Structures and Electronic Properties of the Bi−Sb Superlattice

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Structures and Electronic Properties of the Bi-Sb Superlattice Nanowires and Core-Shell Structural Bi/Sb Nanowires Jingshan Qi, Daning Shi,* Hongxia Chen, and Baolin Wang Department of Physics, Nanjing UniVersity of Aeronautics and Astronautics, Nanjing 210016, China ReceiVed: March 30, 2009; ReVised Manuscript ReceiVed: May 26, 2009

We systematically study the structural and electronic properties of the Bi-Sb superlattice nanowires and core-shell structural Bi/Sb nanowires by first-principles calculations. The relaxed structures of these heterostructural nanowires are first obtained and found to be similar to those of homogeneous Bi nanowires. For the Bi-Sb superlattice nanowires, band lineups of Bi and Sb zones result in multiple quantum wells, where specific states at the band edges and in band continua are confined. The confined electrons (holes) become more localized if the width of the barrier is larger. For the core-shell structural Bi/Sb nanowires, the electronic properties show dependence on the size, the atom type of core, and the chemical composition. Meanwhile, the valence bands are less affected by the chemical composition, while the conduction bands depend on it. These findings might have important implications for understanding the structural and electronic properties of the heterostructural nanowires and further utilizing them as the potential thermoelectric materials. Introduction Thermoelectric phenomena, which involve the conversion between thermal and electrical energy and thus provide a method for heating and cooling materials, are expected to play an increasingly important role in meeting the energy challenges of the future. The maximum efficiency of a thermoelectric material for both power generation and cooling is determined by its figure of merit (ZT): ZT ) S2σT/κ, where S, σ, T, and κ are, respectively, the Seebeck coefficient, electrical conductivity, temperature, and thermal conductivity.1 The electronic conductivity is proportional to electron and hole mobilities, which are inversely proportional to the effective masses of electron and hole, while the Seebeck coefficient is proportional to the effective mass of the carriers. The electronic thermal conductivity depends on the electronic band structure, electron scattering, and electron-phonon interactions. The quantities S, σ, and κ for conventional three-dimensional (3D) crystalline systems are interrelated in such a way that it is very difficult to control these variables independently so that ZT could be increased.2 This is due to the fact that for conventional 3D crystalline systems, an increase in S usually results in a decrease in σ and produces a decrease in the electronic contribution to κ, following the Wiedemann-Franz law.3 However, in the mid 1990s, theoretical predictions first suggested that the thermoelectric efficiency could be greatly enhanced in one-dimensional (1D) and twodimensional (2D) systems compared to the bulk materials, due to both a sharper density of states in low-dimensional systems for enhanced thermopower (S2σ) and an increased phonon scattering for reduced lattice thermal conductivity.4,5 The recent experiment further showed that sized and engineered heterostructures may decouple the Seebeck coefficient and electrical conductivity due to electron filtering6 that could result in high ZT. As we know, much of the recent interest in thermoelectricity stems from theoretical and experimental evidence of greatly enhanced ZT in nanostructured superlattices4,7-14 and wires15-17 * Author to whom correspondence should be addressed. E-mail: [email protected].

due to enhanced Seebeck coefficients and reduced thermal conductivity.18,19 Superlattice nanowires, which consist of a series of interlaced nanodots of two different materials, benefit from both the superlattice and nanowire structures and are especially attractive for thermoelectric applications. The heterogeneous interfaces between the nanodots can reduce the lattice thermal conductivity by increasing the phonon scattering at the segment interfaces. The thermopower can be enhanced due to sharper density of states than 1D homogeneous nanowires. The electronic structure and the thermoelectrical properties of lead salt superlattice nanowires have been theoretically investigated by Lin et al.,20 indicating a series of novel features and significantly larger ZT values than those of their corresponding alloy nanowires. One remarkably notable material with very high potential for thermoelectric applications is bismuth (Bi) or the Bi-related compounds because of the high S of the Bi L-point electron carriers.18 Furthermore, both the theories and experiments5,21-23 have indicated that low-dimensional Bi is a better thermoelectrical material than the bulk one. Researchers have successfully synthesized many highly crystalline semiconductor superlattice nanowires,24-26 including Bi-Sb superlattice nanowires.27 As the superlattice nanowire introduces new variables into the system, a comprehensive understanding of how structural, electronic, and transport properties depend on the geometry, such as the length of each of the nanowire segments, is necessary. In addition, the core-shell nanowire structures such as Si/Ge28 and InAs/InP29 have been synthesized in the experiments, and the theory has pointed out that thermal conductivity of core-shell nanowire is significantly smaller than that of the bulk.30 This also motivates us to investigate the structural and electric properties of core-shell Bi/Sb nanowires for further thermoelectric applications. In the previous paper,31 we have systematically studied the stability and electronic properties of single-crystalline Bi nanowires and nanotubes oriented preferentially along the [012] direction using first-principles approaches. All the most stable Bi nanowires are indirect-band gap semiconductors, and their band gaps decrease with increasing diameter, which can be

10.1021/jp902844e CCC: $40.75  2009 American Chemical Society Published on Web 06/04/2009

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understood by the strong quantum size effects. In the present paper, we further study the structural and electronic properties of Bi-Sb superlattice nanowires and core-shell structural Bi/ Sb nanowires. Upon heterostructure formation, superlattice electronic states form subbands in momentum space. The confined states are clearly demonstrated by isosurface plots of charge densities. The band lineup and resulting electronic structure depend on the length and cross-sectional geometry of the constituent Bi and Sb nanowires. For core-shell structural Bi/Sb nanowires, we show that the band structures of nanowires rely on both the atom type of the core and the chemical composition. Computational Procedures The first-principles calculations were performed in the framework of density functional theory (DFT) with the generalized-gradient approximation (GGA)32 by the PW91 functional for the exchange-correlation interaction and projector augmented wave (PAW) pseudopotentials for ion-electron interaction,33 as implemented in the Vienna ab initio simulation package (VASP).34 The plane-wave cutoff, vacuum space, and k-points sampling convergence are all well tested to ensure the accuracy of the total energy within 1 meV/atom. We used an energy cutoff of 220 eV for the plane-wave basis. The dimension of the tetragonal supercell in the lateral plane was adjusted to maintain a sufficiently large separation between adjacent wires (>10 Å from surface to surface). The 1D Brillouin zone integrations are carried out by using six irreducible k-points for a single unit cell and four irreducible k-points for the larger cells along the nanowire axis. On the basis of test calculations, we apply the smearing method of Gaussian broadening with the smearing parameter 0.1 eV for the atomic relaxation and 0.04 eV for the electronic properties calculations. The supercell length along the nanowire axis and the atomic coordinates within the supercell are fully optimized without any symmetry constraints. Geometry optimizations were done for all configurations with a criterion of maximum force less than 0.01 eV/Å. The detailed computational procedure for Bi nanowires along the [012] orientation has been presented in our recent paper.31 The structural optimizations have also been performed for bulk Bi with hexagonal crystal structure and a neutral Bi2 dimer. The overall satisfactory agreement between the theoretical calculations and experiments for bulk and dimer Bi indicates that the accuracy of current computational methods is reasonable and can be applied to Bi or the Bi-related nanowire system. Results and Discussion 1. Bi-Sb Superlattice Nanowires. In this section, we consider longitudinal BinSbm superlattice nanowires and also Bi and Sb nanowires as constituent structures. We have obtained the most stable configurations of the Bi nanowires oriented along the [012] direction. Therefore, the BinSbm superlattice nanowires we consider here are oriented along the [012] direction and have the same cross-sectional shape as the most stable Bi nanowires. For homogeneous Bi or Sb nanowires, we consider N atoms in a single unit cell, denoted as BiN or SbN nanowire. Here we take N ) 24 and N ) 48 as two special prototypes for comparing the effect of different diameters shown in Figure 1. The diameters of Bi24 and Bi48 nanowire are, respectively, about 1 and 1.6 nm. A BinSbm superlattice nanowire has n ()sN) Bi atoms at one side and m ()tN) Sb atoms at the other side of the single unit cell, s and t being integer numbers. m and n can be used for indicating each segment length of the BinSbm superlattice nanowires. For Bi and Sb crystals, the lattice

Figure 1. Structural view of the Bi-Sb superlattice nanowires. Big (purple) and small (gray) balls represent Bi and Sb atoms, respectively.

Figure 2. Band structures of the Bi-Sb superlattice nanowires with 1 nm diameter. Labels correspond to those in Figure 1.

mismatch at the heterogeneous interfaces is minimal, and one has found that in superlattice nanowires, the lattice strain can be laterally relaxed to avoid defects at the interface.35 At the interface Bi atoms are bonded to Sb atoms pseudomorphically, and thus these atoms in BinSbm have the same coordination as BiN or SbN. This means that the interface is atomically flat. Then,

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Figure 3. Band structures of the Bi-Sb superlattice nanowires with 1.7 nm diameter. Labels correspond to those in Figure 1.

Figure 4. Isosurface charge distributions of the band edge states near the band gap in the superlattice unit cell for superlattice nanowires Sb24Bi24 and Sb48Bi48 with 1 nm diameter. The left (red) and right (blue) balls in superlattice nanowires represent Bi and Sb atoms, respectively.

atomic positions and lattice constant are relaxed to obtain the optimized structure. Figure 1 shows the atomic structures in a single unit cell of all studied BinSbm superlattice nanowires. The relaxed structures of SbN and BinSbm are found to be very similar

to that of BiN because of the same configuration of valence electrons for Bi and Sb, i.e., s2p3 type. To consider the effect of the length of each segment, i.e., the lattice constant, on electronic properties of the superlattice

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Figure 5. Density of states (DOS) for nanowires Bi24, Sb24, Sb24Bi24, and Sb48Bi48 with 1 nm diameter.

nanowire, we first examine how the electronic energy bands of nanowire BinSbm evolve with different n and m values. The electronic band structures of BinSbm, BiN, and SbN nanowires with 1 nm diameter are shown in Figure 2. Compared with homogeneous nanowires BiN or SbN, the remarkable feature of superlattice nanowire BinSbm is that all bands including the lowest conduction band and the highest valence band become flatter with the formation of minibands. In this respect, the band gap becomes more uniform as n or m increases, which indicates that the effective mass of electron and hole becomes larger. For instance, in the case of a constant length of Sb segment, from

Figure 7. Variation of the diameter D (a) and lattice parameter C (b) with the composition x for Bi-core/Sb-shell (black square) and Sbcore/Bi-shell (red circle) nanowires.

Figure 2b, c, and d we can see that the energy band becomes more and more flat and the band gap becomes smaller and smaller, respectively, 0.54, 0.50, and 0.49 eV, as the length of the Bi segment increases. These similar variations also happen for BinSbm nanowires with a constant length of Bi segment,

Figure 6. Cross-sectional view of the core-shell structural Bi/Sb nanowires. Big (purple) and small (gray) balls represent Bi and Sb atoms, respectively.

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Figure 8. Band structures of the core-shell nanowires with 1.7 nm diameter. Labels correspond to those in Figure 6.

shown in Figure 2b, f, and g. For BisNSbtN with s ) t, i.e., Bi24Sb24 and Bi48Sb48, as t or s increases, additional minibands occur and they become flatter, accompanied by the decrease of band gap from 0.54 to 0.44 eV as shown in Figure 2b and h, respectively. We also like to point out that the DFT band gaps are usually lower than the experimental values. So, the calculated gaps cannot be directly related to any experimental estimates of gaps in these systems. Furthermore, we consider the size effect on the electronic properties by calculating superlattice nanowires with 1.6 nm diameter. In Figure 3 the band structures of superlattice nanowires show the same varying trend as those of superlattice nanowires with 1 nm diameter. The difference is that the band gap does not monotonously decrease with the increase of the length of segment. The band gap mainly depends on the ratio of Bi and Sb constituent and increases with the increase of Bi

constituent. This should be reasonable because the band gap of Bi48 is 0.44 eV, much larger than that of Sb48, 0.27 eV. These geometry effects on the electronic properties of the surperlattice nanowires can also be well understood in terms of a multiple quantum well structure.36 Because the conduction and valence band edges of different zones (Bi zone and Sb zone) in the superlattice nanowires have different energies, the diagram of conduction and valence band edge along the axis of superlattice nanowires will display a multiple quantum well structure like a Kronig-Penny model. Electrons in the well region of a zone should decay in the adjacent zones having higher conduction band edge, since their energy will fall into the band gap of this barrier zone. As a result, the states of these confined electrons are propagating in the well but decaying in the barrier. Usually, the confined electrons have low group

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Figure 9. Band structures of the core-shell structural nanowires with 2.3 nm diameter. Labels correspond to those in Figure 6.

velocity. They may become more localized if the barrier is high and the width of barrier is large. We further examine whether the states near the band gap can be longitudinally confined by analyzing the charge densities of the states of the band edges of superlattice nanowires. The isosurface charge distributions in the superlattice unit cell for 1 nm superlattice nanowires are shown in Figure 4. For comparison we depict the isosurface charge distributions for superlattice nanowires with different lengths of segment. The states of the highest valence miniband at the band edges are confined in the Sb zone, while the states of the lowest conduction miniband at the band edges are confined in the Bi zone. And we can see that those confined electrons (holes) in Bi48Sb48 become more localized than those in Bi24Sb24. Meanwhile, similar results have been obtained for the superlattice nanowires with 1.6 nm diameter. All in all, the confined states are clearly demonstrated by the isosurface plots of charge densities. The associated band becomes flatter if the width of the barrier is larger, which should produce higher effective masses and therefore larger Seebeck coefficients. Finally, we also investigate the density of states (DOS) projected on Bi and Sb atoms. In Figure 5 we show the DOS of Bi24, Sb24, Sb24Bi24, and Sb48Bi48 with 1 nm diameter. We find a sharper DOS near the Fermi surface (EF) for Bi48Sb48 with the increase of the length of segment as compared with Bi24Sb24. This is a consequence of stronger quantum confinement effects, which means that the confined states become more localized if the width of the barrier is larger. The DOS of the highest valence miniband comes mainly from Sb atom, while

that of the lowest conduction miniband mainly originates from Bi atom. This is also consistent with the results from the charge densities of states of the band edges. 2. Core-Shell Structural Bi/Sb Nanowires. In this section, we consider Bi/Sb core-shell structural nanowires oriented along the [012] direction with the same cross-sectional shape as the most stable Bi nanowires. We take Bi48 and Bi80 nanowires as two special prototypes for comparing the effect of different diameters. The diameters of Bi48 and Bi80 nanowires are about 1.6 and 2.2 nm, respectively. Depending upon the atom’s type (Bi or Sb) in the core and shell subsets, one can obtain either Bi-core/Sb-shell or Sb-core/Bi-shell models of the nanowire heterostructures. For Bi-core/Sb-shell structural nanowires, we designate them as BinSbm nanowires which have n Bi atoms in the core and m Sb atoms in the shell. For Sb-core/ Bi-shell structural nanowires, we label them as SbnBim nanowires which have n Sb atoms in the core and m Bi atoms in the shell. The numbers of m and n determine the chemical composition x ) m/(m + n). The different m and n (or x) can be used for comparing the effects of different chemical compositions. Then, atomic positions and lattice constants are relaxed to obtain the optimized structures which have been shown in Figure 6. The relaxed structures are also similar to that of BiN due to the same configuration of valence electrons for Bi and Sb. Structural parameters should change with variation of the chemical composition. The analysis of structural parameters can provide important information on physical and chemical characteristics of the systems. For alloys, following Vegard’s law37 the relaxed lattice parameter of a two-component system is a

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Figure 10. Isosurface charge distributions of the HOMO and LUMO states at some special k-points corresponding to the energy extremum for the core-shell structural nanowires with 2.3 nm diameter. Labels correspond to those in Figure 6. The red and blue balls represent Bi and Sb atoms, respectively.

linear function of the composition. Figure 7 shows the lattice parameter c and diameter D of the nanowire as a function of chemical composition x. These clearly exhibit nonlinear dependence. More importantly, the variation of structural parameters with the composition depends strongly on the type of nanowires (Sb-core/Bi-shell or Bi-core/Sb-shell). In the case of Sb-core/ Bi-shell nanowires with tensile strained Sb core, the deviations from linearity are negative, while for Bi-core/Sb-shell nanowires with compressive strained Bi core these deviations are positive. For the smaller diameter nanowires, similar characteristics are also observed, indicating fairly weak size dependence. Therefore the relationship between structural parameters and chemical composition of Bi/Sb-core-shell structural nanowires does not follow Vegard’s law. Our result is also consistent with that of Si/Ge-core-shell structural nanowires.38 In the following we analyze the energy band structures of all core-shell structural nanowires. In Figure 8 we show the band structures of the nanowires with about 1.6 nm diameter. The highest valence bands and the lowest conduction bands are respectively indicated by the blue (dotted) and red (dashed) curves in the band structures plots. All nanowires are indirectband gap semiconductors with the valence band maximum at the Γ point. However, the position of the conduction band minimum is different and depends on the chemical composition. First of all, the atom type of the core is crucial. For example,

the band structure of Bi24Si24 is similar to that of Bi48, while the band structure of Sb24Bi24 is similar to that of Sb48. Moreover, the chemical composition influences the position of the conduction band minimum. It is between the Γ and Z points when the number of Bi atom composition is larger than that of Sb atom composition, while it is at the Z point when the number of Sb atom composition is larger than that of Bi atom composition. For instance, the conduction band minimum of Sb8Bi40 is between the Γ and Z points which is the same as that of Bi48, while the conduction band minimum of Bi8Sb40 is at the Z point which is consistent with that of Sb48. Finally, we find that the band gap of core-shell structural nanowire depends strongly on the atom type of the core and is almost independent of the chemical composition. The band gaps of Bi-core structural nanowires are larger than those of Sb-core structural nanowires. It can be seen that the band gaps of Bi48, Bi24Sb24, and Bi8Sb40 are 0.44, 0.44, and 0.46 eV, respectively, while the band gaps of Sb48, Sb24Bi24, and Sb8Bi48 are 0.28, 0.31, and 0.33 eV, respectively. The band structures of nanowires with about 2.3 nm diameter are shown in Figure 9. It clearly shows that as the size of nanowire increases, Bi80 is still an indirect-band gap semiconductor but Sb80 becomes a semimetal, which makes the variation of band structures with the chemical composition more complicated. Overall, the valence bands are also less affected by

Properties of the Bi-Sb Nanowires the chemical composition, but both the atom type of the core and the chemical composition have influence on the conduction band structures. For Sb-core/Bi-shell nanowires, with the increase of Bi chemical composition they change from semimetal into semiconductor as the conduction band moves up. However, as for the Bi-core/Sb-shell nanowires, with the increase of Sb chemical composition they change from semiconductor into semimetal. Although there is no report on the experimental fabrication of core-shell structural Bi/Sb nanowires, the experiments39 on the alloy Bi1-xSbx nanowires have demonstrated that the transition from semiconductor into semimetal is strongly dependent on the concentration of Sb, which is qualitatively consistent with our calculated results. Therefore, we know that the size, the atom type of core, and the chemical composition have important effects on the electronic properties of core-shell Bi/Sb nanowires. We further analyze the isosurface charge distributions of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). Figure 10 plots the band decomposed electronic charge density isosurfaces of HOMO and LUMO states of the nanowires with 2.3 nm diameter. We find that the distributions of HOMO and LUMO states are independent of the structures. The HOMO states are localized at the outer shell zone of nanowires, while the isosurface charge distribution of the LUMO states depends on the position of conduction band minimum value in the K-space. The LUMO states are localized at the core zone for Sb48Bi32, Sb24Bi56, and Sb8Bi72 nanowires with the band minimum value near the Z point, while for other nanowires with the band minimum value at or near the Γ point, the LUMO states are localized at the outer shell. Similar results are also obtained for the nanowires with 1.6 nm diameter. These results are also consistent with the fact mentioned above that the valence band structures are less affected by the chemical composition while the conduction band structures depend on the chemical composition. Conclusion In conclusion, we systematically study the structural and electronic properties of Bi-Sb superlattice nanowires and core-shell structural Bi/Sb nanowires. The relaxed structures of these heterostructural nanowires are very similar to that of BiN nanowires due to the same configuration of valence electrons for Bi and Sb elements. For Bi-Sb superlattice nanowires, the confined states that offer interesting device applications are clearly demonstrated by isosurface plots of charge densities. We show that the confined electrons (holes) become more localized and the associated band becomes flatter if the width of the barrier is larger. For core-shell structural Bi/Sb nanowires, the size, the atom type of core, and the chemical composition have important effects on the electronic properties. The valence bands are less affected by the chemical composition, while the conduction bands depend on it. Our results provide a comprehensive understanding of the structural and electronic properties of Bi-Sb superlattice nanowires and core-shell structural Bi/Sb nanowires. Acknowledgment. This work is supported by the Natural Science Foundation of China (NSFC, Nos.10772084, 10874052)

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