Effects of Morphology and Doping on the Electronic and Structural

We study the electronic and atomic structures of hydrogenated silicon nanowires (SiNWs) by ... orientation using state-of-the-art density functional c...
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NANO LETTERS

Effects of Morphology and Doping on the Electronic and Structural Properties of Hydrogenated Silicon Nanowires

2006 Vol. 6, No. 5 920-925

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

ABSTRACT We study the electronic and atomic structures of hydrogenated silicon nanowires (SiNWs) by changing the mean diameter, morphology, and orientation using state-of-the-art density functional calculations. Most of the SiNWs are found to have large and direct band gaps, which make them very interesting for silicon-based nano-optoelectronic devices and lasers. The band gap increases with decreasing diameter in all cases because of quantum confinement, but the scaling is dependent on the morphology of the SiNWs. For thin [112] SiNW, the calculated band gap agrees well with the recent experiments. Variation in hydrogen concentration is used to explore the sensing capabilities of different surface morphologies and the associated surface reconstructions. Further studies on p- or n-doping show bulklike modifications in the electronic structure with several advantages that can be used to design nanoscale devices of SiNWs.

Silicon nanowires (SiNWs) are currently attracting great attention as they could be potential candidates and materials of choice for nanoelectronics because of their novel electrical and optical properties,1 controlled production,2-7 and promising new applications such as molecular-scale sensors.8-13 The vast knowledge of dealing with silicon surfaces is a tremendous advantage for developing functional devices. Doping of SiNWs by boron and phosphorus has been achieved to develop p- and n-type elements for active devices,14,15 and even integration of such devices to perform some of the basic computations16 has been demonstrated. SiNWs are biocompatible and their potential as biological as well as chemical sensors8-13 even at the molecular scale has been shown. These applications rely heavily on the electronic structure of SiNWs and require precise control of the surface atomic and electronic structures. For the rapid development of this field, advances in the understanding of the electronic structure of SiNWs and the various possible ways to modify it are very important. There are several ways that the electronic structure of SiNWs can be modified, for example, by changing the thickness, orientation, surface morphology, hydrogen concentration, and doping. Knowledge of the structure-property * Corresponding author. 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/nl052505z CCC: $33.50 Published on Web 04/07/2006

© 2006 American Chemical Society

relation can help experimentalists grow SiNWs suitable for a particular application. Getting this information from experiments could be a challenging task, and so far there is only one study1 where the diameter and orientation dependence of the band gap has been measured. Scanning tunneling microscopy (STM) has been used to obtain atomic structure but generally this needs further verification from calculations. Nanowires with ∼1 nm diameters can now be produced experimentally1 and are ideally suited for study by ab initio calculations. Such theoretical studies on hydrogenated SiNWs are currently few.17 SiNWs oriented along the [100] direction have been studied previously18-21 for understanding luminescence from porous silicon and quantum confinement effects, but their geometries differ from SiNWs produced experimentally. A recent theoretical study17 on nanowires oriented along the [110] and [111] directions using local density approximation (LDA) also showed thickness-dependent optical properties. Experimentally, however, the thinnest hydrogenated SiNWs, grown with ∼1 nm diameter, are oriented along [112] direction.1 Larger diameter nanowires tend to grow along the [110] direction.4 Here we present results of ab initio calculations on hydrogenated SiNWs with different diameters, orientations, and morphologies and show for the first time the effects of the variation in hydrogen concentration as well as P and B doping on the electronic and atomic structures. These results could be used as representative of the sensing ability of the nanowires and

Figure 1. Cross sections of the optimized structures of SiNWs. (a) NW1, (b) NW2, (c) NW3, (d) NW4, and (e) NW5. Red and blue balls represent H and Si atoms, respectively. NW1 and NW2 are oriented along [110], NW3 and NW4 along [100], while NW5 is oriented along the [112] direction. Part f shows the dimerization of those Si atoms (yellow balls) that have only one terminal H on the (100) surface. On one (100) face (front side in the figure) of NW2 the dimerization is perpendicular to the nanowire axis but on the opposite (100) face (backside) it is along the nanowire axis. Similar Si dimers are formed on the (100) surface of NW3 also. Part g shows the (111) surface of NW5. The main features of the structure are the same as those observed in experiments except that in our calculations each surface Si atom is terminated with one H.

could provide guidance for preparing n- and p-type SiNWs. The physical and chemical characteristics of SiNWs including the mean diameter, surface composition, and electronic properties can, in principle, be controlled during synthesis.2-7 The thinnest nanowires grown so far have diameters of about 1.3 nm and are oriented along the [112] direction.1 To compare the properties and understand the possible reason for the preferential growth, we have studied geometries of nanowires grown along the [110], [100], and [112] crystallographic directions. Five different classes of nanowires differing in orientation and surface morphology Nano Lett., Vol. 6, No. 5, 2006

are considered. These are referred to as NWn (n ) 1-5) and are shown in Figure 1. The nanowires are cut from a bulk silicon crystal and are bounded by low index surfaces. The geometry of NW1 is the same as that inferred from experiments1 on larger diameter nanowires. It is oriented along the [110] direction and has a hexagonal cross section with four (111) and two (100) surfaces. NW2 is also oriented along [110]. However, it is bounded by two (100) and two (110) planes in lateral directions. NW3 differs from NW2 only in orientation because it is bounded by similar surfaces as NW2 but oriented along [100]. NW4 is bounded by (110) planes in all lateral directions and is oriented along the [100] 921

Figure 2. Electronic band structures and band gaps of NWn (n ) 1-5) nanowires with comparable mean diameters. Arrows are drawn to show the indirect band gaps in NW3 and NW4. Major ticks on the y axis are equivalent to 1 eV.

direction. Finally, the geometry of NW5 is similar to the thinnest experimentally observed SiNW. It is oriented along the [112] direction and bounded by two (110) and two (111) surfaces in lateral directions. The dangling bonds on the surface are terminated with H atoms so that each Si atom lying on the surface of the nanowires is tetracoordinated. However, in NW2 and NW3, the tetravalency of Si atoms lying on Si(100) facets is ensured by taking into account Si dimer formation, which is usually observed on bulk Si(100) surface. The optimizations are performed using an ab initio ultrasoft pseudopotential22 plane wave supercell method23-25 with periodic boundary conditions and the conjugate gradient technique within the generalized gradient approximation26 (GGA) for the exchange-correlation energy. The cutoff energy for the plane wave expansion is taken to be 227 eV. The Brillouin zone is sampled by 5 k-points along the nanowire axis for achieving atomic optimizations. The structures are considered to be fully relaxed when the absolute value of the force on each ion becomes less than 0.001 eV/Å. More than 10 Å vacuum space is used in lateral directions to avoid any interactions between the replicas of the nanowire. Also to allow atomic relaxations and reconstructions, we use a large unit cell length along the nanowire axis, which is also optimized. For bulk Si the calculated lattice parameter (5.46 Å) and cohesive energy (4.73 eV/ atom) are in excellent agreement with the experimental values of 5.43 Å and 4.63 eV/atom, respectively. The optimized structures of nanowires are highly symmetric (Figure 1a-g) and in general lack any surface reconstruction due to the passivation of the dangling bonds by H except for NW2 and NW3 in which case the tricoordinated Si atoms on Si(100) surfaces get dimerized as shown in Figure 1f. For NW2, the dimer layers on the two opposite facets are perpendicular to each other and the dimers are planar (Figure 1f). This is in contrast to (100) surface of bulk Si and pristine Si nanowires27 where the Si atoms remain tricoordinated even after dimer formation (except for a special case where the dimers get tetracoordinated and become planar27) and this leads to buckling in the 922

dimer layers. The reconstructions on the (100) facets of hydrogenated SiNWs are very similar to monohydride formation on the H adsorbed (100) 2 × 1 surface28 of bulk Si. Furthermore, the morphology of the hydrogenated NW3 has Wulff construction. After hydrogenation and optimization (Figure 1c), the dimer formation induces curvature on the facets. This leads to a very beautiful reconstruction where four semicircular parts get joined together such that the structure becomes fourfold symmetric along the nanowire axis. The core of the nanowire has the bulk Si structure along the [100] direction. Similar to NW2, the dimers on (100) facets of NW3 are also planar. As we shall show, these reconstructions have important consequences on the electronic structure of the nanowires. The Si-Si dimer length on (100) facets is 2.43 and 2.40 Å for NW2 and NW3, respectively. In the case of NW1, as proposed in experiment, all of the dangling bonds are saturated by H atoms on the (100) facets that resemble the dihydrated (100) 1 × 1 surface of bulk Si. It has been shown29 that with an increase in H chemical potential monohydride 2 × 1 Si(100):H can transform to a dihydride surface. In the case of NW5, the thinnest experimentally1 observed SiNW, the structure of the (111) facet is very similar to the STM images (Figure 1g). The calculated Si-Si and Si-H bond lengths (3.85 and 1.5 Å) on the (111) facet agree well with the experimental values1 of 3.80 and 1.5 Å, respectively. However, the experimental interpretation of the STM data that the dots on top of the silicon atoms are SiH3 complexes differs in our work because we hydrogenate these atoms with only one H because each Si atom has only one dangling bond (Figure 1g). Any additional H atom will induce strain in the structure and could lead to distortions. However, the STM image shows no sign of distortions on this facet. The electronic structures of the nanowires are shown in Figure 2. Except for NW3 and NW4, interestingly the nanowires are direct band-gap semiconductors. The band gap changes with the orientation and thickness of the nanowires (Table 1 and Figure 3). NW1 and NW2 are oriented along the same direction and have similar band gaps (∼1.34 eV). However, though NW3 and NW4 are oriented along the same Nano Lett., Vol. 6, No. 5, 2006

Table 1. Stoichiometry Representing the Number of Atoms in the Unit Cell, Mean Diameter, and the Band Gap of SiNWsa system NW1 NW2 NW2 (i) NW2 (ii) NW3 NW3 (i) NW3 (ii) NW4 NW4 (i) NW4 (ii) NW5

stoichiometry Si168H80 Si160H64 Si88H48 Si56H36 Si144H96 Si64H32 Si42H24 Si144H96 Si80H64 Si52H48 Si100H60

mean diameter (nm)

band gap (eV)

1.77 1.56 1.17 0.97 1.78 1.20 1.00 1.40 1.21 1.02 1.35

1.30 1.34 1.52 1.71 1.63 (I) 1.97 2.08 1.36 (I) 1.56 2.27 1.83

a (I) indicates indirect band gap; within the same family of nanowires the band gap increases with decreasing mean diameter because of quantum confinement.

Figure 3. Plot of the band gap vs mean diameter of the nanowires shows that in general the gap increases with decreasing diameter and it depends on the orientation of the nanowire. The dependence on mean diameter is similar for NW2 and NW3 but very different for NW4 showing a strong dependence on the morphology of the nanowire.

direction, the band gaps for nanowires with even nearly the same mean diameters differ by as much as 0.40 eV because of the different surface morphologies. Also, the scaling of the band gap with diameter depends strongly on the nanowire morphology. As shown in Figure 3, the band gap increases strongly for NW4 with decreasing mean diameter as compared to the case of NW3 even though both of the nanowires are oriented along the same direction. Therefore it is not possible to fit them in a universal function, as was reported previously.17 The calculated band gap for NW5 is 1.80 eV, and it is the largest among all of the nanowires with comparable mean diameter. The actual band gap is expected to be significantly higher because of the underestimation within the GGA. For small diameter [110] and [111] SiNWs, Zhao et al.17 calculated a correction to the band gap using the GW method and found it to be about 100% of the LDA value. Accordingly, we expect the true band gap in our case to be in very good agreement with the experimental value Nano Lett., Vol. 6, No. 5, 2006

of 3.53 eV. Importantly, the band gap is direct (not determined in experiments) and it is detrimental to the optical applications of the nanowires. The effect of thickness on the band gaps of nanowires is studied by considering three cases for NW2, NW3, and NW4.30 The features of the bands in NW3 and NW4 are similar because they are oriented along the same direction. Near the top of the valence band there are two bands that cross and their maxima lie at nearly the same energy (difference being only 0.005 eV). Nevertheless, it makes these two nanowires indirect band-gap semiconductors. The profile of the band structure does not change when the diameter is decreased. However, the valence band with the maximum energy gets pushed down and it makes the thinner nanowires direct band-gap semiconductors. The band gap of the nanowires increases monotonically with decreasing thickness (Figure 3), as has also been found in previous studies. This is due to the quantum confinement of the carriers, which is particularly strong in the range of diameters we have studied. The largest GGA band gap (2.27 eV) is found for the thinnest nanowire (mean diameter 1.02 nm) in the NW4 family, for which the actual band gap is expected to lie in the ultraviolet region. This result shows that it could be possible to prepare SiNWs with desired band gaps by varying the thickness and orientation and performing bandgap engineering. It could open up avenues for their potential applications in optoelectronics, photonics, and miniaturized lasers. Our results show that though orientation and surface morphology modify the band gap, the change is more systematic with the thickness variation. Besides optical applications, SiNWs have been shown to hold great promise for label-free detection of biological and chemical species.8-13 The electrical detection of species by SiNW sensors is based on the principle of solid-state field effect transistor (FET) in which p- or n-doped nanowires are used and the gating is achieved chemically by a change in the surface charge when a species binds on the surface leading to a change in the conductance. For the detection of specific biological molecules, the surface of SiNWs in such devices is modified by attaching receptors that bind selectively the species to be detected. In another setup the surface of a SiNW was modified for measuring pH so that it could undergo protonation and deprotonation.8 Such a change in the surface charge gates the nanowire without applying any voltage and again a change in conductance could be used for detection. In contrast to bulk surfaces where the changes in the electronic structure are confined to the surface, the effects of receptor-legend chemistry on the surface of a nanowire go deeper into the core of the nanowire and this further increases the sensitivity of the sensors to the point of single molecule detection.8-13 Unlike oxidized nanowires where the layers of silica are generally thick, the surfaces of hydrogenated nanowires have only one layer of H to pacify the dangling bonds. Therefore, surfaces of hydrogenated nanowires could be even more sensitive and any changes in surface chemistry could have a pronounced effect on the sensing capability of nanowires. As a first step, we study 923

Figure 4. Band structures of (a) defect and (b) defect-free nanowire NW4. The inset shows the cross section and side views of the nanowire with band decomposed charge density isosurfaces. Yellow and purple colors correspond to VBM and CBM of nanowire with H defects.

the effects of changing the concentration of H on the surface of NW4 nanowires because they involve only (110) facets. Removal of one H atom from each of the corner Si atoms of the NW4 nanowire (8 H atom/unit cell) has an effect of creating unpaired electrons on the surface and it leads to a drastic change in the band structure (Figure 4) of fully relaxed atomic structure. The electronic states associated with defects have energies lying within the band gap and it leads to a dramatic reduction in the band gap of the SiNWs. To demonstrate the origin of the defect states, in Figure 4 we show the charge densities arising from the defect states. It is seen that the charge densities arising from the valence band maximum (VBM) and conduction band minimum (CBM) are strongly localized on the eight corner Si atoms, showing clearly that these bands originate from hydrogen defect sites. Importantly, these sites can act as centers of attraction for various receptors. In contrast to this result, we find that SiNWs with (100) facets can easily offset the effects of the H deficit on the surface by dimerization as we discussed in the case of NW2 and NW3 earlier. Therefore, on such surfaces the band gap and electronic properties are unlikely to be affected by H defects. This shows that the electronic properties of nanowires with (100) surfaces cannot be modified easily and therefore are poor candidates for the sensors. Nanowires with (110) or (111) surfaces are ideal for sensors because their electronic properties could be modified drastically by changing H concentration. Most of the electronic or sensing applications of SiNWs have been shown for p- or n-doped nanowires having thicknesses8 in the range of 10-30 nm and oxidized layers on the surface. With the advent of hydrogenated thinner nanowires, it is important to know the effects of doping on the electronic structure of such nanowires. Since we found significant differences in the electronic properties of NW1 and NW4 by a change in hydrogen concentration, we considered them as our prototypes and doped them with B 924

Figure 5. Band structures of n- and p- type nanowires: (a) NW1 and (b) NW4. The red dotted line shows the Fermi energy. The inset shows the charge density decomposed on the donor and acceptor bands crossing the Fermi energy. For NW1 also, the charge density around the dopant site spreads to several neighbors but it is more along the nanowire axis.

and P to have p- and n-type nanowires, respectively. After optimizations, the band structures of the doped nanowires show (Figure 5) a shift of the Fermi level toward the valence and conduction band for the p- and n-type SiNW, respectively. This behavior is quite universal and is observed in both types of nanowires (Figure 5) irrespective of their orientation and surface morphology. However, few subtle differences are observed that arise not because of doping but because of the difference in the surface morphologies of the nanowires. For example, the dispersion in the valence band of p-NW1 is more than that in the case of p-NW4, implying heavier holes in p-NW4 in comparison to p-NW1; likewise, better conduction properties are expected in p-NW1. A comparison of the band structures of the doped and undoped nanowires (Figure 2 and Figure 5) shows that the dispersion of the conduction or valance bands does not change much upon doping. Nanowires grown along different directions and with different surface morphologies have different dispersions (Figure 2) in their conduction and valence bands and this information can be used to design doped semiconductors with better conduction properties. In our calculations, one dopant in the unit cell represents about 0.4% dopant concentration and it is clearly a case of heavy doping. The band structures show that the Fermi level lies in the acceptor/donor bands for the p-/n-type nanowires. Nano Lett., Vol. 6, No. 5, 2006

The electronic charge density decomposed on CBM for the n-type and VBM for the p-type nanowire shows that these bands originate from the dopant site. Interestingly, for the p-type nanowire the electronic charge extends up to 3rd and 4th nearest neighbors and we expect that even for lower doping concentrations a similar effect would be observed. It can enhance the sensing capabilities of thin nanowires further. Similar to bulk Si or oxidized thicker SiNWs, our results show that thin hydrogenated SiNWs can also work as both p- and n-type semiconductors and have the potential to be one of the most important circuit elements for nanoscale devices. In summary, state-of-the-art ab initio calculations on atomic and electronic structures of hydrogenated silicon nanowires show them to be direct band-gap semiconductors in most cases. The band gaps are large and can be tuned by changing thickness, orientation, and morphology as well as doping or changing H concentration leading to the possibilities of band-gap engineering. A strong dependence of the band gap on the morphology of the nanowires implies that experimental determination of the morphology would be important for their optical applications. Our results of the band gap of the thinnest experimentally obtained nanowire are in good agreement with the measurements. These nanowires could be ideal for applications such as optoelectronic devices, lasers, and sensors. Furthermore, we have shown for the first time that H defects on nanowires with (110) facets modify their electronic properties significantly so that they could be used as sensors and that the behavior of n- or p- type doping in hydrogenated SiNWs is very similar to bulk or oxidized thicker nanowires, therefore establishing them to be the smallest possible building blocks for silicon-based nanoscale devices. 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 a JSPS fellowship. V.K. acknowledges partial support from NAREGI Nano Science Project, Ministry of

Nano Lett., Vol. 6, No. 5, 2006

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