Electron Mean Free Path Research Articles

Photographic Analysis of a Low-Current, Vacuum Electric Arc Using an Ultrafast Camera

The main component of vacuum interrupters responsible for ensuring the correct flow of current is the contact system. In a vacuum environment, due to the higher values of the mean free path of electrons and particles in the contact gap, the material and condition of the contacts exert the greatest influence on the development of the arc discharge. To accurately analyze the phenomenon of discharge development in vacuum insulating systems, the authors conducted a time-lapse photographic analysis of a vacuum electric arc. For this purpose, they used a test setup comprising a discharge chamber, a vacuum pump set, a power and load assembly, an ultra-high-speed camera, and an oscilloscope with dedicated probes. The measurement process involved connecting the system, determining the power supply, load, and measurement parameters and subsequently performing contact opening operations while simultaneously recording the process using the oscilloscope and ultra-high-speed camera. An analysis of a low-current vacuum arc in a residual helium gas environment, with a pressure of p = 1.00 × 101 Pa was carried out. Different phases of vacuum arc burning between electrodes in the discharge chamber were identified. In the stable phase, the arc voltage remained constant, while in the unstable phase, the arc voltage increased. The results of the time-lapse analysis were compared with the characteristics recorded by the oscilloscope, revealing a correlation between the increase in vacuum arc voltage and the intensity of flashes in the interelectrode space. The movement of microparticles ejected from the surface of the contacts—either reflecting or adhering to one of the electrodes—was observed. This analysis provides a deeper understanding of the processes involved in discharge formation and development under reduced pressure conditions. Understanding these mechanisms can support the design of vacuum interrupters, particularly in the selection of suitable contact materials and shapes.

Nonclassical Optical Response of Particle Plasmons With Quantum‐Informed Local Optics

AbstractAs the dimensions of plasmonic structures or the field confinement length approach the mean free path of electrons, mesoscopic optical response effects, including nonlocality, electron spill‐in or spill‐out, and Landau damping, are expected to become observable. In this work, a quantum‐informed local analogue model (QILAM) that maps these nonclassical optical responses onto a local dielectric film is presented. The primary advantage of this model lies in its compatibility with the highly efficient boundary element method (BEM), which includes retardation effects with relatively large particle sizes. Furthermore, the approach offers a unified framework that connects two important semiclassical theories: the generalized nonlocal optical response (GNOR) theory and the Feibelman d‐parameters formalism. It is envisioned that QILAM can evolve into a multiscale electrodynamic tool for exploring nonclassical optical responses in diverse plasmonic structures in the future. This can be achieved by directly translating mesoscopic effects into observable phenomena, such as plasmon resonance energy shifts and linewidth broadening in the scattering spectrum.

(Invited) Epitaxial Electrodeposition of Metals for Interconnects Beyond Cu

Cu has been the metal of choice for interconnects in silicon microprocessors since the mid-1990s. The continuous scaling of these interconnects in CMOS technology has not only produced a challenge with respect to power consumption and computing performance, but also with respect to reliability. As the critical dimensions of interconnects are scaled towards, and then below the electron mean free path (EMFP) of Cu (39 nm at room temperature), the resistivity is found to increase. This increase, termed the resistivity size-effect, results in resistance scaling beyond Ohm’s law dimensional scaling and leads to even larger power consumption and further limits improvements in computing performance. The resistivity rise with decreasing dimension is a result of electron scattering at grain boundaries and surfaces (vs. phonons). Given that electron scattering from grain boundaries is the major contributor to the resistivity rise in nanoscale interconnects, there has been increasing interest in producing and evaluating epitaxial, single-crystal conductors absent of grain boundaries. In this presentation, epitaxial electrodeposition of Co, Ru and Cu at room-temperature is reviewed. The choice of seed layer for electrodeposition, the role of symmetry of the seed layer and the epitaxial orientation relationship of the electrodeposited film and the seed layer are discussed. In addition, the impact of underpotential deposition on film nucleation and growth morphology is examined. The effects of electrolyte, ion concentration and pH are also addressed. Potential pathways for implementation of epitaxial electrodeposition in back-end-of-line processing will be discussed.

(Invited) New Materials for High-Conductivity Interconnects

The resistivity of interconnect lines and vias increases with decreasing dimensions. This is due to diffuse electron scattering at surfaces and grain boundaries and leads to, for example, a 10-fold resistance increase for 10-nm-wide Cu lines, causing power consumption and signal delay. Alternative interconnect materials have the potential to outperform Cu if they have a small electron mean free path to render electron scattering at surfaces and grain boundaries negligible. In addition, high-conductivity is facilitated by engineering metal-liner interfaces which minimize charge transfer, leading to specular surface scattering. This talk presents experimental and computational results to illustrate approaches to minimize the resistivity size effect, including transport measurements on epitaxial layers which quantify the intrinsic resistivity scaling and electron interface scattering. It also discusses new materials solutions for high conductivity interconnects including materials with anisotropic Fermi surfaces with preferential transport along the wire direction and compounds with topologically protected conductive surface states.

Plasmonic properties of silicon nitride encapsulated copper

We investigated the optical properties (i.e. plasmonic loss) of thin-film copper that was deposited and processed in a 300mm CMOS pilot line. The optical properties at 1550 nm (QSPP,Cu = 3921 ± 350) were evaluated by measuring the propagation loss of dielectric loaded plasmonic waveguides on samples with high and low root mean square surface roughness (Rq) with and without a silicon nitride diffusion barrier and at room temperature and cryogenic temperatures. In our fabrication result, the average grain size is 2.08±0.05μm, which is much larger than the mean free path of free electrons in copper, so the surface roughness becomes the main cause of the waveguide propagation loss from the fabrication constrains. Further, we show that copper can be encapsulated by a 15 nm silicon nitride diffusion and oxidation barrier without degrading the optical properties.

Evaluating size effects on the thermal conductivity and electron-phonon scattering rates of copper thin films for experimental validation of Matthiessen’s rule

As metallic nanostructures shrink towards the size of the electronic mean free path, thermal conductivity decreases due to increased electronic scattering rates. Matthiessen’s rule is commonly applied to assess changes in electron scattering rates, although this rule has not been validated experimentally at typical operating temperatures for most of the electronic systems (e.g., near room temperature). In this study, we experimentally evaluate the validity of Matthiessen’s rule in determining the thermal conductivity of thin metal films by measuring the in-plane thermal conductivity and electronic scattering rates of copper (Cu) films with varying thicknesses (27 nm — 5 µm), microstructures, and grain boundary segregation. Comparing total electron scattering rates measured with infrared ellipsometry to infrared ultrafast pump-probe measurements, we find that the electron-phonon coupling factor is independent of film thickness, whereas the total electronic scattering rate increases with decreasing film thickness. Our findings provide experimental validation of Matthiessen’s rule for electron transport in thin metal films at room temperature and also introduce an approach to discern critical heat transfer processes in thin metal interconnects, which holds significance for the advancement of future CMOS technology.

Plasmonic enhancement of Faraday rotation with gold nanodisks with low height-to-diameter aspect ratios

We investigate the Faraday rotation induced in gold nanodisks with low height-to-diameter aspect ratios. Through a systematic study, we analyze the phenomenon using electrostatic theory with the modified long-wavelength approximation. We show that the Faraday rotation is enhanced at the localized surface plasmon resonance when the nanodisk’s effective mean free path is equal to the mean free path of the conduction electrons in the bulk metal, where light absorption dominates over light scattering. We also show that the Faraday rotation is largely enhanced at shorter rather than longer wavelengths.

High-Performance Planar Broadband Hot-Electron Photodetection through Platinum-Dielectric Triple Junctions.

Recently, planar and broadband hot-electron photodetectors (HE PDs) were established but exhibited degraded performances due to the adoptions of the single-junction configurations and the utilizations of absorbable films with thicknesses larger than the electronic mean free path. In this work, we present a five-layer design for planar HE PDs assisted by triple junctions in which an ultrathin Pt layer dominates the broadband and displays strong optical absorption (>0.9 from 900 nm to 1700 nm). Optical studies reveal that the optical admittance matching between optical admittances of designed device and air at all interested wavelengths is responsible for broadband light-trapping that induces prominent energy depositions in Pt layers. Electrical investigations show that, benefitting from suppressed hot-electron transport losses and increased hot-electron harvesting junctions, the predicted responsivity of the designed HE PD is up to 8.51 mA/W at 900 nm. Moreover, the high average absorption (responsivity) of 0.96 (3.66 mA/W) is substantially sustained over a broad incidence angle regardless of the polarizations of incident light. The comparison studies between five-layer and three-layer devices emphasize the superiority of five-layer design in strong optical absorption in Pt layers and efficient hot-electron extraction.

Achieving a Noise Limit with a Few-layer WSe2 Avalanche Photodetector at Room Temperature.

We engineered a two-dimensional Pt/WSe2/Ni avalanche photodetector (APD) optimized for ultraweak signal detection at room temperature. By fine-tuning the work functions, we achieved an ultralow dark current of 10-14 A under small bias, with a noise equivalent power (NEP) of 8.09 fW/Hz1/2. This performance is driven by effective dark barrier blocking and a record-long electron mean free path (123 nm) in intrinsic WSe2, minimizing dark carrier replenishment and suppressing noise under an ultralow electric field. Our APD exhibits a high gain of 5 × 105 at a modulation frequency of 20 kHz, effectively balancing gain and bandwidth, a common challenge in traditional photovoltaic-based APDs. By addressing the typical challenges of high noise and low gain and minimizing dependence on high electric fields, this work highlights the potential of 2D materials in developing efficient, low-power, and ultrasensitive photodetections.

The Effect of Relative Humidity in Conductive Atomic Force Microscopy.

Conductive atomic force microscopy (CAFM) analyzes electronic phenomena in materials and devices with nanoscale lateral resolution, and it is widely used by companies, research institutions, and universities. Most data published in the field of CAFM is collected in air at a relative humidity (RH) of 30-60%. However, the effect of RH in CAFM remains unclear becauseprevious studies often made contradictory claims, plus the number of samples and locations tested is scarce. Moreover, previous studies on this topic didnot apply current limitations, which can degrade the CAFM tips and generate false data. This article systematically analyzes the effect of RH in CAFM by applying ramped voltage stresses at over 17,000 locations on ten different samples (insulating, semiconducting, and conducting) under seven different RH. An ultra-reliable setup with a 110-pA current limitation during electrical stresses is employed, andexcellent CAFM tip integrity after thousands of tests is demonstrated. It is found that higher RH results in increased currents due to the presence of a conductivewater meniscus at the tip/sample junction, which increases the effective area forelectron flow. This trend is observed in insulators and ultra-thin semiconductors; however, in thicker semiconductors the electron mean free path is high enough to mask this effect. Metallic samples show no dependence on RH. This study clarifies the effect of relative humidity in CAFM, enhances understanding of the technique, and teaches researchers how to improve the reliability of their studies in this field.

The electron resistance of a single skyrmion within ballistic approach

An alternative way of skyrmion quasi-particle detection is simulated at low voltage bias. The point contact (PC), attached to the strip with a Néel-type skyrmion, can detect it with a higher efficiency than a magnetic tunnel junction. The method is based on detecting the skyrmion via the ballistic magnetoresistance ratio (BRR). PC's resistance with skyrmion significantly differs from the one without it. BRR is estimated in the framework of the point contact model for two directions of spin-polarized current: perpendicular to the transport direction (case 1) and along one (case 2). Skyrmion's size is assumed to be around 3.6 nm in diameter—smaller, or comparable, to the mean free path of electrons, allowing it to utilize the ballistic transport approach. As a result, resistance values for the considered Néel type skyrmion within the related size are estimated as 157 Ω for case 1 and 452.2 Ω for case 2 with optimistic BRR 101.3% and 291.7%, respectively. BRR for case 2 is higher due to the spin-filtering effect. The method also has the potential to detect the skyrmion type, or other magnetic nano structures such as bimeron, domain wall (DW), etc.

A Detailed Survey of the Parallel Mean Free Path of Solar Energetic Particle Protons and Electrons

In this work, more than a dozen solar energetic particle (SEP) events are identified where the source region is magnetically well connected to at least one spacecraft at 1 au. The observed intensity–time profiles, for all available proton and electron energy channels, are compared to results computed using a numerical one-dimensional SEP transport model in order to derive the parallel mean free paths (pMFPs) as a function of energy (or rigidity) at 1 au. These inversion results are then compared to theoretical estimates of the pMFP, using observed turbulence quantities with observationally motivated variations as input. For protons, a very good comparison between inversion and theoretical results is obtained. It is shown that the observed inter-event variations in the inversion pMFP values can be explained by natural variations in the background turbulence values. For electrons, there is relatively good agreement with pMFPs derived assuming the damping model of dynamical turbulence, although the theoretical values are extremely sensitive to the details of the turbulence dissipation range, which themselves display a high level of variation.

The Growth of V5S8 Single Crystals by Chemical Vapour Transport

Single crystals of the d-electron antiferromagnetic metal V5S8 can be prepared by chemical vapour transport with gaseous iodine as a transport agent. We present the outcomes of an endeavour to synthesise high-purity single crystals of V5S8 with reduced crystalline disorder, important to the formation of novel quantum orders. We report results on the residual resistivity ratio of the single crystals as growth parameters are varied including growth temperature, temperature gradient and pre-growth processing of the initial apparatus and reagents. We demonstrate that single crystals of at least a few mm in size can be successfully grown at relatively low temperatures in the range 550–600 °C. The optimisation of this method may imply a better crystallographic organisation, reducing sulphur vacancies and increasing vanadium positional order. The resulting longer electron mean free paths may enhance the probability of finding exotic quantum states of matter at low temperatures. The results presented here may also be of relevance to the development of vanadium sulphide-based energy storage and spintronic devices.

Field, frequency, and temperature dependencies of the surface resistance of nitrogen diffused niobium superconducting radio frequency cavities

We investigate the rf performance of several single-cell superconducting radio-frequency cavities subjected to low temperature heat treatment in nitrogen environment. The cavities were treated at temperature 120–165 °C for an extended period of time (24–48 h) either in high vacuum or in a low partial pressure of ultrapure nitrogen. The improvement in Q0 with a Q rise was observed when nitrogen gas was injected at ∼300 °C during the cavity cooldown from 800 °C and held at 165 °C, without any degradation in accelerating gradient over the baseline performance. The treatment was applied to several elliptical cavities with frequency ranging from 0.75 to 3.0 GHz, showing an improved quality factor as a result of low temperature nitrogen treatments. The Q rise feature is similar to that achieved by nitrogen alloying Nb cavities at higher temperature, followed by material removal by electropolishing. The surface modification was confirmed by the change in electronic mean free path and tuned with the temperature and duration of heat treatment. The decrease of the temperature-dependent surface resistance with increasing rf field, resulting in a Q rise, becomes stronger with increasing frequency and decreasing temperature. The data suggest a crossover frequency of ∼0.95 GHz above that the Q rise phenomenon occurs at 2 K. Some of these results can be explained qualitatively with an existing model of intrinsic field-dependence of the surface resistance with both equilibrium and nonequilibrium quasiparticle distribution functions. The change in the Q slope below 0.95 GHz may result from masking contribution of trapped magnetic flux to the residual surface resistance. Published by the American Physical Society 2024

Time-dependent density-functional theory study on nonlocal electron stopping for inertial confinement fusion

Understanding laser–target coupling is of the utmost importance for achieving high performance in laser-direct-drive (LDD) inertial confinement fusion (ICF) experiments. Thus, accurate modeling of electron transport and deposition through ICF-relevant materials and conditions is necessary to quantify the total thermal conduction and ablation. The stopping range is a key transport quantity used in thermal conduction models; in this work, we review the overall role that the electron mean free path (MFP) plays in thermal conduction and hydrodynamic simulations. The currently used modified Lee–More model employs various physics approximations. We discuss a recent model that uses time-dependent density functional theory (TD-DFT) to eliminate these approximations in both the calculation of the electron stopping power and corresponding MFP in conduction zone polystyrene (CH) plasma. In general, the TD-DFT calculations showed a larger MFP (lower stopping power) than the standard modified Lee–More model. Using the TD-DFT results, an analytical model for the electron deposition range, λTD−DFT(ρ,T,K), was devised for CH plasmas between ρ=[0.05−1.05] g/cm3, kBT=[100−1000] eV. We implemented this model into LILAC, for simulations of a National Ignition Facility-scale LDD implosion and compared key physics quantities to ones obtained by simulations using the standard model. The implications of the obtained results and the path moving forward to calculate this same quantity in conduction-zone deuterium–tritium plasmas are further discussed, to hopefully close the understanding gap for laser target coupling in LDD-ICF simulations.

Electrical and thermal properties of bio-inspired laminated Cu/Ti3SiC2/C composites reinforced by graphene nanoplatelets

Taking inspiration from the unique hierarchical structure of bio-materials like pearl oyster, this study employs bio-inspired composites technological route using flake powder metallurgy to prepare laminated Cu/Ti3SiC2/C composites. The prepared composites have clear laminated structure, uniform dispersion of reinforcing phase and clean interface. At a Cu-plated GNPs content of 0.5 wt%, the composites displayed tensile strength of 300.65 MPa, compressive strength of 575.32 MPa, electrical conductivity of 26.31 MS/m, and thermal conductivity of 285.87 W·m−1·K−1. The reinforcement of composites is caused by the load transfer effect of the laminated structure. During the loading process, the laminated structure creates multiple paths for deflecting cracks, which leads to the redistribution of the applied load. Moreover, the homogeneous distribution of GNPs throughout the laminated structure extends the mean free path of both free electrons and phonons within the material, consequently bolstering the electrical and thermal conductivity of the composites.

Dynamic characteristics of edge plasma profiles during the opening of edge islands on the J-TEXT tokamak

On the J-TEXT tokamak, the dynamics of edge magnetic topology during the opening of the edge magnetic islands induced by the external Resonant Magnetic Perturbation (RMP) are investigated. The edge island chain is pushed outward by increasing plasma toroidal current to intersect the poloidally and toroidally localized divertor plate, forming an open magnetic island in the Scrape-Off Layer (SOL). The location of the strike points on the divertor plate predicted by the HINT code is in agreement with the experimental observations. The influence of the magnetic topology on edge plasma profiles has also been investigated using Langmuir probes. The properties of edge Te , ne , Pe and Er profiles are studied as function of three magnetic structures in qa -dependence experiments and two magnetic structures in RMP configuration-dependence experiments. Some common features are observed. Inside the edge closed and SOL remnant islands, flat Pe but non-flat Te and ne profiles are detected. When transitioning from the edge closed island to the partially open island with remnant island, the local flat Pe profile is shifted outward accompanied by a narrower flattened Pe region. The steep slopes of Te , ne and Pe are measured in the SOL regions characterized by a long connection length Lc , and the longer Lc , the steeper slopes. Er exhibits a negative well inside the remnant island with infinite Lc and in the SOL regions where Lc significantly exceeds than the electron mean free path λe , but develops a positive value in the SOL regions where Lc is relatively short.

RuAl intermetallic compound of low resistivity scaling and high thermal stability as potential interconnect metallization

Thin films of single-phase ruthenium aluminide (RuAl) intermetallic compound were deposited by magnetron co-sputtering. An ordered B2 body-centered cubic structure of high crystallinity was formed after rapid thermal annealing at 800 °C for 1 min. Data fittings using the Fuchs–Sondheimer and Mayadas–Shatzkes models suggested the very short mean free path of electrons of below 5 nm and the high specularity parameter of 0.9. The short mean free path and the much reduced diffuse scattering of electrons at the interface effectively suppressed the resistivity scaling of the B2 RuAl intermetallic compound as compared to ruthenium metal. At an ultra-small film thickness of below 5 nm, the reflection of electrons by grain boundaries or domain walls might alternatively dominate the increase in resistivity. The RuAl intermetallic compound with an ordered B2 structure and a high cohesive energy (a large negative mixing enthalpy) also demonstrated a superior thermal stability at an extreme temperature up to 900 °C. It could be a promising candidate for potential use as the next-generation interconnect metallization without the need of a diffusion barrier.

Properties of low-resistivity molybdenum metal thin film deposited by atomic layer deposition using MoO2Cl2 as precursor

Challenges have arisen in selecting suitable candidates for interconnects and metal contacts due to the exponential increase in metal resistivity at scaled pitches. Molybdenum (Mo) has emerged as a promising alternative to the traditional metals such as copper or tungsten owing to its low electrical resistivity and electron mean free path. In this study, we investigated the formation of a molybdenum film grown by thermal atomic layer deposition (ALD) using a MoO2Cl2 solid precursor and H2 and NH3 gases as the reducing agents. A molybdenum nitride film served as the seed layer on a SiO2 substrate before molybdenum film deposition. The analysis focused on the film's phase, morphology, chemical bonding states, and resistivity across various thicknesses. X-ray diffraction (XRD) confirmed the presence of polycrystalline BCC planes. Our analyses confirmed the successful growth of the molybdenum metal thin film, which, at a thickness of 10 nm, exhibited a record-low resistivity of approximately 13 μΩ cm.

Electron-phonon coupling dictates electron mean free paths and negative thermal diffusion in metals

The spatiotemporal dynamics of the fundamental energy carriers in metals underpin the efficiency of a wide array of technologies. Although much progress in our understanding of the temporal response of electronic relaxation processes following an external field perturbation has been achieved, the spatial relaxation dynamics of electrons after excitation remains unclear. Here, we employ a scanning ultrafast microscopy with high spatial resolution to directly measure the mean free paths of electrons in different metals. We show that the strength of electron-phonon coupling not only dictates the mean free paths, but also controls a peculiar spatial shrinking of the electronic temperature profile immediately after the electrons have thermalized with the ‘colder’ lattice. More specifically, from our experimental tracking of the spatial relaxation profiles, a clear observation of an effective negative thermal diffusion is apparent for metals with weaker electron-phonon coupling, while for metals with stronger electron-phonon coupling, the negative thermal diffusion effect is not observable. Our spatiotemporal modeling based on the two-temperature approach provides evidence that although negative diffusion occurs universally for materials with two different species that have varying diffusivities and are thermodynamically coupled, effective negative diffusion is masked for cases with stronger coupling between the species.