Thermodynamic constraints and substrate influences on the growth of high-quality Bi₂Te₃ thin films by pulsed laser deposition

The celebrity status of tetradymites ¹⁾ stems from their hitherto unparalleled thermoelectric power. ^2,3) Yet, the discovery of topological states in these layered materials ^4,5) brought renowned attention, particularly in condensed matter physics. These topological states offer an entirely new degree of controllability to potential application devices using Majorana fermion, ⁶⁾ quantum anomalous Hall effect, ⁷⁾ and current-spin conversion. ⁸⁾ To access these exotic phenomena, heterostructures based on topological insulators with atomically flat and abrupt heterointerface are necessary.

Bi₂Te₃ is known as a typical topological insulator. It is a layered structured material, where Bi and Te layers are stacked upon each other. While there have been reports on the synthesis of Bi₂Te₃ thin films by molecular beam epitaxy (MBE), ^9–13) the potentials of pulsed laser deposition (PLD) technique, which enables the rapid synthesis of thin films under non-equilibrium conditions, ^14–16) have not yet been fully investigated. The main culprit for the subpar quality of epitaxially grown Bi₂Te₃ film roots in the extraordinary high vapor pressure of tellurium, ^17–19) which requires that Te loss in the deposited films has to be compensated. Furthermore, an appropriate choice in substrate material and orientation presents an additional hurdle because the lattice mismatch between the substrates and Bi₂Te₃ may cause in-plane multiple domain orientations. For exploring exotic topological physics occurring in heterostructures based on Bi₂Te₃, the first challenges are to improve the local crystal quality of Bi₂Te₃ films and control their domain orientations.

Here we approach this problem by utilizing highly off-stoichiometric targets for the synthesis of Bi₂Te₃ thin films. Throughout the experiments here, we used a target stoichiometry of Bi:Te = 1:10, which corresponds to more than 6 times the Te required content. For substrate materials, we used CaF₂ and BaF₂ while using Ar atmosphere in the pressure range of ∼10⁻³ to 10 Torr. Generally, the higher background pressure results in a lower re-evaporation rate of tellurium. ^20,21) If the background gas pressure, however, is too high the deposition process cannot take place. Certainly, other geometric aspects such as the target-substrate distance (60–70 mm) contributes to these limitations.

Under tellurium-rich conditions we were able to increase the synthesis temperature of Bi₂Te₃ thin films close to the liquefaction point of tellurium (449.5 °C ²²⁾). The key to the effective use of such high growth temperatures is to change the substrate temperature from the initial stage of crystal growth on the substrate to the subsequent steady growth. We increased the substrate temperature monotonically from an initial temperature (T₁) up to an endpoint temperature (T₂); rather than the ordinary two-step growth, which cannot prevent Te sublimation during heating of the substrate temperature. Such high synthesis temperatures promote the formation of large area domains of Bi₂Te₃ thin films—an important prerequisite to accessing the unique electronic properties of topological insulators.

The as-received substrates were cut into 5 × 2.5 mm² pieces and annealed at 500 °C for 10 min under ultra-high vacuum (UHV). The Bi₂Te₃ films were grown onto (111) CaF₂ and (111) BaF₂ substrates using a KrF excimer laser (COHERENT COMPEX205) with a wavelength of 248 nm. A rectangular area of the beam was focused onto a 3.4 × 1.0 mm² spot on the target. The substrate temperature was controlled using a laser (808 nm) heating system and pyrometer (Japan Sensor FTK9 1.95–2.5 μm) assuming black body radiation with an emissivity coefficient of 0.2 of the SiC holder. ^23,24) The substrates were bound by silver paste to the SiC holder. The targets were pressed using Bi:Te = 1:10 stoichiometric powder mixture at 40 MPa. The synthesis parameters are listed in Table I. Simultaneously with the start of the Bi₂Te₃ thin films synthesis, we linearly ramped the substrate temperature from T₁ up to T₂ with a ramping rate adjusted for 7200 pulses at 20 Hz (1.0 J cm⁻²). The resulting Bi₂Te₃ thin film thickness was 150 nm. We systematically varied T₁, T₂, Ar pressure, laser-repetition rate, and laser fluence.

The stacking sequence of Bi and Te in Bi₂Te₃ directly influences the c-axis lattice parameter of Bi₂Te_3−δ . ¹¹⁾ We determined the c-axis lengths of the Bi₂Te_3−δ thin films with a precision of ±5 pm, using the Nelson–Riley function. ²⁵⁾ Complementary crystal structure analysis was performed using a high-resolution transmission electron microscope (HRTEM) (JEOL 200F). The morphology of the substrates and Bi₂Te_3−δ films were characterized using a Bruker Dimension FastScan atomic force microscopy (AFM) with FastScan-A silicon probes.

In Figs. 1(a), 1(b), we show XRD scans of Bi₂Te₃ film grown on the (111) CaF₂ and (111) BaF₂ substrates, respectively. The (003), (006), and (0015) diffraction peaks are clearly visible, whereas the (009) and (0012) diffraction peaks are absent due to weak scattering amplitude. Note, the X-ray source used here contains Cu${K}_{{\alpha }_{\mathrm{1,2}}}$ and K_β radiation.

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We mapped the XRD intensities of (0015) peaks as a function of T₁ and T₂ while keeping other growth parameters constant. If T₁ = T₂ [dashed line in Fig. 1(c), 1(d)], Bi₂Te₃ thin films do form and their crystalline qualities stay below their prospects. Instead, if T₁ is lower than T₂, the coherent volume associated with the (0015) peak intensity can be significantly enhanced. If T₁ < T₂, high-quality Bi₂Te₃ thin films can be grown, particularly within the vicinity of T₁ ∼ 320 °C and T₂ ∼ 440 °C on the CaF₂ substrates [Fig. 1(c)]. However, if T₁ is larger than T₂, the film quality rapidly deteriorates. All subsequent experiments were conducted at T₁ smaller than T₂. Yet, the optimum synthesis (in the dashed triangle, Fig. 1) temperatures were markedly different for Bi₂Te₃ thin films when grown on the (111) BaF₂ substrates. In fact, T₁ for the optimal growth conditions may differ more than 100 °C between the two substrate materials. The endpoint temperature, however, is independent of the substrate material. We assign the difference in initial temperature T₁ to the distinctively different lattice mismatch.

We consistently recorded c-axis lengths from the Bi₂Te₃ 10 (00l) diffraction peaks that are even longer than those determined from bulk samples (30.44 Å ²⁶⁾). Several reasons might be considered to be accountable for the observed differences. Let us briefly consider Bi₂Te₃ as an ionic compound with Bi⁺³ and Te⁻². The associated ionic radii ²⁷⁾ are 1.17 Å and 2.21 Å, respectively. Apparently, anti-site defects can be considered to be the primary reason for the observed c-axis length expansion.

In Fig. 2, we show high-resolution scanning transmission electron microscopy (HRSTEM) cross-sectional images of Bi₂Te₃ on the CaF₂ (a) and BaF₂ (b) substrates. As Bi₂Te₃ is built from three individual quintuple layers (QLs) of Te–Bi–Te–Bi–Te, for both substrate materials these QLs were clearly observed. Here, the substrate material has a highly ionic bond character and additional Te layers are not observed. Therefore, the Bi₂Te₃ phase directly forms on the CaF₂ or BaF₂.

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While such HRSTEM images are of great value to determine the local quality of the Bi₂Te₃ thin films, it provides little information about the long-range order. Instead, high-resolution XRD (HRXRD) techniques provide a deeper insight. In Fig. 3, we show the HRXRD data for (001)Bi₂Te₃/(111)CaF₂ and (001)Bi₂Te₃/(111)BaF₂. In addition to the diffraction peaks of the substrates, the (003m) diffraction peaks of Bi₂Te₃ with m = 1...12 are clearly visible. The c-axis value for Bi₂Te₃/CaF₂ (Bi₂Te₃/BaF₂) is 30.613 (30.584) Å which is slightly longer than the bulk value (30.44 Å ²⁶⁾). Note that additional diffraction peaks, e.g. (015) and (012) Bi₂Te₃ are visible. Moreover, as the surface tends to oxidize rapidly, polycrystalline diffraction peaks of TeO₂ and Bi₂O₃ were observed (see SI, available online at stacks.iop.org/APEX/15/065502/mmedia). It is worth noting that energy-dispersive X-ray scattering experiments (see SI) revealed no accumulation of either Bi or Te along grain boundaries.

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An established method of revealing the epitaxial relation between film and substrate are using high-resolution reciprocal space maps (HRRSMs). In Figs. 3(c) and 3(d), HRRSMs are shown for Bi₂Te₃/(111)CaF₂ and Bi₂Te₃/(111)BaF₂ in the vicinity of the $(1\bar{1}20)$ diffraction peaks. The $(1\bar{1}20)$ peak of Bi₂Te₃ and (331) peak of the substrate are not vertically aligned (${Q}_{x}^{\mathrm{film}}\ne {Q}_{x}^{\mathrm{substrate}}$) which means the films are fully relaxed. In Table II, the diffraction peak positions and FWHM of ($1\bar{1}20$) determined from the HRRSMs are listed. From the Q_x values in Figs. 3(c) and 3(d), we determined the in-plane lattice constants a as 4.395 Å and 4.368 Å for Bi₂Te₃ on the CaF₂ and BaF₂ substrates, respectively. The deviation from the bulk value (4.395 Å ²⁶⁾) is negligible. The coherent volumes, which can be roughly estimated domain sizes, of the thin films on Bi₂Te₃/BaF₂ were estimated as 15 × 15 × 20 nm³ using the Debye–Scherrer formula. In contrast, that of the Bi₂Te₃ on the CaF₂ substrates was significantly larger (80 × 80 × 90 nm³). Remarkably, the lattice mismatch of Bi₂Te₃ on the CaF₂ substrates was 14% whereas it was 0.1% on the BaF₂ substrates.

Bi₂Te₃ growth is highly susceptible towards the formation of multi-domain orientations. ³⁰⁾ An established method to determine a possible domain arrangement of Bi₂Te₃ thin films on (111) halide substrates are pole figure measurements. We plot the $(1\bar{1}20)$ and $(1\bar{1}16)$ Bi₂Te₃ diffraction peaks of Bi₂Te₃ on the CaF₂ [Fig. 4 (a)] and BaF₂ [Fig. 4 (b)] substrates, respectively. If Bi₂Te₃ were grown as a single domain form, symmetry considerations predict that the $(1\bar{1}20)$ and $(1\bar{1}16)$ diffraction peaks would appear three times for a 360° scan. For Bi₂Te₃ thin films grown on the (111) CaF₂ substrates, however, this is not the case. Instead, the $(1\bar{1}20)$ diffraction peak appears six times [Fig. 4(a)].

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Each peak position is separated precisely by 60° and the absolute intensities of these $(1\bar{1}20)$ diffraction peaks systematically recover every 120°. We conclude that there are two domains which are rotated by 60° to each other. Second, there is a dominant domain as judged by the XRD intensities. Remarkably, for Bi₂Te₃ films grown on the (111) BaF₂ substrates, the $(1\bar{1}16)$ diffraction peaks repetition was as expected (three times). Moreover, the absolute intensities of these three diffraction peaks did not vary. Consequently, for Bi₂Te₃ films grown on the (111) BaF₂ substrates, single-domain orientation was possible. We note that the single-domain orientation of Bi₂Te₃ on the BaF₂ substrates grown by MBE has been reported. ³¹⁾ Using the information from the HRRSM (Fig. 3) and the pole-figure (Fig. 4), the epitaxial relation can be written as follows:

$$\begin{eqnarray}\begin{array}{rcl}(001){\mathrm{Bi}}_{2}{\mathrm{Te}}_{3} & \parallel & (111){\mathrm{BaF}}_{2}\\ (1\bar{1}0){\mathrm{Bi}}_{2}{\mathrm{Te}}_{3} & \parallel & (11\bar{2}){\mathrm{BaF}}_{2}.\end{array}\end{eqnarray} \tag{ 1 }$$

Figure 4(e) illustrates the epitaxial relation [Eq. (1)] for domain A. In addition, the formation of a twin domain with a 60° rotation is also depicted in Fig. 4(e) where a domain boundary is shown along the [110] direction.

In real space [Fig. 4(e)], a 60° domain rotation gives rise to a non-commutative sequence of the stacking order in Bi₂Te₃. This is also commonly observed for Bi₂Te₃ films grown on covalent substrates, i.e. (111) Si or (111) Ge, ³¹⁾ where an additional layer of Te is sandwiched between substrate and Bi₂Te₃ film. The coherent crystalline volume picked up by XRD [Figs. 3(c), 3(d) and Figs. 4(a), 4(b)] can be directly observed using AFM [Fig. 4(c), 4(d)]. A rough estimation of the lateral dimensions of Bi₂Te₃ domains provides 1.5 × 1.5 μm² for the (111) CaF₂ substrates, whereas 0.5 × 0.5 μm² for the (111) BaF₂ substrates. For a lattice-mismatched substrate material, e.g. (001) Al₂O₃ ³²⁾ or (111) Si, ³³⁾ it was reported that embedding a sandwich layer of Bi or Te significantly minimizes the twinning tendencies of Bi₂Te₃ film. Our results for the lattice-matched substrate [(111) BaF₂] indicate that, even with direct synthesis on the substrate, twin formation can be significantly suppressed. To use these films for the study of topological phenomena, we need to increase the Bi₂Te₃ domain size because carrier scattering at domain boundaries may affect the transport properties.

In conclusion, we found that over-stoichiometric Bi₂Te₃ target, high-Ar pressure, and optimized growth temperature sequence are prerequisites to synthesize stoichiometric Bi₂Te₃ thin films by PLD. Furthermore, lattice matching between Bi₂Te₃ film and substrate is vital for the formation of single oriented Bi₂Te₃ films. Using a monotonically increasing substrate temperature during the deposition process at high Ar pressures, thin films with nearly stoichiometric Bi₂Te₃ composition and single-oriented domains were grown on the (111) BaF₂ substrates from excessively (1:10) Te rich targets. Our HRSTEM data did not reveal the existence of an interface Te layer between Bi₂Te₃ films and substrate. The lattice matched (111) BaF₂ substrate is preferred to grow Bi₂Te₃ for the further development of topological electronics.

Acknowledgments