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Role of Chemical Potential in Tuning Equilibrium Crystal Shape and Electronic Properties of Wurtzite GaAs Nanowires Mengting Jin,† Haibo Shu,*,†,‡ Pei Liang,† Dan Cao,§ Xiaoshuang Chen,‡ and Wei Lu‡ †

College of Optical and Electronic Technology, China Jiliang University, 310018 Hangzhou, China National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, 200083 Shanghai, China § College of Science, China Jiliang University, 310018 Hangzhou, China ‡

S Supporting Information *

ABSTRACT: GaAs nanowires (NWs) often exhibit wurtzite crystal structure during the vapor−liquid−solid (VLS) growth, and their sidewalls are generally composed of {11̅00} and {112̅0} facets. Owing to the large surface-to-volume ratio, the sidewall structures of NWs are sensitive to the chemical environment. However, the impact of chemical environment on the sidewall structures and electronic properties of wurtzite GaAs NWs is still not clear. Here we present detailed first-principles calculations to investigate the atomic structure of sidewall facets, equilibrium crystal shape, and electronic properties of wurtzite GaAs NWs under different chemical potential conditions. On the basis of the surface energies of sidewall facets, the equilibrium crystal shape (ECS) of NWs is evaluated using the Wulff construction. The ECS of NWs demonstrates a shape evolution from a dodecagonal prism to a hexagonal prism with increasing As chemical potential, which is in agreement with the experimental observations. Meanwhile, the increasing As chemical potential results in a direct−indirect band gap transition in wurtzite GaAs NWs due to the structural change of NW sidewalls. This result can be applied successfully to explain an existing experimental controversy for the band gap of wurtzite GaAs NWs.

I. INTRODUCTION The III−V semiconductor nanowires (III−V NWs) have received great interest in the past decade due to their unique physical properties and technological importance in developing the future nanodevices.1−3 Among these semiconductor nanowires, GaAs NWs are one of the most extensively studied targets since they present many advantages, including high electron mobility and absorption coefficients as well as their compatibility with Si technology,4−6 which make them potential building blocks in nanoelectronics and optoelectronics such as nanoscale field-effect transistors,7 single-photon sources,8 photodetectors,9 and solar cells.10 The application of GaAs NWs in these nanodevices requires well-controlled NW size, morphology, and crystal structure so as to the reliable manufacturing of practical devices. To obtain the high-quality GaAs NWs with controllable morphology and crystal structure, a variety of growth technologies have been developed, including metal−organic chemical vapor deposition (MOCVD),11 molecular beam epitaxy (MBE),12 and chemical beam epitaxy (CBE).13 Based on the experimental methods, GaAs NWs are generally grown via the vapor−liquid−solid (VLS) mechanism14 using metal nanoparticles as catalysts. This mechanism is also widely used in the synthesis of other III−V NWs, such as InAs, InP, and © XXXX American Chemical Society

GaP. Interestingly, the VLS-grown III−V NWs often exhibit wurtzite (WZ) crystal phase or the rotational twin structure including both zinc blende (ZB) and WZ segments,15−18 despite the fact that their bulk materials and epitaxial thin films present ZB crystal phase. For instance, Paiman et al. reported the InP NWs grown by the MOCVD method prefer to form WZ phase at high V/III ratios.15 Joyce et al. demonstrated the crystal-structure transition of InAs NWs from the ZB to WZ phase by adjusting the V/III ratio and growth temperature.16 Recently, Han et al. reported the large-scale synthesis of purephase wurtzite GaAs NWs on amorphous SiO2/Si substrates.17 In these experiments, the wurtzite NWs were found to be featured with either hexagonal prism with six {112̅0} (or {11̅00}) facets or dodecagonal shape with both {11̅00} and {112̅0} facets.16−19 The change of crystalline structure brings the changes in the electronic band structure of GaAs NWs. The experimental studies on the electronic band structure of wurtzite GaAs NWs were still a subject of controversy in the past few years. Martelli et al.20 reported a luminescence emission of GaAs nanostrucReceived: July 29, 2013 Revised: October 4, 2013

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tures at 1.522 eV. Hoang et al.21 indicated the emission for wurtzite GaAs NWs in the range 1.53−1.54 eV. On the basis of the photoluminescence (PL) measurements, Heiss et al.22 reported a band gap of 1.50 eV for wurtzite GaAs NWs. Recently, Spirkoska et al.23 demonstrated a type II band alignment in GaAs NWs with a mixture of ZB and WZ phases. In their studies, the NWs with 30% and 70% WZ phase were found to present two different ranges of PL peaks (1.43−1.47 eV for the 30% WZ-NWs and 1.46−1.51 eV for the 70% WZNWs). The apparent difference of these literature results was habitually ascribed to quantum size effect and the formation of quantum heterostructures; very little24 has been focused on the impact of surface chemistry of NWs. Owing to the large surface-to-volume ratio of NWs, their sidewall structures are sensitive to the chemical environment during the growth. The different conditions of chemical potential may cause the reconstruction of NW sidewalls which results in the changes in the crystal shape and electronic structure of NWs. However, how the shape and electronic structure of WZ GaAs NWs affected by the chemical potential is not clear. Theoretical investigations of electronic structures of GaAs NWs have also been widely carried out in the past few years. For example, Cahangirov and Ciraci25 reported electronic structures of different types of bare and hydrogenated GaAs NWs based on the density-functional calculations. They demonstrated the size dependence of band gap in wurtizte GaAs NWs. On the basis of ab initio calculations, Rosini and Magri predicted the structural stability and electronic structures of GaAs NWs with different sidewalls and ridge configurations.26 They found that NW surfaces (side facets plus ridges) determined the NW stability and electronic structure. Recently, Copple et al.27 have studied the effect of uniaxial strain on the electronic structure of wurtzite GaAs NWs using the first-principles calculations. The theoretical studies provided much important information to insight into the electronic structures of GaAs NWs, but most of their results were obtained based on the models that were directly cut from the bulk GaAs. The GaAs NWs with the nonstoichiometric surface have not been considered in their studies. Therefore, it is necessary to understand the role of chemical potential in the sidewall structure of NWs, which is crucial to insight into the electronic properties of GaAs NWs. In this work, we present for the first time a comprehensive study on the role of chemical potential in the sidewall configuration, equilibrium crystal shape, and electronic structures of wurtzite GaAs NWs employing ab initio calculations. First, we investigate the surface phase diagram of GaAs(11̅00) and GaAs(112̅0) as a function of As chemical potential by comparing the structural stability of potential surface configurations. On the basis of the result of surface energies, we further study the equilibrium crystal shape of NWs under different conditions of As chemical potential by applying the Wulff construction theory. Finally, we investigate the electronic structures of wurtzite GaAs NWs under different As chemical potentials. Our calculations elucidate that the chemical potential plays an important role in tuning the equilibrium crystal shape and electronic properties of wurtzite GaAs NWs and resolve an existing experimental controversy on the band gap of wurtzite GaAs NWs.

(VASP).28,29 The exchange-correlation energy is treated in the generalized-gradient approximation (GGA) using the PBE functional.30 The kinetic energy cutoff for the plane-wave expansion is set to 500 eV, using the projector augmented wave (PAW) potentials31 to describe the electron−ion interactions. For the geometry optimization, the convergence criterion in energy and force is set to 10−3 eV and 0.01 eV/Å, respectively. The sidewall facets of wurtzite GaAs NWs are modeled by GaAs(110̅ 0) and GaAs(1120̅ ) surfaces which are created on the basis of WZ crystal structure by using the slab geometry with eight GaAs layers. The surfaces with in-plane periodicity are separated by ∼10 Å vacuum layers to prohibit the interactions of neighboring surface slabs. The bottom surface is terminated by artificial hydrogen atoms32 with fractional charges of 1.25 e and 0.75 e for Ga and As atoms, respectively. During the geometry optimizations, all atoms except for three bottommost GaAs layers and pseudo-hydrogen atoms have been relaxed. The Monkhorst−Pack grids of k-point are used to sample the surface Brillouin zone. The k-point meshes are set 6 × 8 × 1 and 6 × 6 × 1 for GaAs(11̅00) and GaAs(112̅0) surfaces, respectively. The wurtzite GaAs NWs are modeled by the supercell approach, in which neighboring wires are separated by at least 10 Å vacuum to minimize their mutual interactions. Two types of NWs have been considered in the present study: one is the NWs present six {110̅ 0} or {1120̅ } facets, forming a hexagonal cross section, and the other is the NWs with a dodecagonal cross section that includes both {11̅00} and {112̅0} facets. The Brillouin zone summations are performed on a Monkhorst−Pack mesh of 1 × 1 × 8. In the band structure calculations, a total of 15 k-points are included along the K vector direction Γ (0, 0, 0) to Z (0, 0, 0.5). To determine the thermodynamic stability of GaAs(11̅00) and GaAs(1120̅ ) surfaces, the surface energies (γs) of their cleaved surfaces are first calculated by the formula γs = (E T − nEGaAs)/2A

(1)

where ET and EGaAs are the energies of cleaved surface and the Ga−As pair in wurtzite GaAs bulk, respectively. A is the area of cleaved surface, and n is the number of Ga−As pairs in the cleaved surface. Taking the cleaved surface as a reference, the surface energies of other potential surface configurations can be achieved as follows: γ = γs + [ΔE T − ΔnGaμGaAs − (ΔnAs − ΔnGa)μAs ]/A (2)

where ΔET is the total energy difference between a given structure and the cleaved surface. μGaAs is the chemical potential of bulk GaAs, and μAs is the chemical potentials of As atom. The allowed value of μAs is in the range of μAs(bulk) − ΔHf ≤ μAs ≤ μAs(bulk). The upper (lower) limit of μAs corresponds to the As-rich (Ga-rich) condition, and ΔHf is the heat of formation of wurtzite GaAs. The calculated ΔHf is 0.76 eV. ΔnGa (ΔnAs) is the difference between the number of Ga (As) atoms in the given structure and the cleavage surface.

III. RESULTS AND DISCUSSION We start our discussion with the structural stability and electronic structures of GaAs(11̅00) and GaAs(112̅0) surfaces. Figure 1a shows three possible surface atomic configurations of (1 × 1)GaAs(11̅00), including of cleavage surface (Ga−As), As-covered surface (As−As), and Ga-covered surface (Ga−Ga). The absolute surface energies of GaAs(11̅00) with three

II. COMPUTATIONAL DETAILS The density-functional theory (DFT) calculations are carried out by using the Vienna ab initio Simulation Package B

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Figure 2. Band structures of GaAs(11̅00) with the (a) Ga−As and (b) As−As surface configurations. The position of Fermi level is set to energy zero.

Figure 1. (a) Top and side views of optimized surface configurations of GaAs(11̅00) with As−As dimer, Ga−As dimer, and Ga−Ga dimer. (b) Surface energies of GaAs(11̅00) surface with the three different surface structures as a function of ΔμAs.

different configurations as a function of ΔμAs (ΔμAs = μAs − μAs(bulk)) are shown in Figure 1b. It is found that the Ga−As structure is the most stable surface structure in the mostly allowed range of As chemical potential (ΔμAs ≤ −0.05 eV), and the As−As structure becomes energetically favorable only under the As-rich condition. The result agrees very well with the recent theoretical investigation.33 For the Ga−Ga structure, it is still a metastable state. The stabilization mechanism of GaAs(11̅00) can be explained by the electron counting rule (ECR).34,35 According to the definition of ECR, the dangling bonds of anions and cations on a stable semiconductor surface are fully filled and empty, respectively. For the GaAs(110̅ 0) surface, the Ga−As structure allows Ga and As atoms to form Ga−As dimer on the surface, and it satisfies ECR. Thus, the Ga−As structure has a high stability. Although the As−As structure does not satisfy ECR, it is stable due to the fact that As atoms are relatively easy to be incorporated onto the surface under the As-rich condition. Figure 2 shows the band structures of Ga−As and As−As structures. The Ga−As structure indicates a typical direct band gap character with both the conduction band minimum (CBM) and the valence band maximum (VBM) at the Γ point, which meets the definition of ECR where a stable surface is semiconducting. In contrast, the band structure of As−As structure shows an obvious change relative to that of Ga−As structure. Its VBM state is located at the VB peak along the Γ− K direction, and the CBM state is located at the CB valley along the Γ−X direction. Thus, the As−As structure has an indirect band gap. The further analysis of charge−density isosurfaces (see Figure 3a) and partial density of states (see Figure S1a in Supporting Information) indicates that the VBM and CBM of Ga−As structure mainly originate from the 4p states of As atoms and 4s states of Ga and As atoms, respectively, while the VBM and CBM of As−As structure derive from the 4p states of bulk and surface As atoms (see Figure 3b and Figure S1b),

Figure 3. Charge-density isosurfaces of VBM and CBM for GaAs(110̅ 0) with (a) Ga−As and (b) As−As surface configurations.

respectively. In other words, the band structure of GaAs(11̅00) undergoes a direct−indirect band gap transition as As chemical potential increases. The band-structure change originates from the upward shift of Ga 4s states and the downward shift of As 4p states at the conduction band edge when the surface structure changes from Ga−As to As−As (see Figure S1). GaAs(112̅0) is another frequently appearing sidewall facet of wurtzite GaAs NWs during the VLS growth. To explore the surface structure of GaAs(112̅0), five different surface configurations are considered, including of Ga2As2, Ga1As3, As4, Ga3As1, and Ga4 (see Figure 4a). Ga2As2 is a cleavage surface (or clean surface) with the same number of Ga and As atoms, Ga1As3 (Ga3As1) is the Ga2As2 surface with one Ga (As) atom replaced by an As (Ga) atom, and As4 and Ga4 are the Ascovered and Ga-covered surfaces, respectively. The surface energies of five different surface configurations as a function of ΔμAs are shown in Figure 4b. For a large range of As chemical potential, the cleavage surface (Ga2As2) is the energetically most favorable. In the As-rich environment, the As-covered surface (As4) becomes the most stable surface structure. Other surface configurations are still metastable structures in the allowed range of As chemical potential. The stability mechanism of the GaAs(112̅0) surface can be understood by the ECR. For instance, the Ga2As2 structure satisfies ECR and has a high stability. For other high-energy surface configurations (e.g., Ga1As3, Ga3As1, and Ga4), they do not satisfy the ECR. C

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Figure 4. (a) Top and side views of optimized surface configurations of GaAs(112̅0) with Ga2As2, Ga1As3, As4, Ga3As1, and Ga4. (b) Surface energies of GaAs(1120̅ ) surface with the five different surface structures as a function of ΔμAs.

Figure 5 shows the band structures of GaAs(112̅0) with Ga2As2 and As4 structure. It is found that the Ga2As2 structure

sidewall structures of wurtzite GaAs NWs can be tuned by the chemical potential. However, what is the relationship between the sidewall of GaAs NWs and chemical potential? How does the chemical potential affect the electronic structure of GaAs NWs? To answer the questions, the equilibrium crystal shape (ECS) of wurtzite GaAs NWs needs to be confirmed first. According to the Wulff construction theory, the ECS of NWs m ) and can depends on the surface energy of crystal planes γs(⇀ be determined by the formula36,37 ⎛ γ(m⃗ ) ⎞ R(h ⃗) = min⎜ ⎟ ⎝ m⃗ ·h ⃗ ⎠

(3)

⇀ where R( h ) represents the radius of the crystal shape in the ⇀ m denotes the orientation of crystal planes. direction h and ⇀ The ECS is given by the interior envelope of the family of m . In principle, all possible wurtzite planes perpendicular to ⇀ GaAs surfaces should be evaluated to determine the ECS of wurtzite GaAs NWs. However, the high Miller indices surfaces are energetically unfavorable relative to (110̅ 0) and (1120̅ ) surfaces. Moreover, the extensive experiments16−19 also found that the sidewall of wurtzite III−V NWs prefers to be featured with {11̅00} and {112̅0} facets. So we only consider the surface energies of (110̅ 0) and (1120̅ ) facets to plot the cross-section shape of NWs. Owing to the chemical potential dependence of the surface energies of GaAs surfaces (see Figure 6a), the ECS of NWs is thus a function of As chemical potential. The cross-section shape of wurtzite GaAs NWs at three different As chemical potential conditions are presented in Figure 6b−6d. Figure 6b indicates the cross-section shape of NWs at ΔμAs < 0.10 eV. It is found that NWs have a dodecagonal shape with six {110̅ 0} and six {1120̅ } facets, and the area of {11̅00} facets is slightly larger than that of {112̅0} facets due to its relatively low surface energy. In the range of chemical potential (ΔμAs < 0.10 eV), both {11̅00} and {112̅0}

Figure 5. Band structures of GaAs(112̅0) surface with the (a) Ga2As2 and (b) As4 structures. The position of Fermi level is set to energy zero.

exhibits a direct band gap with both VBM and CBM at the Γ point, while the As4 structure presents an indirect band gap with the VBM state at the VB peak along the Γ−X direction and the CBM state at the CB valley along the M−X direction. Similar to the case of GaAs(110̅ 0), the band structure of the GaAs(112̅0) surface also undergoes a direct−indirect band gap transition with the increasing As chemical potential. Meanwhile, the structural transition from Ga2As2 to As4 causes the band gap change from 0.69 to 0.94 eV. On the basis of above analysis, the surface configurations and electronic structures of GaAs(11̅00) and GaAs(112̅0) are sensitive to the chemical environment: the cleavage surfaces are stable for a large range of As chemical potential and have a direct band gap; the As-covered surfaces become energetically favorable under the As-rich condition and have an indirect band gap. The result implies that the electronic properties and D

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Figure 6. (a) Surface energies of GaAs(11̅00)and GaAs(112̅0) as a function of ΔμAs. (b−d) The cross section (shaded region) of ECS of wurtzite GaAs NWs at three different As chemical potentials, including of ΔμAs < 0.10 eV, ΔμAs = 0.09 eV, and As-rich (ΔμAs = 0 eV) conditions. The dashed lines denote two types of crystal surfaces.

atoms during the geometry optimizations. With the increasing NW size, the corner effect on the stability of GaAs NWs will be further reduced. Now we want to know the role of chemical potential in the electronic properties of wurtzite GaAs NWs. On the basis of the result of ESC of NWs, we considered three types of GaAs NWs which correspond to the As chemical potential at ΔμAs < −0.10 eV (named by NW1), ΔμAs = −0.09 eV (named by NW2), and the As-rich condition (named by NW3). The NW1 has a dodecagonal cross section in which all (11̅00) and (112̅0) facets are the cleavage surfaces, the NW2 is a dodecagonal prism in which six {112̅0} facets are the As-covered surface and six {11̅00} facets are the cleavage surface, and the NW3 is a hexagonal prism in which all six {112̅0} facets are the Ascovered surface. To provide a comparison, the hexagon-shaped NW with six cleaved {1120̅ } facets has also been investigated (named by NW4). In the calculations, the size of NWs is located at ∼3 nm. Figure 7 shows the optimized atomic structures and band structures of 3 nm GaAs NWs with four different surface configurations. The NW1 and NW2 have a direct band gap with both VBM and CBM located at the Γ point (Figure 7a,b), and the NW3 is an indirect band gap semiconductor with the VBM at the Γ point and the CBM at the CB valley along the Γ−Z direction (Figure 7c). The result suggests that GaAs NWs undergo a direct−indirect band gap transition as the As chemical potential increases. We calculated the energy difference ΔEC in four GaAs NWs between the CBM at the Γ point (ΓC) and at the valley along the Γ−Z direction (ΔC). It is found that the ΔEC is 0.35, 0.01, and −0.06 eV for NW1, NW2, and NW3, respectively. In other words, the increasing As chemical potential causes the evolution of NW sidewalls from the cleavage surface to the As-covered one, which results in a direct−indirect band gap transition in wurtzite GaAs NWs. We have also investigated the band structures of 2 nm wurtzite GaAs NWs. The band-structure

facets of NWs are cleavage surfaces. With the increase of As chemical potential increases, six {112̅0} facets of NWs turn into the As-covered surfaces. When the As chemical potential arrives at ΔμAs = −0.09 eV, the ECS of NWs becomes a regular dodecagonal prism (Figure 6c). With the further increasing As chemical potential, six {110̅ 0} facets decrease and the NW sidewall is dominated by six {112̅0} facets. Therefore, the ECS of NWs gradually transforms from a dodecagonal prism to a hexagonal one, which agrees with the experimental observations.18,19,38 Under the As-rich environment, the NWs are a regular hexagonal prism with six {1120̅ } facets, as shown in Figure 6d. Moreover, all facets of NW sidewall are the Ascovered surfaces. It needs to be noted that the ECS and thermodynamic stability of NWs are possible to be affected by surface stress and corner (or edge) effects as the NW size decreases. In order to gain insight into the stress and corner effects on the thermodynamic stability of wurtzite GaAs NWs, we carried out a comparison of surface energies among GaAs surfaces and NWs, as listed in Table S1 of the Supporting Information. With the same surface configuration, the difference of surface energies is very small among GaAs surface and NWs. Taking the cleavage (11̅00) surface as an example, the surface energy of GaAs(11̅00) is 30.0 meV/Å2 and the surface energies of GaAs nanowires with the diameter of 2 and 3 nm are 30.9 and 30.6 meV/Å2, respectively. For other surface configurations, the surface-energy difference of GaAs nanostructures with the same surface configuration is less than 3 meV/Å2. Such a result suggests that the stress effect on the stability of GaAs NWs is not very sensitive to the NW size. Meanwhile, the thermodynamic stability of GaAs NWs is not significantly affected by the corner (or edge) effect. It is because the coordination number of all surface atoms (including of corner and facet atoms) of NWs is 3; thus, the relaxation and reconstruction of corner atoms are very similar to that of facet E

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Figure 8. Charge-density isosurface distributions of VBM (lower panels) and CBM (upper panels) of 3 nm GaAs nanowires with (a) six cleavage {11̅00} and six cleavage {112̅0} facets (NW1), (b) six cleavage {11̅00} and six As-covered {112̅0} facets (NW2), (c) six Ascovered {112̅0} facets (NW3), and (d) six cleavage {112̅0} facets (NW4).

Figure 7. Top and side views of optimized atomic structures and band structures of 3 nm GaAs nanowires with (a) six cleavage {11̅00} and six cleavage {112̅0} facets (NW1), (b) six cleavage {11̅00} and six Ascovered {112̅0} facets (NW2), (c) six As-covered {112̅0} facets (NW3), and (d) six cleavage {112̅0} facets (NW4). The position of Fermi level is set to energy zero. ΓC and ΔC denote CBM at the Γ point and the CB valley along the Γ−X direction, respectively.

As atoms (Figure 8c), respectively. The further analysis of partial density of states of Ga and As atoms in the four NWs (see Figure S2) shows that the electronic states of CBM gradually change from the 4s states of inner Ga and As atoms to the 4p states of outer As atoms with the increasing As chemical potential, which is the main reason for the band gap change of wurtzite GaAs NWs. The result suggests the possibility to engineer the band structure of GaAs NWs by adjusting the As chemical potential.

characteristic of 2 nm NWs is the same as that of 3 nm NWs. In other words, the band-structure characteristic of GaAs NWs is not sensitive to the NW size (see Table S1). Although previous theoretical studies25,27 reported the direct−indirect band gap transition of wurtzite GaAs NWs in the size range of 1.5−2.0 nm, such smaller sized NWs are difficult to synthesize in experiment. On the other hand, the band gap of GaAs NWs is also strongly sensitive to the structure of NW sidewalls which is determined by the chemical potential. For instance, NW1 and NW2 have the same shape but different surface structures. We find that the calculated band gap of NW2 is 0.18 eV larger than that of NW1. Similarly, NW3 and NW4 have same shape but different facet structures. However, the NW4 has a direct band gap (Figure 7d), while the NW3 is an indirect band gap semiconductor. The calculated band gap of NW3 is 0.06 eV larger than that of NW4. The sidewall structure dependence of NW bandgap is also observed in 2 nm GaAs NWs. Therefore, the changing the NW sidewalls from the cleavage surface to the As-covered one will result in the band gap change of NWs. The result can be applied to explain the experimental controversy20−24 on the band gap of wurtzite GaAs NWs. When the growth environment is changed, the band gap of NWs may become different. Our results suggest that the band gap of wurtzite GaAs NWs depend on not only the NW size but also the surface configuration. To further understand the influence of chemical potential on the electronic structures of NWs, the charge-density isosurface distributions of VBM and CBM (Figure 8) in four GaAs NWs have been investigated. The sidewalls of NW1 and NW4 are the cleavage surfaces. Their VBM and CBM originate from the 4p states of inner As atoms and the 4s states of Ga and As atoms (see Figure 8a,d), respectively. For the NW2, its VBM is mainly from the 4p states of As atoms and its CBM arises from the contributions of the 4s states of inner Ga and As atoms and the 4p states of outer As atoms (Figure 8b), while the VBM and CBM of NW3 are mainly from the 4p states of inner and outer

IV. CONCLUSIONS In summary, we performed a detailed theoretical investigation on the role of chemical potential in the sidewall, equilibrium crystal shape, and electronic structures of wurtzite GaAs NWs. The calculated surface energies of GaAs(11̅ 0 0) and GaAs(112̅0) indicate that the cleavage surfaces are stable in a large range of As chemical potentials, and the As-covered surfaces become energetically favorable only under the As-rich condition. On the basis of the result of surface energies, the equilibrium crystal shape of wurtzite GaAs NWs can be determined by applying Wulff construction theory and demonstrates a shape evolution from a dodecagonal prism to hexagonal one with the increasing As chemical potential, which agrees very well with the experimental observations. Meanwhile, the increasing As chemical potential causes the structural change of NW sidewall, which results in a direct−indirect band gap transition in GaAs NWs. Our results open the possibility to engineer the electronic properties of wurtzite GaAs NWs by adjusting the chemical environment during the growth.

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ASSOCIATED CONTENT

S Supporting Information *

Partial density of states for Ga and As atoms of GaAs(11̅00) surfaces, the comparison of surface energies, band-structure characteristic, and band gap value Eg of wurtzite GaAs surfaces and nanowires, and partial density of states for the Ga and As atoms of 3 nm wurtzite GaAs nanowires. This material is available free of charge via the Internet at http://pubs.acs.org. F

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Ph +86-0571-86875622 (H.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by Zhejiang Provincial Natural Science Foundation of China (Y1110777 and LQ13A040001) and the National Natural Science Foundation of China (61006051, 10990104, and 60976092). Computational resources from the Tianjin Supercomputer Center are acknowledged.

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