Introduction

Since the topological Dirac semimetal state in Cd3As2 has been theoretically predicted and experimentally verified1,2,3, a variety of its syntheses, such as by melt growth1,2,3,4,5, Cd flux growth6,7,8,9, chemical vapour transport10,11,12,13, and chemical vapour deposition14 have been reported so far. On the other hand, Cd3As2 has long been known as a high-mobility semiconductor15, and growth of rather thick films, mainly by thermal evapouration and pulsed-laser evapouration, has been reported since the 1970s16,17,18,19,20,21,22. Following the discovery of the Dirac semimetal state, molecular beam epitaxy (MBE) has been employed to investigate quantum transport phenomena in Cd3As2 thin films23,24,25. However, crystallinity and flatness of these films are still limited, mainly due to the low temperature (~200 °C) growth necessary for avoiding the revapourisation of Cd3As2 itself. To overcome this issue, we have recently developed a high-temperature annealing method which allows to fabricate very thin (12 nm ~ 20 nm) Cd3As2 films which exhibit a clear quantum Hall effect with zero resistance26. Here we report the detailed structural characterisation of rather thick three-dimensional (100 nm) Cd3As2 films annealed at various temperatures and elucidate the evolution of their epitaxial crystallisation and its relation to transport properties.

Results

High-quality Cd3As2 epitaxial films are fabricated on (001) SrTiO3 substrates by high temperature annealing. The SrTiO3 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 Cd3As2 film is amorphous just after the deposition at room temperature, necessitating an annealing process for crystallisation. Si3N4 and TiO2 were deposited in-situ on the Cd3As2 film as capping layers, which prevent re-evapouration of the Cd3As2 film during the high-temperature annealing. This combination of the capping layers is chosen due to the chemical inertness of TiO2 against Cd3As2 even if there is direct contact between two and the mechanical toughness of Si3N4 covering the whole film. The optimised capping layers enable annealing at temperatures as high as 600 °C, where the vapour pressure of Cd3As2 becomes increasingly high (~10 Torr at 600 °C27). Detailed growth conditions are described in Methods section.

To better understand the epitaxial relation between Cd3As2 and SrTiO3, their lattice structures are presented in Fig. 1. Cd3As2 forms a solid phase having a cubic Cd-deficient antifluorite (Cd4As2) structure below 715 °C, and gets successively distorted to form \(\sqrt{2}\times \sqrt{2}\times 2\) and 2 × 2 × 4 superstructures below 600 °C and 475 °C, respectively, accompanied with ordered displacements of Cd atoms28. In this 2 × 2 × 4 Cd3As2, 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 SrTiO3 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) Cd3As2 plane and the (001) SrTiO3 plane, realizing epitaxial growth of the Cd3As2 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) SrTiO3 plane (white arrow in the right panel). Consequently, there are two distinct stacking patterns of the (112) Cd3As2 plane on the (001) SrTiO3 plane, where the [11\(\overline{1}\)] in-plane Cd3As2 axis is along either the [100] or [010] direction in SrTiO3, 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 Cd3As2 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 TiO2 layers are formed at the heterointerface. Such surface termination with a few TiO2 layers is known to usually occur when SrTiO3 substrates are annealed at such high temperature29,30.

Figure 1
figure 1

Epitaxial relation between Cd3As2 and SrTiO3. (a) Top and (b) side views of crystal structures, representing epitaxial [112] Cd3As2/[001] SrTiO3 relation. The green hexagons in (a) represent the As triangular lattice in Cd3As2. There are two possible in-plane alignments on the Ti square lattice (right). (c) HAADF-STEM image showing atomic arrangement at the heterointerface between Cd3As2 film and SrTiO3 substrate. (d) Depth profile of Cd, As, Sr, Ti, and O, obtained by integrating EDX counts along the horizontal direction in (c). Incidentally, Sr EDX counts in the depth profile are certainly suppressed in the interfacial layers as compared to the respective Ti and O results, indicating that a few TiO2 layers are formed by high-temperature annealing29,30. The STEM and EDX measurements were performed with a low acceleration voltage of 80 kV to reduce the damage at the Cd3As2 interface, resulting in the lower resolution image compared to those of the central region26 taken at 200 kV. The damage is inevitable to some extent, causing deviation from the Cd/As stoichiometric composition at the interface. (e) Epitaxial relation of the (112) oriented Cd3As2 film on the (001) SrTiO3 substrate. Projected lattice distances of the triangular-lattice As atoms and the square-lattice Ti atoms are almost the same.

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XRD θ-2θ scans and rocking curves of the film peaks are summarised in Fig. 2 for the Cd3As2 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 CdAs2 phases are detected when annealing at this temperature. By increasing the annealing temperature up to 600 °C, a (112)-oriented single-phase Cd3As2 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 samples7. 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 Cd3As2 films (\(\le \)20 nm), this background is not discernible. Presumably, some disorder is present for thicker films away from the Cd3As2/SrTiO3 interface.

Figure 2
figure 2

XRD characterisation of the Cd3As2 films annealed at high temperatures. XRD θ-2θ scans and corresponding rocking curves of the (224) Cd3As2 film peaks (a) before annealing and (b,c) after annealing at 500 °C, (d,e) 550 °C, and (f,g) 600 °C. (h) Sample structure and changes of the crystalline nature in each layer due to the annealing. (i–k) In-plane reciprocal space mappings and (l)–(n) ϕ-scans along the red curves in the reciprocal space mappings. The ϕ-scan pattern shown in (n) represents two sets of 6-fold peaks. Major and minor in-plane stacking patterns of the As triangular lattice are denoted by dark and light green hexagons as shown in the right panel of Fig. 1(a).

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In-plane reciprocal space mappings and ϕ-scans for the (4\(\overline{4}\)0) Cd3As2 peak are presented in Fig. 2(i–n). For the Cd3As2 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 Cd3As2 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 (4\(\overline{4}\)0) 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 SrTiO3 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 μm2. 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 Cd3As2 [112]. All these three diffraction patterns correspond to the major stacking pattern of the (112) Cd3As2 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 Cd3As2 (4\(\overline{4}\)0) 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.

Figure 3
figure 3

Plane-view TEM characterisation of the Cd3As2 film. (a) Planar TEM picture of the film annealed at the highest temperature of 600 °C. Dotted curves are overlaid on discernible domain boundaries. Crystal axes of the SrTiO3 substrate are shown in the inset for reference. (b) Higher-resolution magnified image focusing on a tri-sectional grain boundary in the boxed area in (a). Electron diffraction patterns taken in the respective domains are shown in the insets. The brightest spot at the center is the zeroth diffraction spot. The diffraction patterns in each grain are slightly tilted as compared to the simulated one (right bottom), where the in-plane crystallographic axes of the Cd3As2 film are assumed to be completely aligned with the respective SrTiO3 axes.

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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.

Figure 4
figure 4

Evolution of crystallinity and transport properties. (a) Annealing temperature dependence of the rocking curve width for the out-of-plane (224) Cd3As2 film peak and the in-plane (4\(\overline{4}\)0) film peak. (b) Same plots for longitudinal conductivity σ xx , carrier density n, and the electron mobility μ at 2 K. (c) Normalised longitudinal magnetoresistance.

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The carrier density (n, orange) and electron mobility (μ, blue) of the Cd3As2 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 × 1018 cm−3 and it is significantly reduced to 9 × 1017 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 CdAs2) are confirmed, presumably resulting in arsenic deficiency in the Cd3As2 phase. Since Cd3As2 is known to be naturally n-type due to As deficiency, n of the Cd3As2 films heated at 600 °C is reduced by the annealing-induced chemical reaction towards a more stoichiometric phase. The mobility μ reaches 3.4 × 104 cm2/Vs after annealing at 600 °C, while it is 1.5 × 103 cm2/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 Cd3As2 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 Cd3As2 films grown on dielectric oxides provides the foundation to prepare higher-quality Cd3As2 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 TiO2/Si3N4 and (001) SrTiO3, respectively26. For preparing a Cd3As2 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 Cd3As2 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/cm2 and 10 Hz, respectively. Subsequently, 30 nm TiO2 and 100 nm Si3N4 capping layers were deposited by ablating their targets with a laser fluence of 4.0 J/cm2 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 Cd3As2. Thicknesses of the respective layers were confirmed from Laue oscillations in the XRD θ-2θ scan.