Candidate TLS Defects at the Al-Si Interface in a Superconducting Qubit from STEM-based Structure Refinement
Soohyun Im, Venkata Surya Chaitanya Kolluru, Keith G. Ray, Vito Iaia, Loren D. Alegria, Vincenzo Lordi, Yaniv Jacob Rosen, Maria K. Y. Chan, Paul M. Voyles
Two-level systems (TLSs) are the dominant source of decoherence in superconducting qubits, a leading platform for quantum computing. While TLSs are believed to arise from atomic-scale tunneling defects, their precise structural origins, particularly at complex and disordered interfaces in real devices, have remained elusive. Conventional structural characterization is extremely challenging because these interfaces are non-periodic, containing steps and roughness, and device-relevant TLS defects involve only atomic motions with small energy differences. We have determined the atomic character of candidate TLSs at the Al-Si interface of a superconducting qubit using aberration-corrected scanning transmission electron microscopy (STEM) combined with experiment-constrained 3D structure modeling and computational defect searching. High-angle annular dark-field (HAADF) STEM images were obtained from a disordered interface containing a prominent step defect and localized strain. Structure modeling started with 3D models created in the Ingrained framework to match the experimental projections, accounting for mistilt and uniform strain. These models were then refined using FANTASTX (Fully Automated Nanoscale To Atomistic Structure from Theory and eXperiments), a multi-objective optimizer that simultaneously minimizes disagreement with the experimental image via structural similarity and the ab initio (DFT) total system energy. Transition-state searches with the activation relaxation technique nouveau (ARTn) on the refined models identified many atomic configurations occupying double-well potentials corresponding to TLS. Statistical analysis of over 1500 TLSs shows that candidate TLS with tunneling energies and asymmetries in the range relevant to superconducting qubits (∼5 GHz) predominantly involve Al atoms located near the interface. These atoms exhibit smaller median tunneling displacements (∼0.44 Å) than the non-candidate TLS and reside in locally disordered environments with marginally longer and less dense first-neighbor shells than those of non-candidate TLSs. The most probable candidate TLSs feature cooperative motion of one or two Al atoms, and sometimes with Si, in directions largely parallel to the interface. This work provides the first direct atomic-scale insight into the structural defects that may be responsible for decoherence at a realistic, device-relevant interface. It also demonstrates a scalable, generalizable workflow for solving the atomic structure of complex, disordered interfaces by integrating aberration-corrected STEM with advanced computational refinement and defect searching. The methodology is directly applicable to other materials systems and heterointerfaces critical to quantum devices [5].
Two-level systems (TLSs) are the dominant source of decoherence in superconducting qubits, a leading platform for quantum computing. While TLSs are believed to arise from atomic-scale tunneling defects, their precise structural origins, particularly at complex and disordered interfaces in real devices, have remained elusive. Conventional structural characterization is extremely challenging because these interfaces are non-periodic, containing steps and roughness, and device-relevant TLS defects involve only atomic motions with small energy differences. We have determined the atomic character of candidate TLSs at the Al-Si interface of a superconducting qubit using aberration-corrected scanning transmission electron microscopy (STEM) combined with experiment-constrained 3D structure modeling and computational defect searching. High-angle annular dark-field (HAADF) STEM images were obtained from a disordered interface containing a prominent step defect and localized strain. Structure modeling started with 3D models created in the Ingrained framework to match the experimental projections, accounting for mistilt and uniform strain. These models were then refined using FANTASTX (Fully Automated Nanoscale To Atomistic Structure from Theory and eXperiments), a multi-objective optimizer that simultaneously minimizes disagreement with the experimental image via structural similarity and the ab initio (DFT) total system energy. Transition-state searches with the activation relaxation technique nouveau (ARTn) on the refined models identified many atomic configurations occupying double-well potentials corresponding to TLS. Statistical analysis of over 1500 TLSs shows that candidate TLS with tunneling energies and asymmetries in the range relevant to superconducting qubits (∼5 GHz) predominantly involve Al atoms located near the interface. These atoms exhibit smaller median tunneling displacements (∼0.44 Å) than the non-candidate TLS and reside in locally disordered environments with marginally longer and less dense first-neighbor shells than those of non-candidate TLSs. The most probable candidate TLSs feature cooperative motion of one or two Al atoms, and sometimes with Si, in directions largely parallel to the interface. This work provides the first direct atomic-scale insight into the structural defects that may be responsible for decoherence at a realistic, device-relevant interface. It also demonstrates a scalable, generalizable workflow for solving the atomic structure of complex, disordered interfaces by integrating aberration-corrected STEM with advanced computational refinement and defect searching. The methodology is directly applicable to other materials systems and heterointerfaces critical to quantum devices [5].
In superconducting transmon qubits, macroscopic characterization is the primary method for probing performance metrics, such as relaxation T1 and dephasing T2 times, resonance frequency, and quality factor. While these measurements can aid our understanding of the dielectric loss of a transmon, they do not allow us to characterize the structural and chemical inhomogeneity of the interfaces which directly impacts this energy loss. These fundamental materials problems must be studied using transmission electron microscopy (TEM) to provide insight into these defects across different qubit interfaces at an atomic scale. In this contribution, we will examine qubits, such as those shown in Figure 1, fabricated at Fermi National Accelerator Laboratory (SQMS Center) [1]. The qubit devices consist of superconducting metal base layers, typically sputter deposited Nb or Ta, and Al/AlOx/Al junctions, where the AlOx barrier is roughly 3nm in thickness and prepared through in-situ oxidation [2]. Characterizing this system prior to its integration within a superconducting radio frequency cavity establishes a baseline for the system, allowing us to isolate fabrication-induced defects before they manifest in performance degradation during quantum measurements. With the samples and fabrication process well known on a macroscopic scale, we study the atomic structure and chemistry of different heterointerfaces within the Josephson junction (JJ) of the transmon qubit and between the sapphire substrate and Nb resonator pads to identify potential defects contributing to the decoherence for qubits constructed with particular geometries. To resolve these defects, atomic-resolution imaging, energy-dispersive X-ray spectroscopy (EDS), and electron-energy loss spectroscopy (EELS) are performed using the JEOL-ARM200CF, an aberration-corrected scanning transmission electron microscope (STEM). Figure 2 provides a clear image of the stacked layers formed as the JJ, but with the addition of a platinum and carbon protective coating added during the focus ion beam (FIB) milling process to preserve pristine Al/AlOx/Al interfaces. 4D-STEM approaches, such as ptychography, orientation mapping and nanoscale diffraction will be employed to further study the layered interfaces and defects in real space and reciprocal space. These techniques can also provide insight into any damage that incurs during lamella preparation using the FIB [3]. Magnetic field-free atomic resolution imaging, differential phase contrast mapping, and monochromated EELS can be achieved using the new MARS-MONO STEM (JEM-Z200MF) without inducing current fluctuations or magnetic field related distortions [4]. By integrating this work across the functional interfaces of the transmon qubits and their different geometries, we will identify possible structural and chemical defects which limit device performance using our multi-modal approach [5]. SQMS fabricated transmon qubits fabricated on HEMEX sapphire substrate imaged via a) ZEISS optical microscope, b) SEM and c) EDS. TEM image of Josephson Junction layered interface at on JEOL-ARM200CF on the ClearView camera with a 200kV accelerating voltage.
Superconducting qubit technology is among the most promising hardware platform for quantum computing due to its fast gate operation, manufacturing scalability, and architectural flexibility [1]. A key figure of merit that dictates quantum computing functionality is the qubit’s coherence time, which needs to be maximized in order to bring quantum computing to the practical and scalable realm [2]. In particular, the T1 relaxation time—now on the order of milliseconds—can be enhanced with materials engineering, as amorphous dielectrics and crystallographic defects, among other factors, are known to induce decoherence [3-7]. Current state-of-the-art superconducting qubit devices use amorphous AlOx sandwiched between two superconducting Al electrodes as the Josephson junction (JJ), a key element in the transmon qubit, but amorphous dielectrics introduce two-level system (TLS) loss that underlie decoherence [8]. For this reason, numerous efforts have explored crystalline dielectrics as a replacement for amorphous AlOx, since single-crystal materials do not suffer from the lack of long-range order and sub-stoichiometry that comprise TLS defects [9-12]. However, none of these alternative materials choices have been able to surpass, let alone replicate, the performance of Al-AlOx-Al JJs. In this work, we fabricate superconducting quantum devices using a novel heteroepitaxial TiN/γ-Al2O3/TiN tri-layer stack grown on sapphire (Fig. 1a) and find that the measured microwave loss of the single-crystal γ-Al2O3 dielectric is lower than that of amorphous AlOx by two orders of magnitude. For qubits made with this tri-layer to transcend the coherence of incumbent Al-AlOx-Al, the structural, chemical, and electronic defects that induce TLS loss in these materials need to be well understood. Towards this end, we combine scanning transmission electron microscopy (STEM) and scanning electron microscopy (SEM) methods to highlight structural and interfacial complexity across length scales, ultimately identifying loss sources in the TiN/γ-Al2O3/TiN heteroepitaxial tri-layer. With atomic-resolution imaging and four-dimensional (4D-)STEM nanobeam electron diffraction (NBED), we find that the dielectric γ-Al2O3 layer, though single-crystalline (Fig. 1b), suffers from the formation of antiphase boundaries (Fig. 1c), which can host strong local electric fields and enhance lossy dielectric response [13]. Correlated with these nanoscale planar defects is uniformly distributed elastic strain, on the order of 6%, between the lattice-mismatched γ-Al2O3 and TiN (Fig. 1d). In other words, the dielectric layer is fully strained to match the underlying metal layer; such high strain can distort local bonding environments and thus create new TLSs or shift existing TLSs into resonance. Beyond imperfections within the bulk of the dielectric layer, there are noteworthy interfacial defects: roughening of both TiN/γ-Al2O3 interfaces deviate from atomically flat boundaries (Fig. 1c), while anion interdiffusion across both interfaces, as evident from core-loss electron energy-loss spectral (EELS) maps (Fig. 1e), leave behind vacancies and undercoordinated metal atoms, thereby creating 1.5 – 2 nm nonstoichiometric diffuse interfacial layers, both of which can cause TLS loss. In the superconducting TiN layers, we again use NBED to identify 180°-reflected specular twinned domains, indicating distinct heteroepitaxial relationships of [111]TiN//[0006]Al2O3 and [002¯]TiN//[22¯02¯]Al2O3 (Fig. 2a) [14]. Crystal twinning of the TiN epilayer is not only spatially distributed at the nanoscale, as shown using virtual dark-field (VDF) images (Fig. 2b), but is also widespread at the microscale, as shown using SEM electron backscatter diffraction (EBSD) (Fig. 2c). While microwave performance is not limited by a single factor, it is clear that defective quantum microstructure across length scales collectively contribute to dielectric loss, and in turn, TLS-related decoherence. By correlating nanoscale crystallographic and spectroscopic information with microscale diffraction measurements, our work can guide interface engineering during material growth, paving the way towards further improvements in quantum device performance. Cross-sectional samples were prepared by subsequent 30 kV, 8 kV and 5 kV Xe+ plasma focused ion beam (FIB) using the Thermo Scientific Helios 5 Hydra CX DualBeam Plasma FIB/SEM. Samples were then plasma cleaned using South Bay Technology PC-2000 Plasma Cleaner with a 3:1 mixture of Ar:O2 gas at 20∼40 W RF power for 15 s at 150 mTorr. High-angle annular dark-field (HAADF-) and annular bright-field (ABF-) STEM images were collected on a probe-corrected JEOL JEM-ARM200CF S/TEM operating at 200 kV using JEOL detectors. The STEM convergence angle, HAADF collection angle, and ABF collection angle were 27 mrad, 90 – 370 mrad, and 23 mrad, respectively. EELS data were collected on a JEOL JEM-ARM300F GrandARM S/TEM operating at 300 kV using the Gatan GIF Continuum K3 IS system. The data were collected using a 2.5 mm aperture and a 750 eV wide energy slit at a dispersion of 0.18 eV/Ch and a camera length of 2 cm. 4D-STEM data were collected on the same microscope and detector system using a 0.5 – 1.5 mrad convergence angle and a 20 eV wide energy slit at a camera length of 4 cm. All STEM data processing was performed using the Gatan Microscopy Suite software. Top-down EBSD measurements were performed in the Thermo Scientific Helios 5 CX DualBeam FIB/SEM at 25 kV using the Oxford Symmetry S3 detector. EBSD data processing was performed using the Oxford AZtecCrystal software [15]. Defects in γ-Al2O3. a) HAADF-STEM image of a TiN/γ-Al2O3/TiN tri-layer stack on a α-Al2O3 (0001) substrate. The thickness of γ-Al2O3 is approximately 13.5 nm. b) 4D-STEM NBED pattern of the γ-Al2O3 layer, confirming the {111} out-of-plane orientation. c) Fourier-filtered atomic-resolution ABF-STEM image of the γ-Al2O3 dielectric layer, taken from the cyan-colored square region in a), emphasizing the planar defects along both TiN/γ-Al2O3 interfaces and within the γ-Al2O3 layer itself–interfacial roughness (yellow lines) and antiphase boundaries (colored parallelograms), respectively. The scale bar is 2 nm. d) In-plane and out-of-plane strain maps of the heteroepitaxial tri-layer stack, with approximately 6.5∼6.8% strain in both directions. The units of the intensity bar are such that 100% strain would be equivalent to 1.0. e) STEM-EELS maps of Ti-L2,3, N-K, and O-K edges, along with a superimposed image of the three, taken from the same region as c). The scale bars are all 5 nm. Defects in TiN. a) 4D-STEM NBED patterns and b) VDF images of nanoscale TiN {111} and {002} twins. c) SEM EBSD pole figures in the three face-centered cubic crystallographic directions, revealing that the 60° rotation twinning behavior (with the [111] twin axis) is spread across the microscale.
The low-temperature physics of structurally amorphous materials is governed by low-energy two-level system (TLS) defects. Being impervious to most traditional condensed matter probes, the exact origin and nature of TLS remain elusive. Recent advances toward realizing stable high-coherence quantum computing platforms have increased the importance of studying TLS in solid-state quantum circuits, as they are a persistent source of decoherence and instability. Here, performing scanning gate microscopy on a live superconducting NbN resonator at millikelvin temperatures, we locate individual TLS, directly revealing their microscopic nature. Mapping and visualizing the most detrimental TLS in the bath pinpoints the dominant sources of ubiquitous 1/ f dielectric noise and energy relaxation. We also deduce the three-dimensional orientation of individual TLS electric dipole moments. Combining these insights with structural information of the underlying materials can help unravel the detailed microscopic nature and chemical origin of TLS, directing targeted strategies for their eventual mitigation.
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.
The development of quantum computers, capable of surpassing classical computing in solving specific complex problems, hinges on breakthroughs in materials science, precision device fabrication, and the optimization of quantum architectures [1]. Among the leading candidates for quantum computation, superconducting qubits, particularly those based on transmon designs, have shown promising advances with coherence times reaching hundreds of microseconds [2]. However, to fully unlock the potential of scalable quantum computing, further enhancements in coherence are necessary. The intricate structure-coherence relationship within these devices, especially at critical interfaces such as metal-air, metal-dielectric, and metal-substrate in Josephson junctions (JJs), poses a significant challenge due to the potential for two-level-system loss channels. Here, we detail our pioneering efforts to understand these structure-coherence relationships utilizing advanced electron microscopy techniques. Focusing on the Al-AlOx and Al-Si substrate interfaces in Josephson Junctions, we employ a combination of low-loss and core-loss electron energy loss spectroscopy (EELS) and four-dimensional scanning transmission electron microscopy (4D-STEM) conducted at room and ultra-low temperatures (sub-6 K). This approach allows for an unprecedented examination of the chemical composition, bonding environments, and nanoscale structures of key surfaces and interfaces critical to the quantum coherence. Figure 1 presents a typical superconducting architecture at the chip level; each superconducting qubit consists of a Josephson Junction in parallel with an ultra-low-loss capacitor to create a resonant structure in the 3-6GHz range. JJs are highlighted in the area boxed in Fig. 1A and can be observed in detail in Fig. 1B. Lamella cross-sections (as shown in Fig. 1C) were prepared using a dual-beam focused ion beam (FIB) FEI-SEM Helios Nanolab. The lift-off was performed using 30 kV Ga+ ions, and the final cleaning step was carried out at 2 kV to remove surface damage on the area of interest, resulting in a final sample thickness of 50-100 nm. Transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) data were collected on a probe-corrected JEOL ARM200 S/TEM operating at 200 kV. The convergent angle for ADF-STEM imaging was 25 mrad. Electron energy loss spectra (EELS) were acquired at 200 kV using a Gatan GIF Quantum on a K2 pixelated detector. Data processing (background subtraction, plural scattering removal, and signal mapping) was conducted using Gatan GMS software. Four-dimensional STEM (4D-STEM) data were collected by a K3 and STELA cameras. The convergent angles were 0.5-1.5 mrad, and the camera length was 6-10 cm. The step size was 5-10 Å. Merging microscopic insights with electrical data and theoretical frameworks, we aim to reveal how atomic-scale irregularities affect coherence times. Our results highlight key decoherence mechanisms in superconducting qubits and suggest specific improvements for qubit design and manufacturing. By linking electron microscopy findings to device performance, we outline strategies to reduce decoherence, essential for achieving reliable quantum computing. This work bridges materials science and quantum engineering, driving efforts in making scalable quantum computers forward [3]. A) Microscopic view of a superconducting transmon qubit, highlighting its symmetric design with central island and capacitor pads. B) SEM image of a JJ displaying their Al top and bottom contacts. C) STEM image of a JJ showing its key components and interfaces: Al top and bottom contact, AlOx tunnel barrier, Si substrate and Al-Si interface. A) EELS chemical maps of two interfaces, Al/Al and Al/Si using K-edges of oxygen, aluminum and silicon of a Josephson junction. It is possible to detect a formation of oxides at both interfaces. Plots showing Al and Si K-edge at 1560 eV and 1839 eV, respectively, and the ELNES are shown on the right side (Scale bar in A – 20 nm). B) Analysis of the disordered Al phases at the interfaces utilizing ePDF.
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.