Showing 1–44 of 44 results for author: Forbes, R

Elucidating Norrish Type-I reactive pathways by ultrafast X-ray absorption spectroscopy

Authors: Martin Graßl, Pablo Unzueta, Andreas E. Hillers-Bendtsen, Yusong Liu, Diptarka Hait, Alice E. Green, Xinxin Cheng, Felix Allum, Taran Driver, Ruaridh Forbes, James. M. Glownia, Erik Isele, Kirk A. Larsen, Xiang Li, Ming-Fu Lin, Razib Obaid, Adam Summers, Emily Thierstein, Jun Wang, James P. Cryan, Matthias F. Kling, Todd J. Martinez, Thomas J. A. Wolf

Abstract: Norrish type I reactions selectively cleave carbon-carbon bonds directly adjacent to carbonyl groups. Despite their broad use in combination with aromatic carbonyls for additive manufacturing and dental UV curing applications, the nature of the photochemically active state and its population mechanism remain insufficiently understood. Detailed mechanistic insight requires mapping of the photoexcit… ▽ More Norrish type I reactions selectively cleave carbon-carbon bonds directly adjacent to carbonyl groups. Despite their broad use in combination with aromatic carbonyls for additive manufacturing and dental UV curing applications, the nature of the photochemically active state and its population mechanism remain insufficiently understood. Detailed mechanistic insight requires mapping of the photoexcited population flow involving internal conversion and intersystem crossing. We present a time-domain study of gas phase acetophenone as a prototypical aromatic carbonyl combining soft X-ray time-resolved near-edge X-ray absorption fine structure (TR-NEXAFS) spectroscopy at the oxygen K-edge with ab initio multiple spawning (AIMS) simulations. Exploiting the specific sensitivity of TR-NEXAFS spectroscopy to states with $nπ^*$ character, we observe population transfer from the initially excited $^1ππ^*$ state to the $^1nπ^*$ state with a time constant of $(0.13 \pm 0.02)$ ps after an initial induction period of $(0.12 \pm 0.02)$ ps without population transfer, in quantitative agreement with the AIMS simulations. The population in the $^1nπ^*$ state subsequently decays via intersystem crossing, likely mediated by a $^3ππ^*$ state, within $(3.17 \pm 0.66)$ ps to a long-lived $^3nπ^*$ state, which is presumed to be active towards Norrish type I chemistry. △ Less

Submitted 18 March, 2026; originally announced March 2026.

Probing the structure of cyclic hydrocarbon molecules with X-ray-induced Coulomb explosion imaging

Authors: Kurtis D. Borne, Rebecca Boll, Thomas M. Baumann, Surjendu Bhattacharyya, Martin Centurion, Keyu Chen, Benjamin Erk, Alberto De Fanis, Ruaridh Forbes, Markus Ilchen, Edwin Kukk, Huynh V. S. Lam, Xiang Li, Lingyu Ma, Tommaso Mazza, Michael Meyer, Terence Mullins, J. Pedro F. Nunes, Asami Odate, Shashank Pathak, Daniel Rivas, Philipp Schmidt, Florian Trinter, Sergey Usenko, Anbu S. Venkatachalam , et al. (5 additional authors not shown)

Abstract: Coulomb explosion imaging (CEI) is a powerful experimental technique that maps a molecule's geometric structure onto the momenta of ionic molecular fragments produced by rapid multiple ionization. Here, we apply CEI induced by pulses from an X-ray free-electron laser in order to image and distinguish complex hydrocarbon isomers with the chemical formula C7H8: toluene, cycloheptatriene, and 1,6-hep… ▽ More Coulomb explosion imaging (CEI) is a powerful experimental technique that maps a molecule's geometric structure onto the momenta of ionic molecular fragments produced by rapid multiple ionization. Here, we apply CEI induced by pulses from an X-ray free-electron laser in order to image and distinguish complex hydrocarbon isomers with the chemical formula C7H8: toluene, cycloheptatriene, and 1,6-heptadiyne. The measured fragment-ion momentum distributions show discernible differences between the three isomers and provide signatures of specific carbon and hydrogen sites in the molecule. In contrast to previous work, we demonstrate that distinct 'marker atoms' are not strictly required for constructing a meaningful molecular frame of reference for the interpretation of the momentum-space data. Our work paves the way for tracking the ultrafast motion of nuclei during isomerization reactions in pure hydrocarbons. △ Less

Submitted 3 February, 2026; originally announced February 2026.

Highly efficient DUV generation at 100 kHz via Yb pumped four-wave mixing in stretched hollow-core fibers

Authors: Ruaridh Forbes, Paul Hockett, Rune Lausten

Abstract: We report the generation of the fifth harmonic of Yb at 206 nm with pulse energies exceeding 16 $μ$J and durations of approximately 100 fs at a repetition rate of 100 kHz. The deep ultraviolet pulses are produced using four-wave difference frequency mixing in a He-filled stretched hollow-core fiber, driven by a pump at 343 nm and seeded at 1030 nm. Guided by simulations, we carefully optimize the… ▽ More We report the generation of the fifth harmonic of Yb at 206 nm with pulse energies exceeding 16 $μ$J and durations of approximately 100 fs at a repetition rate of 100 kHz. The deep ultraviolet pulses are produced using four-wave difference frequency mixing in a He-filled stretched hollow-core fiber, driven by a pump at 343 nm and seeded at 1030 nm. Guided by simulations, we carefully optimize the process, resulting in a conversion efficiency of $\sim$30% from the 343 nm pump beam. △ Less

Submitted 12 November, 2025; originally announced November 2025.

Journal ref: Forbes, R., Hockett, P. and Lausten, R. (2025), Optics Letters, 50(18), pp. 5893-5896

An update to ECMWF's machine-learned weather forecast model AIFS

Authors: Gabriel Moldovan, Ewan Pinnington, Ana Prieto Nemesio, Simon Lang, Zied Ben Bouallègue, Jesper Dramsch, Mihai Alexe, Mario Santa Cruz, Sara Hahner, Harrison Cook, Helen Theissen, Mariana Clare, Cathal O'Brien, Jan Polster, Linus Magnusson, Gert Mertes, Florian Pinault, Baudouin Raoult, Patricia de Rosnay, Richard Forbes, Matthew Chantry

Abstract: We present an update to ECMWF's machine-learned weather forecasting model AIFS Single with several key improvements. The model now incorporates physical consistency constraints through bounding layers, an updated training schedule, and an expanded set of variables. The physical constraints substantially improve precipitation forecasts and the new variables show a high level of skill. Upper-air hea… ▽ More We present an update to ECMWF's machine-learned weather forecasting model AIFS Single with several key improvements. The model now incorporates physical consistency constraints through bounding layers, an updated training schedule, and an expanded set of variables. The physical constraints substantially improve precipitation forecasts and the new variables show a high level of skill. Upper-air headline scores also show improvement over the previous AIFS version. The AIFS has been fully operational at ECMWF since the 25th of February 2025. △ Less

Submitted 23 September, 2025; originally announced September 2025.

Imaging valence electron rearrangement in a chemical reaction using hard X-ray scattering

Authors: Ian Gabalski, Alice Green, Philipp Lenzen, Felix Allum, Matthew Bain, Surjendu Bhattacharyya, Mathew A. Britton, Elio G. Champenois, Xinxin Cheng, James P. Cryan, Taran Driver, Ruaridh Forbes, Douglas Garratt, Aaron M. Ghrist, Martin Graßl, Matthias F. Kling, Kirk A. Larsen, Mengning Liang, Ming-Fu Lin, Yusong Liu, Michael P. Minitti, Silke Nelson, Joseph S. Robinson, Philip H. Bucksbaum, Thomas J. A. Wolf , et al. (2 additional authors not shown)

Abstract: We have observed the signatures of valence electron rearrangement in photoexcited ammonia using ultrafast hard X-ray scattering. Time-resolved X-ray scattering is a powerful tool for imaging structural dynamics in molecules because of the strong scattering from the core electrons localized near each nucleus. Such core-electron contributions generally dominate the differential scattering signal, ma… ▽ More We have observed the signatures of valence electron rearrangement in photoexcited ammonia using ultrafast hard X-ray scattering. Time-resolved X-ray scattering is a powerful tool for imaging structural dynamics in molecules because of the strong scattering from the core electrons localized near each nucleus. Such core-electron contributions generally dominate the differential scattering signal, masking any signatures of rearrangement in the chemically important valence electrons. Ammonia represents an exception to the typically high core-to-valence electron ratio. We measured 9.8 keV X-ray scattering from gas-phase deuterated ammonia following photoexcitation via a 200 nm pump pulse to the 3s Rydberg state. We observed changes in the recorded scattering patterns due to the initial photoexcitation and subsequent deuterium dissociation. Ab initio calculations confirm that the observed signal is sensitive to the rearrangement of the single photoexcited valence electron as well as the interplay between adiabatic and nonadiabatic dissociation channels. The use of ultrafast hard X-ray scattering to image the structural rearrangement of single valence electrons constitutes an important advance in tracking valence electronic structure in photoexcited atoms and molecules. △ Less

Submitted 23 June, 2025; originally announced June 2025.

Shake-down spectroscopy as state- and site-specific probe of ultrafast chemical dynamics

Authors: Henry J. Thompson, Matteo Bonanomi, Jacob Pedersen, Oksana Plekan, Nitish Pal, Cesare Grazioli, Kevin C. Prince, Bruno N. C. Tenorio, Michele Devetta, Davide Faccialà, Caterina Vozzi, Paolo Piseri, Miltcho B. Danailov, Alexander Demidovich, Alexander D. Brynes, Alberto Simoncig, Marco Zangrando, Marcello Coreno, Raimund Feifel, Richard J. Squibb, David M. P. Holland, Felix Allum, Daniel Rolles, Piero Decleva, Michael S. Schuurman , et al. (5 additional authors not shown)

Abstract: Tracking the multifarious ultrafast electronic and structural changes occurring in a molecule during a photochemical transformation is a challenging endeavor that benefits from recent experimental and computational progress in time-resolved techniques. Measurements of valence electronic states, which provide a global picture of the bonding structure of the molecule, and core electronic states, whi… ▽ More Tracking the multifarious ultrafast electronic and structural changes occurring in a molecule during a photochemical transformation is a challenging endeavor that benefits from recent experimental and computational progress in time-resolved techniques. Measurements of valence electronic states, which provide a global picture of the bonding structure of the molecule, and core electronic states, which provide insight into the local environment, traditionally require different approaches and are often studied separately. Here, we demonstrate that X-ray pulses from a seeded free-electron laser (FEL) enable the measurement of high-resolution, time-resolved X-ray photoelectron spectra (XPS) that capture weak satellite states resulting from shake-down processes in a valence-excited molecule. This approach effectively combines the advantages of both valence- and core-state investigations. We applied this method to investigate photoexcited CS$_2$ molecules, where the role of internal conversion (IC) and intersystem crossing (ISC) in determining the pre-dissociation dynamics is controversial. We present XPS spectra from photoexcited CS$_2$, obtained at the FERMI FEL. High-resolution measurements, compared to the corresponding spectra obtained from accurate multireference quantum chemical calculations, reveal that shake-down satellite channels are highly sensitive to both valence electronic and geometric changes. Previous studies of the pre-dissociation dynamics have led to uncertain assignments of the branching between singlet and triplet excited states. We derive a propensity rule that demonstrates the spin-selectivity of the shake-downs. This selectivity allows us to unequivocally assign contributions from the bright and dark singlet excited states, with populations tracked along the pre-dissociation dynamic pathway. △ Less

Submitted 4 August, 2025; v1 submitted 17 June, 2025; originally announced June 2025.

Imaging the Photochemistry of Cyclobutanone using Ultrafast Electron Diffraction: Experimental Results

Authors: A. E. Green, Y. Liu, F. Allum, M. Graßl, P. Lenzen, M. N. R. Ashfold, S. Bhattacharyya, X. Cheng, M. Centurion, S. W. Crane, R. G. Forbes, N. A. Goff, L. Huang, B. Kaufman, M. F. Kling, P. L. Kramer, H. V. S. Lam, K. A. Larsen, R. Lemons, M. -F. Lin, A. J. Orr-Ewing, D. Rolles, A. Rudenko, S. K. Saha, J. Searles , et al. (5 additional authors not shown)

Abstract: We investigated the ultrafast structural dynamics of cyclobutanone following photoexcitation at $λ=200$ nm using gas-phase megaelectronvolt ultrafast electron diffraction. Our investigation complements the simulation studies of the same process within this special issue. It provides information about both electronic state population and structural dynamics through well-separable inelastic and elas… ▽ More We investigated the ultrafast structural dynamics of cyclobutanone following photoexcitation at $λ=200$ nm using gas-phase megaelectronvolt ultrafast electron diffraction. Our investigation complements the simulation studies of the same process within this special issue. It provides information about both electronic state population and structural dynamics through well-separable inelastic and elastic electron scattering signatures. We observe the depopulation of the photoexcited S$_2$ state of cyclobutanone with n3s Rydberg character through its inelastic electron scattering signature with a time constant of $(0.29 \pm 0.2)$ ps towards the S$_1$ state. The S$_1$ state population undergoes ring-opening via a Norrish Type-I reaction, likely while passing through a conical intersection with S$_0$. The corresponding structural changes can be tracked by elastic electron scattering signatures. These changes appear with a delay of $(0.14 \pm 0.05)$ ps with respect the initial photoexcitation, which is less than the S$_2$ depopulation time constant. This behavior provides evidence for the ballistic nature of the ring-opening once the S$_1$ state is reached. The resulting biradical species react further within $(1.2 \pm 0.2)$ ps via two rival fragmentation channels yielding ketene and ethylene, or propene and carbon monoxide. Our study showcases both the value of gas-phase ultrafast diffraction studies as an experimental benchmark for nonadiabatic dynamics simulation methods and the limits in the interpretation of such experimental data without comparison to such simulations. △ Less

Submitted 14 April, 2025; v1 submitted 19 February, 2025; originally announced February 2025.

Efficient ($\sim$10$\%$) Generation of Vacuum Ultraviolet Femtosecond Pulses via Four-Wave Mixing in Hollow-Core Fibers

Authors: Ruaridh Forbes, Paul Hockett, Quentin Leterrier, Rune Lausten

Abstract: We report the generation of the 5th harmonic of Ti:sapphire, at 160 nm, with more than 4~$μ$J of pulse energy, and a pulse length of 37 fs with a 1 kHz repetition rate. The VUV pulses are produced using Four-Wave Difference Frequency Mixing (FWDFM) in a helium-filled stretched Hollow-Core Fiber (HCF), driven by a pump at 267 nm and seeded at 800 nm. Guided by simulations using Luna.jl, we are able… ▽ More We report the generation of the 5th harmonic of Ti:sapphire, at 160 nm, with more than 4~$μ$J of pulse energy, and a pulse length of 37 fs with a 1 kHz repetition rate. The VUV pulses are produced using Four-Wave Difference Frequency Mixing (FWDFM) in a helium-filled stretched Hollow-Core Fiber (HCF), driven by a pump at 267 nm and seeded at 800 nm. Guided by simulations using Luna.jl, we are able to optimize the process carefully. The result is a conversion efficiency of $\sim$10$\%$ from the 267 nm pump beam, rivaling the efficient optical mixing schemes in nonlinear crystals. △ Less

Submitted 28 March, 2024; v1 submitted 10 February, 2024; originally announced February 2024.

Experimental Demonstration of Attosecond Pump-Probe Spectroscopy with an X-ray Free-Electron Laser

Authors: Zhaoheng Guo, Taran Driver, Sandra Beauvarlet, David Cesar, Joseph Duris, Paris L. Franz, Oliver Alexander, Dorian Bohler, Christoph Bostedt, Vitali Averbukh, Xinxin Cheng, Louis F. DiMauro, Gilles Doumy, Ruaridh Forbes, Oliver Gessner, James M. Glownia, Erik Isele, Andrei Kamalov, Kirk A. Larsen, Siqi Li, Xiang Li, Ming-Fu Lin, Gregory A. McCracken, Razib Obaid, Jordan T. ONeal , et al. (25 additional authors not shown)

Abstract: Pump-probe experiments with sub-femtosecond resolution are the key to understanding electronic dynamics in quantum systems. Here we demonstrate the generation and control of sub-femtosecond pulse pairs from a two-colour X-ray free-electron laser (XFEL). By measuring the delay between the two pulses with an angular streaking diagnostic, we characterise the group velocity of the XFEL and demonstrate… ▽ More Pump-probe experiments with sub-femtosecond resolution are the key to understanding electronic dynamics in quantum systems. Here we demonstrate the generation and control of sub-femtosecond pulse pairs from a two-colour X-ray free-electron laser (XFEL). By measuring the delay between the two pulses with an angular streaking diagnostic, we characterise the group velocity of the XFEL and demonstrate control of the pulse delay down to 270 as. We demonstrate the application of this technique to a pump-probe measurement in core-excited para-aminophenol. These results demonstrate the ability to perform pump-probe experiments with sub-femtosecond resolution and atomic site specificity. △ Less

Submitted 26 January, 2024; originally announced January 2024.

Comments: 55 pages, main manuscript (5 figures) + supplementary materials (25 figures), 30 figures total. Submitted to Nature Photonics

Monitoring the evolution of relative product populations at early times during a photochemical reaction

Authors: Joao Pedro Figueira Nunes, Lea Maria Ibele, Shashank Pathak, Andrew R. Attar, Surjendu Bhattacharyya, Rebecca Boll, Kurtis Borne, Martin Centurion, Benjamin Erk, Ming-Fu Lin, Ruaridh J. G. Forbes, Nate Goff, Christopher S. Hansen, Matthias Hoffmann, David M. P. Holland, Rebecca A. Ingle, Duan Luo, Sri Bhavya Muvva, Alex Reid, Arnaud Rouzée, Artem Rudenko, Sajib Kumar Saha, Xiaozhe Shen, Anbu Selvam Venkatachalam, Xijie Wang , et al. (9 additional authors not shown)

Abstract: Identifying multiple rival reaction products and transient species formed during ultrafast photochemical reactions and determining their time-evolving relative populations are key steps towards understanding and predicting photochemical outcomes. Yet, most contemporary ultrafast studies struggle with clearly identifying and quantifying competing molecular structures/species amongst the emerging re… ▽ More Identifying multiple rival reaction products and transient species formed during ultrafast photochemical reactions and determining their time-evolving relative populations are key steps towards understanding and predicting photochemical outcomes. Yet, most contemporary ultrafast studies struggle with clearly identifying and quantifying competing molecular structures/species amongst the emerging reaction products. Here, we show that mega-electronvolt ultrafast electron diffraction in combination with ab initio molecular dynamics calculations offer a powerful route to determining time-resolved populations of the various isomeric products formed after UV (266 nm) excitation of the five-membered heterocyclic molecule 2(5H)-thiophenone. This strategy provides experimental validation of the predicted high (~50%) yield of an episulfide isomer containing a strained 3-membered ring within ~1 ps of photoexcitation and highlights the rapidity of interconversion between the rival highly vibrationally excited photoproducts in their ground electronic state. △ Less

Submitted 21 November, 2023; originally announced November 2023.

Journal ref: J. Am. Chem. Soc. 2024, 146, 6, 4134-4143

High Repetition-Rate Pulse Shaping of a Spectrally Broadened Yb Femtosecond Laser

Authors: Julia Codere, Michael Belmonte, Brian Kaufman, Michael Wahl, Eric Jones, Martin G Cohen, Thomas Weinacht, Ruaridh Forbes

Abstract: We demonstrate compression and shaping of few cycle pulses from a high average power Ytterbium laser system. The pulses from a commercial 20 W, 100 kHz Yb laser system are spectrally broadened in two-stages using gas-filled, stretched hollow-core fibers and then compressed and shaped in an acousto-optic modulator-based pulse-shaper. The pulse-shaper allows for compression, characterization, and sh… ▽ More We demonstrate compression and shaping of few cycle pulses from a high average power Ytterbium laser system. The pulses from a commercial 20 W, 100 kHz Yb laser system are spectrally broadened in two-stages using gas-filled, stretched hollow-core fibers and then compressed and shaped in an acousto-optic modulator-based pulse-shaper. The pulse-shaper allows for compression, characterization, and shaping all in one system, producing ~10 fs pulses with 50 uJ of energy △ Less

Submitted 17 November, 2023; originally announced November 2023.

Progress on the journey to put field electron emission onto a better scientific basis

Authors: Richard G. Forbes, Sergey V. Filippov, Anatoly G. Kolosko, Eugeni O. Popov

Abstract: This paper forms part of a long-term project to put field electron emission (FE) onto a better scientific basis, by seeking reliable quantitative agreement between theory and experiment, especially as regards emission-current values. The main paper aims are: (1) to respond to remarks made in recent papers; (2) to restate the thinking behind our 2022 methodology for choosing between different FE mo… ▽ More This paper forms part of a long-term project to put field electron emission (FE) onto a better scientific basis, by seeking reliable quantitative agreement between theory and experiment, especially as regards emission-current values. The main paper aims are: (1) to respond to remarks made in recent papers; (2) to restate the thinking behind our 2022 methodology for choosing between different FE models using experiments; (3) to assess progress; and (4) to make further suggestions about improved approaches. △ Less

Submitted 23 May, 2023; originally announced May 2023.

Comments: 3 pages, 6 tables, 1 figure. Conference paper for IVNC2023 in Boston, Mass., July 2023. To be published electronically by IEEE Explore

Femtosecond electronic and hydrogen structural dynamics in ammonia imaged with ultrafast electron diffraction

Authors: Elio G. Champenois, Nanna H. List, Matthew Ware, Mathew Britton, Philip H. Bucksbaum, Xinxin Cheng, Martin Centurion, James P. Cryan, Ruaridh Forbes, Ian Gabalski, Kareem Hegazy, Matthias C. Hoffmann, Andrew J. Howard, Fuhao Ji, Ming-Fu Lin, J. Pedro Nunes, Xiaozhe Shen, Jie Yang, Xijie Wang, Todd J. Martinez, Thomas J. A. Wolf

Abstract: Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross-sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of th… ▽ More Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross-sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of the nuclear and corresponding electronic structure changes resulting from the dissociation dynamics in the time-dependent diffraction. Both assignments are confirmed by ab initio simulations of the photochemical dynamics and the resulting diffraction observable. While the temporal resolution of the experiment is insufficient to resolve the dissociation in time, our results represent an important step towards the observation of proton dynamics in real space and time. △ Less

Submitted 6 March, 2023; originally announced March 2023.

Ultrafast Molecular Frame Quantum Tomography

Authors: Luna Morrigan, Simon P. Neville, Margaret Gregory, Andrey E. Boguslavskiy, Ruaridh Forbes, Iain Wilkinson, Rune Lausten, Albert Stolow, Michael S. Schuurman, Paul Hockett, Varun Makhija

Abstract: We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically non-adiabatic wavepacket in ammonia (NH$_3$). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the sys… ▽ More We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically non-adiabatic wavepacket in ammonia (NH$_3$). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH$_3$, we observe that electronic coherences are induced by nuclear dynamics which non-adiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is non-adiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer time scales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes. △ Less

Submitted 9 October, 2023; v1 submitted 6 March, 2023; originally announced March 2023.

Journal ref: Phys. Rev. Lett. 131, 193001 (2023)

Field emitter electrostatics: efficient improved simulation technique for highly precise calculation of field enhancement factors

Authors: Fernando F. Dall'Agnol, Thiago A. de Assis, Richard G. Forbes

Abstract: When solving the Laplace equation numerically via computer simulation, in order to determine the field values at the surface of a shape model that represents a field emitter, it is necessary to define a simulation box and, within this, a simulation domain. This domain must not be so small that the box boundaries have an undesirable influence on the predicted field values. A recent paper discussed… ▽ More When solving the Laplace equation numerically via computer simulation, in order to determine the field values at the surface of a shape model that represents a field emitter, it is necessary to define a simulation box and, within this, a simulation domain. This domain must not be so small that the box boundaries have an undesirable influence on the predicted field values. A recent paper discussed the situation of cylindrically symmetric emitter models that stand on one of a pair of well-separated parallel plates. This geometry can be simulated by using two-dimensional domains. For a cylindrical simulation box, formulae have previously been presented that define the minimum domain dimensions (MDD) (height and radius) needed to evaluate the apex value of the field enhancement factor for this type of model, with an error-magnitude never larger than a "tolerance" $ε_{\rm{tol}}$. This MDD criterion helps to avoid inadvertent errors and oversized domains. The present article discusses (in greater depth than previously) a significant improvement in the MDD method; this improvement has been called the MDD Extrapolation Technique (MDDET). By carrying out two simulations with relatively small MDD values, it is possible to achieve a level of precision comparable with the results of carrying out a single simulation using a much larger simulation domain. For some simulations, this could result in significant savings of memory requirements and computing time. Following a brief restatement of the original MDD method, the MDDET method is illustrated by applying it to the hemiellipsoid-on-plane (HEP) and hemisphere-on-cylindrical-post (HCP) emitter shape models. △ Less

Submitted 7 February, 2023; originally announced February 2023.

Comments: 9 pages, 4 figures. Accepted for publication in JVSTB

Effect of ZrB$_2$ additions on the thermal stability of polycrystalline diamond

Authors: Melisha Jivanji, Roy Peter Forbes, Humphrey Sithebe, Johan Ewald Westraadt

Abstract: This study investigates the effect of ZrB$_2$ additions on the microstructure, thermal stability, and thermo-mechanical wear behaviour of polycrystalline diamond. Following high-pressure high-temperature (HPHT) sintering, the ZrB$_2$-PCD material showed a full conversion of the binder phase to cobalt-boride (Co2B and Co$_{23}$B$_6$) phases. In-situ PXRD and TEM vacuum annealing experiments observe… ▽ More This study investigates the effect of ZrB$_2$ additions on the microstructure, thermal stability, and thermo-mechanical wear behaviour of polycrystalline diamond. Following high-pressure high-temperature (HPHT) sintering, the ZrB$_2$-PCD material showed a full conversion of the binder phase to cobalt-boride (Co2B and Co$_{23}$B$_6$) phases. In-situ PXRD and TEM vacuum annealing experiments observed that the onset of bulk graphitisation occurred above $1000^{\circ}C$ for the ZrB$_2$-PCD material, compared to $850^{\circ}C$ for the STD-PCD material. The ZrB$_2$-PCD tools showed excellent thermo-mechanical wear behaviour, exhibiting increased durability and a steady wear scar progression during high-temperature dry-VTL testing. However, lowered abrasion wear resistance was observed for the ZrB2-PCD tools during low-temperature wet-VTL testing, probably due the reduced diamond contiguity in the ZrB2 additive sample. Further optimisation of the ZrB$_2$ additive phase content, mixing methodology, or sintering conditions could be explored to improve the abrasive wear resistance of this novel PCD material. △ Less

Submitted 7 February, 2023; originally announced February 2023.

Filming Enhanced Ionization in an Ultrafast Triatomic Slingshot

Authors: A. J. Howard, M. Britton, Z. L. Streeter, C. Cheng, R. Forbes, J. L. Reynolds, F. Allum, G. A. McCracken, I. Gabalski, R. R. Lucchese, C. W. McCurdy, T. Weinacht, P. H. Bucksbaum

Abstract: Filming atomic motion within molecules is an active pursuit of molecular physics and quantum chemistry. A promising method is laser-induced Coulomb Explosion Imaging (CEI) where a laser pulse rapidly ionizes many electrons from a molecule, causing the remaining ions to undergo Coulomb repulsion. The ion momenta are used to reconstruct the molecular geometry which is tracked over time (i.e. filmed)… ▽ More Filming atomic motion within molecules is an active pursuit of molecular physics and quantum chemistry. A promising method is laser-induced Coulomb Explosion Imaging (CEI) where a laser pulse rapidly ionizes many electrons from a molecule, causing the remaining ions to undergo Coulomb repulsion. The ion momenta are used to reconstruct the molecular geometry which is tracked over time (i.e. filmed) by ionizing at an adjustable delay with respect to the start of interatomic motion. Results are distorted, however, by ultrafast motion during the ionizing pulse. We studied this effect in water and filmed the rapid "slingshot" motion that enhances ionization and distorts CEI results. Our investigation uncovered both the geometry and mechanism of the enhancement which may inform CEI experiments in many other polyatomic molecules. △ Less

Submitted 24 October, 2022; originally announced October 2022.

Photon Energy-Resolved Velocity Map Imaging from Spectral Domain Ghost Imaging

Authors: Jun Wang, Taran C. Driver, Felix Allum, Christina C. Papadopoulou, Christopher Passow, Günter Brenner, Siqi Li, Stefan Düsterer, Atia Tul Noor, Sonu Kumar, Philip H. Bucksbaum, Benjamin Erk, Ruaridh Forbes, James P. Cryan

Abstract: We present an approach that combines photon spectrum correlation analysis with the reconstruction of three-dimensional momentum distribution from velocity map images in an efficient, single-step procedure. We demonstrate its efficacy with the results from the photoionization of the $2p$-shell of argon using the FLASH free-electron laser~(FEL). Distinct spectral features due to the spin-orbit split… ▽ More We present an approach that combines photon spectrum correlation analysis with the reconstruction of three-dimensional momentum distribution from velocity map images in an efficient, single-step procedure. We demonstrate its efficacy with the results from the photoionization of the $2p$-shell of argon using the FLASH free-electron laser~(FEL). Distinct spectral features due to the spin-orbit splitting of Ar$^+(2p^{-1})$ are resolved, despite the large average bandwidth of the ionizing pulses from the FEL. This demonstrates a clear advantage over the conventional analysis method, and it will be broadly beneficial for velocity map imaging experiments with FEL sources. The retrieved linewidth of the binding energy spectrum approaches the resolution limitation prescribed by the spectrometers used to collect the data. Our approach presents a path to extend spectral-domain ghost imaging to the case where the photoproduct observable is high-dimensional. △ Less

Submitted 20 March, 2023; v1 submitted 17 October, 2022; originally announced October 2022.

Comments: 14 pages

Journal ref: New J. Phys. 25 033017 (2023)

Rehybridization dynamics into the pericyclic minimum of an electrcyclic reaction imaged in real-time

Authors: Yusong Liu, David M. Sanchez, Matthew R. Ware, Elio G. Champenois, Jie Yang, J. Pedro F. Nunes, Andrew Attar, Martin Centurion, James P. Cryan, Ruaridh G. Forbes, Kareem Hegazy, Matthias C. Hoffmann, Fuhao Ji, Ming-Fu Lin, Duan Luo, Sajib K. Saha, Xiaozhe Shen, Xijie Wang, Todd J. Martínez, Thomas J. A. Wolf

Abstract: Electrocyclic reactions are characterized by the concerted formation and cleavage of both σ and π bonds through a cyclic structure. This structure is known as a pericyclic transition state for thermal reactions and a pericyclic minimum in the excited state for photochemical reactions. However, the structure of the pericyclic geometry has yet to be observed experimentally. We use a combination of u… ▽ More Electrocyclic reactions are characterized by the concerted formation and cleavage of both σ and π bonds through a cyclic structure. This structure is known as a pericyclic transition state for thermal reactions and a pericyclic minimum in the excited state for photochemical reactions. However, the structure of the pericyclic geometry has yet to be observed experimentally. We use a combination of ultrafast electron diffraction and excited state wavepacket simulations to image structural dynamics through the pericyclic minimum of a photochemical electrocyclic ring-opening reaction in the molecule α-terpinene. The structural motion into the pericyclic minimum is dominated by rehybridization of two carbon atoms, which is required for the transformation from two to three conjugated π bonds. The σ bond dissociation largely happens after internal conversion from the pericyclic minimum to the electronic ground state. These findings may be transferrable to electrocyclic reactions in general. △ Less

Submitted 27 September, 2022; originally announced September 2022.

Comments: Combined manuscript and supplementary information

Post-field ionization of Si clusters in atom probe tomography: A joint theoretical and experimental study

Authors: Ramya Cuduvally, Richard J. H. Morris, Giel Oosterbos, Piero Ferrari, Claudia Fleischmann, Richard G. Forbes, Wilfried Vandervorst

Abstract: A major challenge for Atom Probe Tomography (APT) quantification is the inability to decouple ions which possess the same mass/charge-state ($m/n$) ratio but a different mass. For example, $^{75}{\rm{As}}^{+}$ and $^{75}{\rm{As}}{_2}^{2+}$ at ~75 Da or $^{14}{\rm{N}}^+$ and $^{28}{\rm{Si}}^{2+}$ at ~14 Da, cannot be differentiated without the additional knowledge of their kinetic energy or a signi… ▽ More A major challenge for Atom Probe Tomography (APT) quantification is the inability to decouple ions which possess the same mass/charge-state ($m/n$) ratio but a different mass. For example, $^{75}{\rm{As}}^{+}$ and $^{75}{\rm{As}}{_2}^{2+}$ at ~75 Da or $^{14}{\rm{N}}^+$ and $^{28}{\rm{Si}}^{2+}$ at ~14 Da, cannot be differentiated without the additional knowledge of their kinetic energy or a significant improvement of the mass resolving power. Such mass peak overlaps lead to ambiguities in peak assignment, resulting in compositional uncertainty and an incorrect labelling of the atoms in a reconstructed volume. In the absence of a practical technology for measuring the kinetic energy of the field-evaporated ions, we propose and then explore the applicability of a post-experimental analytical approach to resolve this problem based on the fundamental process that governs the production of multiply charged molecular ions/clusters in APT, i.e., Post-Field Ionization (PFI). The ability to predict the PFI behaviour of molecular ions as a function of operating conditions could offer the first step towards resolving peak overlap and minimizing compositional uncertainty. We explore this possibility by comparing the field dependence of the charge-state-ratio for Si clusters ($\rm{Si}_2$, $\rm{Si}_3$ and $\rm{Si}_4$) with theoretical predictions using the widely accepted Kingham PFI theory. We then discuss the model parameters that may affect the quality of the fit and the possible ways in which the PFI of molecular ions in APT can be better understood. Finally, we test the transferability of the proposed approach to different material systems and outline ways forward for achieving more reliable results. △ Less

Submitted 11 July, 2022; originally announced July 2022.

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling

Authors: Thiago A. de Assis, Fernando F. Dall'Agnol, Richard G. Forbes

Abstract: This review of quantitative field emitter electrostatics, covering analytical, numerical and fitted-formula approaches, is thought the first of its kind. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is polarity independent; thus the review applies to both fiel… ▽ More This review of quantitative field emitter electrostatics, covering analytical, numerical and fitted-formula approaches, is thought the first of its kind. The review relates chiefly to situations where emitters operate in an electronically ideal manner, and zero-current electrostatics is applicable. Terminology is carefully described and is polarity independent; thus the review applies to both field electron and field ion emitters. It also applies more generally to charged, pointed electron-conductors that exhibit the "electrostatic lightning-rod effect", but are poorly discussed in general electricity and magnetism literature. Modern electron-conductor electrostatics is an application of the chemical thermodynamics and statistical mechanics of electrons. The review focuses chiefly on the electrostatics of two common basic emitter forms: the needle-shaped emitters used in traditional projection technologies; and the post-shaped emitters often used in modelling large-area multi-emitter electron sources. In the post-on-plane context, we consider in detail both the electrostatics of the single post and the interaction between two identical posts that occurs as a result of electrostatic depolarization (often called "screening" or "shielding"). Core to the review are discussions of the "minimum domain dimensions" method for implementing effective finite-element-method electrostatic simulations, and of the variant that leads to very precise estimates of dimensionless field enhancement factors (error typically less than 0.001 % in situations where analytical comparisons exist). Brief outline discussions, and core references, are given for each of many "related considerations" that are relevant to the electrostatic situations, methods and results described. Many areas of field emitter electrostatics are suggested where further research and/or separate mini-reviews would probably be useful. △ Less

Submitted 18 June, 2022; originally announced June 2022.

Comments: 39 pages, 24 figures. Invited Review, submitted for refereeing

Journal ref: J. Phys.: Condens. Matter 34, 493001 (2022). (Open Access)

Interpretation of field emission current-voltage data: background theory and detailed simulation testing of a user-friendly webtool

Authors: Mohammad M. Allaham, Richard G. Forbes, Alexandr Knapek, Dinara Sobola, Daniel Burdaa, Petr Sedlak, Marwan S. Mousa

Abstract: In field electron emission (FE) studies, to interpret current-voltage data and extract characterization parameters, we use smooth planar metal-like emitter (SPME) methodology and a data-analysis plot. Three types exist: Millikan-Lauritsen (ML), Fowler-Nordheim (FN) and Murphy-Good (MG) plots. In SPME methodology, ML and FN plots are slightly curved but a MG plot is nearly straight. 1956 MG FE theo… ▽ More In field electron emission (FE) studies, to interpret current-voltage data and extract characterization parameters, we use smooth planar metal-like emitter (SPME) methodology and a data-analysis plot. Three types exist: Millikan-Lauritsen (ML), Fowler-Nordheim (FN) and Murphy-Good (MG) plots. In SPME methodology, ML and FN plots are slightly curved but a MG plot is nearly straight. 1956 MG FE theory is better physics than 1928 FN theory, so we expect MG plots to be more precise than ML or FN plots. Current-voltage data are often converted: measured voltage to (apparent) macroscopic field, current to macroscopic current density. Thus, four different data-input forms exist. Over-simplified models of system behaviour are widely assumed. Whether simple use of a data-analysis plot is a valid interpretation method is often neglected. Published FE studies seem to contain a high incidence of spurious values for "field enhancement factor". A procedure (the "Orthodoxy Test") described in 2013 allows a validity check: around 40 % of a small sample of results were spuriously high. To assist data interpretation and validity checks, a simple user-friendly webtool has been designed by the lead author. As inputs, this needs system specification data and "range-limits" data from any of the three plot forms, using any of the four data-input forms. The webtool then applies the Orthodoxy Test, and -- if passed -- extracts characterization parameters. This study reports: (1) systematic tests of webtool functionality, using simulated input data prepared using Extended MG FE theory; and (2) systematic comparisons of the three different data-plot types, to check how well extracted parameter values match simulation input values. A summary review of relevant theory is given. For formal emission areas, the MG plot performs better than FN and ML plots. This is important for FE science. △ Less

Submitted 3 July, 2022; v1 submitted 9 May, 2022; originally announced May 2022.

Comments: 16 printed pages, 8 figures. Open-access published version

Journal ref: Mater. Today Commun. 31, 103654 (2022)

Time Correlation Filtering Reveals Two-Path Electron Quantum Interference in Strong-Field Ionization

Authors: Nicholas Werby, Andrew S. Maxwell, Ruaridh Forbes, Carla Figueira de Morisson Faria, Philip H. Bucksbaum

Abstract: Attosecond dynamics in strong-field tunnel ionization are encoded in intricate holographic patterns in the photoelectron momentum distributions (PMDs). These patterns show the interference between two or more superposed quantum electron trajectories, which are defined by their ionization times and subsequent evolution in the laser field. We determine the ionization time separation between interfer… ▽ More Attosecond dynamics in strong-field tunnel ionization are encoded in intricate holographic patterns in the photoelectron momentum distributions (PMDs). These patterns show the interference between two or more superposed quantum electron trajectories, which are defined by their ionization times and subsequent evolution in the laser field. We determine the ionization time separation between interfering pairs of electron orbits by performing a differential Fourier analysis on the measured momentum spectrum. We identify electron holograms formed by trajectory pairs whose ionization times are separated by less than a single quarter cycle, between a quarter cycle and half cycle, between a half cycle and three fourths of a cycle, and a full cycle apart. We compare our experimental results to the predictions of the Coulomb quantum orbit strong-field approximation (CQSFA), with significant success. We also time-filter the CQSFA trajectory calculations to demonstrate the validity of the technique on spectra with known time correlations. As a general analysis technique, the filter can be applied to all energy- and angularly-resolved datasets to recover time correlations between interfering electron pathways, providing an important tool to analyze any strong-field ionization spectra. △ Less

Submitted 14 May, 2022; originally announced May 2022.

Comments: 11 pages, 7 figures, submitted to Physical Review X

Field emission: calculations supporting a new methodology of comparing theory with experiment

Authors: Sergey V. Filippov, Anatoly G. Kolosko, Eugeni O. Popov, Richard G. Forbes

Abstract: This paper presents a new methodology for making comparisons between the theory of field electron emission (FE) and experiment, and is intended as a "demonstration of concept". This methodology is based on the value of the exponent kappa that describes the power to which voltage is raised in the pre-exponential of a mathematical equation that describes (for an electronically ideal FE system) the d… ▽ More This paper presents a new methodology for making comparisons between the theory of field electron emission (FE) and experiment, and is intended as a "demonstration of concept". This methodology is based on the value of the exponent kappa that describes the power to which voltage is raised in the pre-exponential of a mathematical equation that describes (for an electronically ideal FE system) the dependence of measured emission current on measured voltage. The aim is to use experimental exponent-values kappa^expt in an attempt to decide between two alternative FE theories, for both of which allowable (but different) ranges of kappa have been established. At present, there is limited information on what contribution to the "total theoretical kappa" is made by the voltage-dependence of the notional emission area: this paper reports simulations intended to add to our knowledge about this, for four common assumed shapes of an emitter apex. The methodology is then applied to the choice between 1928/29 Fowler-Nordheim (FN) FE theory and 1956 Murphy-Good (MG) FE theory (which is a situation where it is theoretically certain that 1956 MG FE theory is "better physics" than 1928/29 FN FE theory). Like all previous attempts to reach the known correct theoretical conclusion by experimentally based argument, the outcome of the new methodology tends to favour MG FE theory, but is formally indecisive at this stage of discussion. There seems an urgent need for better methods of measuring kappa^expt and of establishing reliable experimental error limits. △ Less

Submitted 4 July, 2022; v1 submitted 4 May, 2022; originally announced May 2022.

Comments: 23 pages, 5 figures. Tables 3 and 4 have been updated as a result of additional calculations, but this makes no changes in qualitative conclusions. A missing reference has been added

21st Century Planar Field Emission Theory and its Role in Vacuum Breakdown Science

Authors: Richard G. Forbes

Abstract: For explaining electrical breakdown, field electron emission (FE) is a mechanism of interest. In the period 2006 to 2010 there were significant developments in basic FE theory, but these have not yet fully entered general thinking in technological FE areas, which are often still based on 1960s thinking or (in some contexts) 1920s thinking about FE theory. This paper outlines the history of FE theo… ▽ More For explaining electrical breakdown, field electron emission (FE) is a mechanism of interest. In the period 2006 to 2010 there were significant developments in basic FE theory, but these have not yet fully entered general thinking in technological FE areas, which are often still based on 1960s thinking or (in some contexts) 1920s thinking about FE theory. This paper outlines the history of FE theory and provides an overview of modern developments and of some related topics, in so far as these affect the interpretation of experiments and the explanation of physical phenomena. The paper concentrates on principles, with references given where details can be found. Some suggestions are made about moving to the use of "21st-Century" FE theory. In addition, an error in Feynman's treatment of the electrostatics of pointed conductors is displayed, and it is found that Zener tunneling is implausible as a primary cause of vacuum breakdown from a CuO overlayer. △ Less

Submitted 3 July, 2022; v1 submitted 19 July, 2021; originally announced July 2021.

Comments: 8 pages, 1 figure. Originally presented at the 29th International Symposium on Discharges and Electrical Insulation in Vacuum (hosted virtually from Padova, September 2021). This version (v2) corrects typographic errors (including two in an equation) in the original arXiv verwion and the published version

Journal ref: Proc. 2020 29th International Symposium on Discharges and Electrical Insulation in Vacuum (ISDEIV) (IEEE Explore, 2021)

Conformer-specific Chemistry Imaged in Real Space and Time

Authors: E. G. Champenois, D. M. Sanchez, J. Yang, J. P. F. Nunes, A. Attar, M. Centurion, R. Forbes, M. Gühr, K. Hegazy, F. Ji, S. K. Saha, Y. Liu, M. -F. Lin, D. Luo, B. Moore, X. Shen, M. R. Ware, X. J. Wang, T. J. Martínez, T. J. A. Wolf

Abstract: Conformational isomers or conformers of molecules play a decisive role in chemistry and biology. However, experimental methods to investigate chemical reaction dynamics are typically not conformer-sensitive. Here, we report on a gas-phase megaelectronvolt ultrafast electron diffraction investigation of α-phellandrene undergoing an electrocyclic ring-opening reaction. We directly image the evolutio… ▽ More Conformational isomers or conformers of molecules play a decisive role in chemistry and biology. However, experimental methods to investigate chemical reaction dynamics are typically not conformer-sensitive. Here, we report on a gas-phase megaelectronvolt ultrafast electron diffraction investigation of α-phellandrene undergoing an electrocyclic ring-opening reaction. We directly image the evolution of a specific set of α-phellandrene conformers into the product isomer predicted by the Woodward-Hoffmann rules in real space and time. Our experimental results are in quantitative agreement with nonadiabatic quantum molecular dynamics simulations, which provide unprecedented detail of how conformation influences time scale and quantum efficiency of photoinduced ring-opening reactions. Due to the prevalence of large numbers of conformers in organic chemistry, our findings impact our general understanding of reaction dynamics in chemistry and biology. △ Less

Submitted 8 July, 2021; originally announced July 2021.

Strong Field Ionization of Water II: Electronic and Nuclear Dynamics En Route to Double Ionization

Authors: Chuan Cheng, Zachary L. Streeter, Andrew J. Howard, Michael Spanner, Robert R. Lucchese, C. William McCurdy, Thomas Weinacht, Philip H. Bucksbaum, Ruaridh Forbes

Abstract: We investigate the role of nuclear motion and strong-field-induced electronic couplings during the double ionization of deuterated water using momentum-resolved coincidence spectroscopy. By examining the three-body dicationic dissociation channel, D$^{+}$/D$^{+}$/O, for both few- and multi-cycle laser pulses, strong evidence for intra-pulse dynamics is observed. The extracted angle- and energy-res… ▽ More We investigate the role of nuclear motion and strong-field-induced electronic couplings during the double ionization of deuterated water using momentum-resolved coincidence spectroscopy. By examining the three-body dicationic dissociation channel, D$^{+}$/D$^{+}$/O, for both few- and multi-cycle laser pulses, strong evidence for intra-pulse dynamics is observed. The extracted angle- and energy-resolved double ionization yields are compared to classical trajectory simulations of the dissociation dynamics occurring from different electronic states of the dication. In contrast with measurements of single photon double ionization, pronounced departure from the expectations for vertical ionization is observed, even for pulses as short as 10~fs in duration. We outline numerous mechanisms by which the strong laser field can modify the nuclear wavefunction en-route to final states of the dication where molecular fragmentation occurs. Specifically, we consider the possibility of a coordinate-dependence to the strong-field ionization rate, intermediate nuclear motion in monocation states prior to double ionization, and near-resonant laser-induced dipole couplings in the ion. These results highlight the fact that, for small and light molecules such as D$_2$O, a vertical-transition treatment of the ionization dynamics is not sufficient to reproduce the features seen experimentally in the strong field coincidence double-ionization data. △ Less

Submitted 10 May, 2021; v1 submitted 12 April, 2021; originally announced April 2021.

Comments: 14 pages, 13 figures

Journal ref: Phys. Rev. A 104, 023108 (2021)

Dissecting Sub-Cycle Interference in Photoelectron Holography

Authors: Nicholas Werby, Andrew S. Maxwell, Ruaridh Forbes, Philip H. Bucksbaum, Carla Figueira de Morisson Faria

Abstract: Multipath holographic interference in strong-field quantum tunnel ionization is key to revealing sub-Angstrom attosecond dynamics for molecular movies. This critical sub-cycle motion is often obscured by longer time-scale effects such as ring-shaped patterns that appear in above-threshold ionization (ATI). In the present work, we overcome this problem by combining two novel techniques in theory an… ▽ More Multipath holographic interference in strong-field quantum tunnel ionization is key to revealing sub-Angstrom attosecond dynamics for molecular movies. This critical sub-cycle motion is often obscured by longer time-scale effects such as ring-shaped patterns that appear in above-threshold ionization (ATI). In the present work, we overcome this problem by combining two novel techniques in theory and experimental analysis: unit-cell averaging and time-filtering data and simulations. Together these suppress ATI rings and enable an unprecedented highly-detailed quantitative match between strong-field ionization experiments in argon and the Coulomb-quantum orbit strong-field approximation (CQSFA) theory. Velocity map images reveal fine modulations on the holographic spider-like interference fringes that form near the polarization axis. CQSFA theory traces this to the interference of three types of electron pathways. The level of agreement between experiment and theory allows sensitive determination of quantum phase differences and symmetries, providing an important tool for quantitative dynamical imaging in quantum systems. △ Less

Submitted 23 February, 2021; originally announced February 2021.

Comments: 13 Pages, 8 figures

Journal ref: Phys. Rev. A 104, 013109 (2021)

Comment on 'Design and circuit simulation of nanoscale vacuum channel transistors' by J. Xu, Y. Qin, Y. Shi, Y. Yang and X. Zhang, Nanoscale Adv. 2020, 2, 3582

Authors: Richard G. Forbes

Abstract: These comments aim to correct some apparent weaknesses in the theory of field electron emission given in a recent paper about nanoscale vacuum channel transistors, and to improve the presentation of this theory. In particular, it is argued that a "simplified" formula stated in the paper should not be used, because this formula is known to under-predict emission current densities by a large factor… ▽ More These comments aim to correct some apparent weaknesses in the theory of field electron emission given in a recent paper about nanoscale vacuum channel transistors, and to improve the presentation of this theory. In particular, it is argued that a "simplified" formula stated in the paper should not be used, because this formula is known to under-predict emission current densities by a large factor (typically around 300 for an emitting surface with local work function 4.5 eV). Thus, the "simplified" formula may significantly under-predict the practical performance of a nanoscale vacuum channel transistor. △ Less

Submitted 22 February, 2021; originally announced February 2021.

Comments: 5 pages; version as submitted and accepted for publication after review

Strong Field Ionization of Water: Nuclear Dynamics Revealed by Varying the Pulse Duration

Authors: A. J. Howard, C. Cheng, R. Forbes, G. A. McCracken, W. H. Mills, V. Makhija, M. Spanner, T. Weinacht, P. H. Bucksbaum

Abstract: Polyatomic molecules in strong laser fields can undergo substantial nuclear motion within tens of femtoseconds. Ion imaging methods based on dissociation or Coulomb explosion therefore have difficulty faithfully recording the geometry dependence of the field ionization that initiates the dissociation process. Here we compare the strong-field double ionization and subsequent dissociation of water (… ▽ More Polyatomic molecules in strong laser fields can undergo substantial nuclear motion within tens of femtoseconds. Ion imaging methods based on dissociation or Coulomb explosion therefore have difficulty faithfully recording the geometry dependence of the field ionization that initiates the dissociation process. Here we compare the strong-field double ionization and subsequent dissociation of water (both H$_2$O and D$_2$O) in 10-fs and 40-fs 800-nm laser pulses. We find that 10-fs pulses turn off before substantial internuclear motion occurs, whereas rapid internuclear motion can take place during the double ionization process for 40-fs pulses. The short-pulse measurements are consistent with a simple tunnel ionization picture, whose predictions help interpret the motion observed in the long-pulse measurements. △ Less

Submitted 28 January, 2021; originally announced January 2021.

Comments: 9 pages, 5 figures

Journal ref: Phys. Rev. A 103, 043120 (2021)

The pre-exponential voltage-exponent as a sensitive test parameter for field emission theories

Authors: R. G. Forbes, E. O. Popov, A. G. Kolosko, S. V. Filippov

Abstract: For field electron emission (FE), an empirical equation for measured current I_m as a function of measured voltage V_m has the form I_m = C*(V_m)^k*exp[-B/(V_m)], where B is a constant and C and k are constants or vary weakly with V_m. Values for k can be extracted (a) from simulations based on some specific FE theory, and in principle (b) from current-voltage measurements of sufficiently high qua… ▽ More For field electron emission (FE), an empirical equation for measured current I_m as a function of measured voltage V_m has the form I_m = C*(V_m)^k*exp[-B/(V_m)], where B is a constant and C and k are constants or vary weakly with V_m. Values for k can be extracted (a) from simulations based on some specific FE theory, and in principle (b) from current-voltage measurements of sufficiently high quality. This paper shows that comparison of theoretically derived and experimentally derived k-values could provide a sensitive and useful tool for comparing FE theory and experiment, and for choosing between alternative theories. Existing methods of extracting k-values from experimental or simulated current-voltage data are discussed, including a modernised "least residual" method, and existing knowledge concerning k-values is summarised. Exploratory simulations are reported. Where an analytical result for k is independently known, this value is reliably extracted. More generally, extracted k-values are sensitive to details of the emission theory used, but also depend on assumed emitter shape; these two influences will need to be disentangled by future research, and a range of emitter shapes will need examination. Other procedural conclusions are reported. Some scientific issues that this new tool may be able to help investigate are indicated. △ Less

Submitted 22 February, 2021; v1 submitted 3 December, 2020; originally announced December 2020.

Comments: 29 submitted pages, 3 figures, + intended Electronic Supplementary Material; modified version as submitted after review and accepted for publication

Comment on "Advanced field emission measurement techniques for research on modern cold cathode materials and their applications for transmission-type x-ray sources" [Rev. Sci. Instrum. 91, 083906 (2020)]

Authors: Richard G. Forbes

Abstract: This Comment suggests that technological field electron emission (FE) papers, such as the paper under discussion [P. Serbun et al.,, Rev. Sci. Instrum. 91, 083906 (2020)], should use FE theory based on the 1956 work of Murphy and Good (MG), rather than a simplified version of FE theory based on the original 1928 work of Fowler and Nordheim (FN). Use of the 1928 theory is common practice in technol… ▽ More This Comment suggests that technological field electron emission (FE) papers, such as the paper under discussion [P. Serbun et al.,, Rev. Sci. Instrum. 91, 083906 (2020)], should use FE theory based on the 1956 work of Murphy and Good (MG), rather than a simplified version of FE theory based on the original 1928 work of Fowler and Nordheim (FN). Use of the 1928 theory is common practice in technological FE literature, but the MG treatment is known to be better physics than the FN treatment, which contains identifiable errors. The MG treatment predicts significantly higher emission current densities and currents for emitters than does the FN treatment. From the viewpoint of the research and development of electron sources, it is counterproductive (and unhelpful for non-experts) for the technological FE literature to use theory that undervalues the performance of field electron emitters. △ Less

Submitted 1 December, 2020; originally announced December 2020.

Comments: 2 published pages

Journal ref: Rev. Sci. Instrum. 91 (2020) 107101

Disentangling the Sub-Cycle Electron Momentum Spectrum in Strong-Field Ionization

Authors: Nicholas Werby, Adi Natan, Ruaridh Forbes, Philip Bucksbaum

Abstract: Quantum calculations of tunneling in strong-field ionization (SFI) predict intricate momentum distributions due to sub-laser-cycle attosecond electron dynamics. These are obscured in most experiments by the dominance of inter-cycle interference patterns which are the hallmark of above-threshold ionization (ATI). Highly controlled 1- to 2-cycle laser pulses produce less inter-cycle interference but… ▽ More Quantum calculations of tunneling in strong-field ionization (SFI) predict intricate momentum distributions due to sub-laser-cycle attosecond electron dynamics. These are obscured in most experiments by the dominance of inter-cycle interference patterns which are the hallmark of above-threshold ionization (ATI). Highly controlled 1- to 2-cycle laser pulses produce less inter-cycle interference but cannot accurately recreate the sub-cycle features produced by uniform cycle calculations due to the effect of the carrier envelope of the pulse. We present a simple and effective technique to recover these sub-cycle features in experimental multi-cycle spectra. We time-filter the momentum distribution to highlight features originating from the interference of electron trajectory pairs with ionization times less than one field cycle apart. This method removes the ATI patterns and reveals sub-cycle interference structures in unprecedented detail. We can resolve new modulations in holographic structures that have not been previously noted in earlier experiments and which provide a new reference for comparing to calculations. △ Less

Submitted 1 June, 2021; v1 submitted 21 August, 2020; originally announced August 2020.

Comments: 7 pages, 4 figures, Published in PRResearch

Journal ref: Phys. Rev. Research 3, 023065 (2021)

Implementation of the orthodoxy test as a validity check on experimental field emission data

Authors: Mohammad M. Allaham, Richard G. Forbes, Alexander Knapek, Marwan S. Mousa

Abstract: In field electron emission (FE) studies, it is important to check and analyse the quality and validity of experimental current-voltage data, which is usually plotted in one of a small number of standard forms. These include the so-called Fowler-Nordheim (FN), Millikan-Lauritsen (ML) and Murphy-Good (MG) plots. The Field Emission Orthodoxy Test is a simple quantitative test that aims to check for t… ▽ More In field electron emission (FE) studies, it is important to check and analyse the quality and validity of experimental current-voltage data, which is usually plotted in one of a small number of standard forms. These include the so-called Fowler-Nordheim (FN), Millikan-Lauritsen (ML) and Murphy-Good (MG) plots. The Field Emission Orthodoxy Test is a simple quantitative test that aims to check for the reasonableness of the values of the parameter "scaled field" that can be extracted from these plots. This is done in order to establish whether characterization parameters extracted from the plot will be reliable or, alternative, likely to be spurious. This paper summarises the theory behind the orthodoxy test, for each of the plot forms, and confirms that it is easy to apply it to the newly developed MG plot. A simple web tool has been developed that extracts scaled-field values from any of these three plot forms, and tests for lack of field emission orthodoxy. △ Less

Submitted 15 June, 2020; originally announced June 2020.

Comments: 14 typescript pages, 2 figures

Journal ref: J. Electr. Eng. Slovak. 71, 37 (2020)

Applying the field emission orthodoxy test to Murphy-Good plots

Authors: Mohammad M. Allam, Richard G. Forbes, Marwan S. Mousa

Abstract: In field electron emission (FE) studies, it is important to check and analyse the quality and validity of results experimentally obtained from samples, using suitably plotted current-voltage [I(V)] measurements. For the traditional plotting method, the Fowler-Nordheim (FN) plot, there exists a so-called "orthodoxy test" that can be applied to the FN plot, in order to check whether the FE device/sy… ▽ More In field electron emission (FE) studies, it is important to check and analyse the quality and validity of results experimentally obtained from samples, using suitably plotted current-voltage [I(V)] measurements. For the traditional plotting method, the Fowler-Nordheim (FN) plot, there exists a so-called "orthodoxy test" that can be applied to the FN plot, in order to check whether the FE device/system generating the results is "ideal". If it is not ideal, then emitter characterization parameters deduced from the FN plot are likely to be spurious. A new form of FE I(V) data plot, the so-called "Murphy-Good (MG) plot" has recently been introduced (R.G. Forbes, Roy. Soc. Open Sci. 6 (2019) 190912. This aims to improve the precision with which characterization-parameter values (particularly values of formal emission area) can be extracted from FE I(V) data. The present paper compares this new plotting form with the older FN and Millikan-Lauritsen (ML) forms, and makes an independent assessment of the consistency with which slope (and hence scaled-field) estimates can be extracted from a MG plot. It is shown that, by using a revised formula for the extraction of scaled-field values, the existing orthodoxy test can be applied to Murphy-Good plots. The development is reported of a prototype web tool that can apply the orthodoxy test to all three forms of FE data plot (ML, MG and FN). △ Less

Submitted 13 June, 2020; originally announced June 2020.

Comments: 26 typescript pages, 3 figures

Tracking the Ultraviolet Photochemistry of Thiophenone During and Beyond the Initial Ultrafast Ring Opening

Authors: Shashank Pathak, Lea M. Ibele, Rebecca Boll, Carlo Callegari, Alexander Demidovich, Benjamin Erk, Raimund Feifel, Ruaridh Forbes, Michele Di Fraia, Luca Giannessi, Christopher S. Hansen, David M. P. Holland, Rebecca A. Ingle, Robert Mason, Oksana Plekan, Kevin C. Prince, Arnaud Rouzée, Richard J. Squibb, Jan Tross, Michael N. R. Ashfold, Basile F. E. Curchod, Daniel Rolles

Abstract: Photoinduced isomerization reactions, including ring-opening reactions, lie at the heart of many processes in nature. The mechanisms of such reactions are determined by a delicate interplay of coupled electronic and nuclear dynamics unfolding on the femtosecond scale, followed by the slower redistribution of energy into different vibrational degrees of freedom. Here we apply time-resolved photoele… ▽ More Photoinduced isomerization reactions, including ring-opening reactions, lie at the heart of many processes in nature. The mechanisms of such reactions are determined by a delicate interplay of coupled electronic and nuclear dynamics unfolding on the femtosecond scale, followed by the slower redistribution of energy into different vibrational degrees of freedom. Here we apply time-resolved photoelectron spectroscopy with a seeded extreme ultraviolet free electron laser to trace the ultrafast ring opening of gas phase thiophenone molecules following photoexcitation at 265 nm. When combined with cutting edge ab initio electronic structure and molecular dynamics calculations of both the excited and ground state molecules, the results provide unprecedented insights into both electronic and nuclear dynamics of this fundamental class of reactions. The initial ring opening and non-adiabatic coupling to the electronic ground state is shown to be driven by ballistic SC bond extension and to be complete within 350 femtoseconds. Theory and experiment also allow clear visualization of the rich ground-state dynamics involving formation of, and interconversion between, several ring opened isomers and the reformed cyclic structure, and fragmentation (CO loss) over much longer timescales. △ Less

Submitted 14 March, 2020; v1 submitted 1 December, 2019; originally announced December 2019.

Comments: 40 pages, 21 figures Changes from the previous version: 1) Added theoretical calculations for explaining long timescale changes in shown in Figure 4(a). 2) Reworked on fitting (modelling) of the experimental data in Figure 2(b). Added another panel i.e. Figure 2(c). 3) Other minor changes and rewording in response to questions and suggestions by the referees

Comments on the continuing widespread and unnecessary use of a defective emission equation in field emission related literature

Authors: Richard G. Forbes

Abstract: Field electron emission (FE) has relevance in many different technological contexts. However, many related technological papers use a physically defective elementary FE equation for local emission current density (LECD). This equation takes the tunneling barrier as exactly triangular, as in the original FE theory of 90 years ago. More than 60 years ago, it was shown that the so-called Schottky-Nor… ▽ More Field electron emission (FE) has relevance in many different technological contexts. However, many related technological papers use a physically defective elementary FE equation for local emission current density (LECD). This equation takes the tunneling barrier as exactly triangular, as in the original FE theory of 90 years ago. More than 60 years ago, it was shown that the so-called Schottky-Nordheim (SN) barrier, which includes an image-potential-energy term (that models exchange-and-correlation effects) is better physics. For a metal-like emitter with work-function 4.5 eV, the SN-barrier-related Murphy-Good FE equation predicts LECD values that are higher than the elementary equation values by a large factor, often between around 250 and around 500. By failing to mention/apply this 60-year-old established science, or to inform readers of the large errors associated with the elementary equation, many papers (aided by defective reviewing) spread a new kind of "pathological science", and create a modern research-integrity problem. The present paper aims to enhance author and reviewer awareness by summarizing relevant aspects of FE theory, by explicitly identifying the misjudgment in the original 1928 Fowler-Nordheim paper, by explicitly calculating the size of the resulting error, and by showing in detail why most FE theoreticians regard the 1950s modifications as better physics. Suggestions are made, about nomenclature and about citation practice, that may help to diminish misunderstandings. △ Less

Submitted 27 June, 2019; v1 submitted 24 June, 2019; originally announced June 2019.

Comments: Submitted for publication; in v2 a correction to historical information (with no numerical consequences) has been made in Appendix A

Field emission: Why converting LAFE voltages to macroscopic fields before making a Fowler-Nordheim plot has often led to spurious characterization results

Authors: Richard G. Forbes

Abstract: An important parameter used to characterize large-area field electron emitters (LAFEs) is the characteristic apex field enhancement factor γ_C. This parameter is normally extracted from the slope of a Fowler-Nordheim (FN) plot. Several years ago, the development of an "orthodoxy test" allowed a sample of 19 published FN plots relating to LAFEs to be tested, and it was found that about 40% of the r… ▽ More An important parameter used to characterize large-area field electron emitters (LAFEs) is the characteristic apex field enhancement factor γ_C. This parameter is normally extracted from the slope of a Fowler-Nordheim (FN) plot. Several years ago, the development of an "orthodoxy test" allowed a sample of 19 published FN plots relating to LAFEs to be tested, and it was found that about 40% of the related papers were reporting spuriously high values for γ_C. In technological papers relating to LAFE characterization, common practice is to pre-convert the measured voltage into an (apparent) value of macroscopic field before making and analyzing a FN plot. This paper suggests that the cause of the "spurious-FEF-value" problem is the widespread use of a pre-conversion equation that is defective (for example, not compatible with ordinary electrical circuit theory) when it is applied to so-called "non-ideal" field emission devices/systems. Many real devices/ systems are non-ideal. The author argues that FN plots should be made using raw experimental current-voltage data, and that an orthodoxy test should be applied to the resulting FN plot before any more-detailed analysis, and that (in view of growing concerns over the reliability of published "scientific" results) reviewers should scrutinize field emission materials-characterization papers with enhanced care. △ Less

Submitted 29 May, 2019; originally announced May 2019.

Comments: Article submitted for publication

The Murphy-Good plot: a better method of analysing field emission data

Authors: Richard G. Forbes

Abstract: Measured field electron emission (FE) current-voltage Im(Vm) data are traditionally analysed via Fowler-Nordheim (FN) plots, as ln{Im/(Vm)**2} vs 1/Vm. These have been used since 1929, because in 1928 FN predicted they would be linear. In the 1950s, a mistake in FN's thinking was found. Corrected theory by Murphy and Good (MG) made theoretical FN plots slightly curved. This causes difficulties whe… ▽ More Measured field electron emission (FE) current-voltage Im(Vm) data are traditionally analysed via Fowler-Nordheim (FN) plots, as ln{Im/(Vm)**2} vs 1/Vm. These have been used since 1929, because in 1928 FN predicted they would be linear. In the 1950s, a mistake in FN's thinking was found. Corrected theory by Murphy and Good (MG) made theoretical FN plots slightly curved. This causes difficulties when attempting to extract precise values of emission characterization parameters from straight lines fitted to experimental FN plots. Improved mathematical understanding, from 2006 onwards, has now enabled a new FE data-plot form, the "Murphy-Good plot". This plots ln{Im/(Vm)**(2-(η/6)} vs 1/Vm, where η depends only on local work function. Modern ("21st century") MG theory predicts that a theoretical MG plot should be "almost exactly" straight. This makes precise extraction of well-defined characterization parameters from ideal I_m(V_m) data much easier. This article gives the theory needed to extract characterization parameters from MG plots, setting it within the framework of wider difficulties in interpreting FE Im(Vm) data (among them, use of the "planar emission approximation"). Careful use of MG plots could also help remedy other problems in FE technological literature. It is argued MG plots should now supersede FN plots. △ Less

Submitted 18 May, 2019; originally announced May 2019.

Comments: Intended article

Quantum Beat Photoelectron Imaging Spectroscopy of Xe in the VUV

Authors: Ruaridh Forbes, Varun Makhija, Jonathan Underwood, Albert Stolow, Iain Wilkinson, Paul Hockett, Rune Lausten

Abstract: Time-resolved pump-probe measurements of Xe, pumped at 133~nm and probed at 266~nm, are presented. The pump pulse prepared a long-lived hyperfine wavepacket, in the Xe $5p^5(^2P^{\circ}_{1/2})6s~^2[1/2]^{\circ}_1$ manifold ($E=$77185 cm$^{-1}=$9.57 eV). The wavepacket was monitored via single-photon ionization, and photoelectron images measured. The images provide angle- and time-resolved data whi… ▽ More Time-resolved pump-probe measurements of Xe, pumped at 133~nm and probed at 266~nm, are presented. The pump pulse prepared a long-lived hyperfine wavepacket, in the Xe $5p^5(^2P^{\circ}_{1/2})6s~^2[1/2]^{\circ}_1$ manifold ($E=$77185 cm$^{-1}=$9.57 eV). The wavepacket was monitored via single-photon ionization, and photoelectron images measured. The images provide angle- and time-resolved data which, when obtained over a large time-window (900~ps), constitute a precision quantum beat spectroscopy measurement of the hyperfine state splittings. Additionally, analysis of the full photoelectron image stack provides a quantum beat imaging modality, in which the Fourier components of the photoelectron images correlated with specific beat components can be obtained. This may also permit the extraction of isotope-resolved photoelectron images in the frequency domain, in cases where nuclear spins (hence beat components) can be uniquely assigned to specific isotopes (as herein), and also provides phase information. The information content of both raw, and inverted, image stacks is investigated, suggesting the utility of the Fourier analysis methodology in cases where images cannot be inverted. △ Less

Submitted 2 March, 2018; originally announced March 2018.

Journal ref: Phys. Rev. A 97, 063417 (2018)

Time-resolved multi-mass ion imaging: femtosecond UV-VUV pump-probe spectroscopy with the PImMS camera

Authors: Ruaridh Forbes, Varun Makhija, Kévin Veyrinas, Albert Stolow, Jason W. L. Lee, Michael Burt, Mark Brouard, Claire Vallance, Iain Wilkinson, Rune Lausten, Paul Hockett

Abstract: The Pixel-Imaging Mass Spectrometry (PImMS) camera allows for 3D charged particle imaging measurements, in which the particle time-of-flight is recorded along with $(x,y)$ position. Coupling the PImMS camera to an ultrafast pump-probe velocity-map imaging spectroscopy apparatus therefore provides a route to time-resolved multi-mass ion imaging, with both high count rates and large dynamic range, t… ▽ More The Pixel-Imaging Mass Spectrometry (PImMS) camera allows for 3D charged particle imaging measurements, in which the particle time-of-flight is recorded along with $(x,y)$ position. Coupling the PImMS camera to an ultrafast pump-probe velocity-map imaging spectroscopy apparatus therefore provides a route to time-resolved multi-mass ion imaging, with both high count rates and large dynamic range, thus allowing for rapid measurements of complex photofragmentation dynamics. Furthermore, the use of vacuum ultraviolet wavelengths for the probe pulse allows for an enhanced observation window for the study of excited state molecular dynamics in small polyatomic molecules having relatively high ionization potentials. Herein, preliminary time-resolved multi-mass imaging results from C$_2$F$_3$I photolysis are presented. The experiments utilized femtosecond UV and VUV (160.8~nm and 267~nm) pump and probe laser pulses in order to demonstrate and explore this new time-resolved experimental ion imaging configuration. The data indicates the depth and power of this measurement modality, with a range of photofragments readily observed, and many indications of complex underlying wavepacket dynamics on the excited state(s) prepared. △ Less

Submitted 2 February, 2017; originally announced February 2017.

Run 2 Upgrades to the CMS Level-1 Calorimeter Trigger

Authors: B. Kreis, J. Berryhill, R. Cavanaugh, K. Mishra, R. Rivera, L. Uplegger, L. Apanasevich, J. Zhang, J. Marrouche, N. Wardle, R. Aggleton, F. Ball, J. Brooke, D. Newbold, S. Paramesvaran, D. Smith, M. Baber, A. Bundock, M. Citron, A. Elwood, G. Hall, G. Iles, C. Laner, B. Penning, A. Rose , et al. (39 additional authors not shown)

Abstract: The CMS Level-1 calorimeter trigger is being upgraded in two stages to maintain performance as the LHC increases pile-up and instantaneous luminosity in its second run. In the first stage, improved algorithms including event-by-event pile-up corrections are used. New algorithms for heavy ion running have also been developed. In the second stage, higher granularity inputs and a time-multiplexed app… ▽ More The CMS Level-1 calorimeter trigger is being upgraded in two stages to maintain performance as the LHC increases pile-up and instantaneous luminosity in its second run. In the first stage, improved algorithms including event-by-event pile-up corrections are used. New algorithms for heavy ion running have also been developed. In the second stage, higher granularity inputs and a time-multiplexed approach allow for improved position and energy resolution. Data processing in both stages of the upgrade is performed with new, Xilinx Virtex-7 based AMC cards. △ Less

Submitted 18 November, 2015; originally announced November 2015.

Comments: 10 pages, 7 figures

Fowler-Nordheim Plot Analysis: a Progress Report

Authors: Richard G. Forbes, Jonathan H. B. Deane, Andreas Fischer, Marwan S. Mousa

Abstract: The commonest method of characterizing a cold field electron emitter is to measure its current-voltage characteristics, and the commonest method of analysing these characteristics is by means of a Fowler-Nordheim (FN) plot. This tutorial/review-type paper outlines a more systematic method of setting out the Fowler-Nordheim-type theory of cold field electron emission, and brings together and summar… ▽ More The commonest method of characterizing a cold field electron emitter is to measure its current-voltage characteristics, and the commonest method of analysing these characteristics is by means of a Fowler-Nordheim (FN) plot. This tutorial/review-type paper outlines a more systematic method of setting out the Fowler-Nordheim-type theory of cold field electron emission, and brings together and summarises the current state of work by the authors on developing the theory and methodology of FN plot analysis. This has turned out to be far more complicated than originally expected. Emphasis is placed in this paper on: (a) the interpretation of FN-plot slopes, which is currently both easier and of more experimental interest than the analysis of FN-plot intercepts; and (b) preliminary explorations into developing methodology for interpreting current-voltage characteristics when there is series resistance in the conduction path from the high-voltage generator to the emitter's emitting regions. This work reinforces our view that FN-plot analysis is best carried out on the raw measured current-voltage data, without pre-conversion into another data format, particularly if series resistance is present in the measuring circuit. Relevant formulae are given for extracting field-enhancement-factor values from such an analysis. △ Less

Submitted 1 July, 2016; v1 submitted 23 April, 2015; originally announced April 2015.

Comments: v7 is publication version, but with correction of typographic errors on pages 138 and 141 of published version

Journal ref: Jordan Journal of Physics 8 (2015) 125-147

Extraction of emission parameters for large-area field emitters, using a technically complete Fowler-Nordheim-type equation

Authors: Richard G. Forbes

Abstract: In papers on cold field electron emission from large area field emitters (LAFEs), it has become widespread practice to publish a misleading Fowler-Nordheim-type (FN-type) equation. This equation over-predicts the LAFE-average current density by a large highly-variable factor thought to usually lie between 1000 and 1000 000 000. This equation, although often referenced to FN's 1928 paper, is a simp… ▽ More In papers on cold field electron emission from large area field emitters (LAFEs), it has become widespread practice to publish a misleading Fowler-Nordheim-type (FN-type) equation. This equation over-predicts the LAFE-average current density by a large highly-variable factor thought to usually lie between 1000 and 1000 000 000. This equation, although often referenced to FN's 1928 paper, is a simplified equation used in undergraduate teaching, does not apply unmodified to LAFEs, and does not appear in the 1928 paper. Technological LAFE papers often do not cite any theoretical work more recent than 1928, and often do not comment on the discrepancy between theory and experiment. This usage has occurred widely, in several high-profile American and UK applied-science journals, and in various other places. It does not inhibit practical LAFE development, but can give a misleading impression of potential LAFE performance to non-experts. This paper shows how the misleading equation can be replaced by a conceptually complete FN-type equation that uses three high-level correction factors. One of these, or a combination of two of them, may be useful as an additional measure of LAFE quality; this paper describes how to estimate factor values using experimental data. Suggestions are made for improved engineering practice in reporting LAFE results. Some of these should help to prevent situations arising whereby an equation appearing in high-profile applied-science journals is used to support statements that an engineering regulatory body might deem to involve professional negligence. △ Less

Submitted 29 January, 2012; v1 submitted 30 November, 2011; originally announced November 2011.

Comments: 36 pages, including two figures, and list of acronyms (to be electronic supplementary materiaL). Version scientifically equivalent to corrected proof for publication in Nanotechnology. Some minor typographical errors have been corrected

Journal ref: Nanotechnology 23 (2012) 095706