Weak antilocalization in topological crystalline insulator SnTe films deposited using amorphous seeding on SrTiO₃ Open Access

Topological crystalline insulators (TCIs) are a subclass of topological materials that possess conducting surface and edge states due to band inversion at locations of high crystal symmetry in the Brillouin zone.^1,2 The prototypical TCI, SnTe (and its family of Pb-alloyed rocksalt compounds), has been thoroughly studied because the crystal symmetry protection of TCIs offers new methods for control of its topological states.^3–5 Contrasting with conventional TIs, applying strain or an electric field can break the crystal symmetry, gapping the topological states.^1,2,6–8 A topological transistor based on this principle using gated SnTe has been proposed, with an applied electric field breaking the SnTe crystalline symmetry.⁸ 

Angle-resolved photoelectron spectroscopy and scanning tunneling microscopy^9–18 have identified topological surface states in flakes and discontinuous films of SnTe; however, synthesizing SnTe films with uniform crystalline orientation and continuity to engineer devices has proven difficult.^17–23 Techniques such as molecular beam epitaxy and chemical vapor deposition have been favored over exfoliation, commonly used for other 2D materials,²⁴ because of the strong interlayer bonds in SnTe. Yet, on substrates both with and without close lattice matches, SnTe forms discontinuous films with multiple crystalline orientations, not suitable for gate-controlled devices. A modified molecular beam epitaxy technique called co-sublimation-deposition (coSubDep) has been shown to produce SnTe films as thin as 10 u.c. on SrTiO₃ with higher continuity and crystalline uniformity.²⁵ With its high dielectric constant and large bandgap, SrTiO₃ is a promising substrate for gated-SnTe, with SrTiO₃ serving as an insulating buffer layer between SnTe and a conducting oxide gate.²⁶ 

In this work, we present advances in the coSubDep deposition technique, dramatically increasing the achievable in-plane crystalline uniformity of SnTe(001) thin films. We implement a thin templating SnTe layer that is crystallized after amorphous deposition, followed by molecular beam epitaxy growth monitored with high resolution laser ellipsometry to control both deposition and evaporation of the SnTe film. The thin template layer results in high quality, continuous SnTe films with markedly higher in-plane crystalline uniformity than previously achieved. We perform magnetoconductivity measurements to characterize the topological states of uniform SnTe thin films, specifically to quantify the number of independent topological channels present and the inelastic mean free path of topological carriers as a function of film thickness.

SnTe films are deposited in an ultrahigh vacuum chamber (base pressure 1 × 10⁻⁹) devoted to chalcogenide molecular beam epitaxy deposition. Molecular SnTe is evaporated from an effusion cell at a deposition rate of ∼1.5 unit cells per minute on TiO₂-terminated SrTiO₃(001) substrates purchased from Crystec GmbH. Reflection high-energy electron diffraction (RHEED) and ellipsometry are measured in situ during growth. Following the deposition, the crystalline structure is characterized using ex situ x-ray diffraction. Transport measurements are performed ex situ in a Quantum Design DynaCool Physical Property Measurement System using the Electrical Transport Option, which utilizes an AC lock-in amplifier. Rectangular bars are mechanically fabricated for transport measurements using stainless steel tweezers, and Au pads are deposited for electrical contacts. Representative van der Pauw and linear four-point devices are shown in Fig. S1(a).

As described previously,²⁵ coSubDep is used to achieve continuous SnTe films with single (001) orientation. We deposit thick SnTe films (>150 u.c.) by conventional molecular beam epitaxy and then elevate the substrate temperature under constant SnTe flux until we reach a net negative growth rate of the film thickness. Previously, multiple trials with different evaporation times were used to achieve films with the desired thickness.²⁵ Here, we utilize laser ellipsometry to track the sublimation step of coSubDep in real time. Ellipsometry allows us to reproducibly stop evaporation at the desired thickness. This method is sensitive to film thickness at small values due to the high absorption coefficient of SnTe at the wavelength of the helium–neon laser (632 nm).²⁷ The laser, polarizer, and analyzer are mounted to the windows of the growth chamber, with a specular reflection angle of ∼40° with respect to the sample normal. Two values parameterizing the shift in polarization upon reflection, ∆ and Ψ, are measured and are sufficient to characterize the thickness using known values of the complex index of refraction for SnTe.²⁷ An accurate calibration of the ellipsometry insensitive to geometrical details such as the sample position and orientation of the polarizers is performed by measuring the values of ∆ and Ψ with respect to the thickness determined by a quartz crystal monitor. As shown in Fig. 1(a), the value of Ψ is a particularly sensitive measure of thickness from 0 to 75 u.c. of SnTe. A plot of these values over deposition of 200 u.c. SnTe is shown in Fig. 1(a). To achieve films of 10–20 u.c., we target Ψ = 15, which corresponds to a thickness of ∼25 u.c. We target a Ψ corresponding to a greater thickness than desired because the SnTe continues to evaporate while the sample is cooled.

Following growth of SnTe(001) thin films by coSubDep, we characterize the SnTe crystalline orientation by measuring x-ray diffraction. Specular diffraction measurements reveal (0 0 1) SnTe [Fig. S1(b)] fully relaxed from the SrTiO₃ lattice. Because the SnTe film consists only of (0 0 1) oriented crystals, the film is terminated with a (0 0 1) plane at the SrTiO₃ interface, which consists of both Sn and Te atoms. We determine the in-plane crystalline orientation of SnTe(001) by measuring ϕ-rocking curves at the SnTe (2 0 6) and SrTiO₃ (1 0 6) Bragg reflections. The SnTe ⟨1 0 0⟩ direction is typically oriented parallel to the SrTiO₃ ⟨1 1 0⟩.^15,25 However, for many SnTe films, there are multiple (2 0 6) Bragg peaks observed when varying ϕ, indicating domains of SnTe with different in-plane orientations [Fig. 1(b)]. In the case of the film displayed in Fig. 1(b), we identify four SnTe (2 0 6) reflections over a range of 90°, which indicates four distinct in-plane orientations.

The observation of multiple in-plane orientations suggests that the (001) face of SnTe is able to nucleate with multiple orientations on the SrTiO₃ surface. To prevent multiple orientation formation, and thus formation of domain boundaries between orientations, we have discovered alternate growth conditions that promote single-orientation nucleation. Rather than depositing at a substrate temperature that results in a highly crystalline film, we deposit an amorphous layer of 5 unit cells (u.c.) of SnTe at room temperature and then anneal at 350 °C to crystallize the layer. After crystallization, we observe formation of single orientation SnTe(001) in RHEED [Figs. 1(c) and 1(d)], which agrees with ex situ XRD measurements [Fig. S1(b)]. After the crystallization anneal, 195 u.c. SnTe is deposited at 350 °C for a total thickness of 200 u.c.

To achieve films thinner than 20 u.c., we begin growth with the deposition of an amorphous layer of SnTe and recrystallization, as described above, followed by the deposition of 195 u.c. at a substrate temperature of 350 °C, and then use the coSubDep process to reduce the film thickness. We grow the seeded films thicker and then sublimate them to the desired thickness using coSubDep, rather than directly growing from the seeded layer to the desired thickness, for two reasons: first, we do occasionally observe (111) reflections in RHEED after the seeding layer is crystallized, which coSubDep is able to remove, and second, the seeding layer quickly transitions to forming 3D domains after crystallization (rather than a continuous film), and coSubDep has proven to be a reliable way to achieve single orientation and uniform films.

Measuring ϕ-rocking curves after utilizing the amorphous layer to nucleate SnTe, we observe a marked improvement in film uniformity—only a single (001) orientation is present [Fig. 1(b)], with SnTe ⟨1 0 0⟩ parallel to SrTiO₃ ⟨1 1 0⟩. Using amorphous layer nucleation combined with ellipsometry tracking during evaporation, we are able to reproducibly grow SnTe films down to 10 u.c. with only a single in-plane orientation of SnTe. AFM measurements confirm the formation of continuous films with a small density of physical holes in films thinner than 10 u.c. (Fig. 2), consistent with previous coSubDep growths.²⁵ 

To characterize the nature of the topological states in these continuous SnTe films, we perform magnetoconductivity measurements to observe quantum interference effects (more details about transport measurements are given in the supplementary material). The sheet resistance, carrier density, and mobility of the SnTe films are consistent with previous studies of SnTe thin films (Fig. S2).²⁵ Extracted magnetoconductivity (MC) exhibits weak antilocalization (WAL) behavior, or an enhancement of conductivity, near zero out-of-plane magnetic field [Fig. 3(a)]. This MC behavior is consistent with transport through topological states.^20,28–31 Although the interior of a SnTe film is conducting and exhibits strong spin–orbit coupling and thus should also exhibit WAL, the observed MC corresponds to topological surface state transport, as we show in Fig. 3. In addition, previous studies show that surface carriers in SnTe films as thin as 10 u.c. make up nearly 95% of the total carriers.²⁵ 

To quantify the phase coherence length and number of independently conducting channels (i.e., conduction paths that can be electrically isolated from one another), we fit the MC data to a Hikami–Larkin–Nagaoka(HLN) model,³² 

where l_φ is the phase coherence length, N is the number of channels, B is the applied magnetic field perpendicular to the film surface, ψ is the digamma function, and the value of α identifies the nature of conduction. For topological insulators, we expect α = −1/2 for a single channel. Since we have two geometric surfaces for a thin film that can host topological states (i.e., at the SnTe/SrTiO₃ and SnTe/vacuum interfaces), we may expect either N = 2 if the surfaces are isolated or N = 1 if the bulk is sufficiently conducting, and the two surfaces behave as a single channel.²⁸ We perform MC measurements for four film thicknesses grown using an amorphous seed and coSubDep—10, 17.5, 50, and 200 u.c.—over a temperature range of 2–10 K and ±4000 Oe. Data beyond ±4000 Oe are excluded because conventional MC dominates the WAL effect.

The data from a 10 u.c.-thick film at 2 K fit the measured data over the range of ±4000 Oe. However, single-channel fits noticeably deviate from the data measured from 17.5 to 50 u.c. films at 2 K [Fig. 3(b)]. The origins of this deviation may be the coexistence of topologically trivial states from the SnTe bulk, which could give the opposite effect, weak localization (WL), with the non-trivial states expected at the SnTe surfaces.^29,33,34

Another potential source may be the presence of Kondo scattering from magnetic impurities.³⁵ However, the MC response from Kondo scattering generally occurs at larger magnetic field strength than observed here (>±4000 Oe),³⁵ and measurements of the magnetic properties of SnTe films, using a Quantum Design Magnetic Properties Measurement System, reveal no magnetic moment, eliminating Kondo scattering as a source of this observed deviation.

We can model the coexistence of WAL and WL by adding a WL contribution to Eq. (1),

where we fix α₁ = −1/2 and α₂ = +1 for the WAL and WL states, respectively, and allow the number of channels, N_m, to vary independently. The fits incorporating both WL and WAL deviate less from data from every film [Fig. 3(b)], strongly suggesting the presence of trivial states in addition to the topological states.

The extracted values of N < 1 are smaller than the expected value of N = 1 for a single conduction channel for both WAL and WL contributions [Figs. 4(a) and S3(a), respectively]. Considering the presence of trivial states is likely due to band edge fluctuations on the film opening up small areas of primarily bulk conduction,^29,33,34 the value of N₂ < 1 can be understood as a low density of fluctuations. The value of N₁ < 1 [Fig. 4(a)] suggests that either the film is not topologically non-trivial across the entire film area or there are additional trivial states that offset the WAL. Additional WL states may be possible since Eq. (2) can only separate different conduction channels with sufficiently different l_φ. If the difference in l_φ is less than 7%, we are unable to isolate the presence of multiple conduction channels over our experimental range of ±4000 Oe. Future experiments utilizing gated SnTe field-effect devices could isolate any additional WL states by tuning the Fermi level to the bulk bandgap at the SnTe–SrTiO₃ interface.

The phase coherence lengths for the topological states, which are limited by inelastic scattering,³⁶ are in the range of 50–500 nm with a T^−p/2 dependence [Fig. 4(b)], consistent with previous measurements of topological materials.^{20,25,28–31,37} Fitting the temperature dependence gives values of p equal to ∼1.5 for the 10 u.c. and 17.5 u.c. films and decreasing to ∼1 for the 50 and 200 u.c. films [Fig. 4(b)]. The value of p in thinner films is consistent with previous studies of topological insulators^{20,28–31,33,38,39} and suggests a scattering mechanism of both electron–electron and electron–phonon scattering in the topological surface states—for thin films, a value of p = 1 corresponds to electron–electron scattering^38,40 and a value of p = 2 corresponds to electron–phonon scattering.⁴¹ The decrease in p with increasing film thickness (Fig. S4) implies a decrease in electron–phonon scattering, which is likely due to increased film continuity in thicker films.^39–41 This transition may also be due to a difference in the dominant scattering mechanism between the bulk and surface conduction states; previous work demonstrates that in a 10 u.c. film, 95% of the conduction is through topological surface states at the buried SnTe/SrTiO₃ interface, while in a 200 u.c. film, <20% of the conduction is expected through the topological surface states.²⁵ Since the value of p = 0.82 in the 200 u.c. film is less than p = 1, this possibly suggests another change in scattering mechanism as thin films approach bulk behavior; however, additional experiments are necessary to further explore this possibility.

In addition, the magnitude of WAL coherence length in the topological states increases with thickness, from a coherence length of ∼150 nm in the 10 u.c. film to ∼500 nm in the 200 u.c. film. The transition from mixed scattering in thin films to electron–electron dominated in thicker films is not sufficient to understand this trend. The increase in coherence length with film thickness may be due to decreasing interaction between the two sets of surface states at the SrTiO₃/SnTe and SnTe/vacuum interfaces, respectively. This would be consistent with previous theoretical work that demonstrated that surface states occupy a non-zero depth into the interior of a film, and two sets of parallel surface states will interact when they begin to overlap in thin enough films.⁸ The ability to tune the Fermi level in a next generation of gated SnTe field-effect devices, built on the foundation of this work, would lead to a better understanding of the topological behavior of SnTe, from the scattering mechanism in thicker films to the potential interactions between parallel surface states in thinner films.

The presence of WL indicates conduction through a channel with small spin–orbit coupling length relative to the phase coherence length, suggesting that the spin–orbit length for SnTe bulk states is on the order of 10 nm. Although bulk states in conventional topological insulators and SnTe experience the same strong spin–orbit coupling that gives rise to the topological band inversion, previous studies have identified conduction through bulk subbands, arising from the quantum confinement effect, as a potential source of WL behavior in other topological systems.^33,34,42 Considering the band bending observed near the SnTe/vacuum interface,²⁵ local variations to the Fermi level at the SrTiO₃/SnTe interface due to inhomogeneities in the substrate surface, such as the presence of trapped charges²⁶ or misfit and threading dislocations due to the SnTe relaxation relative to the substrate, could result in partial conduction through bulk subbands, giving WL behavior with N₂ < 1. Measuring the band profile through the SnTe film could elucidate the origin of the WL behavior and its relation to interface inhomogeneities. Since the precise band profile of SnTe/SrTiO₃ has yet to be characterized,²⁵ we cannot conclusively identify the origin of WL states without further experiments to determine the band profile, such as high energy x-ray photoemission spectroscopy (HXPES).

The extracted coherence length of the WL states does not present an observable pattern [Fig. S3(b)]. This is likely due to the relatively small contribution of WL to the overall data, which means there is little precision in this fitting parameter. However, the particularly small WL coherence length (<10 nm) observed in the 200 u.c. film indicates a vanishingly small contribution of WL states in this film. Considering the likely origin of WL states—bulk subbands crossing the Fermi level due to local inhomogeneities—this observation is consistent with the removal of bulk subbands as they transition into a three-dimensional continuum of states in thicker films.

This work characterizes the conduction behavior of topological states in high quality SnTe films, providing a pathway to the development of gate-controlled SnTe devices. We demonstrate the parameters for a growth process for synthesizing uniform SnTe films on SrTiO₃, which begins with an amorphous seed layer to advance previous deposition procedures. The SnTe films presented here display magnetoconductivity consistent with transport through a single topological channel, with inelastic mean free paths of several hundred nanometers. Comparing the scattering mechanism in thick and thin films suggests greater electron–phonon scattering from more discontinuities at the interfaces of the thinnest SnTe films, presenting further opportunity for SnTe growth optimization. Continued improvements to SnTe growth on SrTiO₃, building from the growth procedures presented here, could be used to construct gated Hall bars that enable a more detailed understanding of the band profile within SnTe films and magnetoconductivity character of SnTe topological states.

See the supplementary material for a representative photograph of the devices used for electrical measurement, specular x-ray diffraction results, and more transport measurements of SnTe thin films.

This work was supported by the Air Force Office of Scientific Research (AFOSR) under Grant No. FA9550-21-1-0173. S.D.A. acknowledges the Kouvel fellowship at Yale.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.