Spin caloritronics with superconductors: Enhanced thermoelectric effects, generalized Onsager response-matrix, and thermal spin currents

It has recently been proposed and experimentally demonstrated that it is possible to generate large thermoelectric effects in ferromagnet/superconductor structures due to a spin-dependent particle-hole asymmetry. Here, we theoretically show that quasiparticle tunneling between two spin-split superconductors enhances the thermoelectric response manyfold compared to when only one such superconductor is used, generating Seebeck coefficients ($\mathcal{S} > 1$ mV/K) and figures of merit ($ZT \simeq 40$) far exceeding the best bulk thermoelectric materials, and also becomes more resilient toward inelastic scattering processes. We present a generalized Onsager response-matrix which takes into account spin-dependent voltage and temperature gradients. Moreover, we show that thermally induced spin currents created in such junctions, even in the absence of a polarized tunneling barrier, also become largest in the case where a spin-dependent particle-hole asymmetry exists on both sides of the barrier. We determine how these thermal spin currents can be tuned both in magnitude and sign by several parameters, including the external field, temperature, and the superconducting phase-difference.Comment: 7 pages, 5 figures. v2: Added several new results, such as the response matrix for spin-dependent biases and the evaluation of thermal spin currents. Accepted for publication in Phys. Rev.

Conversion pathways of primary defects by annealing in proton-irradiated n-type 4H-SiC

The development of defect populations after proton irradiation of n-type 4H-SiC and subsequent annealing experiments is studied by means of deep level transient (DLTS) and photoluminescence (PL) spectroscopy. A comprehensive model is suggested describing the evolution and interconversion of irradiation-induced point defects during annealing below 1000{\deg}C. The model proposes the EH4 and EH5 traps frequently found by DLTS to originate from the (+/0) charge transition level belonging to different configurations of the carbon antisite-carbon vacancy (CAV) complex. Furthermore, we show that the transformation channel between the silicon vacancy (VSi) and CAV is effectively blocked under n-type conditions, but becomes available in samples where the Fermi level has moved towards the center of the band gap due to irradiation-induced donor compensation. The annealing of VSi and the carbon vacancy (VC) is shown to be dominated by recombination with residual self-interstitials at temperatures of up to 400{\deg}C. Going to higher temperatures, a decay of the CAV pair density is reported which is closely correlated to a renewed increase of VC concentration. A conceivable explanation for this process is the dissociation of the CAV pair into separate carbon anitisites and VC defects. Lastly, the presented data supports the claim that the removal of free carriers in irradiated SiC is due to introduced compensating defects and not passivation of shallow nitrogen donors

Cross-Sectional Carrier Lifetime Profiling and Deep Level Monitoring in Silicon Carbide Films Exhibiting Variable Carbon Vacancy Concentrations

The carrier lifetime control over 150 μm thick 4H-SiC epitaxial layers via thermal generation and annihilation of carbon vacancy (VC) related Z1/2 lifetime killer sites is reported. The defect developments upon typical SiC processing steps, such as high- and moderate-temperature anneals in the presence of a carbon cap, are monitored by combining electrical characterization techniques capable of VC depth-profiling, capacitance–voltage (CV) and deep-level transient spectroscopy (DLTS), with a novel all-optical approach of cross-sectional carrier lifetime profiling across 4H-SiC epilayer/substrate based on imaging time-resolved photoluminescence (TRPL) spectroscopy in orthogonal pump-probe geometry, which readily exposes in-depth efficacy of defect reduction and surface recombination effects. The lifetime control is realized by initial high-temperature treatment (1800 °C) to increase VC concentration to ≈1013 cm−3 level followed by a moderate-temperature (1500 °C) post-annealing of variable duration under C-rich thermodynamic equilibrium conditions. The post-annealing carried out for 5 h in effect eliminates VC throughout the entire ultra-thick epilayer. The reduction of VC-related Z1/2 sites is proven by a significant lifetime increase from 0.8 to 2.5 μs. The upper limit of lifetimes in terms of carrier surface leakage and the presence of other nonradiative recombination centers besides Z1/2, possibly related to residual impurities such as boron are discussed.publishedVersio

Point defects in silicon carbide for quantum technologies: Identification, tuning and control

Point defects strongly affect the electrical and optical properties of semiconductors, and are therefore of vast importance for device performance. Over recent years, however, point defects have been shown to possess properties that are highly suitable for applications related to quantum computing, sensing and communication. Single-photon emission and coherent spin manipulation at room temperature have been established for several systems, with the nitrogen-vacancy center in diamond counting among the first solid-state and semiconductor-based quantum platforms. Despite the long coherence times and established entanglement protocols of diamond-based qubit systems, diamond is only marginally compatible with advanced device fabrication methodology, and methods for integration of quantum emitters with electrically and optically controlled devices remain immature. For this reason, silicon carbide (SiC) has gained the attention of the quantum community, having a wide band gap, low spin-orbit coupling, mature device fabrication, and playing host to several promising quantum emitters of both extrinsic and intrinsic type. In this work, electrically and optically active point defects in silicon carbide have been studied using a combination of theoretical and experimental methods, with the aim of elucidating the role of different defects in power electronics and quantum technology devices. Hybrid density functional theory (DFT) calculations were employed to establish defect formation energies and chargestate transition levels, explore defect migration, and develop a new framework for studying the effect of electric fields on defect quantum emission. The calculations are correlated to experimental findings, where deep level transient spectroscopy (DLTS) and photo/cathodoluminescence (PL/CL) measurements reveal electrical and optical defect properties, respectively. The thesis places a particular emphasis on the silicon vacancy (VSi) in SiC, a room temperature single-photon source and qubit candidate exhibiting long spin coherence times. By monitoring VSi emission and comparing to DLTS spectra of proton-irradiated 4H-SiC samples, the VSi(-/2-) and VSi(2-/3-) charge-state transitions are assigned to the S-center, enabling electrical control over the VSi charge state. Depositing Schottky barrier diodes (SBDs) on the 4H-SiC sample surface enhances VSi emission by almost an order of magnitude, and sequential biasing of the SBD results in VSi charge-state switching, as detected by monitoring the V1 and V10 zero-phonon lines attributed to the negatively charged VSi at a hexagonal lattice site. The framework of bulk 4H-SiC epitaxial layers is compared to that of a microparticle matrix of predominantly the 6H polytype, with the former ensuring a homogeneous environment for the qubit defect and the latter enabling self-assembly, flexibility and ease of addressability. Importantly, both external and internal perturbations to the solid-state matrix wherein the VSi is embedded are shown to influence the emitted photon energies, as evidenced by an electric field-induced Stark effect and strain tuning in SiC microparticles. Furthermore, a set of emitters observed in the vicinity of the V1/V10 lines and having consistent subset spacings of 1.45 meV and 1.59 meV are tentatively attributed to vibronic replicas of the VSi emission. The VSi is unstable at elevated temperatures, and this thesis addresses the topics of VSi conversion and defect migration in p-type, intrinsic and n-type 4H-SiC material at 400 °C and above. Indeed, we find that hydrogen and VSi are likely to form complexes in the case that both species are present and in close proximity. In the absence of H, the VSi may convert to the carbon antisitevacancy (CAV) pair in p-type material, however, temperatures above 1000 °C are needed in n-type 4H-SiC, where both recombination with interstitials and divacancy formations prove to be more favorable annealing pathways for the VSi. The carbon vacancy (VC) is far more stable than VSi, and by comparing the two defect species using muon spin rotation (μSR) spectroscopy, we establish the μSR technique as a powerful tool for distinguishing different defect relaxation mechanisms and probing near-surface semiconductor defects in a non-destructive and depth-resolved manner. Annealing temperatures above 1200 °C are shown to be needed to induce VC migration, which is further demonstrated to be anisotropic in 4H-SiC, with the VC favoring in-plane atomic hops over the axial migration path. Finally, above temperatures of 2300 °C the lattice atoms themselves become mobile, and secondary ion mass spectrometry (SIMS) is employed to investigate the influence of a carbon cap covering the surface during annealing on self-diffusion of Si and C in 4H-SiC

Strongly Coupled Spin, Heat and Charge Currents in Superconducting Hybrids

We study the large thermoelectric effects arising as a result of strongly coupled spin, heat and charge currents in superconducting hybrids theoretically. Two new frameworks for calculating thermoelectric coefficients are presented, one including the possibility of spin-dependent bias application to homogeneously magnetized materials, and the other utilizing the quasiclassical framework allowing for spin-splitting polarizations along more than one axis. The thermoelectric coefficient governing pure thermal spin currents, the Seebeck coefficient S and the thermoelectric figure of merit ZT are all maximized when tunneling is considered to be across an insulating barrier between two Zeeman-split superconducting reservoirs. The disadvantage of such a configuration is the large external magnetic fields which need be applied for the thermoelectric effects to arise. Therefore, we here present results indicating large thermoelectric effects of similar orders of magnitude arising in superconducting hybrids wherein the particle-hole symmetry is broken without the use of large external magnetic fields. Within the low-field material systems studied, all tunneling occurs from the middle of the central layer in a Josephson junction into a normal-metal electrode. The central nanowire in the Josephson junction (i) contains spatially varying magnetization, (ii) is coupled to spin-active interfaces (such as magnetic insulators) or (iii) has intrinsic spin-orbit interaction of Rashba type

Spin Seebeck effect and thermoelectric phenomena in superconducting hybrids with magnetic textures or spin-orbit coupling

We theoretically consider the spin Seebeck effect, the charge Seebeck coefficient, and the thermoelectric figure of merit in superconducting hybrid structures including either magnetic textures or intrinsic spin-orbit coupling. We demonstrate that large magnitudes for all these quantities are obtainable in Josephson-based systems with either zero or a small externally applied magnetic field. This provides an alternative to the thermoelectric effects generated in high-field (~1 T) superconducting hybrid systems, which were recently experimentally demonstrated. The systems studied contain either conical ferromagnets, spin-active interfaces, or spin-orbit coupling. We present a framework for calculating the linear thermoelectric response for both spin and charge of a system upon applying temperature and voltage gradients based on quasiclassical theory which allows for arbitrary spin-dependent textures and fields to be conveniently incorporated

First-principles calculations of Stark shifts of electronic transitions for defects in semiconductors: the Si vacancy in 4H-SiC

Point defects in solids are promising single-photon sources with application in quantum sensing, computing and communication. Herein, we describe a theoretical framework for studying electric field effects on defect-related electronic transitions, based on density functional theory calculations with periodic boundary conditions. Sawtooth-shaped electric fields are applied perpendicular to the surface of a two-dimensional defective slab, with induced charge singularities being placed in the vacuum layer. The silicon vacancy (VSi) in 4H-SiC is employed as a benchmark system, having three zero-phonon lines in the near-infrared (V1, V1' and V2) and exhibiting Stark tunability via fabrication of Schottky barrier or p-i-n diodes. In agreement with experimental observations, we find an approximately linear field response for the zero-phonon transitions of VSi involving the decay from the first excited state (named V1 and V2). However, the magnitude of the Stark shifts are overestimated by nearly a factor of 10 when comparing to experimental findings. We discuss several theoretical and experimental aspects which could affect the agreement

Stability, Evolution and Diffusion of Intrinsic Point Defects in 4H-SiC

Silicon carbide (SiC) is a wide band-gap semiconductor of great technological importance, showing promise for application areas ranging from quantum computing and communication to power devices. Vital in both the contexts of power devices and quantum technology is the understanding of intrinsic defects that are introduced during various device processing steps, both immediately after their formation and over the course of defect evolution with temperature. Here we monitor the formation and evolution of intrinsic point defects in n-type 4H-SiC after proton irradiation at room temperature and subsequent annealing in the temperature range 300-1000 °C, and discuss the nature and origin of the EH4 and EH5 deep level defects observed by deep level transient spectroscopy around 400-500 K. In particular, the controversy on the nature of the EH5 trap in particular is addressed, where we propose the presence of two overlapping defect peaks: one metastable level that appears after low energy electron irradiation below the silicon displacement limit, and one more stable level that gradually decreases in concentration until an annealing temperature of 1000°C. We argue that the former is likely related to carbon interstitials, while the latter was recently tentatively attributed to the carbon antisite-vacancy pair.ISSN:0255-5476ISSN:1662-975

Formation of carbon interstitial-related defect levels by thermal injection of carbon into n-type 4 H-SiC

Electrical properties of point defects in 4 H-SiC have been studied extensively, but those related to carbon interstitials (C i) have remained elusive until now. Indeed, when introduced via ion irradiation or implantation, signatures related to C i observed by deep level transient spectroscopy tend to overlap with those of other primary defects, making the direct identification of C i-related levels difficult. Recent literature has suggested to assign the so-called M center, often found in as-irradiated 4 H-SiC, to charge state transitions of the C i defect in different configurations. In this work, we have introduced excess carbon into low-doped n-type 150 μm thick 4 H-SiC epilayers by thermal annealing, with a pyrolyzed carbon cap on the sample surface acting as a carbon source. Because the layers exhibited initially low concentrations of carbon vacancies ([V C] = 10 11 cm), this enabled us to study the case of complete V C annihilation and formation of defects due to excess carbon, i.e., carbon interstitials C i and their higher-order complexes. We report on the occurrence of several new levels upon C injection, which are likely C i-related. Their properties are different from those found for the M center, which point toward a different microscopic identity of the detected levels. This suggests the existence of a rich variety of C i-related defects. The study will also help generating new insights into the microscopic process of V C annihilation during carbon injection processes.ISSN:0021-8979ISSN:1089-755

Influence of hydrogen implantation on emission from the silicon vacancy in 4H-SiC

The silicon vacancy (VSi) in 4H-SiC is a room temperature single-photon emitter with a controllable high-spin ground state and is a promising candidate for future quantum technologies. However, controlled defect formation remains a challenge, and, recently, it was shown that common formation methods such as proton irradiation may, in fact, lower the intensity of photoluminescence (PL) emission from VSi as compared to other ion species. Herein, we combine hybrid density functional calculations and PL studies of the proton-irradiated n-type 4H-SiC material to explore the energetics and stability of hydrogen-related defects, situated both interstitially and in defect complexes with VSi, and confirm the stability of hydrogen in different interstitial and substitutional configurations. Indeed, VSi-H is energetically favorable if VSi is already present in the material, e.g., following irradiation or ion implantation. We demonstrate that hydrogen has a significant impact on electrical and optical properties of VSi, by altering the charge states suitable for quantum technology applications, and provide an estimate for the shift in thermodynamic transition levels. Furthermore, by correlating the theoretical predictions with PL measurements of 4H-SiC samples irradiated by protons at high (400 C) and room temperatures, we associate the observed quenching of VSi emission in the case of high-temperature and high-fluence proton irradiation with the increased mobility of Hi, which may initiate VSi-H complex formation at temperatures above 400 C. The important implication of hydrogen being present is that it obstructs the formation of reliable and efficient single-photon emitters based on silicon vacancy defects in 4H-SiC