Structure and topological transport in Pb-doping topological crystalline insulator SnTe (001) film

1. Introduction

A new quantum matter, that is topological crystalline insulators (TCI), supplies a great application expectation to future quantum devices, because of its novel surface conductive states being immune to surface impurities or defects to avoid the possible thermal dissipation [1], [2]. The surface conductive sates of TCI arise from the crystal symmetries protection and its band structure usually consists of even number of Dirac cones in contrast to conventional topological insulator with odder Dirac cones [3], [4], [5], [6]. The first theoretically predicted TCI is the compound SnTe and its metallic surface states, originating from the even number of Dirac cones on high-symmetry crystal surfaces {001}, {110} and {111}, can be demonstrated by the band structural observation and electronic transport. The angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) experiments firstly confirmed the presence of topological surface states (TSSs). The Dirac cones with linear dispersion relation have been clearly observed in single crystalline SnTe and their doping alloys Sn_xPb_1-xTe and Pb_1-xSn_xSe [7], [8]. Based on the band structure confirmation of the topological surface state, the SnTe system become a significant platform to study the valley-degenerate topological systems in transport experiments for promoting TCI to be a potential quantum electronic device in future. The transport properties of SnTe system is focused on the high-symmetry crystal surfaces {001}, {110} and {111} with typical topological surface state and they are generally realized by the epitaxial growth on the corresponding single crystalline substrate SrTiO₃(111), BaF₂(001), BaF₂(111) via the molecular beam epitaxy (MBE) [9], [10], [11], [12], [13], [14]. However, on the SrTiO₃ (111) substrate, the epitaxial film SnTe (or SnSe) only growing along [001] while not [111] indicates a novel match relation between film and substrate, but this match relation is still not to be clarified. To construct the lattice match mechanism, the SnTe epitaxial film grown on SrTiO₃ (111) is needed to be as a model system for presenting the corresponding structural detail and formation mechanism [15], [16], [17]. It will pave an important structural basement to understand its transport properties. Furthermore, the effect of element doping and film thickness on the transport behavior of the novel epitaxial SnTe (001) film on SrTiO₃ (111) is significant for understanding the topological characteristics of TCI SnTe. The modulation of doping or film thickness will open up a continuously tunable band gap on the surface, which may lead to wide-ranging applications in thermoelectric and tunable electronics.

In this work, we systematically investigate the lattice structure of the SnTe (001) film grown on the SrTiO₃ (111) substrate and construct a structural model for illustrating the lattice match correlation between SnTe film and SrTiO₃ substrate. To suppress the bulk transport to enhance the surface conductive states contribution, the decrease of the film thickness and Pb-doping was used. The SnTe (001) film with thinner film thickness 15 nm presents larger sheet resistance indicating the enhancement of the TSSs in the general transport of the film. By introducing the Pb doping, an enhancement of phase coherent length and mobility but a decrease of the carrier density shows an increase of the TSSs and a suppression of the bulk carrier in general transport of the Pb-doping film.

2. Experimental

The thin films were prepared by molecular beam epitaxy system (MBE) with the based vacuum better than 1.5 × 10^-10 mbar. The SnTe and Sn_0.7Pb_0.3Te films were grown on SrTiO₃ (111) substrate by simultaneously evaporating pure Sn (99.999 wt.%), Te (99.999 wt.%) and Pb (99.999 wt.%) sources from the Knudsen cells. Before growth process, the SrTiO₃ (111) substrate was performed degas circulation under 600 °C and then the substrate temperature was kept at 300 °C during film growth. The relatively narrow diffraction stripe from the in-situ reflection high energy electron diffraction (RHEED) indicates perfect single crystalline substrate (Fig. 1(a)) and good epitaxial growth of the thin film (Fig. 1(b)). In Fig. 1(c), the X-ray diffraction (XRD) spectrum of SnTe film further proves the grown orientation along [001] direction. The controllable thickness of SnTe film was achieved by controlling the growing rate with 1 nm/min. The Pb doping was realized by exactly controlling its evaporating ratio with Sn and Te elements whose exact content was detected by X-ray photoelectron spectroscopy (XPS) analysis at different depth of film (Fig. S1 in Supplementary materials). The cross-sectional atomic structure of the film was detected by the high resolution transmission microscopy (HRTEM). The transport behavior of the grown films was measured by a standard four-terminal Hall bar device, in which the schematic is shown in the inset of Fig. 1(d).

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Fig. 1.   (a) RHEED pattern of substrate SrTiO₃ (111) and (b) SnTe (001) film with thickness 15 nm; (c) XRD pattern of SnTe film in which the inset shows the lattice structure of SnTe; (d) transport measurement geometry with the Hall bar of the SnTe film.

3. Results and discussion

In Fig. 1(b), the RHEED pattern of a represented SnTe film with 15 nm thickness indicates good epitaxial growth. The faint RHEED streaks between three bright streaks indicate the multi-domain structure of the SnTe (001) film. The low-energy electron diffraction pattern of this film proves the existence of the multi-domain structure (Fig. S2). The similar domain structure was also observed in literature [13]. The diffraction peak in the XRD pattern is indexed as (002) reflection indicates the [001] growth of the SnTe film on SrTiO₃ (111). The similar situation was observed in SnSe film on SrTiO₃ (111), which suggests that SnTe or SnSe is easy to epitaxially grow along [001] on the (111) plane of SrTiO₃ substrate [10], [18]. The atomic match correlation between the (001) plane of SnTe and the (111) plane of SrTiO₃ is definitely responsible for this special epitaxial growth. In Fig. 2(a), the cross-sectional HRTEM image shows the interface structure of SnTe (001)/SrTiO₃ (111). The characterized (002) and (200) crystalline planes of SnTe film were confirmed by measuring their typical d-spacing of 3.15 Å in two directions. The d-spacing of 2.76 Å and 2.25 Å correspond to (110) and (111) crystalline planes of SrTiO₃ substrate. After the annealing procedure, the Ti-O plane always appears on the surface of SrTiO₃ (111) and becomes the grown plane for SnTe film [19], therefore, the hexagonal Ti-O lattice on the (111) plane decides the atomic match of the SnTe film. In Fig. 2(c), the hexagonal atomic arrangement of Ti-O plane shows two different atomic distances between two Ti atoms along [110] and [$\bar{1}$10] directions that are a₁ = 9.5 Å and a₂ = 5.52 Å respectively. For SnTe film with a cubic rock salt structure, its (001) plane displays a square lattice with the shortest atomic distance b₁ = 3.15 Å while its (111) plane shows a triangle lattice with the shortest atomic distance b₂ = 4.48 Å. The lattice match between of SnTe and SrTiO₃ is decided by their integer or integer multiple relation of lattice parameters, whose detailed geometry configurations are shown in Fig. 2(c) and (d).

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Fig. 2.   (a) Cross section HRTEM image of SnTe(001)/SrTiO₃(111) along the lattice axis [112]; (b) atomic arrangement and atomic distance of the (001) and (111) planes of SnTe film; (c) lattice structural model for the match correlation between SnTe (001), SnTe (111) and SrTiO₃ (111); (d) cross-section model image between SnTe (001) and SrTiO₃ (111).

For realizing appropriate atomic match, the atomic arrangement of SnTe (001) tends to along the [110] and [$\bar{1}$10] direction on the Ti-O plane, because the distance 9.5 Å of two Ti atoms at [110] direction corresponds to three times atomic distance (3 × 3.15 Å = 9.45 Å) on (001) plane of SnTe film; the distance 11.07 Å of three Ti atoms at [$\bar{1}$10] direction corresponds to four times atomic distance (4 × 3.15 Å = 12.6 Å) on (001) plane of SnTe film (Fig. 2(c). Through present atomic arrangement, the square lattice of SnTe (001) can be epitaxially grown on the hexagonal Ti-O plane of SrTiO₃ (111). The different integer time’s atomic arrangement on two directions will induce a dislocations on the interface between SrTiO₃ substrate and SnTe film. According to above atomic match, the distance of three Ti atoms corresponding to four Sn(Te) atoms on [$\bar{1}$10] direction means that the four Sn(Te) atoms epitaxial match with three Ti atoms and it obviously lead to the dislocations on [$\bar{1}$10] direction. The interfacial HRTEM image of SnTe (001)/SrTiO₃ (111) shown in Fig. 2(a) provides a solid evidence for the existence of the dislocations on the interface. For clearly understanding the produce of the dislocations, the interfacial model was accordingly constructed in Fig. 2(d) and the dislocations are indicated by the red arrows.

There is no related report on the SnTe (111) films directly epitaxial growth on the SrTiO₃ (111). The reason is due to the improper atomic match correlation between the (111) planes of SnTe and SrTiO₃. Referring above atomic arrangement model, the lattice geometry of (111) of SnTe is an equilateral triangle with side length 8.95 Å, in which the Te atom is located on the vertex and the Sn atom is located on the center position of the SnTe (111) triangle lattice (Fig. 2(b)). For realizing an epitaxial match, the triangle geometry of SnTe (111) should have integer or integer multiple relations with the SrTiO₃ (111). On the Ti-O plane of SrTiO₃ (111), two types of triangle lattice geometry are presented that are equilateral triangle with side length 5.52 Å and isosceles triangle with long side length 9.5 Å and short side length 5.52 Å (Fig. 2(c)). When comparing the triangle lattices of SnTe and SrTiO₃, there is no proper match for the atomic arrangement of these triangle geometries, although the long side length 9.5 Å is almost two times of the distance 4.48 Å between two Te atoms in triangle lattice of the SnTe (111). Therefore, the severe mismatch between SnTe (111) and SrTiO₃ (111) finally leads to SnTe film cannot be epitaxially grown on the (111) plane of SrTiO₃ substrate.

The temperature dependence of sheet resistance (R_□) of SnTe (001) films with different thickness was shown in Fig. 3(a). All the films display metallic conductance and their conductive behaviors are similar to the SnTe (111) films grown on Bi₂Se₃ and BaF₂ (111) [14]. Generally, the transport of the topological film is simultaneously contributed by its bulk carriers and TSSs. The metallic transport in SnTe (001) film was considered to arise from the charged Sn vacancies in bulk which dominate the general electronic transport properties [20]. Taken SnTe (001) film with thickness 25 nm as a representative, the sheet resistance was fitted as perfect linear correlation from 300K to 100K, but a nonlinear decrease from 100 K to 4 K was observed (Fig. 3(b)). It suggests that the resistance mechanism above 100 K is dominated by the electron-phonon interaction (linear), but the slowly decreased resistance at low temperature range tending to a constant means the gradually enhanced contribution from the electron-electron interactions [21]. When the temperature tends to 4 K, the enhanced electron-electron interaction may induce more obvious surface conductive state contribution at low temperature quantum limitation [11], [14]. For investigating the film thickness influence on the general transport and TSSs, the film thickness was decreased to 15 nm. The resistance magnitude of 15 nm SnTe (001) film quickly increases 5 times over entire temperature range than 25 nm SnTe film. In suggests that the bulk carrier (Sn vacancy) contribution to general transport is decreased when decreasing the film thickness. The TSSs has more possibility to be shown in the SnTe (001) film. With the thickness increase from 25 nm to 60 nm, the resistance magnitude almost keeps unchanged and it indicates the completely bulk transport domination in the SnTe film and the TSSs will be suppressed.

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Fig. 3.   (a) Temperature dependence of the sheet resistance of SnTe (001) films with different thickness and (b) R_□ vs. T of the SnTe (001) films (25 nm thick) with fitting line above 100 K in which the inset shows the Hall curve of SnTe (001) film with 15 nm; (c) ΔG-B curves at the range of 4-40 K and (d) transfer channel of α and phase coherence length of SnTe (001) film with 15 nm.

To clearly characterize the TSSs of the SnTe (001) film, the magnetic field dependence of the conductance difference (ΔG = G(B) - G(0)) ΔG-B curves of the film with 15 nm were measured in low temperature range from 4 K to 40 K. The typical cusp-like curves with rapid conductance decrease when applying a small magnetic field are shown in Fig. 3(c). The cusp-like magneto-conductivity (MC) is attributed to the weak anti-localization (WAL) effect of the carrier transport related to the topological surface sates (TSSs) [22]. The WAL effect is recognized as one of the features of the quantum transport in the diffusive transport regime, arising from destructive interference. During transport of the TSSs, a shift in the Berry phase arises from the spin-momentum locking effect for an electron (or a hole) traveling along a self-intersecting path, which causes a destructive interference of the wave-function, leading to an enhancement of the conductivity [23]. When applying a magnetic field perpendicular to the closed path, it tends to break the destructive interference, giving rise to negative MC to indicate a key signature of WAL [24]. With temperature increasing to 10 K, the absolute values of ΔG progressively decrease and the cusp curve disappears, suggesting the temperature sensitive feature of the WAL in SnTe (001) film. The surface states are quickly suppressed by increased temperature and the enhanced phonon effect is responsible for the gradual disappearance of cusp in ΔG-B curves.

For TCI SnTe (001), its TSS has four Dirac cones along Γ-X line of the first Brillouin zone and the surface transport channel always was determined by the number of Dirac cones on the (001) surface of SnTe film. When combined with top and bottom surface states of SnTe film, the total surface channels should be eight that means the fitting value α should be four when using the classic Hikami-Larkin-Nagaoka (HLN) function (Eq. (1)) to fit the ΔG-B curve (one surface channels should be fitted as 0.5). In Eq. (1), e is the charge of an electron, ћ is Planck’s constant, l_ф is the phase coherent length, Ψ(x) is the digamma function, and α represents a coefficient related to the number of coherent transport channels. In temperature dependence of α curve (α~T) of Fig. 3(d), the fitting value α tends to be α=3 in the range of 4-8 K which is near to the theoretical value α = 4 representing the eight surface transport channels originated from the eight Dirac cones on the top and bottom surface of the SnTe (001) film. The little difference between fitted value and theoretical value is possibly attribute to the interaction among these channels [25]. When the temperature is increased to 10 K, the ΔG-B curves changes from cusp to parabolic indicating the disappearance of the WAL effect, then the enhanced phonon scattering gradually destroy the surface state quantum transport. For another parameter l_ф, it represents the phase coherence length of the Dirac electrons originating from the surface sate. The decreased tendency of the l_ф with the decreased temperature shows a consistence with the diffusive transport theory (Fig. 3(d)) [11], [26], [27]. For analyzing the contribution of TSSs and bulk to general transport of SnTe (001) films at low temperature, the Hall resistance was measured at 4 K and shown in the inset of Fig. 4(b). The positive slope indicates the p-type conductance. It means that the bulk holes as the main carriers is responsible for the general transport of the SnTe (001) films at low temperature. The large carriers density (4.6 × 10²¹ cm^-3) and small mobility (17.38 (cm²/(V s))) derived from Hall curve indicate the holes mainly contribute to the general transport to the SnTe (001) film, although the typical WAL is observed in ΔG-B curve at 4 K.

$\Delta G=G(B)-G(0)=-\alpha\frac{e^{2}}{2 \pi^{2}\hbar}[in(\frac{\hbar}{4Bel^{2}_{\Phi}})-\Psi(\frac{1}{2}+\frac{\hbar}{4Bel^{2}_{\Phi}})]$ (1)

For further decreasing the influence of bulk carriers on general transport and inducing stronger surface state in SnTe (001) film, the n-type Pb-doping was introduced to inhibit the formation of Sn vacancy and decrease the number of holes. The transport study of Sn_0.7Pb_0.3Te (001) film was carried out to check whether more TSSs contribution to general electronic transport is obvious. In Fig. 4(a), the R_□-T curve of Sn_0.7Pb_0.3Te (001) film with 30 nm thickness indicates a semi-conductive behavior in which the sheet resistance increases with decreasing temperature and a platform appears when the temperature decrease to 30 K. It indicates that Pb-doping in SnTe may open a gap at the Dirac point on (001) to induce a transition from metallic conductive SnTe to semi-conductive Sn_0.7Pb_0.3Te. The appearance of the resistance platform below 30 K indicates the gradually increased contribution from the electron-electron interaction coming from the TSSs of Pb-doping Sn_0.7Pb_0.3Te(001) film. Furthermore, the carrier density and mobility was obtained from the Hall curve of Sn_0.7Pb_0.3Te (001) film, as shown in the inset of Fig. 4(a). The positive slope shows that the p-type carriers still maintain the major contribution to the general transport, but the carrier density is really decreased to 9.3 × 10¹⁹ cm^-3 which is decreased two orders comparing to the SnTe (001) film. The mobility of the film is also quickly increased to 361.64 cm²/(V s) with almost two orders increase when comparing the SnTe (001) film. It indicates that Pb-doping really decreases the holes number in bulk and leads the enhancement of the surface state in present Sn_0.7Pb_0.3Te (001) film. The typical WAL effect in Sn_0.7 Pb_0.3Te (001) film from 4 K to 15 K are observed in Fig. 4(b) and the critical temperature for WAL effect disappearing is raised to 15 K when comparing with un-doped SnTe film. These facts suggest that the Pb-doping really suppresses the formation of p-type vacancy and strengthens the topological non-trivial state in the present film. With HLN functions, the parameters, including the transfer channel α and phase coherent length l_ф, were also fitted from the ΔG-B curves of Sn_0.7Pb_0.3Te film. From 4 K to 15 K, the α value is kept as reasonable value and the existing temperature for the reasonable α value is maintained to be little higher than the SnTe film, which suggests that the strengthened TSSs can weaken the phonon effect when temperature increasing. At the same time, the phase coherent length l_ф of present Sn_0.7Pb_0.3Te film was found to be quickly enhanced than SnTe film (inset of Fig. 4(c)). It indicates that the Pb-doping not only decreases the influence of bulk carrier density on the surface transport of the film, but also enhances the l_ф to induce the increase of the surface mobility of the TCI film.

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Fig. 4.   (a) Temperature dependence of sheet resistance of Sn_0.7Pb_0.3Te(001) film; (b) ΔG-B curves at range of 4-30 K of Sn_0.7Pb_0.3Te(001) film; (c) transfer channel of α and coherent length of Sn_0.7Pb_0.3Te(001).

4. Conclusion

The SnTe (001) film was prepared on the single crystalline substrate SrTiO₃ (111) by MBE system. The epitaxial growth of SnTe (001) film on SrTiO₃ (111) was confirmed by the XRD pattern HRTEM analysis. The corresponding structural model was proposed according to their atomic match correlation. The severely atomic mismatch between the SnTe (111) and SrTiO₃ (111) explains the non-epitaxial growth of SnTe (111). The WAL correlated the TSSs was observed in the SnTe (001) films, but the metallic transport indicates the bulk holes mainly contribute to the general transport of the film. Through Pb-doping to reduce the bulk holes in SnTe film, the general transport is induced to semi-conductive behavior in Sn_0.7Pb_0.3Te (001) film and the TSSs is enhanced. With the strengthen TSSs in Sn_0.7Pb_0.3Te (001) film, the WAL existing temperature and phase coherent length are simultaneously enhanced, which indicates that Pb-doping is the effective strategy for suppressing the bulk transport and promote the TSSs in TCI SnTe system.

Acknowledgment

This work was supported financially by the National Natural Science Foundation of China (Nos. 51571195 and 51590883) and the National Key R&D Program of China (No. 2017YFA0206301).

Appendix A. Supplementary data

Supplementary material related to this article can be found, in the online version, at doi: https://doi.org/10.1016/j.jmst.2019.10.033.

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