and {001} facets hydrogenated NWs exhibit semimetallic character. This is quite different from the metallic and semimetallic behav- iour proposed in Si NWs along the [001] direction [24]. Since both p -bonded chain and p(2  1) reconstructions on Si(111) and Si(001), respectively, exhibit semiconductor behaviour, such elec- tronic structures are typical for NWs containing pristine facets edges. In order to clarify the origin of semimetallic character, we ana- lyze the character of wave functions in the {0 0 1} facets hydroge- nated nanowire shown in Fig. 2b. Fig. 4a and b show the contour plots of wave functions for symmetrically equivalent two highest occupied (HO) and four lowest unoccupied (LU) states, respec- tively. By comparing the distribution of wave functions for the p - bonded chain on Si(111) surface (insets of Fig. 4), we find that the wave functions of the doubly-degenerate HO states and four LU states correspond to the p -like bands of edge atoms and the Fig. 1. Calculated formation energies of NWs grown along the [110] direction for various surface reconstructions as a function of hydrogen chemical potential. (a) Formation energy over wide temperature range and (b) that for narrow range where partially hydrogenated structures are stabilized (represented by vertical dotted lines). Dashed lines denote metastable structures. The temperature of H 2 -gas temperature at 1 atom is also shown. Fig. 2. Cross-sectional views of (a) pristine, (b) {111} facets hydrogenated, (c) {001} facets hydrogenated, and (d) completely H-terminated NWs. Open and filled circles represent Si and H atoms, respectively. The six-membered rings which constitute nanowire edges between adjacent {111} facets are represented by grey areas in (a) and (b). T. Akiyama et al. / Surface Science 602 (2008) 3033–3037 3035 p * -like bands on {111} facets, respectively. This is because nano- wire edges between adjacent {1 11} facets consist of six-membered ring (grey area in Fig. 2a and b) while surface atoms of normal p - bonded chain on {111} facets belong to seven-membered ring: the difference in atomic configuration causes the suppression of lattice relaxation for edge atoms. Indeed, the p * -like bands for the edge atoms are located $0.2 eV above the p -like bands for the edge atoms, implying that the suppression of lattice relaxation results in the weakness of surface bound states. As a result, the en- ergy of p -like bands on nanowire edge becomes close to the p * -like bands on {111} facets. We note, however, that more elaborate cal- culations beyond DFT calculations, such as GW approximation [25], should be required to exclude the possibility that such a semi- metallic behaviour comes from the limitation of DFT calculation. For completely H-terminated nanowire, as shown in Fig. 3d, the surface related electronic states are completely eliminated around the band gap. More importantly, the gap energy (0.94 eV) is large compared to that in bulk Si (0.74 eV) and the direct band gap char- acter is found. The band structure of monohydride nanowire is qualitatively consistent with the calculated results for Si NWs with dihydride surface in the previous calculations [9–11]. As explained in the previous study [9,10], this character can be understood in terms of the projection of energy band in bulk Si and confinement effect: the confinement decreases the energy of HO states and in- creases the energy of the LU states, but the magnitude of the en- ergy shift depends on their effective masses. Due to the large effective mass along the longitudinal direction of the LU states lo- cated at $85% along C to X in bulk Si, which is projected at the C - point for NWs grown along the [110] direction, the energy shift of the projected LU states becomes small, resulting in the direct band gap character. 4. Summary We have investigated atomic and electronic structures of silicon NWs along the [110] direction based on first-principles pseudopo- tential calculations. For atomic structure, we found that partially hydrogenated NWs as well as H-terminated and pristine NWs can be formed depending on hydrogen chemical potential. The existence of the nanowire edges between different nanowire facets causes the stabilization of p -bonded chain on {111} facets, which results in the appearance of partially hydrogenated NWs with p - bonded chain configuration. We have also confirmed the direct band gap character with larger gap energy than bulk value for com- pletely hydrogenate nanowire, consistent with previous theoreti- cal studies. Surface related electronic states caused by nanowire facets appear for pristine and partially hydrogenated NWs result in semimetallic nature different from flat surfaces. This semimetal- lic nature originates from the suppression of lattice relaxation for edge atoms which results in the weakness of surface bound states. Although the size dependence on the structural and electronic properties have been left in the present study, the calculated re- sults imply that over wide range of the nanowire diameter the reconstruction on nanowire edge crucially affects the structural Energy (eV) Energy (eV) Energy (eV) Energy (eV) -1 0 1 X -1 0 1 X -1 0 1 X -1 0 1 X ΓΓ ΓΓ abcd Fig. 3. Energy bands of (a) pristine, (b) {111} facets hydrogenated, (c) {001} facets hydrogenated, and (d) completely H-terminated NWs. The zero of energy is set to the Fermi level. Arrows in (b) and (c) represent the surface related electronic states due to p -bonded chain on {111} facets and dangling bonds on p(2  1) surface of {001} facets, respectively. Arrowheads in (b) indicate the electronic states related to p -bonded chain of nanowire edges between adjacent {111} facets. The calculated gap energy in bulk Si is 0.73 eV. Fig. 4. Cross-sectional views of the wave functions at zone boundary of (a) two highest occupied and (b) four lowest unoccupied states in the {0 01} facets hydrogenated nanowire. The density of isosurfaces is 1.5  10 À3 e/Å 3 . The wave functions of p - and p * -like bands on Si(111)-(2  1) surfaces are also shown on the inset of (a) and (b), respectively. 3036 T. Akiyama et al. / Surface Science 602 (2008) 3033–3037 and electronic properties of Si NWs grown along the [110] direction. Acknowledgements This work was supported in part by Grant-in-Aid for Scientific Research from JSPS under Contract No. 18560020. Codes used in this work are based on Tokyo Ab-initio Program Package (TAPP). Computations were performed at RCCS (National Institutes of Nat- ural Sciences) and ISSP (University of Tokyo). References [1] J.D. Holmes, K.P. Johnston, R.C. Doty, B.A. Korgel, Science 287 (2000) 1471. [2] D.D.D. Ma, S.C. Lee, F.C.K. Au, S.Y. Tong, S.T. Lee, Science 299 (2003) 1874. [3] Y.F. Zhang, Y.H. Tang, N. Wang, D.P. Yu, C.S. Lee, I. Bello, S.T. Lee, Appl. Phys. Lett. 72 (1998) 1835. [4] N. Wang, Y.F. Zhang, Y.H. Tang, C.S. Lee, S.T. Lee, Appl. Phys. Lett. 73 (1998) 3902. [5] Y. Cui, L.J. Lauhon, M.S. Gudiksen, J. Wang, C.M. Lieber, Appl. Phys. Lett. 78 (2001) 2214. [6] S. Hofmann, C. Ducati, R.J. Neill, S. Piscanec, A.C. Ferrari, J. Geng, R.E. Dunin- Borkowski, J. Robertson, J. Appl. Phys. 94 (2003) 6005. [7] Y. Wu, Y. Cui, L. Huynh, C.J. Barrelet, D.C. Bell, C.M. 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The appearance of p - bonded chain implies that the stability of {11 1} facets is similar to that in clean Si( 11 1). atoms of Si( 11 1)-(2  1) p -bonded chain surface are identical within 0. 01 eV and 0. 01 Å, respectively. 2 Although the size of unit cell along the [11 0] direction