NANO LETTERS
Pristine Semiconducting [110] Silicon Nanowires
2005 Vol. 5, No. 11 2302-2305
Abhishek Kumar Singh,*,† Vijay Kumar,†,‡,§ Ryunosuke Note,† and Yoshiyuki Kawazoe† Institute for Materials Research, Tohoku UniVersity, Aoba-ku, Sendai 980-8577, Japan, Research Institute for Computational Sciences (RICS), National Institute of AdVanced Industrial Science and Technology (AIST), AIST Tsukuba Central 2, Umezono 1-1-1, Tsukuba 305-8568, Japan, and Dr. Vijay Kumar Foundation, 45 Bazaar Street, K. K. Nagar (West), Chennai 600 078, India Received August 31, 2005; Revised Manuscript Received September 28, 2005
ABSTRACT We report results of ab initio calculations on silicon nanowires oriented along the [110] direction and show for the first time that these pristine silicon nanowires are indirect band gap semiconductors. The nanowires have bulk Si core and are bounded by two (100) and two (110) planes in lateral directions. The (100) planes are atomically reconstructed with dimerization in a manner similar to the (100) surface of bulk Si but the dimer arrays are perpendicular to each other on the two (100) planes. An interesting consequence of surface reconstruction is the possibility of polytypism in thicker nanowires. We discuss its effects on the electronic structure. These findings could have important implications for the use of silicon nanowires in nanoscale devices as experimentally [110] nanowires have been found to grow preferentially in the small diameter range.
Silicon nanowires (SiNWs) are currently attracting great interest, as these are the most promising building blocks for the “bottom-up” approach to future nanoscale devices. Remarkable developments have taken place in recent years that show applications of SiNWs as electronic devices1,2 and as biological and chemical sensors.3 Even basic computations have already been performed using logic-gate structures formed4 from the crossed nanowires. Most exciting are the applications in optical and photonic devices5sa domain that is almost forbidden for bulk silicon. The reason for this versatility of SiNWs lies in the increased number of controllable parameters at the nanoscale as compared to bulk. In the case of SiNWs, the growth direction, thickness, morphology, and the way the surface is pacified (via oxidation or hydrogenation) can be controlled to modify their electronic properties. Furthermore, the quantum confinement of carriers that occurs at the nanoscale could lead to their very useful size dependent optical properties. Experimentally, SiNWs with less than 10 nm diameter can now be synthesized with control in growth direction and thickness. In recent experiments nanowires are grown along [110] and [112] directions6 with the diameter in the range of 1.3-7 nm. A detailed analysis shows7 that smaller diameter SiNWs are oriented along [110], while larger * To whom correspondence may be addressed. E-mail:
[email protected]. † Institute for Materials Research, Tohoku University. ‡ Research Institute for Computational Sciences (RICS), National Institute of Advanced Industrial Science and Technology (AIST). § Dr. Vijay Kumar Foundation. 10.1021/nl051739f CCC: $30.25 Published on Web 10/19/2005
© 2005 American Chemical Society
diameter nanowires are oriented along [112] or [111] direction. Though these astonishing developments show the capabilities achieved in controlling the growth at the nanoscale, there are only a few theoretical studies of these systems. The size and possible surface reconstructions make a comprehensive quantum mechanical study of pristine SiNWs still challenging. H-terminated SiNWs have been studied but often with bulk atomic structure due to the passivation of dangling bonds. The band gap of these semiconducting nanowires exhibits quantum confinement induced widening.8-10 In a different approach, assembly of stable silicon nanoclusters has been used to study the stability of SiNWs.11 Recent experiments, however, convincingly show that pristine SiNWs grow around a crystalline bulk core, but the atomic structure on the facets and edges could have important effects on their properties as has been shown for [100] SiNWs.12 Rurali et al. have shown13 that SiNWs grown along the [100] direction are metallic or semimetallic due to the presence of surface states. Such metallic nanowires are important as interconnects; the semiconducting nanowires are essential for band gap engineering that could proliferate their applications in various interdisciplinary fields. Here we consider pristine thin SiNWs with ≈1 nm diameter and axis along [110] direction as observed and show for the first time that these are semiconducting. The calculations have been performed within the ab initio density functional theory using the ultrasoft gradient corrected pseudopotentials14-16 and the generalized gradient
Table 1. The Mean Initial and Final Cross Sections (Å × Å), Number of Atoms (N), Length of the Optimized Unit Cell (L) in Å, BE in eV/atom, and Band Gaps (eV) of the Optimized SiNWs SiNWs NW1 NW2 NW3
Figure 1. SiNW NW2: Gr. I and II represent the initial and final atomic structures in the unit cell, respectively. Part a shows the cross section along the axis while parts b and c show the (100) and (110) facets, respectively. Twelve layers of Si atoms can be seen in the unit cells shown in parts b and c. For clarity, the surface Si atoms that form dimers are shown in red and yellow on the two opposite (100) facets (i) and (ii) in part b. The orientation of the dimers on the two facets is perpendicular. The red balls can be seen in part c to lie in a plane so that there is no buckling of these dimers. Also the (110) facets of the nanowire do not reconstruct but have significant relaxation near the edges.
approximation (GGA)17 for the exchange-correlation functional. The valence electron wave functions are expanded using a plane wave basis set with a kinetic energy cutoff of 150.6 eV. The Brillouin zone integrations are carried out using 5 k-points along the nanowire axis. The cell length along the nanowire axis (taken as z-axis) and the atomic positions in each cell are optimized without any symmetry constraints. Sufficient vacuum space is kept in the x and y directions to create an infinite one-dimensional system. We consider SiNWs oriented along [110] direction with three different average diameters to understand the diameter dependence of the properties and call them NW1, NW2, and NW3. These nanowires were cut from bulk silicon in rectangular shapes and are bounded by two (100) and two (110) facets in lateral directions (Figure 1). To allow for possible reconstructions on the surface and eliminate artifacts of periodic boundary conditions, 12 or more layers of Si are considered in a unit cell along the nanowire axis. This leads to unit cell sizes that are the biggest ever taken for an ab initio calculation of the SiNWs and has led to interesting possibilities of polytypism in these systems. The initial and final cross sections (CS), number of atoms, length of the unit cell, binding energy (BE), and band gaps of the optimized nanowires are given in Table 1. The initial structure of the thinnest SiNW (NW1) has an array of Si atoms with three dangling bonds due to the Nano Lett., Vol. 5, No. 11, 2005
CS (initial)
CS (final)
N
L
BE
5.91 × 8.54 5.93 × 8.79 84 22.7 4.12 7.68 × 10.86 7.25 × 10.65 132 22.8 4.21 15.35 × 10.86 14.20 × 11.33 240 22.9 4.31
band gap 0.37 0.01 0.28
presence of (100) facets and the way the facets meet at the edges. Consequently, the nanowire undergoes severe reconstruction, strongly driven by the tendency of Si atoms to reduce the number of dangling bonds at the surface. Such severe reconstructions of very thin SiNWs could change their overall structure, as was also found in the study18 of cluster assembly of nanowires. Here we emphasize the semiconducting nature of this thin nanowire and an important feature of the reconstruction that shows the formation of Si dimer layer at the (100) facets. The dimers on the two (100) faces are perpendicular to each other and get buckled similar to the reconstruction observed on infinite Si(100) surfaces. These features are quite general in this family of SiNWs and would be clear in the following where we discuss results on NW2 and NW3 in detail. The initial and optimized structures of the thicker SiNW (NW2) are shown in (Figure 1). Unlike NW1, in this case none of the Si atoms in the initial structure has three dangling bonds. The driving force for the reconstructions on the (100) facets is again reduction in the number of the dangling bonds. In the initial structure (Figure 1a), Si atoms on the (100) surface of the nanowire are bounded to only two neighbors and therefore each of these has two dangling bonds. By dimerization two dangling bonds per dimer are removed quite similar to the way one observes on a Si(100) surface.19,20 This leads to significant reduction in energy of the nanowires. Also similar to NW1, the arrays of dimer layers formed at the two opposite (100) facets (Figure 1b, i and ii) are perpendicular to each other. The dimer length (2.31 Å) is less than the bulk value. This increases the bond order and lowers the energy further. Compared to surfaces of bulk materials, nanowires have facets that have infinite extent only in one lateral direction and finite in the other. This has further implications for the reconstructions of the nanowires. In the present case one of the dimer layers shown by yellow balls in Figure 1b(i) lies along the nanowire axis and it resembles very closely the reconstruction found on the (100) surface of bulk Si. The dimers are buckled symmetrically.19 On the opposite (100) facet, there are three dimer arrays in the unit cell, each with two dimers as shown in Figure 1b(ii) by red balls. Unlike bulk surfaces, these dimer arrays do not have an infinite extent and are terminated at the edges of the nanowires. We find that the pair of Si atoms forming a dimer on this face makes an additional bond with the Si atom in the adjacent (110) facet. This way the remaining dangling bonds on the dimer atoms are weakened and it lowers the energy further. This also leads to contraction in mean diameter (Table 1) in the (100) direction. 2303
Figure 2. Optimized atomic structure of the NW3 SiNW in the unit cell. (a), (b), and (c) are similar to those in Figure 1. In (c) there are different reconstructions of red atoms and these are marked with A and B. B is the reflection of A and the plane of reflection is shown by a line.
These dimers are not buckled unlike the (100) surface of bulk Si and remain planar (see Figure 1c). The (110) facets, however, do not reconstruct but relaxation occurs which is more significant for the edge atoms. It is partly due to the fact that most of the atoms on these facets are already tricoordinated and any additional bond formation requires large strain energy that is not compensated by the bond formation energy. The optimized structure shows that the actual periodicity of the unit cell consists of four Si layers along the nanowire axis. For the thickest nanowire (NW3) that we studied, the reconstruction again triggers at the (100) facets as shown in Figure 2. Similar to the case of NW2, the dimer layers form on the two (100) facets in perpendicular directions with buckling not only on the dimer layer along the nanowire axis but also on the opposite (100) facet (Figure 2c). This leads to expansion in the mean thickness along the (110) direction (Table 1). As the thickness of the nanowire is increased, the number of dimers in an array on this (100) facet increases to four (Figure 2b(ii)). The dimers that are in the middle of these arrays are tricoordinated and the Si atoms in the core of the nanowires are tetracoordinated as in bulk. This leads to buckling features similar to infinite surfaces. Also the edge dimers are tricoordinated and buckled with slightly longer (2.42 Å) bond length as compared to the value (2.34 Å) for the other two inner dimers. So for thicker nanowires, the effects of terminating the facets are more and more localized on the edges and elsewhere the reconstruction resembles one of the low energy reconstructions observed on the (100) surface of bulk Si. We therefore expect that similar reconstructions will take place on thicker SiNWs. A characteristic feature of the atomic structure of NW3 SiNW is that there are two consecutive arrays of dimers on a (100) facet that have mirror symmetry in a plane perpendicular to the axis of the nanowire as shown in Figure 2304
Figure 3. Optimized atomic structure of NW3 SiNW in the unit cell with eight silicon layers. Two ways of reconstruction are shown such that the dimer sequences are A A or A B type. (a and c) and (b and d) show the (100) and (110) facets, respectively, of the A B (A A) sequence. The A B sequence has the lowest energy, but A A is almost degenerate.
2c by A and B. The third array is similar to one of the other two arrays. To further clarify the growth behavior, we studied nanowires with eight Si layers in a unit cell such that (1) there are two dimer arrays with a reflection symmetry (Figure 3(a and c)) and (2) two arrays with similar consecutive arrangement (Figure 3b,d)). After optimization the structures remain nearly the same and in both cases the energies are also nearly degenerate, though in case 1 the energy lies 0.04 eV lower than the value for case 2. This suggests a possibility of polytypism in the growth of these nanowires with different sequences of A and B type blocks of layers. Interestingly, in all the cases, the nanowires are semiconducting with nearly the same value of the band gap. Therefore such a polytypism will not affect the properties significantly. The band structure of the NW3 nanowire shows it to be an indirect band gap semiconductor (Figure 4) while NW2 is a semimetal. The characters of the bands near the top of the valence and bottom of the conduction bands are further analyzed by plotting the band decomposed electronic charge density. In the case of NW2 (Figure 5a), the electronic charge density of the topmost valence band originates from sp3 type orbitals on the edge atoms. The separations between the lobes are 3.77 and 3.83 Å along the nanowire axis, and this results in weak overlap and relatively flat bands. The electronic charge density from the bottom of the conduction band state comes from pz type orbitals as the atomic arrangement on the face becomes flat and the bonding more sp2 type as can be seen in Figure 5a. The separations between the lobes are 3.69 and 3.92 Å, respectively. Therefore the dispersion of the corresponding band is again small, and the band is narrow. The characteristics of the other two bands lying above (not shown in figure) the bottom of conduction band Nano Lett., Vol. 5, No. 11, 2005
Figure 4. Parts a and b show the band structures of NW2 and the lowest energy NW3 eight-layer nanowires, respectively. The arrows show the indirect band gap. Dashed line shows the Fermi level of NW2.
semiconducting irrespective of morphology of other facets. A detailed study on these results will be published elsewhere. In summary we have shown for the first time from ab initio calculations that semiconducting pristine SiNWs can be formed if the nanowires are grown in the [110] direction. These results gain significance from the point of view of applications as experiments show preference for [110] nanowires in the small diameter range as studied here. We find a systematic pattern of the atomic reconstructions at the (100) facets of these nanowires and even thicker nanowires can be expected to have similar reconstructions. These results would be helpful in identification of atomic structures of facets in experiments as well as in the understanding of the properties of such SiNWs. Also we find the possibility of polytypism in the surface reconstruction. However, this does not affect the semiconducting properties significantly. Acknowledgment. We thankfully acknowledge the support of the staff of the Center for Computational Material Science, IMR, Tohoku University for the use of SR8000/ H64 supercomputer facilities. A.K.S. is also thankful for the support of JSPS fellowship. V.K. acknowledges partial support from NAREGI Nano Science Project, Ministry of Education, Culture, Sports, Science and Technology, Japan and the hospitality at IMR as well as RICS, AIST.
Figure 5. Band decomposed electronic charge density of (a) NW2 and (b) the lowest energy NW3 SiNWs. Brown and green show band decomposed electronic charge density isosurfaces from the top of the valence band and the bottom of the conduction band, respectively.
are also similar. These as well as the three bands near the top of the valence band originate from the folding of the same bands as actual periodicity is of 4 Si layers and we have taken 12 layers in the unit cell. In the case of NW3 the band decomposed electronic charge density (Figure 5b) on the topmost valence band originates at the edges of the nanowire. The lobes are sp3 type and are separated by 3.89 and 3.75 Å. Again the corresponding dispersion is small and results in a narrow band. The electronic charge density from the bottom of conduction band states shows again pz character and originates from one of the dimer atoms that lie along the axis of the nanowire. These results show that the bands corresponding to the conduction band minima and valence band maxima of these nanowires originate at two different facets of the nanowire. This is in contrast to the character of metallic/semimetalic bands observed in the nanowires grown along the [100] direction, where they lie invariably on the dimer atoms.13 Our results indicate that the origin of the semiconducting gap is inherent to this particular family of the nanowires. 21 The sizable band gap of the NW3 nanowire and a consistent reconstruction behavior show a strong possibility of the formation of thicker semiconducting nanowires also in this family. Currently, extensive work is going on not only involving (100) or (110) facets but also considering several other facets including (111) facet. The initial results show that the nanowires oriented along [110] direction and involving (100) facet, are Nano Lett., Vol. 5, No. 11, 2005
References (1) Chung, S.-W.; Yu, J.-Y.; Heath, J. R. Appl. Phys. Lett. 2000, 76, 2068. (2) Zheng, G.; Lu, W.; Jin, S.; Lieber, C M. AdV. Mater. 2004, 16, 1890. (3) Cui, Y.; Wei, Q.; Park, H.; Lieber, C. M. Science 2001, 293, 1289. (4) Huang, Y.; Duan, X.; Cui, Y.; Lauhon, L. J.; Kim, K.-H.; Lieber, C. M. Science 2001, 294, 1313. (5) Guiksen, M. S.; Lauhon, L. J.; Wang, J.; Smith, D. C.; Lieber, C. M. Nature 2002, 415, 617. (6) Ma, D. D. D.; Lee, C. S.; Au, F. C. K.; Tong, S. Y.; Lee, S. T. Science 2003, 299, 1874. (7) Wu, Y.; Cui, Y.; Huynh, L.; Barrelet, C. J.; Bell, D. C.; Lieber, C. M. Nano Lett. 2004, 4, 433. (8) Delley, B.; Steigmeier, E. F. Appl. Phys. Lett. 1995, 67, 2370. (9) Reeds, A. J.; Needs, N. J.; Nash, K. J.; Canham, L. T.; Calcott, P. D. J.; Quteish, A. Phys. ReV. Lett. 1992, 69, 1232. (10) Landman, U.; Barnett, R. N.; Scherbakov, A. G.; Avouris, P. Phys. ReV. Lett. 2000, 85, 1958. (11) Li, B. X.; Cao, P. L.; Zhang, R. Q.; Lee, S. T. Phys. ReV. B 2002, 65, 125305. (12) Ismail-Beigi, S.; Arias, T. Phys. ReV. B 1998, 57, 11923. (13) Rurali, R.; Lorente, N. Phys. ReV. Lett. 2005, 94, 026805. (14) Vanderbilt, D. Phy. ReV. B 1990, 41, 7892. (15) ] Kresse, G.; Hafner, J. J. Phys.: Condens. Matter 1994, 4, 8245. (16) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169; Comput. Mater. Sci. 1996, 6, 15. (17) Perdew. J. P. In Electronic Structure of Solids ’91; Ziesche, P., Eschrig, P., Eds.; Akademie Verlag: Berlin, 1991. (18) Singh, A. K.; Kumar, V.; Briere, T. M.; Kawazoe, Y. Nano Lett. 2002, 2, 1243. (19) Roberts N.; Needs, R. J. Surf. Sci. 1990, 236, 112 and references therein. (20) Fritsch, J.; Pavone, P. Surf. Sci. 1995, 344, 159. (21) As the thickness of the nanowires increases, the fraction of the surface to bulk atoms as well as the surface to bulk states decreases. The ratio of tri- to more than tricoordinated Si atoms (the tri-, tetra-, and pentacoordinated Si atoms are 54, 72, and 6 for NW2 and 94, 144, and 2 for NW3, respetively) reduces from 0.69 for NW2 to 0.63 for NW3.
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