Large variations in the energy relaxation time (T1) of superconducting qubits make it difficult to accurately evaluate and compare new qubit materials and fabrication processes, or to perform studies that require precise measurements of energy loss. To address this issue, we present techniques for characterizing qubit quality factors by applying electric fields to TLS in the vicinity of qubits. Introducing low-frequency (<1 Hz) AC fields allows us to stabilize the measured T1 by averaging over the accessible TLS configurations, producing a robust estimate of T1 that is difficult to replicate with hundreds of measurements over long periods, without applied fields. In a complementary technique, we apply a randomly selected DC field to the qubit and measure T1. Repeated ‘fast-random’ measurements reveal a distribution of T1 values whose harmonic mean is consistent with that obtained through AC measurements but illustrates a wider range of qubit lifetimes induced by TLS interactions. We implement these TLS control techniques in various ways, including demonstrating a simple T1 improvement protocol and precise measurements of T1 vs temperature. These techniques will facilitate our understanding of how to improve qubit coherence by enabling better measurements in shorter times or with fewer devices.

Superconducting qubits have been used in the most advanced demonstrations of quantum information processing, and they can be manufactured at-scale using proven semiconductor techniques. This makes them one of the leading technologies in the race to demonstrate useful quantum computers. Since their initial demonstration, advances in design, fabrication, and materials have extended the timescales over which fragile quantum information can be stored and manipulated on superconducting qubits. Ubiquitous atomic-scale material defects have been identified as a primary cause of qubit energy-loss and decoherence. Here we study transmon qubits that exhibit energy relaxation times exceeding 2.5 ms. Even at these long timescales, our qubit energy loss is dominated by two level systems (TLS). We observe large variations in these energy-loss times that would make it extremely difficult to accurately evaluate and compare qubit fabrication processes and to perform studies that require precise measurements of energy loss. To address this issue, we present a technique for characterizing qubit quality factor. In this method, we apply a slowly varying electric field to TLS near the qubit to stabilize the measured energy relaxation time, enabling us to replace hundreds of hours of measurements with ones that span several minutes.

Quantum computing relies on the operation of qubits in an environment as free of noise as possible. This work reports on measuring the impact of environmental radiation on lifetimes of fixed frequency transmon qubits with various capacitor pad geometries by varying the amount of shielding used in the measurement space. It was found that the qubit lifetimes are robust against these shielding changes until the most extreme limit was tested without a mixing chamber shield in the refrigerator. In contrast, the quasiparticle tunneling rates were found to be extremely sensitive to all configurations tested, indicating these devices are not yet limited by losses related to superconducting quasiparticles.

Non-equilibrium quasiparticles are possible sources for decoherence in superconducting qubits because they can lead to energy decay or dephasing upon tunneling across Josephson junctions (JJs). Here, we investigate the impact of the intrinsic properties of two-dimensional transmon qubits on quasiparticle tunneling (QPT) and discuss how we can use quasiparticle dynamics to gain critical information about the quality of JJ barrier. We find the tunneling rate of the non-equilibrium quasiparticles to be sensitive to the choice of the shunting capacitor material and their geometry in qubits. In some devices, we observe an anomalous temperature dependence of the QPT rate below 100 mK that deviates from a constant background associated with non-equilibrium quasiparticles. We speculate that this behavior is caused by high transmission sites/defects within the oxide barriers of the JJs, leading to spatially localized subgap states. We model this by assuming that such defects generate regions with a smaller effective gap. Our results present a unique in situ characterization tool to assess the uniformity of tunnel barriers in qubit junctions and shed light on how quasiparticles can interact with various elements of the qubit circuit.

The performance of next-generation, nanoelectronic devices relies on a precise understanding of strain within the constituent materials. However, the increased flexibility inherent to these three-dimensional device geometries necessitates direct measurement of their deformation. Here we report synchrotron x-ray diffraction-based non-destructive nanoscale mapping of Si/SiGe nanosheets for gate-all-around structures. We identified two competing mechanisms at different length scales contributing to the deformation. One is consistent with the in-plane elastic relaxation due to the Ge lattice mismatch with the surrounding Si. The second is associated with the out-of-plane layering of the Si and SiGe regions at a length scale of film thickness. Complementary mechanical modeling corroborated the qualitative aspects of the deformation profiles observed across a variety of nanosheet sample widths. However, greater deformation is observed in the SiGe layers of the nanosheets than the predicted distributions. These insights could play a role in predicting carrier mobilities of future devices.

Silicon-germanium (SiGe) is a material that possesses a multitude of applications ranging from transistors to electro-optical modulators and quantum dots. The diverse properties of SiGe also make it attractive to implementations involving superconducting quantum computing. Here, we demonstrate the fabrication of transmon quantum bits on SiGe layers and investigate the microwave loss properties of SiGe at cryogenic temperatures and single photon microwave powers. We find relaxation times of up to 100 mu s, corresponding to a quality factor Q above 4 M for large pad transmons. The high Q values obtained indicate that the SiGe/Si heterostructure is compatible with state-of-the-art performance of superconducting quantum circuits.

The progress witnessed within the field of quantum computing has been enabled by the identification and understanding of interactions between the state of the quantum bit (qubit) and the materials within its environment. Beginning with an introduction of the parameters used to differentiate various quantum computing approaches, we discuss the evolution of the key components that comprise superconducting qubits, where the methods of fabrication can play as important a role as the composition in dictating the overall performance. We describe several mechanisms that are responsible for the relaxation or decoherence of superconducting qubits and the corresponding methods that can be utilized to characterize their influence. In particular, the effects of dielectric loss and its manifestation through the interaction with two-level systems (TLS) are discussed. We elaborate on the methods that are employed to quantify dielectric loss through the modeling of energy flowing through the surrounding dielectric materials, which can include contributions due to both intrinsic TLS and extrinsic aspects, such as those generated by processing. The resulting analyses provide insight into identifying the relative participation of specific sections of qubit designs and refinements in construction that can mitigate their impact on qubit quality factors. Additional prominent mechanisms that can lead to energy relaxation within qubits are presented along with experimental techniques which assess their importance. We close by highlighting areas of future research that should be addressed to help facilitating the successful scaling of superconducting quantum computing.

A strategy aimed at decreasing dielectric loss in coplanar waveguides (CPWs) and qubits involves the creation of trenches in the underlying substrate within the gaps of the overlying metallization. Participation of contamination layers residing on surfaces and interfaces in these designs can be reduced due to the change in the effective dielectric properties between the groundplane and the conductor metallization. Although finite element method approaches have been previously applied to quantify this decrease, an analytical method is presented that can uniquely address geometries possessing small to intermediate substrate trench depths. Conformal mapping techniques produce transformed CPW and qubit geometries without substrate trenching but a nonuniform contamination layer thickness. By parametrizing this variation, one can calculate surface participation through use of a 2-D, analytical approximation that properly captures singularities in the electric field intensity near the metallization corners and edges. Examples demonstrate two regimes with respect to substrate trench depth that capture an initial increase in substrate-to-air surface participation due to the trench sidewalls and an overall decrease in surface participation due to the reduction in the effective dielectric constant and are compared with experimental measurements to extract loss tangents on this surface.

Throughout his career, Dr. Stephen Rossnagel and his co-workers have had a profound influence on thin film deposition. His seminal work includes the development of reactive, collimated, and ionized methods of DC and RF magnetron sputtering, as well as plasma-enhanced atomic layer deposition. Most importantly, his contributions have been widely adopted within the microelectronics community in its efforts to produce finer layers with increased uniformity and functionality. While applications span a very broad range, from complementary metal oxide semiconductor device metallization to DNA sensing, Dr. Rossnagel has also conducted fundamental investigations into microstructural effects on electronic scattering. In this manuscript, the authors will highlight some of Steve’s contributions to these areas and their continued relevance to current and future microelectronic device scaling.

The discovery of auxetic behavior (negative Poisson's ratio) within elements and alloys had focused attention on their elastic anisotropy in an effort to understand the range of crystal orientations that manifest this property. A comparison of elastic constant data to atomistic models based on pair-wise, central force models provides key insights into deformation behavior of cubic crystals over a wide range of anisotropy, including, for the first time, those with Zener anisotropy ratios less than 1. A simple criterion is derived which dictates all cases in which a crystal whose atomic ordering obeys cubic symmetry will display auxetic deformation, where the extrema in Poisson's ratio involves (110) orientations. In the field of stress determination through x-ray diffraction, these findings also shed light on strain anisotropy in polycrystalline materials, where the elastic incompatibility between adjacent grains alters their overall deformation. By applying these same atomistic models, we can predict the Voigt/Reuss weighting fractions associated with Kröner limit x-ray elastic constants for cubic materials, a necessary component in quantifying stress using diffraction data. We also establish that greater elastic anisotropy in a constituent crystal leads to a more rigid mechanical response in the corresponding polycrystalline aggregate, with implications for auxetic crystal ensembles.

Elastic strain energy within materials due to recrystallization of grains with a specific orientation, or texture, can be calculated through the use of Eshelby inclusions, where a recrystallized grain can be treated as an elastically anisotropic inclusion in an elastically isotropic matrix. The evolution of texture that minimizes elastic strain energy is shown to be dependent on the specific strain state. The interaction strains generated by this elastic incompatibility and corresponding strain energy have been derived for grains with cubic symmetry for general forms of the applied strain tensor. For uniaxial and isotropic, biaxial strain tensors, the interaction strain tensor and corresponding elastic strain energy density are proportional to the orientation parameter, Γ, which relates the Miller indices of the recrystallized grain to the loading direction: either parallel to the uniaxial strain direction or perpendicular to the plane in which isotropic biaxial strain is applied. It is rigorously proven that for elastically isotropic inclusions, corresponding to Γ = 1/5, the interaction strain is zero. Although blanket films often possess an isotropic, biaxial stress state, metallization trenches can exhibit a combination of normal and shear strain components, particularly near the trench corners. It is shown that in cases where shear is present, the resulting elastic strain energy can be lowered by the development of (110) texture despite its higher surface energy, as has been observed in thin films and interconnect trenches. These results suggest that shear strain can play an important role in the evolution of texture in narrow, metallization structures.

Superconducting qubits are sensitive to a variety of loss mechanisms, which include dielectric loss from interfaces. The calculation of participation near the key interfaces of planar designs can be accomplished through an analytical description of the electric field density based on conformal mapping. In this way, a 2-D approximation to coplanar waveguide and capacitor designs produces values of the participation as a function of depth from the top metallization layer as well as the volume participation within a given thickness from this surface by reducing the problem to a surface integration over the region of interest. These quantities are compared to finite-element method numerical solutions, which validate the values at large distances from the coplanar metallization but diverge near the edges of the metallization features due to the singular nature of the electric fields. A simple approximation to the electric field energy at shallow depths (relative to the waveguide width) is also presented that closely replicates the numerical results based on conformal mapping and those reported in prior literature. These techniques are applied to the calculation of surface participation within a transmon qubit design, where the effects due to shunting capacitors can be easily integrated with those associated with metallization comprising the local environment of the qubit junction.

Jörg Maser1,*, Barry Lai1, Vincent De Andrade1, Simon R. Bare2, Mariana Bertoni3, Tonio Buonassisi4, Paul Evans5, David P. Fenning6, Steve Heald1, Chris Johnson7, Tony Lanzirotti8, Conal Murray9, Tijana Rajh10, Volker Rose1,10, Ruben Reininger1, Xianbo Shi1, M. Stuckelberger11, David Tiede7, Stefan Vogt1, Randy Winans1. 1. X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Argonne, IL, USA 2. SSRL, SLAC National Accelerator Laboratory, CA, USA. 3. Arizona State University, Tempe, AZ, USA. 4. Massachusetts Institute of Technology, Cambridge, MA, USA. 5. University of Wisconsin-Madison, WI, USA 6. University of California, San Diego, USA. 7. Chemical Sciences and Engineering Division, Argonne, IL, USA. 8. The University of Chicago, IL, USA. 9. IBM T.J. Watson Research Center, Yorktown Heights, NY, USA. 10 Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL, USA 11 Deutsches Elektronen-Synchrotron, Hamburg, Germany * Corresponding author, maser@anl.gov

The issue of stress in thin films and functional coatings is a persistent problem in materials science and technology that has congregated many efforts, both from experimental and fundamental points of view, to get a better understanding on how to deal with, how to tailor, and how to manage stress in many areas of applications. With the miniaturization of device components, the quest for increasingly complex film architectures and multiphase systems and the continuous demands for enhanced performance, there is a need toward the reliable assessment of stress on a submicron scale from spatially resolved techniques. Also, the stress evolution during film and coating synthesis using physical vapor deposition (PVD), chemical vapor deposition, plasma enhanced chemical vapor deposition (PECVD), and related processes is the result of many interrelated factors and competing stress sources so that the task to provide a unified picture and a comprehensive model from the vast amount of stress data remains very challenging. This article summarizes the recent advances, challenges, and prospects of both fundamental and applied aspects of stress in thin films and engineering coatings and systems, based on recent achievements presented during the 2016 Stress Workshop entitled “Stress Evolution in Thin Films and Coatings: from Fundamental Understanding to Control.” Evaluation methods, implying wafer curvature, x-ray diffraction, or focused ion beam removal techniques, are reviewed. Selected examples of stress evolution in elemental and alloyed systems, graded layers, and multilayer-stacks as well as amorphous films deposited using a variety of PVD and PECVD techniques are highlighted. Based on mechanisms uncovered by in situ and real-time diagnostics, a kinetic model is outlined that is capable of reproducing the dependence of intrinsic (growth) stress on the grain size, growth rate, and deposited energy. The problems and solutions related to stress in the context of optical coatings, inorganic coatings on plastic substrates, and tribological coatings for aerospace applications are critically examined. This review also suggests strategies to mitigate excessive stress levels from novel coating synthesis perspectives to microstructural design approaches, including the ability to empower crack-based fabrication processes, pathways leading to stress relaxation and compensation, as well as management of the film and coating growth conditions with respect to energetic ion bombardment. Future opportunities and challenges for stress engineering and stress modeling are considered and outlined.

Strain within nanoscale strained SiGe FinFET structures has been investigated using a combination of X-ray diffraction and transmission electron microscopy-based nanobeam diffraction (NBD) techniques to reveal the evolution of the stress state within the FinFETs. Reciprocal space maps collected using high-resolution X-ray diffraction exhibited distinct features corresponding to the SiGe fin width, pitch, and lattice deformation and were analyzed to quantify the state of stress within the fins. Although the majority of the SiGe fin volume exhibited a uniaxial stress state due to elastic relaxation of the transverse in-plane stress, NBD measurements confirmed a small interaction region near the SOI interface that is mechanically constrained by the underlying substrate. We have quantitatively characterized the evolution of the fin stress state from biaxial to uniaxial as a function of fin aspect ratio and Ge fraction and confirmed that the fins obey elastic deformation based on a model that depends on the relative difference between the equilibrium Si and SiGe lattice constants and relative fraction of in-plane stress transverse to the SiGe fins. Spatially resolved, nanobeam X-ray diffraction measurements conducted near the SiGe fin edge indicate the presence of additional elastic relaxation from a uniaxial stress state to a fully relaxed state at the fin edge. Mapping of the lattice deformation within 500 nm of this fin edge by NBD revealed large gradients, particularly at the top corner of the fin. The values of the volume averaged lattice deformation obtained by nanoXRD and NBD are qualitatively consistent. Furthermore, the modulation of strain at the fin edge obtained by quantitative analysis of the nanoXRD results agrees with the lattice deformation profile obtained by NBD.

Superconducting qubits are sensitive to a variety of loss mechanisms including dielectric loss from interfaces. By changing the physical footprint of the qubit, it is possible to modulate sensitivity to surface loss. Here, we show a systematic study of planar superconducting transmons of differing physical footprints to optimize the qubit design for maximum coherence. We find that qubits with small footprints are limited by surface loss and that qubits with large footprints are limited by other loss mechanisms, which are currently not understood.

Coherent X-ray microscopy by phase retrieval of Bragg diffraction intensities enables lattice distortions within a crystal to be imaged at nanometre-scale spatial resolutions in three dimensions. While this capability can be used to resolve structure-property relationships at the nanoscale under working conditions, strict data measurement requirements can limit the application of current approaches. Here, we introduce an efficient method of imaging three-dimensional (3D) nanoscale lattice behaviour and strain fields in crystalline materials with a methodology that we call 3D Bragg projection ptychography (3DBPP). This method enables 3D image reconstruction of a crystal volume from a series of two-dimensional X-ray Bragg coherent intensity diffraction patterns measured at a single incident beam angle. Structural information about the sample is encoded along two reciprocal-space directions normal to the Bragg diffracted exit beam, and along the third dimension in real space by the scanning beam. We present our approach with an analytical derivation, a numerical demonstration, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.