Investigation of the deposition of α-tantalum (110) films on a-plane sapphire substrate by molecular beam epitaxy for superconducting circuit

Superconducting coplanar waveguide (SCPW) resonators with low microwave loss are critical elements for quantum computation,^1–4 quantum memories,^5,6 and photon detection.⁷ Two-level system (TLS) is the most prominent source of dielectric loss quantized by an intrinsic (unloaded) quality factor (Q_i) in superconducting circuits.^8–10 According to recent research, the unexplained TLS defects are mainly distributed at substrate–air, metal–air, and metal–substrate interfaces.^11–13 Therefore, it is very important to improve the material growth and fabrication process to decrease the volume of these interfaces for high quality devices.

Aluminum, niobium, and tantalum are mostly used in superconducting circuits.¹⁴ Due to its high superconducting transition temperature and relatively low microwave loss, niobium (Nb) has become more commonly used materials for superconducting circuits.¹⁵ However, the complicated stoichiometry of the native Nb oxide layer is considered to be a major source of complex microwave loss at the metal–air interface.^16,17 In contrast, the surface insulating oxide of tantalum (Ta) is expected to be less lossy in superconducting circuits.^18,19 Record coherence times for two-dimensional transmon qubits have been reported by using the capacitor and microwave resonators fabricated from magnetron sputtered Ta films.^20,21 However, these films always contain other structures, such as β-Ta grains and α-Ta (111) grains, which are harmful to high quality superconducting circuit fabrication. Additionally, comparing with the sputtering method, which is known to damage the substrate surface by ions¹¹ and incorporate contaminants, the molecular beam epitaxy (MBE) technology can keep the surface intact, grow high purity film, and give atomically-flat metal–air and metal–substrate interfaces. Additionally, Ta films grown by MBE usually have a more continuous structure than Ta films with a columnar structure deposited by magnetron sputtering. It is expected that Ta films grown by MBE exhibit very large grain surface area and less grain boundaries, which are related to high residual resistance ratio (RRR) and high superconducting transition temperature T_c.¹⁷ 

In this work, to optimize the MBE growth conditions of α-Ta (110) films on the a-plane (11–20) sapphire substrate, the influences of growth rate and growth temperature have been investigated by using atomic force microscopy (AFM), high-resolution x-ray diffraction (HR-XRD), and scanning transmission electron microscope (STEM). The optimized α-Ta (110) film exhibits a single-crystal structure, with a polished surface and an atomically flat metal–substrate interface. The film with thickness of 30 nm shows a T_c of 4.12 K and a high RRR of 9.53. The resonators of quarter-wavelength CPWs produced by using the 150 nm optimized α-Ta (110) film, demonstrate an intrinsic quality factor exceeding one million under single photon excitation at millikelvin temperature.

The Ta films for the resonators were grown on the a-plane sapphire substrate at high temperatures (500 °C–800 °C) by MBE. The Ta material was evaporated through a scanning electron beam heater. The beam energy is 8 keV and the emission current was around 200 mA. The deposition rate was verified using two methods, namely, atomic absorption spectroscopy (AAS) and quartz crystal microbalance (QCM). To ensure a stable deposition rate, the signal from AAS was used as feedback to control the heating power. A high-purity Ta rod with a purity of 99.998% was used as the source material, tailored to fit the crucible shape. Before deposition, the source material was degassed sufficiently before deposition. Prior to growth, two out-gassing bakes were performed for thermal cleaning of the substrate surface at 200 °C for 2h and followed by 850 °C for 0.5h to remove surface contamination. The growth chamber had an actual pressure of 2 × 10⁻⁹ Torr during growth with the Ta electron-beam hearth operational. The surface morphology and structural properties of these Ta films were characterized using several methods including AFM, STEM, and HR-XRD.

Sapphire is a common substrate for superconducting quantum devices. The crystallographic structure and growth orientation of epitaxial Ta films are strongly affected by the substrate. The epitaxy of bcc Ta (110) can be realized on the a-plane sapphire substrate due to the alignment of the threefold axes in the plane of the metal–substrate interface.²³ The different growth rates lead to various morphologies of the 30 nm-thick Ta (110) films grown by MBE, as shown in Figs. 1(a)–1(d). These AFM images demonstrate the smooth surface of Ta (110) films grown with different growth rates at 550 °C for a scanning area of 1 × 1 μm². The measured RMS roughness values of the surface over 1 × 1 μm² scans are about 0.15 nm. With growth rate of 0.15 A/s, the surface exhibits many pits caused by the appearance of small crystal nucleus and surface defects of substrate, which are diminished as the growth rate increases. This suggests that Ta adatoms with reduced mobility tend to stay near the point of impact, which may not be the minimum free energy lattice sites, resulting in the decrease of pits on surface. However, too large growth rates lead to the appearance of pellets on the surface of Ta films, which may be due to excessively low mobility of Ta atoms on the growth surface.

AFM images of Ta films with a growth rate of 0.22 A/s at 600 and 800 °C are shown in Figs. 1(e) and 1(f), respectively. The 30-nm-thick Ta film grown at 800 °C is in the early stage of coalescence, which is formed by small islands. While the surfaces of films grown at 500 and 600 °C are more continuous than that of the Ta film grown at 800 °C. The measured RMS roughness values of these surface grown at 800 and 600 °C over the 1 × 1 μm² scans are 4.66 and 0.28 nm, respectively. These results indicate that the coalescence of Ta films slows down at higher temperatures, which may be finished within several atomic layers during low temperature growth. Higher growth temperatures promote three-dimensional growth instead of lateral growth, resulting in grooved morphologies on the surface, due to the Ehrlich–Schwoebel (ES) barrier which makes unbalance between descending steps and ascending steps of Ta adatoms.²⁴ As mentioned above, the reduced mobility of Ta adatoms by increasing growth rate will suppress ascending step process and promote lateral growth. Therefore, to match a higher growth temperature, a higher growth rate is required.

After mutually optimized the temperature and growth rate, Figs. 2(a) and 2(c) show AFM images of 150 nm-thick Ta films grown with growth rate of 0.3 A/s at 550 °C and 0.5 A/s at 800 °C, respectively. The measured RMS roughness values in Figs. 2(a) and 2(c) are 0.21 and 0.33 nm for a scanning area of 1 × 1 μm². The surface grown at 550 °C is smoother, and the atomic steps can be clearly observed from AFM images. In Figs. 2(b) and 2(d), the HRXRD spectrum of Ta films on sapphire shows clear peaks corresponding to α-Ta (110) and sapphire (11–20). The peak width of Ta (110) grown at 800 °C is narrower than that of Ta (110) grown at 550 °C. In addition, the peak position of α-Ta (110) grown at 800 °C is further away from the peak of sapphire (11–20). These results suggest that the epitaxial strain is more relaxed at high growth temperatures. It is noteworthy that the diffraction peak of Ta films grown at 550 °C has shoulder on the left. It can be inferred that the epitaxial strain in Ta films grown at low temperatures is inhomogeneous, while at high temperatures, strain is relaxed more rapidly by the formation of misfit dislocation and coalescence of islands. Due to the merging of neighboring islands attracted to each other, it is considered that the formation of grain boundary gives rise to tensile stress which leads to the reduction of compressive stress in Ta films.²⁵ 

As mentioned above, the microwave loss is mainly from the amorphous oxide at surfaces and interfaces of superconducting quantum devices.^11–13 The exposed grain boundaries will deepen the oxidization of the superconductors. In other words, the more grain boundaries, the larger microwave loss volume.¹⁷ A high-quality and structurally continuous film portends good device performance. Therefore, interface atomic structure and performance characterization of Ta films grown with optimized growth conditions (0.3 A/s at 550 °C) was conducted. As shown in Figs. 3(a)–3(c), STEM of Ta film cross sections indeed reveals a continuous structure, with no obvious grain boundary described as Josephson weak links.^26,27 The growth direction is oriented along the [110] axis [Fig. 3(a)]. It can be seen that the amorphous tantalum oxide layer is about 2 nm thick on the top of Ta [Fig. 3(b)], with clear interface between Ta and the oxide layer. The interface between Ta and sapphire is atomically flat and the arrangement pattern of Ta atoms in the film continues the arrangement pattern of Al atoms in the substrate [the inset of Fig. 3(c)], showing an epitaxial growth. In the interfacial region, there is no misfit dislocation found from the STEM image in Fig. 3(c). Finally, combining AFM studies of the Ta surface and cross section from STEM image, it indicates that the Ta films grows layer by layer at 550 °C with proper growth rates, avoiding defects caused by the coalescence of 3D islands. In Fig. 3(d), the Ta (101)-diffraction peak series show four peaks and indicate no twist domains in the Ta film. This is consistent with the analysis of the interface atomic structure of Ta (110) film epitaxy on the a-plane sapphire substrate.

The observed superconducting transition temperature T_c of the Ta film (30 nm-thick) is 4.12 K and RRR is 9.53 as shown in Fig. 4(a), further conforming the high quality of the Ta film. Then, the 150 nm-thick Ta film grown with a growth rate of 0.3 A/s at 550 °C was patterned into the SCPW microwave resonator in the form of a quarter-wavelength segment to extract Q_i from the S₂₁ transmission measurement. The structure of the resonator is shown in Fig. S1(a) in the supplementary material. Q_i was extracted by fitting the S₂₁ vs frequency curve. One fitting example is shown in Figs. S1(b) and S1(c) in the supplementary material.The device was designed with center conductor and insulating gap widths of w = 10 μm and g = 6 μm, respectively. Resonance frequencies f ranged from 5 to 7 GHz. Figure 4(b) shows the dependence of Q_i on the microwave drive power, all resonators with different frequency show Q_i value higher than one million under single photon region. Q_i shows an increasing trend with the increase of power. As the input power increase further, obvious nonlinear effects occur, see Fig. S2 in the supplementary material. It is clear that the high Q_i resonator made from Ta films grown by MBE has been realized, due to the atomically flat interface between Ta and sapphire, and the smooth surface of high-quality Ta films with single-crystal structures.

It is worth noting that the etching rate of Ta films grown by MBE is significantly slower than that of Ta films deposited by magnetron sputtering due to the better compactness of the film, under-etching phenomenon occurred during the preparation process of the CPW microwave resonator. The Q_i value of the resonator made from MBE-grown Ta films is not higher than some resonators made from deposited Ta films by magnetron sputtering in other works, which could be caused by the processing technique of the (a-plane) sapphire and the etching process of CPWs. In other words, both the a-plane sapphire substrate preparation and the repeatability of the optimal etching process for the CPW need to be improved to adapt to MBE-grown Ta films and further research is needed to identify other loss channels.

In conclusion, we optimized the MBE growth conditions of α-Ta (110) films on a-plane sapphire substrates. The effects of growth rate and temperature on the MBE-grown film properties were investigated using various characterization tools, such as AFM, HR-XRD, and STEM. The optimized α-Ta (110) film exhibited a single-crystal structure with a polished surface and an atomic metal–substrate interface. The film with thickness of 30 nm shows a T_c of 4.12 K and a high RRR of 9.53. Resonators based on quarter-wavelength CPWs were fabricated by utilizing the 150 nm optimized α-Ta (110) film, which demonstrated Q_i exceeding one million when subjected to single photon excitation at millikelvin temperature.

K.L.X. acknowledges support from the Youth Innovation Promotion Association of Chinese Academy of Sciences (No. 2019319). J.G.F. acknowledges support from the Start-up foundation of Suzhou Institute of Nano-Tech and Nano-Bionics, CAS, Suzhou (No. Y9AAD110).

The authors have no conflicts to disclose.

Haolin Jia: Data curation (equal); Investigation (equal); Writing – original draft (lead); Writing – review & editing (lead). Boyi zhou: Data curation (equal); Investigation (equal). Tao Wang: Data curation (equal); Investigation (equal). Yanfu Wu: Data curation (supporting); Investigation (supporting). Lina Yang: Data curation (supporting); Investigation (supporting). Zengqian Ding: Data curation (supporting); Investigation (supporting). Shuming Li: Data curation (supporting); Investigation (supporting). Xiao Cai: Investigation (supporting). Kanglin Xiong: Conceptualization (lead); Data curation (lead); Funding acquisition (lead); Investigation (lead); Project administration (lead); Supervision (lead); Writing – original draft (supporting); Writing – review & editing (supporting). Jiagui Feng: Conceptualization (lead); Data curation (lead); Funding acquisition (lead); Investigation (lead); Project administration (lead); Supervision (lead); Writing – original draft (lead); Writing – review & editing (lead).

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