Catalyst-free growth of Bi₂Te₃ nanostructures by molecular beam epitaxy

Topological insulators (TI) are band insulators with gapless time-reversal symmetry protected topological surface states (TSS).^1–3 The theoretical prediction^4,5 and subsequent experimental discovery⁶ of the prototypical 3D TIs in the (Bi,Sb)₂(Se,Te)₃ family has sparked intense experimental work focused on improving material quality and exploring the exotic electronic properties.⁷ However, despite extensive growth efforts, binary 3D TIs continue to suffer from intrinsic defects,⁸ which contribute to undesirably large bulk carrier densities that overshadow the surface state in the overall electronic transport.⁹ Increasing the surface-to-volume ratio by fabricating thin films and nanostructures^10,11 is one strategy to enhance the relative contribution of the TSS.¹² Recently, a binary 3D TI nanowire-based field effect transistor demonstrated superior device performance when compared to conventional semiconductor nanowire transistors.¹³ 

To date, physical and chemical vapor deposition (PVD/CVD) have been the most successful techniques for growing of TI nanostructures and the use of Au nanoparticles as catalysts via the vapor-liquid-solid (VLS) growth route is well established.^14–17 However, the use of Au, as observed for (Bi,Sb)₂Se₃ TIs,¹⁸ is often undesirable for electronic transport applications since the catalyst becomes incorporated into the nanostructure during growth. While alternative catalyst materials such as TiO₂ show promise,¹⁸ catalyst-free techniques offer the cleanest synthesis route for TI nanostructures. The catalyst-free PVD growth of Bi₂Se₃ nanoribbons showing a large number of Shubnikov-de Haas quantum oscillations in magnetotransport measurements has been reported.¹⁹ 

A particularly attractive alternative to PVD/CVD techniques for growing high-purity thin films and nanostructures is molecular beam epitaxy (MBE). MBE is an ultra-high vacuum, non-thermal equilibrium growth technique that gives independent control over the fluxes of the constituent species and the substrate temperature which provides the greatest flexibility for suppressing background impurities and optimizing growth parameters. Here, we report on the catalyst-free growth of Bi₂Te₃ nanostructures by MBE in a detailed growth study as a function of substrate temperature using scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM).

Growth of the prototypical (Bi,Sb)₂(Se,Te)₃ TIs is governed by spiral surface growth (SSG).²⁰ The characteristic growth spirals are, in principle, hexagonal which reflect the rotational symmetry of Bi₂Te₃. They can, however, also adopt a triangular shape. In the framework of the Burton-Cabrera-Frank (BCF) theory, this can be explained when, for certain crystallographic orientations, the distance between corners of the structure is larger than the diffusion length of the surface adatoms.²¹ The growth spirals exhibit a terrace-step morphology in which adjacent terraces are separated by step heights of ∼1 nm, which correspond to one quintuple (Te-Bi-Te-Bi-Te) layer. The growth spirals are either induced by dislocations with a screw component²¹ or, according to a more recent study, by the pinning of 2D growth fronts at irregular substrate steps.²² Based on the BCF model,²³ the critical radius of nucleation was calculated to be 10.5 nm by Ferhata et al.²¹ The formation of screw dislocations in Bi₂Te₃ has been linked to variations in stoichiometry of the deposited nucleation centers due to Te re-evaporation during the initial stages of film growth. Te vacancies lead to an increased stacking-fault energy which is reduced by the formation of screw dislocations.²¹ 

For MBE growth, the flux of the group V material is responsible for controlling the growth rate of the (Bi,Sb)₂(Se,Te)₃ TI, while a large overpressure of the group VI species is typically supplied due to the high probability of re-evaporation. For thin film growth, it has been demonstrated that substrate temperature is the main parameter which determines film quality.^24,25 When the substrate temperature is too low, film growth is typically characterized by small orientationally disordered growth domains.²⁶ At higher growth temperatures, at which fewer nuclei initially form, domains are larger and well-oriented with respect to the underlying substrate. However, the presence of vertical nanostructures has also been observed, which are the subject of this study.²⁶ 

Bi₂Te₃ nanostructures were grown in a home-built MBE system on 10 × 10 mm² c-plane Al₂O₃ substrates (STEP, Shinkosha). The base pressure of the system was ∼5 × 10⁻¹⁰Torr. For this study, the commercial Te cracker cell (Createc) was heated to 470 °C, while the hotlip was kept at 700 °C. The Bi cell (Riber) was kept at 490 °C. The fluxes were calibrated using a quartz crystal microbalance. The Te:Bi flux ratio was ∼10:1 and the typical growth rate was ∼70 Å/min. The growth proceeded for a fixed time of 15 min, giving a nominal Bi₂Te₃ thin film layer thickness of ∼100 nm, determined from cross-sectional SEM. The substrate was radiatively heated with a halogen lamp, and the temperature was calibrated using a thermocouple at the substrate position.

To investigate growth of the vertical features that were found to accompany film growth, a temperature series utilizing a substrate temperature window between T_sub ≈ 180–260 °C was carried out. Figure 1 shows representative results from four temperatures within the investigated temperature range. At all temperatures, a mixed thin film and nanostructure growth regime is observed. Compositional analysis using Auger electron spectroscopy indicates that the nanostructures and surrounding thin film have the same Bi:Te ratio of 2:3. The stoichiometry of the nanoribbons was also confirmed by TEM-based energy-dispersive x-ray spectroscopy (EDS). Note that the brighter appearance of the nanostructures when compared to the underlying film is due to their large surface area which results in an increase in secondary electron emission. The nanostructure growth at low temperatures [208 °C, Fig. 1(a)] is governed by a high density of wide, wedge-shaped structures which are aligned with the steps of the underlying thin film (red close-up). Thinner, plate-like structures are also observed (blue close-up), which are thin film segments growing perpendicular to the surface. Increasing the substrate temperature to 233 °C (b) leads to a decrease of the nanostructure density. The growth is now dominated by nanoribbons which are several 100 nm wide. Their tips are usually terminated by a 30° inclined edge. Further increasing the temperature leads to even narrower nanoribbons (width <100 nm) [241 °C, (c)]. Finally, at 256 °C (d), a sparse distribution of very narrow nanoribbons is found (width <50 nm, blue close-up). Occasionally, some wider ribbons (widths ∼ several 100 nm) appear as well which could be due to the merging of narrower ribbons during growth (red close-up). Despite their nanowire-like appearance, the term nanoribbon is a more appropriate description, since their growth direction is along the [110] direction, and due to their sheet-like appearance. A stacked quintuple layer platelet structure, on the other hand, with a perpendicular growth axis would be expected for a nanowire as described by Kong et al.¹⁰ 

While substrate temperature was found to influence the density and shape of the nanostructures, no correlation between growth rate and nanostructure morphology and density—aside from the obvious length dependence for a fixed growth time—was observed. Experiments with rates between ∼7–70 Å/min yield similar densities and morphologies. At all temperatures, no evidence of tip-catalyzed growth was found. The base, however, appears to play an important role in the nanostructure growth.

AFM was performed in order to investigate the base of the nanostructures in more detail. Figure 2 shows AFM images of the low-temperature sample presented in Fig. 1(a), which was selected for AFM analysis because the typical nanostructure heights were small enough to allow for imaging without significant tip damage. Two features dominate the image, wedge-shaped structures and thinner, plate-like structures. The height profile across a wedge structure in Fig. 2(b) shows a height of ∼40 nm and a width of ∼100 nm. The pseudo-3D image in (c) clearly shows the hexagonal growth spirals typical for the Bi₂Te₃ thin film. Wedge-shaped structures, as shown in (d), were found to occupy a single terrace in width. The growing wedge strongly disturbs the spiral growth of the underlying film and appears to be consuming material from the lower terraces. The plate-like structures [shown in Fig. 2(e); see also Fig. 1(a), blue frame] are most common for low-temperature growth and are multilayered with a stepped surface morphology. Note that the thin sheets appear wider in AFM imaging due to tip-sample convolution. Additional bright features, which appear as small “defects” sitting on the films surface, are clearly visible in the AFM images [cf. black dashed circle in Fig. 2(e)]. These features are commonly found at the lowest point of the surface morphology and correspond to nuclei which have not seeded nanostructure growth, and have yet to be overgrown by the converging islands.

TEM was used to provide detailed structural information on the higher growth temperature sample. Figure 3 shows TEM (top-view) micrographs of two ∼140 nm wide nanoribbon segments grown at 256 °C. The growth is along the [110] (or $[112¯0]$⁠) direction, as indicated in (a). The nanoribbon tip has a slanted edge which is inclined by 30° with respect to the top plane. An additional, shorter edge indicated by the small arrow in (a) reflects the symmetry of the crystal structure and resembles the transition from hexagonal to triangular islands known from film growth. The high-resolution TEM image in Fig. 3(b) reveals the high-quality, single-crystalline nature of the structures. The distance between the lattice planes shown in (b) is ∼2.2 Å, which corresponds to the spacing of the (110) planes. The lattice parameters for hexagonal Bi₂Te₃ are a = 4.395 Å and c = 30.44 Å (JCPDS 82–0358). The Fourier transform is shown in (c) and reveals the hexagonal symmetry of the crystal structure (⁠ $R3¯m$ for Bi₂Te₃).

The above analysis warrants a discussion of the possible growth mechanism for the nanoribbons, which grow along the [110] direction. As shown in the temperature series in Fig. 1 (specifically for the higher resolution images in the lower row) as the temperature is increased, the nanostructures undergo a continuous transformation from densely populated predominately wedge and plate-like growth at low temperatures, to a reduced density consisting of wide nanoribbon features at intermediate temperatures, and finally to sparely populated narrow nanoribbon growth at the higher temperature limit. These results suggest that the seed must play a critical role in the growth of the nanostructures and determine their shape.

In the early stages of film growth, most of the seeds will nucleate spiral islands, which drives the film growth, whereas a few seeds nucleate 3D structures for which the growth rate and direction are different from the regular spiral film growth [cf. circle in Fig. 4(a) and close up in Fig. 4(b)]. The SEM images in Figs. 4(a) and 4(b) illustrate this situation on growth-interrupted samples (nominal film thickness ∼10 nm; grown at 194 °C and 178 °C, respectively). At these low temperatures, the exposed seeds appear to be responsible for nucleating the observed wedge features. As shown in Fig. 1(b), as the substrate temperature is increased, the wedge-shaped nanostructures disappear from the surface, which indicates that the seeds shown in Figs. 4(a) and 4(b) are not responsible for nucleating the higher temperature nanoribbon features.

Careful analysis of the roots of the nanoribbons in Fig. 1 (lower rows) and Figs. 2(c) and 2(d) reveals that the nanoribbons grow from step edges [Fig. 1(c), bottom row] or originate from the center of the film spirals [Fig. 1(c), middle row]. AFM imaging indicates the presence of several small seeds on the film surface [Figs. 2(c) and 2(e)], which are preferentially arranged at step-edges, spiral centers, and the intersection of grain boundaries. The exposed seeds nucleate a laterally confined sheet growth, which occurs simultaneously with the spiral island film growth but will result in the formation of a nanostructure. When the laterally growing sheet reaches the step edge to a lower-lying terrace, the growth direction changes from in-plane to out-of-plane and vertical nanoribbons emerge. Growth of the nanoribbons then continues along the [110] direction as the base of the nanoribbons are aligned with the step edges of the underlying terraces. This growth scenario is schematically illustrated in Fig. 4(c), and supporting SEM data are shown in Fig. 4(d). While the origin the driving force for the upward bending is not yet clear, it is not likely the result of stress due to lattice or thermal expansion mismatch between the film and the ribbon; however, a thermal gradient may develop due to their different thermal radiation characteristics.

In summary, we have presented a systematic study of the catalyst-free MBE growth of high-quality single-crystalline Bi₂Te₃ nanostructures on c-plane sapphire. By keeping the flux ratios of Bi and Te and the growth time constant, nanostructure growth was found to be controlled via substrate temperature. At low temperatures, a high seed density leads to the formation of short and wide nanostructures. At high temperatures, where the seed density is much lower, long and narrow nanoribbons growing along the [110] direction were observed. Understanding and the controlling growth of high quality nanostructures is important for the practical development of TI-based nanostructure devices. The use of MBE, in addition to synthesizing high quality nanostructures, also provides the unique opportunity to grow nanoribbon heterostructures to combine other functionalities with TIs and create novel device structures.

This work was supported by a DARPA MESO Project (No. N66001-11-1-4105) and the Army Research Office through Grant 57267PH. S.E.H. was supported by the DoD through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program and the VPGE (Stanford). P.S. acknowledges funding by EPSRC, Corpus Christi College, and the Studienstiftung. We thank S. Li, T. Sarmiento, A. Lin, A. A. Baker, and T. Kamins for experimental assistance and useful discussion throughout the course of this work.