Letter pubs.acs.org/NanoLett
Single Crystalline Nanostructures of Topological Crystalline Insulator SnTe with Distinct Facets and Morphologies Z. Li,† S. Shao,‡ N. Li,§ K. McCall,† J. Wang,*,‡ and S. X. Zhang*,† †
Department of Physics, Indiana University, Bloomington, Indiana 47405, United States MST-8 and §MPA-CINT, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
‡
S Supporting Information *
ABSTRACT: Topological crystalline insulators (TCIs) are a new class of topological materials that possess unique metallic surface states protected by crystalline mirror symmetry. Their topological surface properties are expected to strongly depend on the surface orientation. By combining density functional theory (DFT) calculations and synthesis experiments, we demonstrate the controlled growth of single crystalline nanostructures of the prototypical TCI SnTe with distinct facets and morphologies. Our calculations suggest that the excess energy of the {111} surfaces can be either higher or lower than that of the {100} surfaces, depending on the stoichiometry, while the {110} is always higher than the {100}. In our synthesis experiment, we qualitatively controlled the stoichiometry by tailoring the growth temperature and obtained two types of single crystalline nanowires: smooth nanowires dominated by {100} facets at high temperatures and zigzag nanowires composed of both {100} and {111} surfaces at low temperatures. Notably, there is no {110} facet in our nanostructures, strongly supporting the DFT calculations. Our device fabrication and electrical characterizations suggest that both types of nanowires are suitable for transport studies of topological surface states. KEYWORDS: Topological crystalline insulators, tin telluride, nanowires, synthesis
T
ratio by synthesizing nanometer-scale structures.15−20 Indeed, for conventional TIs (e.g., Bi2Se3 and Bi2Te3) that also suffer contamination from bulk conduction, clear signatures of surface transport, for example, Aharonov−Bohm interference16,17 and two-dimensional Shubnikov de Haas,21 have been observed in their nanostructures. While the TI nanostructures were grown by different bottom-up synthetic approaches such as thermal vapor deposition,15,22,23 solvothermal method,17,24 and van der Waals epitaxy,25−27 their dominant facets are often found to be (0001) plane of the hexagonal lattice owing to the anisotropic crystallography characteristics. To date, the growth of SnTe nanostructures has been limited to the solution method and the synthesized nanowires28 and nanorods29 have been too short for device fabrication and transport studies. Furthermore, due to the isotropic fcc crystalline structure (Figure 1a) it is unknown which facets of SnTe dominate during nanostructure growth. Understanding the facet formation in SnTe is fundamentally important because recent band structure calculations along with k-p theory suggest that different surface planes have qualitatively distinct topological properties.30,31 For the {111} plane, even the type of surface termination influences the alignment of surface Dirac points with respect to the bulk bandgap.30
he discovery of topological insulators (TIs)1,2 with unique topological surface states protected by time-reversal symmetry has triggered considerable interest in the search for new topological materials.3−5 One of the most prominent examples is the recently proposed topological crystalline insulators (TCIs)5 in which the metallic surface states are protected by crystalline mirror symmetry instead of timereversal symmetry. Theoretical studies predicted such topological states on the high symmetry surfaces (e.g., {100}, {110}, and {111}) of the IV−VI semiconductor SnTe with rock-salt face-centered cubic (fcc) crystal structure.6 Angle-resolved photoemission spectroscopy measurements confirmed the existence of these Dirac surface states on the {100} crystal surface of SnTe7 and related compounds.8,9 Scanning tunneling microscopy studies also demonstrated the formation of massless Dirac fermions and the mechanism of mass generation via crystal-symmetry breaking.10 The unique surface properties of TCIs may open the door for tunable electronic and spintronic applications.11 To develop these applications, it is essential to understand the electrical and spin transport properties of the surface states (SSs). However, the as-grown SnTe bulk crystals are often found to be highly p-type doped because they naturally form with a high concentration of Sn vacancies (p > 10 20 cm−3).7,12−14 As a result, the bulk conduction dominates over the surface contribution, making it very challenging to probe the SSs by transport studies.11,13 One way to magnify the surface contribution is to increase the surface area-to-volume © 2013 American Chemical Society
Received: August 12, 2013 Revised: October 3, 2013 Published: October 18, 2013 5443
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therefore the surface energy does not depend on the chemical potential of a single atomic species. In contrast, the {111} surfaces are either Sn-terminated (denoted as {111}: Sn) or Teterminated (denoted as {111}: Te). In this case, some unpaired Sn or Te atoms exist, and the surface energy depends on the chemical potentials of Sn or Te γ=
1 surf bulk [G − NSnμSn − NTe(gSnTe − μSn )] A
(1)
γ=
1 surf bulk [G − NTeμTe − NSn(gSnTe − μTe )] A
(2)
surf
where G is the Gibbs free energy of the simulated material slab obtained through DFT calculations, Ni is the number of atoms with species i (Sn and Te in this work), and μi is the chemical potential of the atom species i. A is the free surface area of the simulated material slab and gbulk SnTE is the Gibbs free energy per formula unit of the bulk SnTe. Figure 1b shows the energies of the {100}, {110}, and {111} surfaces as functions of the relative Te chemical potential ΔμTe, where ΔμTe = μTe − gTe. The energies of the {100} and {110} surfaces are 0.108 and 0.248 J/m2, respectively, and are independent of ΔμTe. The energies of both types of {111} surfaces are linear functions of ΔμTe, and the {111}: Sn surface has significantly higher energy (0.807−1.088 J/m2) than the {111}: Te surface (0.148−0.429 J/m2). The results clearly indicate that only the {100} and {111}: Te surfaces could be present in a solid SnTe nucleus, in accordance with the relative Te chemical potential ΔμTe. The equilibrium crystal shapes (ECS) under Te-lean (ΔμTe = −0.622 eV) and Te-rich (ΔμTe = 0 eV) conditions are then predicted using the Gibbs-Wulff theory32 according to the surface energies obtained above. Under Te-lean conditions, the ECS is predicted to be a cube having only {100} faces; while under Te-rich conditions, the ECS is a cube having {100} faces with corners truncated by the {111}: Te surfaces. With the increase of Te content, the {111}: Te surfaces dominate over the {100} surfaces. The stoichiometry and the facet formation can be qualitatively controlled by the growth temperature. According to the phase diagram of the Sn−Te compound,33 the SnTe crystal is solidified from the liquid phase of SnTe below the congruent melting temperature of 806 °C, while the compound SnTe + Te is solidified from the liquid phase at a eutectic temperature of 401 °C where Te is in rich. Therefore, at relatively high growth temperatures, vaporized Sn and Te can directly react and form SnTe crystals. However, when the vaporized Sn and Te react at the lower temperatures (toward 400 °C side), the reaction will cause the formation of SnTe+Te, because of the substantially lower surface energy of {111}: Te surface. As a result, we expect to have {100} surface dominated nanostructures at higher growth temperatures and {111} dominated nanostructures at lower temperatures. To test the above predictions, we conduct the synthesis of SnTe nanostructures via thermal vapor deposition, a technique that has been widely used to grow nanostructures of conventional TIs.15,16,21,22 Detailed growth conditions are provided in the Supporting Information. The substrate temperature varies from 525 to 675 °C depending on its position in the furnace (Figure 2a). As shown in Figure 2b, straight and smooth NWs with a typical length of 50−100 μm and diameter/width of 100−900 nm were observed on the high temperature substrate (645∼675 °C). Figure 2c shows a typical SEM image of a NW at its tip where a particle is clearly seen.
Figure 1. (a) A schematic of the face-centered cubic crystalline structure of SnTe; (b) the free energies of the {100}, {110}, {111}: Sn and {111}: Te surfaces as functions of the relative Te chemical potential ΔμTe. Wulff constructions of the thermodynamic equilibrium SnTe crystals at the Te-lean and Te-rich conditions are shown in the inset.
Here we combine density functional theory (DFT) calculations and synthesis experiments to demonstrate the growth of single crystalline SnTe nanostructures with controlled facets and morphologies. Our calculations suggest that the surface energy of {111} can be either higher or lower than the {100} surface, depending on the stoichiometry, while the {110} is always higher than {100}. In our thermal vapor deposition experiment, we qualitatively control the stoichiometry by tailoring the growth temperature and obtained two types of single crystalline nanowires (NWs): smooth NWs dominated by {100} facets at high temperatures versus zigzag NWs composed of both {100} and {111} surfaces at low temperatures. Both types of NWs are suitable for nanodevice fabrication and transport studies. Notably, we do not observe any {110} facet in our nanostructures, strongly supporting the DFT calculations. The energies of the low index surfaces of β-SnTe, {100}, {110}, and {111} were computed using density functional theory. The computational details are provided in the Supporting Information. For {100} and {110} surfaces, there are an equal number of Sn and Te atoms on each surface, 5444
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{100} facets we performed transmission electron microscopy (TEM) studies to characterize their crystalline structures. Figure 3a shows a low-magnification TEM image of a smooth
Figure 3. (a) TEM image of a smooth NW. Inset: diffraction pattern taken along ⟨001⟩ zone axis. (b) HR-TEM image shows the interface between Au particle and the NW; (c) HR-TEM image shows the lattice fringes of the NW.
NW with width/diameter of ∼140 nm and alloy particle ∼80 nm in diameter. Diffraction pattern (DP) was taken along ⟨001⟩ zone axis, parallel to one of the four side facets of the nanowire. The feature of isolated spots in the DP (inset of Figure 3a) clearly indicates that the nanowire is single crystalline with growth direction along ⟨100⟩. On the basis of the known zone axis and the growth direction, the four perpendicular side facets can be identified as {100} planes. The high-resolution TEM (HR-TEM) images in Figure 3b,c suggest that the tapered tip consists of steps of {100} planes. The fringe spacing of 0.32 nm measured from Figure 3c agrees with half of the distance between two {100} planes in SnTe, further confirming the ⟨100⟩ growth direction and the {100} facets. The 3D microsize crystals that coexist with the smooth nanowires are too big/thick (∼50 μm) to perform TEM studies. However, Raman spectroscopy measurements and EDX compositional analysis suggested that they are indeed SnTe with fcc crystal structure (Supporting Information, Figure S2). Since no Au particle was observed on the surface of any of these 3D crystals, the growth is likely to be through vapor− solid (V-S) mechanism. To verify this, we performed a control experiment without using Au nanoparticles and observed 3D crystals with similar size and morphology. The facets of these 3D crystals can be readily identified by their morphologies. As shown in Figure 4a,b, the cubic crystal has six octahedral facets that should be {100} planes, and the smaller triangular facets that cut the eight corners are {111} planes. We now propose how these nanostructures form. Because the growth temperature is relatively high, the early morphology of a solid SnTe nucleus is composed mostly of large {100} surfaces with few small {111} facets according to their surface
Figure 2. (a) Schematic diagram of the tube furnace for nanostructure growth (upper panel); the temperature as a function of position (lower panel); (b) typical SEM image shows 1D smooth NWs and 3D microsize crystals on the high-temperature substrate; (c) magnified SEM image of a smooth NW with a distinguishable nanoparticle at its tip; (d) typical SEM image shows zigzag NWs on the low temperature substrate; (e) magnified SEM image of a zigzag NW. Inset image shows a nanoparticle at the tip.
Energy dispersive X-ray (EDX) analysis (Supporting Information Figure S1) shows that the wire only contains Sn and Te, while the particle is composed of Au, Sn and Te, which suggests the vapor−liquid−solid (V-L-S) growth mechanism. While these NWs are often found to be slightly tapered at the tip toward the alloy particle, the cross-section in the NW body is rectangular, that is, four side facets are perpendicular to each other. In contrast, NWs deposited on lower-temperature substrates (525−625 °C) have zigzag shape and appear to be accumulated stacks of nanocrystals. The length of these NWs as measured in Figure 2d is typically less than 15 μm which is much shorter than the lengths of smooth NWs. The diameter of these NWs decreases from the root (0.5−2 μm) to the tip (
