Structural characterisation of high-mobility Cd3As2 films crystallised on SrTiO3

Cd3As2 has long been known as a high-mobility semiconductor. The recent finding of a topological semimetal state in this compound has demanded growth of epitaxial films with high crystallinity and controlled thickness. Here we report the structural characterisation of Cd3As2 films grown on SrTiO3 substrates by solid-phase epitaxy at high temperatures up to 600 °C by employing optimised capping layers and substrates. The As triangular lattice is epitaxially stacked on the Ti square lattice of the (001) SrTiO3 substrate, producing (112)-oriented Cd3As2 films exhibiting high crystallinity with a rocking-curve width of 0.02° and a high electron mobility exceeding 30,000 cm2/Vs. The systematic characterisation of films annealed at various temperatures allowed us to identify two-step crystallisation processes in which out-of-plane and subsequently in-plane directions occur with increasing annealing temperature. Our findings on the high-temperature crystallisation process of Cd3As2 enable a unique approach for fabricating high-quality Cd3As2 films and elucidating quantum transport by back gating through the SrTiO3 substrate.


Results
High-quality Cd 3 As 2 epitaxial films are fabricated on (001) SrTiO 3 substrates by high temperature annealing. The SrTiO 3 substrates are etched with a buffered hydrofluoric acid by a supplier (SHINKOSHA Co. Ltd). As shown in the x-ray diffraction (XRD) pattern later, the Cd 3 As 2 film is amorphous just after the deposition at room temperature, necessitating an annealing process for crystallisation. Si 3 N 4 and TiO 2 were deposited in-situ on the Cd 3 As 2 film as capping layers, which prevent re-evapouration of the Cd 3 As 2 film during the high-temperature annealing. This combination of the capping layers is chosen due to the chemical inertness of TiO 2 against Cd 3 As 2 even if there is direct contact between two and the mechanical toughness of Si 3 N 4 covering the whole film. The optimised capping layers enable annealing at temperatures as high as 600 °C, where the vapour pressure of Cd 3 As 2 becomes increasingly high (~10 Torr at 600 °C 27 ). Detailed growth conditions are described in Methods section.
To better understand the epitaxial relation between Cd 3 As 2 and SrTiO 3 , their lattice structures are presented in Fig. 1 accompanied with ordered displacements of Cd atoms 28 . In this 2 × 2 × 4 Cd 3 As 2 , a triangular lattice is formed on the (112) lattice plane, which corresponds to the (111) lattice plane of the high-temperature cubic antifluorite structure. The crystal structure of SrTiO 3 is perovskite type with a square lattice on the (001) plane. The green hexagons in Fig. 1(a) depict the in-plane epitaxial relation between the (112) Cd 3 As 2 plane and the (001) SrTiO 3 plane, realizing epitaxial growth of the Cd 3 As 2 film. The length of the perpendicular line in the As triangular lattice is 3.88 Å (white arrow in the left panel), which is very close to the lattice constant of 3.91 Å in the (001) SrTiO 3 plane (white arrow in the right panel). Consequently, there are two distinct stacking patterns of the (112) Cd 3 As 2 plane on the (001) SrTiO 3 plane, where the [111] in-plane Cd 3 As 2 axis is along either the [100] or [010] direction in SrTiO 3 , as shown in the right panel of Fig. 1(a). Figure 1(c) and (d) show cross-section high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image along with a depth profile of each element obtained by energy dispersive x-ray spectroscopy (EDX) for the Cd 3 As 2 film annealed at the highest temperature of 600 °C, and a schematic sketch is shown in Fig. 1(e) indicating a possible atomic structure. Incidentally, Sr EDX counts in the depth profile are suppressed in the interfacial layers as compared to the Ti and O counts, indicating that a few TiO 2 layers are formed at the heterointerface. Such surface termination with a few TiO 2 layers is known to usually occur when SrTiO 3 substrates are annealed at such high temperature 29,30 . XRD θ-2θ scans and rocking curves of the film peaks are summarised in Fig. 2 for the Cd 3 As 2 films annealed at various temperatures. The diffraction pattern of the as-grown film shows no film peaks, indicating that the film is amorphous. For the film annealed at 500 °C, weak film peaks assigned to the (224) and (336) plane reflections are observed in the θ-2θ scan, while a full width at half maximum (FWHM) of the rocking curve for the (224) peak is very broad (9.9°). The θ-2θ scan for the film annealed at 550 °C shows much stronger peaks originating from the {112} lattice planes, and the FWHM of the rocking curve also became much sharper (0.027°). On the other hand, impurity peaks ascribed to As and CdAs 2 phases are detected when annealing at this temperature. By increasing the annealing temperature up to 600 °C, a (112)-oriented single-phase Cd 3 As 2 film is obtained, as shown in Fig. 2(f). The FWHM of the rocking curve is very sharp (0.023°), which is nearly one-fourth of values reported for single-crystalline bulk samples 7 . In both Fig. 2(e) and (f), a rather broad background with weak intensity can be seen (note the logarithmic scale). In case of thinner Cd 3 As 2 films (≤20 nm), this background is not discernible. Presumably, some disorder is present for thicker films away from the Cd 3 As 2 /SrTiO 3 interface.
In-plane reciprocal space mappings and φ-scans for the (440) Cd 3 As 2 peak are presented in Fig. 2(i-n). For the Cd 3 As 2 films annealed at 500 °C and 550 °C, Debye-Scherrer ring patterns are observed in the reciprocal space mappings and no sharp peaks are confirmed in the φ-scans. These results indicate that the Cd 3 As 2 films annealed below 550 °C are not oriented along the in-plane directions, while they are crystallised with the [112] out-of-plane orientation as confirmed in Fig. 2(b) and (d). In contrast, the reciprocal space mapping for the film annealed at 600 °C shows a clear peak from the (440) reflection plane, which exhibits a six-fold symmetry in the φ-scan. In addition, other six peaks with much weaker intensity are observed between the main peaks in the φ-scan. The existence of these two sets of peaks with contrasting intensities indicates that there are two types of stacking patterns originating from the epitaxial relation as shown in Fig. 1(a). One of them becomes dominant through the high-temperature annealing, which is possibly due to a miscut direction of the SrTiO 3 substrates.
To investigate the in-plane orientation in more detail, a planer TEM image is taken for the film annealed at the highest temperature of 600 °C. Figure 3(a) shows the existence of domains as large as >10 μm 2 . A higher-resolution magnified image of a tri-sectional domain boundary is presented in Fig. 3(b). As shown in the insets, the obtained electron diffraction patterns agree well with the one simulated for the incident beam direction along Cd 3 As 2 [112]. All these three diffraction patterns correspond to the major stacking pattern of the (112) Cd 3 As 2 plane depicted as a dark green hexagon in Fig. 1(a), being consistent with the major peaks appearing in in-plane φ-scan for the Cd 3 As 2 (440) plane shown in Fig. 2(n). Although these three domains are in the square epitaxial relation, the in-plane orientation exhibits a small variance of several degrees in the tilting angle. This variance of the in-plane orientation also explains the broad peaks observed in the φ-scan, indicating that the small in-plane misorientation is the origin of the domain formation.

Discussion
Annealing temperature dependences of the film crystallinity and transport properties are summarised in Fig. 4. As detailed in Fig. 2, the FWHM of the rocking curve for the out-of-plane (224) peak sharply drops from 500 °C to 550 °C (red in Fig. 4(a)), whereas annealing at a temperature as high as 600 °C is needed to promote the in-plane orientation alignment (green in Fig. 4(a)). The considerable increase in conductivity occurs between 550 °C and 600 °C, suggesting that the in-plane alignment plays an important role.
The carrier density (n, orange) and electron mobility (μ, blue) of the Cd 3 As 2 films for each annealing temperature are deduced from the Hall measurement, as plotted in Fig. 4(b). The carrier density agrees well with one deduced from the SdH oscillations. Before annealing, n is 7 × 10 18 cm −3 and it is significantly reduced to 9 × 10 17 cm −3 by annealing at temperatures up to 600 °C. This reduction in n may be explained as follows. As shown in the XRD pattern for the film annealed at 550 °C (Fig. 2(d)), arsenic-rich impurity phases (As and CdAs 2 ) are  Fig. 1(a).
confirmed, presumably resulting in arsenic deficiency in the Cd 3 As 2 phase. Since Cd 3 As 2 is known to be naturally n-type due to As deficiency, n of the Cd 3 As 2 films heated at 600 °C is reduced by the annealing-induced chemical reaction towards a more stoichiometric phase. The mobility μ reaches 3.4 × 10 4 cm 2 /Vs after annealing at 600 °C, while it is 1.5 × 10 3 cm 2 /Vs before annealing. The increase in the mobility up to the annealing temperature of  550 °C is mainly attributed to the reduction of the carrier density as seen above. The further increase of the mobility from 550 °C to 600 °C is due to the reduction of grain boundaries from in-plane random to epitaxially locked orientations. Figure 4(c) shows longitudinal magnetoresistances of these samples measured with applying the magnetic field perpendicular to the film plane. They are normalised to the zero-field results. With increasing annealing temperature, Shubnikov-de Haas oscillations and quadratic positive magnetoresistance become more pronounced, demonstrating that quantum transport is achievable in films of high-crystallinity and high-mobility.
In summary, we have performed a detailed structural characterisation of high-crystallinity Cd 3 As 2 films fabricated by high-temperature solid-phase epitaxy. From the systematic characterisation of the films annealed at various high temperatures, successive crystallisation processes take place about the out-of-plane and in-plane orientations. The electron mobility is strikingly enhanced by the epitaxial crystallisation on the square-lattice and the effective reduction of arsenic deficiency. The mobility is expected to be further enhanced by reducing the number of domain boundaries and point defects. Our systematic characterisation of high-quality Cd 3 As 2 films grown on dielectric oxides provides the foundation to prepare higher-quality Cd 3 As 2 films by reducing the in-plane domains and carrier densities as well as to investigate quantum transport phenomena by back gating and chemical substitution.

Methods
Prior to this study, we have screened various materials and tested them for the usefulness as capping layer and substrate. The best results are achieved when using an optimised combination of TiO 2 /Si 3 N 4 and (001) SrTiO 3 , respectively 26 . For preparing a Cd 3 As 2 target, 6N5 Cd and 7N5 As shots were mixed at the stoichiometric ratio and heated at 950 °C for 48 hours in a vacuum-sealed silica tube. After heating the mixture, it was grinded and pelletised and then it was sintered at 250 °C for 30 hours in a vacuum-sealed tube. The Cd 3 As 2 target was ablated using KrF excimer laser at room temperature and a base pressure of about 2 × 10 −7 Torr. The laser fluence and frequency were set to 0.6 J/cm 2 and 10 Hz, respectively. Subsequently, 30 nm TiO 2 and 100 nm Si 3 N 4 capping layers were deposited by ablating their targets with a laser fluence of 4.0 J/cm 2 and a frequency of 20 Hz. After all the layers were deposited, the sample was cut into pieces and each pieces was annealed in air at a temperature of 500 °C, 550 °C, and 600 °C for 5 minutes in a rapid thermal annealing system. Annealing at higher temperatures resulted in cracking of the capping layers due to the high vapour pressure of Cd 3 As 2 . Thicknesses of the respective layers were confirmed from Laue oscillations in the XRD θ-2θ scan.