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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A new mechanism for void-cascade interaction from nondestructive depth-resolved atomic-scale measurements of ion irradiation–induced defects in Fe

The nondestructive investigation of single vacancies and vacancy clusters in ion-irradiated samples requires a depth-resolved probe with atomic sensitivity to defects. The recent development of short-pulsed positron beams provides such a probe. Here, we combine depth-resolved Doppler broadening and positron annihilation lifetime spectroscopies to identify vacancy clusters in ion-irradiated Fe and measure their density as a function of depth. Despite large concentrations of dislocations and voids in the pristine samples, positron annihilation measurements uncovered the structure of vacancy clusters and the change in their size and density with irradiation dose. When combined with transmission electron microscopy measurements, the study demonstrates an association between the increase in the density of small vacancy clusters with irradiation and a remarkable reduction in the size of large voids. This, previously unknown, mechanism for the interaction of cascade damage with voids in ion-irradiated materials is a consequence of the high porosity of the initial microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Interface effect of Fe and Fe 2 O 3 on the distributions of ion induced defects

The stability of structural materials in extreme nuclear reactor environments—with high temperature, high radiation, and corrosive media—directly affects the lifespan of the reactor. In such extreme environments, an oxide layer on the metal surface acts as a passive layer protecting the metal underneath from corrosion. To predict the irradiation effect on the metal layer in these metal/oxide bilayers, nondestructive depth-resolved positron annihilation lifetime spectroscopy (PALS) and complementary transmission electron microscopy (TEM) were used to investigate small-scale defects created by ion irradiation in an epitaxially grown (100) Fe film capped with a 50 nm Fe 2 O 3 oxide layer. In this study, the evolution of induced vacancies was monitored, from individual vacancy formation at low doses—10 –5 dpa—to larger vacancy cluster formation at increasing doses, showing the sensitivity of positron annihilation spectroscopy technique. Furthermore, PALS measurements reveal how the presence of a metal–oxide interface modifies the distribution of point defects induced by irradiation. TEM measurements show that irradiation induced dislocations at the interface is the mechanism behind the redistribution of point defects causing their accumulation close to the interface. Finally, this work demonstrates that the passive oxide layers formed during corrosion impact the distribution and accumulation of radiation induced defects in the metal underneath and emphasizes that the synergistic impact of radiation and corrosion will differ from their individual impacts.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Identification of Auger mechanisms responsible for low energy electron emission from graphene on copper using Auger-gamma coincidence spectroscopy

We have applied positron annihilation induced Auger-gamma coincidence spectroscopy to identify important mechanisms responsible for the emission of low energy electrons following the sudden creation of holes in bilayer graphene on copper substrate. The novel surface spectroscopic method measures the energy of the Doppler shifted annihilation gamma photon in coincidence with the Auger electron emitted following the relaxation of the hole created by the annihilation of a surface electron with a surface trapped positron. By extracting and theoretically modelling the annihilation gamma spectra coincident with low energy electrons, we associate majority of the intensity in the low energy (7 eV–25 eV) region of the Auger spectrum to electron emission following Auger decays of 2s holes in adsorbed oxygen and deep valence holes in graphene. We provide additional support to this conclusion by showing that most of the Auger electrons with energy less than ~ 25 eV are coincident with gamma photons with small Doppler shift (511 keV–512 keV) indicating that the primary electron whose annihilation resulted in low energy Auger electron emission had small momentum parallel to the gamma emission direction. On the other hand, majority of the Auger electrons measured in coincidence with the photons having maximum Doppler shift (515 keV–521 keV) were emitted following the decay of core holes (C 1s and O 1s). Furthermore, by selecting annihilation gamma photons coincident only with the O KVV (from surface adsorbed oxygen), C KVV (graphene), and Cu MVV (copper substrate) Auger electrons, we have also experimentally derived the energy spectrum of Doppler shifted gamma photons resulting from the annihilation of positrons with 1s electrons of O, 1s electrons of C and 3p electrons of Cu respectively. Model Doppler broadened gamma spectra produced using ab-initio calculations agree well with the experimentally derived line shapes. This demonstrates the ability of Auger-gamma coincidence method to experimentally resolve the Doppler broadened annihilation gamma spectrum from surfaces into its veiled electronic level constituents which has, heretofore, relied solely on theoretical analysis. Our results also demonstrate that the line shape of the Doppler broadened annihilation gamma peak reflect the chemical composition of the topmost atomic layer and can thus be used to characterize both external and inaccessible surfaces of porous materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Influence of neutrino-electron scattering and neutrino-pair annihilation on hypermassive neutron star

Here, we investigate the influence of inelastic neutrino microphysics in general-relativistic magnetohydrodynamics simulations of a hypermassive neutron star. In particular, we include species/energy groups coupled neutrino-matter interactions, such as inelastic neutrino-electron scattering and electron-positron annihilation kernels, into simulations up to 50 ms. Neutrino-electron inelastic scattering is known to have effective neutrino-matter energy exchange. We show that, with neutrino-electron inelastic scattering, simulations predict 75% higher disc mass with slightly different mass-averaged compositions, and 18% more ejected mass with similar distributions. The enhancement of the mass of the disc and the ejecta results in stronger baryon pollution, leading to less favorable jet launching environments. Furthermore, neutrino luminosities are about 50%, 40%, and 30% higher for electron neutrino, electron antineutrino, and heavy-lepton neutrinos. In contrast, we do not see any significant impacts due to electron-positron annihilation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Light dark matter searches with positrons

We discuss two complementary strategies to search for light dark matter (LDM) exploiting the positron beam possibly available in the future at Jefferson Laboratory. LDM is a new compelling hypothesis that identifies dark matter with new sub-GeV “hidden sector” states, neutral under standard model interactions and interacting with our world through a new force. Accelerator-based searches at the intensity frontier are uniquely suited to explore it. Thanks to the high intensity and the high energy of the Continuous Electron Beam Accelerator Facility (CEBAF) beam, and relying on a novel LDM production mechanism via positron annihilation on target atomic electrons, the proposed strategies will allow us to explore new regions in the LDM parameters space, thoroughly probing the LDM hypothesis as well as more general hidden sector scenarios.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Identification and Suppression of Point Defects in Bromide Perovskite Single Crystals Enabling Gamma‐Ray Spectroscopy

Abstract Methylammonium lead tribromide (MAPbBr 3 ) stands out as the most easily grown wide‐band‐gap metal halide perovskite. It is a promising semiconductor for room‐temperature gamma‐ray ( γ ‐ray) spectroscopic detectors, but no operational devices are realized. This can be largely attributed to a lack of understanding of point defects and their influence on detector performance. Here, through a combination of crystal growth design and defect characterization, including positron annihilation and impedance spectroscopy, the presence of specific point defects are identified and correlated to detector performance. Methylammonium (MA) vacancies, MA interstitials, and Pb vacancies are identified as the dominant charge‐trapping defects in MAPbBr 3 crystals, while Br vacancies caused doping. The addition of excess MABr reduces the MA and Br defects and so enables the detection of energy‐resolved γ ‐ray spectra using a MAPbBr 3 single‐crystal device. Interestingly, the addition of formamidinium (FA) cations, which converted to methylformamidinium (MFA) cations by reaction with MA + during crystal growth further reduced MA defects. This enabled an energy resolution of 3.9% for the 662 keV 137 Cs line using a low bias of 100 V. The work provides direction toward enabling further improvements in wide‐bandgap perovskite‐based device performance by reducing detrimental defects.

Ni, Zhenyi↗
DOE OSTI2020

The Beam Dump eXperiment

Hadronic matter makes about 14% of the known universe. The remaining 86% is Dark Matter (DM). Since it does not interact with the ordinary matter via electromagnetic force, DM is not visible and, to date, it escaped detection. The search for Dark Matter (DM) is one of the hottest topic in modern physics. Despite the increasing number of astrophysical and cosmological observations proving the existence, so far no particle physics experiment has detected DM yet. Up to now, most of the experimental efforts have been focused on the so called WIMP (Weakly Interacting Massive Particle) paradigm, which predicts heavy DM (10 GeV-10 TeV mass range) interacting with Standard Model (SM) particles via the weak force mediators (W or Z bosons). More recently, due to the lack of clear evidence of WIMPs, other models of DM gained the interest of the physics community. These models consider Light DM particles (LDM), in MeV-GeV mass range. Among LDM theories, the Dark Photon theory predicts the existence of a Dark Sector interacting with SM particles via a new massive vector boson (Dark Photon, Heavy Photon or A0), mediator of a new force. This scenario, despite being theoretically well motivated, is remarkably experimentally unexplored. The Beam Dump eXperiment (BDX), is an approved experiment at Jefferson Lab (JLab), aiming to discover the DM predicted witihn the Dark Photon theory. The experiment uses the CEBAF (Continuous Electron Beam Accelerator Facility) 11 GeV electron beam, impinging on the JLab Hall-A beam-dump, to produce a beam of DM particles, detected by a ~ 1 m3 detector made of thallium doped cesium iodide (CsI(Tl)) crystals located ~ 20 m downstream. In order to achieve excellent background rejection, the experimental setup includes active vetos and passive shielding surrounding CsI(Tl) crystals. Given the weakness of the DM-SM interaction, the scattering of a DM particle in the BDX detector is a rare event. Therefore, the characterization of the expected background is a critical aspect of the experiment. Both cosmogenic and penetrating SM particles produced by the beam interaction in the dump contribute to the background of the experiment. While the cosmogenic contribution can be measured during the experiment when the beam is off, beam-related background can only be estimated via Monte Carlo (MC) simulations. Therefore, a careful assessment of possible systematics introduced by the MC is needed. The beam-correlated background characterization was made by measuring the muon flux produced by the interaction of the CEBAF beam with Hall-A dump in a dedicated experimental campaign in spring 2018 [1]. The comparison to the ?ux predicted by MC allowed us to validate the BDX simulation framework. The reach of BDX, i.e. the region that the experiment can probe in the LDM theory parameter space, depends critically on the background rejection capability and signal detection effciency. For this reason, the detector setup was fine-tuned through a dedicated study. The response to LDM and background events was evaluated for different setups and selection cuts. As a result of this procedure, the configuration resulting in the best sensitivity was selected [2]. The reach calculation was performed taking into account the different LDM production mechanisms, including the contribution of secondary particles produced in the beam-dump. In particular, the effect of the secondary positrons annihilation was found to be extremely significant. In the majority of the sensitivity studies, this contribution is neglected, but recent results [3] [4] demonstrated that this process significantly enhances the sensitivity of lepton beam-dump experiments. Currently, the BDX collaboration is focused on the deployment and operation of a small detector, called BDX-MINI, built to perform a preliminary physics measurement searching for LDM at JLab. This test will pave the way to the realization of the full BDX experiment. The measurement is currently ongoing but results are expected by the end of this year. During my PhD I was involved in all aspects of the BDX experiment: design, simulation, prototyping and data analysis. The main results of my work are reported in this thesis. This manuscript is organized as follows: the first Chapter provides an introduction to the theory of LDM, with particular attention to the Dark Photon paradigm; the second Chapter illustrates the BDX experimental setup, the LDM production and detection mechanisms and the expected backgrounds; Chapter 3 and 4 describe, respectively, the BDX-HODO measurement, with a detailed description of the simulations, and the BDX experimental setup and analysis cuts optimization. Chapter 5 reports about BDXMINI detector characterization, calibration and sensitivity estimate. Finally, Chapter 6 describes in detail the calculation of the secondary positron annihilation contribution to the sensitivity of BDX and other electron-beam thick-target experiment.

Marsicano, Luca↗
DOE OSTI2021

The Energy-Energy Correlation in the back-to-back limit at N 3 LO and N 3 LL'

We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N 3 LO) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation — the jet function — from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at N 3 LO. We combine the newly obtained N 3 LO jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in N = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at N 3 LL' accuracy, resulting in a factor of ~ 4 reduction of uncertainties in the peak region compared to N 3 LL predictions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Microstructural dependence of defect formation in iron-oxide thin films

In this report passivating iron-oxide films are grown atop iron films simulating the corrosion process in a nuclear reactor environment. Two oxide films grown via physical vapor deposition at 600 °C and room temperature exhibited dense-epitactic and columnar-polycrystalline, microstructures respectively. A third oxide film grown in open air at 600 °C exhibited an eqiuaxed, porous morphology. Cubic maghemite and magnetite phases in each oxide film were identified via grazing incidence X-ray diffraction. Positron annihilation spectroscopy was used to characterize point defects and measure their depth and size distributions in each oxide layer and showed a range of average positron lifetimes from 0.23 ns in the high temperature, vapor deposited film, 0.35 ns in the room temperature-grown film, and 0.31 ns in the thermally grown oxide. These data indicate that the film morphology, which varies greatly in these films, leads to very different defect content. Finally, four-dimensional scanning transmission electron microscopy was used to measure the internal stress of each film and was correlated to the strain state presented in the X-ray diffraction spectra. The defect formation in each film is reasoned through using a thin film growth model.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Development of a pulsed, variable-energy positron beam for atomic scale defect studies

Positron annihilation spectroscopy provides a sensitive means of non-destructive characterization of materials, capable of probing single atom vacancies in solids with 10 –7 sensitivity. Here, in this work, we detail the development of a magnetically guided, variable energy, pulsed positron beam designed to conduct depth-dependent defect studies in metals, semiconductors, and dielectrics, which will be the first of its kind in the United States. The design of the target stage provides capabilities for measurements during in situ annealing up to 800 °C and incorporates a new approach to minimize the background due to energetic backscattered positrons. The developed beam at Bowling Green State University provides a powerful tool for characterization of thin films, devices, and ion irradiated materials.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Vacancy complexes in Cd 3 As 2

Epitaxial growth of the three-dimensional topological semimetal Cd 3 As 2 on semiconductor substrates enables its use and integration in device applications. Epitaxy also provides an avenue for varying and controlling point defects through modification of the chemical potential during growth. In turn, knowledge of the point defects that are generated in Cd 3 As 2 epilayers will aid the interpretation of electron transport behavior and guide growth efforts to produce material with low defect densities. Point defects in Cd 3 As 2 epilayers grown by molecular beam epitaxy with varying As/Cd flux ratios are probed by positron annihilation spectroscopy. We find that lower As/Cd flux ratios produce higher concentrations of point defects. Remarkably, the measurements indicate that the average defect size is larger than a monovacancy. The data presented here contribute to an evolving picture of vacancy point defects in Cd 3 As 2 and can be used to direct future investigation of the defect-transport relationships in this emerging electronic material.

36 MATERIALS SCIENCE↗
DOE OSTI2023

CDB-AP: An application for coincidence Doppler broadening spectroscopy analysis

Coincidence Doppler Broadening (CDB) Positron Annihilation Spectroscopy (PAS) is a material analysis technique that can be used to non-destructively measure characteristics of structural defects in samples. Analyzing and comparing large datasets obtained using this technique, however, can be complicated and time intensive. The Coincidence Doppler Broadening Analysis Program (CDB-AP) is a graphical user interface that facilitates rapid analysis of many data files while using transparent processes. It is already used in three laboratories at Idaho National Laboratory and can be used in laboratories worldwide.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Elucidating Primary Degradation Mechanisms in High-Cycling-Capacity, Compositionally Tunable High-Entropy Hydrides

The hydrogen sorption properties of single-phase bcc (TiVNb) 100–x Cr x alloys (x = 0–35) are reported. All alloys absorb hydrogen quickly at 25 °C, forming fcc hydrides with storage capacity depending on the Cr content. Here, a thermodynamic destabilization of the fcc hydride is observed with increasing Cr concentration, which agrees well with previous compositional machine learning models for metal hydride thermodynamics. The steric effect or repulsive interactions between Cr–H might be responsible for this behavior. The cycling performances of the TiVNbCr alloy show an initial decrease in capacity, which cannot be explained by a structural change. Pair distribution function analysis of the total X-ray scattering on the first and last cycled hydrides demonstrated an average random fcc structure without lattice distortion at short-range order. If the as-cast alloy contains a very low density of defects, the first hydrogen absorption introduces dislocations and vacancies that cumulate into small vacancy clusters, as revealed by positron annihilation spectroscopy. Finally, the main reason for the capacity drop seems to be due to dislocations formed during cycling, while the presence of vacancy clusters might be related to the lattice relaxation. Having identified the major contribution to the capacity loss, compositional modifications to the TiVNbCr system can now be explored that minimize defect formation and maximize material cycling performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Effect of rhenium addition on deuterium retention in neutron-irradiated tungsten

In this work, the effects of rhenium (Re) addition on deuterium (D) retention in neutron-irradiated tungsten (W) were investigated. Pure W and W-5Re (5 at.%) alloy samples were irradiated with neutrons at High Flux Isotope Reactor using MFE-RB-19 J capsule. The sample temperature and the damage level were 864 K and 0.35 dpa for pure W and 792 K and 0.26 dpa for W-5Re alloy. A portion of the samples was exposed to D plasma at Tritium Plasma Experiment at Idaho National Laboratory at 823 K to a fluence of 5 × 1025 m -2 . Vacancy-type defects in neutron-irradiated samples were examined using positron annihilation spectroscopy (PAS); D retention after plasma exposure was evaluated by thermal desorption spectrometry (TDS). TDS measurements revealed that D retention in the neutron-irradiated W-5Re alloy was similar to that in the unirradiated W sample, whereas a significant increase in D retention was observed in neutron-irradiated W. Thus, Re addition significantly suppressed the increase in D retention after neutron irradiation. This effect was attributed to the suppression of vacancy-type defect formation, as confirmed by PAS.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Neutron irradiation induced defects in oxides and their impact on the oxide properties

Understanding the irradiation-induced defects in oxides is of interest for a wide range of applications. ZnO is an interesting oxide with mixed ionic and covalent bonding that contains a variety of point defect structures—making it an excellent model for studying irradiation-induced defects and their impact on properties. Here, we investigate the effects of neutron irradiation on the formation of defects and on the structural, optical, and electrical properties of ZnO single crystals. We observe the formation of vacancies and voids via positron annihilation spectroscopy. Neutron irradiation led to a significant deterioration of the ZnO structure and formed a high concentration of point defects, vacancy clusters, and voids with large disparities in their structure across variable irradiation times. It also led to significant changes in the optical properties and sample color. Irradiation for 444 h induced a high concentration of Cu acceptors as well as a high concentration of Ga donors. Additionally, temperature-dependent Hall effect measurements revealed the competing production of donors and acceptors and showed an increase in the slope of the carrier freeze-out curve with increasing irradiation dose. This work demonstrates the combined effects of neutron irradiation in producing a wide range of structural defects, impurities, and dopants in oxides and their enormous impact on modifying the oxide structure and both the optical and electronic properties. It particularly emphasizes the importance of considering the production of new impurities and dopants during the neutron irradiation of oxides.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Gallium vacancy formation in oxygen annealed β-Ga 2 O 3

Here, the formation and character of gallium vacancies (V Ga ) and their complexes in near surface and bulk regions of single crystal β-Ga 2 O 3 were explored using unintentionally doped single crystals grown by the Czochralski method. As-grown and O 2 annealed (up to 1550 °C) samples were investigated using positron annihilation spectroscopy (PAS) to study the top 0.05–6 μm, and also current–voltage measurements and infrared (IR) spectroscopy, with hydrogenated samples to probe V Ga , to study the bulk. After annealing in O 2 > 1000 °C, the β-Ga 2 O 3 resistivity begins increasing, up to ~10 9 Ω cm for 1550 °C treatment, with the top 0.5 mm being many orders of magnitude more resistive. PAS measurements of the top 6 μm (S values) and very near surface 200 nm (diffusion length, L) indicate differential behavior as a function of peak annealing temperature. At least four temperature regimes of behavior are described. V Ga are present in the bulk after growth, but considerable changes occur upon annealing at a temperature ≈1000 °C, where L and S decrease simultaneously, suggesting an increasing defect concentration (L) but a decreasing defect volume (S). Annealing at a temperature ≈1400 °C increases S again, showing an increasing volume concentration of V Ga , with IR absorption showing a large signature of V Ga -2H, indicative of increased V Ga formation that was not present when annealing at a temperature ≈1000 °C. These results suggest that defect changes from annealing in oxygen are depth dependent, and that V Ga configuration may not be the same near the oxygen-exposed surface of the sample and in the bulk.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Defect Generation and Evolution in Irradiated Epitaxial Films and Heterostructures of Fe 3 O 4 and Cr 2 O 3

Abstract The functionality of nuclear structural materials, sensors, and microelectronics in harsh environments such as radiation relies on understanding defect generation and evolution processes in oxide layers. The initial radiation response of epitaxial thin films of Fe 3 O 4 (111), Cr 2 O 3 (0001), and Fe 3 O 4 (111)/Cr 2 O 3 (0001) heterostructures deposited on Al 2 O 3 (0001) by oxygen‐assisted molecular beam epitaxy and irradiated with 200 keV He + is characterized. X‐ray diffraction and X‐ray absorption near edge spectroscopy showed that the Cr 2 O 3 layers underwent significant lattice expansion and disordering under irradiation, whereas the Fe 3 O 4 layers do not exhibit noticeable changes. In contrast, positron annihilation spectroscopy revealed an evolution of cation vacancy point defects in the Fe 3 O 4 layers into larger vacancy clusters with increasing irradiation, while the cation vacancies in Cr 2 O 3 remained primarily as single vacancies and small clusters. The results suggest that the Fe 3 O 4 lattice can utilize the free volume of the larger vacancy clusters to relax but the small vacancies in the Cr 2 O 3 lattice do not facilitate relaxation. Comparing defect concentrations in the single layer films versus the heterostructure suggests that point defects may cross the interface from Fe 3 O 4 into Cr 2 O 3 . Together, these results enhance the understanding of the initial defect evolution mechanisms in oxide layers in harsh irradiation environments.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Positron stopping in multilayer materials

Positron annihilation spectroscopy provides a sensitive toolset for defect characterization. In beam based studies of single-layer targets, the form of implantation profiles is well established, depending on the kinetic energy and angle of incident positrons relative to the target surface and the density and average atomic number of the target. For multilayer systems, the difference in density and across the layers makes derivation of an analytical form difficult. To date, the determination of positron stopping profiles in multilayer targets has primarily involved Monte Carlo simulations. We present here an alternative approach that estimates the energy distribution dN/dE of those positrons transmitted past each layer boundary, by fitting the remaining tail of the stopping profile after each layer with a basis set comprised of calculated stopping profiles in the same material they are transmitted through. The stopping profile in the next layer is then found by summing a series of stopping profiles in the new medium in proportion to the determined distribution dN/dE. The results of our model are compared with simulation results in a system of alternating layers of Al and Au and find reasonable agreement in the predicted profile and excellent agreement in the predicted mean implantation depth. Finally, we derived a simple formula-based approach for the calculation of the mean implantation depth in two-layer systems that provides results in excellent agreement with the full model.

Jones, A. C. L. [Arizona State University, Tempe, ↗