Revealing surface-state transport in ultrathin topological crystalline insulator SnTe films Open Access

Topological insulators (TIs) form a class of bulk insulating materials with gapless surface states (SS) or edge states that are induced by band inversion due to strong spin-orbit coupling, which are protected by time-reversal symmetry. The unique properties of TIs, observed in chalcogenides such as Bi₂Se₃ and Bi₂Te₃, include spin momentum locking, dissipation-free edge conduction, and the quantum anomalous Hall effect.^1–8 Similar properties are also observed in another class of materials, the topological crystalline insulators (TCIs).^9–12 Surface bands in TCIs are protected by crystal mirror symmetry, rather than by time-reversal symmetry. In the first reported group of TCIs, (Pb, Sn)Te, Dirac cone SS have been predicted on both the (001) and (111) surfaces and observed by angle-resolved photoemission spectroscopy (ARPES), magnetotransport, and scanning tunneling spectroscopy (STS).^10–33 

Stoichiometric SnTe is a narrow bandgap semiconductor with a bulk bandgap of ∼0.2 eV.¹⁰ Conduction in the bulk coexists with conduction through SS due to unintentional doping of electrically active Sn vacancies.^34–36 Conduction in the bulk obscures the interesting and potentially useful conduction through topological states of SnTe for films >40 nm-thick or for devices fabricated on individual nanoplates with thickness >100 nm.^19,21,23,37 Another challenge for fabricating SnTe devices is that growth on several substrates, including Bi₂Se₃, 6H-SiC, BaF₂, and Si, results in polycrystalline films or nanoplates with both (001) and (111) orientations.^{13,19,25,26,37–39} Here, we develop a novel method that builds upon molecular beam epitaxy (MBE) in order to grow ultrathin continuous SnTe films on SrTiO₃ with a single orientation, where SS host a majority of carriers and the conduction through SS dominates. In addition, by burying the topologically protected SS at an interface, we overcome a number of challenges for incorporating TIs and TCIs in devices: providing encapsulation of the conducting channel, protecting the topological states from the ambient environment, and creating a high quality interface with an insulator for realizing field effect devices. This approach is widely applicable for other TIs and can be used for future devices based on topological SS, such as the low-dissipation topological transistors proposed in Ref. 11 based on the edge states of two-dimensional (2D) SnTe.

We initially grow SnTe films using a conventional MBE approach by thermally evaporating SnTe source material onto atomically flat single-crystal (001) SrTiO₃ (STO). The STO substrates remain insulating following SnTe growth (see the supplementary material for growth methods). For films 30 unit cells (uc) thick, reflection high-energy electron diffraction (RHEED) images [Fig. 1(a)] show two sets of streaks, marked by triangles and arrows, consistent with the RHEED results reported in Refs. 38 and 39. The second orientation marked by arrows disappears in the RHEED pattern of 400 uc SnTe, as shown in Fig. 1(b). The spacing of the multiple rods in RHEED suggests the coexistence of (001) and (111) orientations. The morphology of grains for both (001) and (111) orientations is shown in Figs. 1(c)–1(f) using atomic force microscopy (AFM) and scanning electron microscopy (SEM). For the thinnest sample (30 uc-thick) [Figs. 1(c) and 1(e)], small grains about 200 nm in diameter appear with holes in the film between grains, indicating the discontinuous nature of the films. In the 400 uc sample [Figs. 1(d) and 1(f)], grains with diameters of approximately 500 nm are observed. Holes between grains no longer exist, yielding a continuous film.

The formation of multiple domains is also observed using x-ray diffraction (XRD, see the supplementary material). The XRD patterns show two orientations of the films [Figs. 1(g)–1(i)], as seen by the appearance of (222) and (004) SnTe reflections. The relative intensities of (222) and (004) peaks change with the thickness of the films, while the peak widths in 2θ decrease with deposited thickness. Rocking curve measurements are carried out for each film to estimate the volume ratio of (111) to (001) grains. The ratios are 1.82, 0.10, and 0.04 for 20 uc, 90 uc, and 400 uc SnTe films, respectively, indicating the increasing dominance of (001) orientation in thick films, in agreement with the RHEED images [Figs. 1(a) and 1(b)]. The picture that emerges from this data is that SnTe nucleates at the STO surface with two out-of-plane orientations. As the films are made thicker, the lateral dimensions of the grains increase, leading to continuous films. The (001) oriented grains grow faster than the (111) oriented grains so that for SnTe films >90 uc thick, the (001) orientation covers more than 90% of the film area. This behavior is expected from the known dependence of grain growth in thin films driven by differences in surface energies; here, the (001) orientation has a lower surface energy than the polar (111) surface.⁴⁰ 

This observation of the relative stability of the two orientations is the basis for modifying the conventional MBE process to achieve single-orientation, ultrathin, and continuous SnTe films for transport measurements and device applications. We adapt a deposition method that controls the growth rate by balancing sublimation from the growing film at elevated substrate temperatures with deposition from the SnTe source. Two-temperature growth methods have been previously introduced for other semiconductors, such as GaAs and CaS.⁴¹ Here, we use this process to thin down SnTe films to a few atomic layers in thickness to achieve single-oriented (001) SnTe films, as described below. For the films measured here, we first deposit 150 uc SnTe on STO at 400 °C, where the sublimation rate is negligible and the ratio of (111) to (001) grains is <0.1. The substrate temperature is then increased to 540 °C to sublimate the thin film while maintaining a constant SnTe flux. These conditions result in a net sublimation of SnTe from the film—a negative growth rate, thus gradually reducing the film thickness. We achieve continuous SnTe films with thicknesses ranging from 10 to 40 uc by this process. Atomically flat crystal terraces are observed on the surface of all films, as seen by AFM and SEM [Figs. 2(b) and 2(c)], with pinholes making up <5% of the area [Fig. 2(b)]. RHEED and XRD measurements confirm that the SnTe films grown by this method only show (001) SnTe grains [Figs. 2(a) and 2(d)].

This co-sublimation-deposition (coSubDep) process completely removes grains with (111) orientation while making the SnTe films thinner. Furthermore, this “gentle polishing” minimizes the bulk volume while maintaining the continuity of the SnTe films, leading to a substantial suppression of carriers in the trivial bulk states, a critical step toward the fabrication of devices with electrical transport dominated by the topological states.

To study the transport properties related to SS, we conduct electrical transport and magnetotransport measurements on SnTe films grown by the coSubDep process (t ≤ 40 uc) (see the supplementary material for more details). For all thicknesses, we observe metallic conduction as the temperature is varied from T = 1.8 K to T = 300 K [Fig. 3(a)]. Hall measurements R_xy(B) are used to determine the 2D total carrier density n_2D [Fig. 3(b)] and are found to be linearly dependent on B up to B = 9 T for all films. One critical feature of the transport in these films is that, besides the conduction through SS, carriers exist in bulk states due to Sn vacancies that contribute to conduction as well. We adapt a simple physical picture and equation to describe the observed transport properties, which is applicable to the general class of materials systems that conduct through both bulk and SS.

In this system, we expect the conduction to occur via three channels: bulk carriers with a thickness-dependent carrier density n_Bt, and SS carriers at the top and bottom interfaces with thickness-independent densities n_{s,SnTe/vacuum} and n_s,SnTe/STO. The Hall measurements of SnTe films are linear up to B = 9 T, indicating that the differences in mobility for the three channels are small enough to assume that the measured 2D carrier density is the sum of the contributing channels, n_2D(t) = n_Bt + n_{s,SnTe/vacuum} + n_s,SnTe/STO. Analysis of this assumption with the magnitude of the carrier mobility (<100 cm²/Vs) shows that the 2D carrier density is self-consistent to within 1%. With transport data from various film thicknesses, we extract the bulk and total surface contributions, n_B and n_S, from n_2D(t) = n_Bt + n_s, where n_s refers to the sum of SS carrier densities of n_{s,SnTe/vacuum} and n_s,SnTe/STO [Fig. 3(c)]. The measured n_2D(t) depends linearly on the thickness t for all thicknesses at each temperature and intersects at the same point on the y-axis [Fig. 3(c)]. From linear fittings using the equation n_2D(t) = n_Bt + n_S, we extract the bulk carrier density n_B = 1.8, 2.1, and 2.5 × 10²⁰/cm³ at 300 K, 240 K, and 140 K, respectively, consistent with previous transport measurements on bulk SnTe.^36,42 This density corresponds to one Sn vacancy or two electrons in every 20 unit cells. We note that the bulk carrier density in SnTe is ∼2–3 orders of magnitude greater than the values reported for Bi₂Te₃/Bi₂Se₃, due to the negative formation energy of Sn vacancies. The excessive amount of Sn vacancies may cause extra scattering, leading to the low mobility observed.

The intercept on the y-axis gives n_S = 5 × 10¹⁴ cm⁻², which is temperature independent. While the bulk part of SnTe is a degenerately doped semiconductor, n_S is temperature independent, distinct from a degenerate system and consistent with the nature of SS states. Furthermore, examination of magnetoconductance measurements reveals weak anti-localization (WAL) behavior [Fig. 3(d)], consistent with conduction through topological SS.^19,37,43,44 Fitting the magnetoconductance from a representative 10 uc film to the Hikami–Larkin–Nagaoka (HLN) equation gives a coherence length of 200 nm. For SnTe films with thickness t ≤ 40 uc, the total carrier density n_2D is mostly composed of the carriers in the surface states n_S. In the 10 uc SnTe film, ∼95% of the hole carriers come from the SS and only ∼5% of the hole carriers come from the bulk states. This approach can be applied to extract the carrier concentrations for SS and bulk in other bulk-doped TIs and TCIs.

One question that arises is whether the measured SS reside at the top surface of the film or the interface between the film and substrate. The SnTe/STO interface is sharp, due to the atomically smooth STO surface, and the STO forms an insulating barrier – STO has a relatively large bandgap, 3.2 eV and a favorable band alignment with SnTe, estimated from the work functions of STO and SnTe.⁴⁵ This band alignment puts the Dirac point of SnTe near the center of the STO bandgap, where negligible band bending and charge transfer from STO occurs [Fig. 4(a)]. However, recent ARPES measurements¹³ of SS in Sn vacancy doped SnTe show that the pristine buried SnTe/STO interface is not replicated at the exposed SnTe/vacuum interface. Bulk doping in these films results in a chemical potential ∼0.3 eV below the top of SnTe valence band.^10,13,34 This is consistent with the films presented here: a comparison between the measured n_B and the calculation of n_B based on the complex band structure of bulk SnTe also puts the Fermi level ∼0.25 eV below the valence band edge.⁴² Measured ARPES, however, which is surface sensitive, shows a Fermi level only ∼0.03 eV below the Dirac point, likely due to band bending and depletion at the top surface of SnTe/vacuum.¹³ It has been proposed that defects or adsorbates at the exposed SnTe surface may be responsible for pinning the SnTe Fermi level. X-ray photoelectron spectroscopy measurements on our SnTe films after exposure to air reveal existence of carbon and oxygen atoms, likely from the adsorbates on the SnTe films. This work demonstrates that this pinning is absent at the SnTe/STO interface, as demonstrated by measurements of the carrier density n_S and WAL behavior, protecting the SS from the environment.

To locate the carriers at the SnTe/STO interface, we first determine the carrier concentration at the SnTe/vacuum interface using scanning tunneling microscopy (STM) and STS measurements (see the supplementary material). These measurements are done on a clean surface, and atomic resolution images are achieved, where the contrast is sensitive to the Sn atoms of the (001) surface with positive bias voltage applied to the sample with respect to the tip [Fig. 4(b)].⁴⁶ For our purposes, the STS measurement [Fig. 4(c)] shows the local density of states (DOS) at the (001) SnTe surface in vacuum. At the Fermi level, the DOS is greater than zero, consistent with gapless SS, as expected for the (001) SnTe surface.³¹ Our STS experiments, as well as previous experiments by ARPES, show that for the surface of SnTe in vacuum, the Fermi level (at zero bias voltage) lies in the SnTe bandgap and close to the Dirac point, compared to the bulk Fermi level, which is ∼0.3 eV lower than the top of the SnTe valence band [Figs. 4(a) and 4(c)]. The resulting band bending leads to carrier depletion at the SnTe/vacuum surface.

Because of this pinning, the density of surface state carriers at the SnTe/vacuum interface n_{s,SnTe/vacuum} is negligible compared to n_s,SnTe/STO. We conclude the large measured SS carrier concentration n_s is dominated by conduction at the SnTe/STO interface. Assuming that the Fermi level in the bulk is ∼0.25 eV below the top of the valence band, as estimated from the measured bulk carrier density,⁴² we estimate a topological surface density of n_S = 1.3 × 10¹⁴ cm⁻² by counting the area of the Fermi surface at 0.25 eV below the valence band as a circle with a radius of k_F = 0.1 Å⁻¹, including the four degenerate Fermi surface sheets. We note that this is an overestimate of the actual Fermi surface, which has an ellipse-like shape with the major axis from the center of the ellipse k ≥ 0.1 Å⁻¹, as shown by ARPES measurements.^11,13 This estimate of n_S agrees within a factor of four with the n_S measured for thin films, 5 × 10¹⁴ cm⁻², indicating the SS contributing to the conduction of the SnTe films are the topological SS of SnTe. In comparison, at the surface of SnTe in vacuum, a Fermi surface 0.03 eV below the Dirac point corresponds to k_F ∼0.02 Å⁻¹ and a surface carrier density of 0.05 × 10¹⁴ cm⁻². We note that n_S at the SnTe/STO interface is one to two orders of magnitude larger than the density achieved using field effect gating of 2D electron gas (2DEG) systems, such as graphene and MoS₂, and is rivaled only by ionic liquid gating.

While it is preferable in designing topological devices for the bulk of a topological film to be insulating and for transport to be solely through SS, our approach of synthesizing high-quality ultrathin TCI films through co-sublimation-deposition allows us to unlock the unique topological properties of SnTe even in the presence of bulk conduction. Combined with our approach of burying the SnTe/STO interface to protect SS carriers, this process may lead to the development of new devices, including low-dissipation electronic devices, spintronic devices, and devices based on the topological magnetoelectric effect. This approach is suitable beyond SnTe and is applicable to broad classes of TI and TCI materials.

See supplementary material for details of sample growth, X-ray diffraction, transport experimental setup, and scanning probe experimental setup.