Spatially encoded measurements of transient optical transmissivity became a standard tool for temporal diagnostics of free-electron-laser (FEL) pulses, as well as for the arrival time measurements in X-ray pump and optical probe experiments. The modern experimental techniques can measure changes in optical coefficients with a temporal resolution better than 10 fs. This, in an ideal case, would imply a similar resolution for the temporal pulse properties and the arrival time jitter between the FEL and optical laser pulses. However, carrier transport within the material and out of its surface, as well as carrier recombination may, in addition, significantly decrease the number of carriers. This would strongly affect the transient optical properties, making the diagnostic measurement inaccurate. Below we analyze in detail the effects of those processes on the optical properties of XUV and soft X-ray irradiated Si[Formula: see text]N[Formula: see text], on sub-picosecond timescales. Si[Formula: see text]N[Formula: see text] is a wide-gap insulating material widely used for FEL pulse diagnostics. Theoretical predictions are compared with the published results of two experiments at FERMI and LCLS facilities, and with our own recent measurement. The comparison indicates that three body Auger recombination strongly affects the optical response of Si[Formula: see text]N[Formula: see text] after its collisional ionization stops. By deconvolving the contribution of Auger recombination, in future applications one could regain a high temporal resolution for the reconstruction of the FEL pulse properties measured with a Si[Formula: see text]N[Formula: see text]-based diagnostics tool.

Center for Free Electron Laser Science CFEL Deutsches Elektronen Synchrotron DESY Notkestrasse 85 22607 Hamburg Germany

Deutsches Elektronen Synchrotron DESY Notkestrasse 85 22607 Hamburg Germany

Elettra Sincrotrone Trieste S C p A 34149 Trieste Basovizza Italy

European XFEL GmbH Holzkoppel 4 22869 Schenefeld Germany

Institut für Experimentalphysik Universität Hamburg Luruper Chaussee 149 22761 Hamburg Germany

Institute for Laser and Optics Hochschule Emden Leer University of Applied Sciences Constantiaplatz 4 26723 Emden Germany

Institute of Nuclear Physics Polish Academy of Sciences Radzikowskiego 152 31 342 Kraków Poland

Institute of Physics Carl von Ossietzky University Carl von Ossietzky Str 9 11 26111 Oldenburg Germany

Institute of Physics CAS v v i Na Slovance 2 182 21 Prague Czech Republic

Institute of Plasma Physics CAS v v i Za Slovankou 3 182 00 Prague Czech Republic

Institute of Radiation Physics Helmholtz Zentrum Dresden Rossendorf e 5 Bautzner Landstrasse 400 01328 Dresden Germany

SLAC National Accelerator Laboratory Menlo Park CA 94025 USA

See more in PubMed

Harmand M, et al. Achieving few-femtosecond time-sorting at hard X-ray free-electron lasers. Nat. Photon. 2013;7:215. doi: 10.1038/nphoton.2013.11. DOI

Riedel R, et al. Single-shot pulse duration monitor for extreme ultraviolet and X-ray free-electron lasers. Nat. Commun. 2013;4:1731. doi: 10.1038/ncomms2754. PubMed DOI

Finetti P, et al. Pulse duration of seeded free-electron lasers. Phys. Rev. X. 2017;7:021043.

Maltezopoulos T, et al. Single-shot timing measurement of extreme-ultraviolet free-electron laser pulses. New J. Phys. 2008;10:033026. doi: 10.1088/1367-2630/10/3/033026. DOI

Teubner U, Wagner U, Foerster E. Sub-ten-femtosecond gating of optical pulses. J. Phys. B. 2001;34:2993. doi: 10.1088/0953-4075/34/15/306. DOI

Medvedev N, Tkachenko V, Lipp V, Li Z, Ziaja B. Various damage mechanisms in carbon and silicon materials under femtosecond X-ray irradiation. 4open. 2018;1:3. doi: 10.1051/fopen/2018003. DOI

Krupin O, et al. Temporal cross-correlation of X-ray free electron and optical lasers using soft X-ray pulse induced transient reflectivity. Opt. Exp. 2012;20:11396–11406. doi: 10.1364/OE.20.011396. PubMed DOI

Casolari F, et al. Role of multilayer-like interference effects on the transient optical response of Si3N4 films pumped with free-electron laser pulses. Appl. Phys. Lett. 2014;104:191104. doi: 10.1063/1.4875906. DOI

Mincigrucci R, et al. Optical constants modelling in silicon nitride membrane transiently excited by EUV radiation. Opt. Exp. 2018;26:11877. doi: 10.1364/OE.26.011877. PubMed DOI

Mincigrucci R, et al. Timing methodologies and studies at the FERMI free-electron laser. J. Synchr. Radiat. 2018;25:44. doi: 10.1107/S1600577517016368. PubMed DOI

Capotondi F, et al. Characterization of ultrafast free-electron laser pulses using extreme-ultraviolet transient gratings. J. Synchr. Radiat. 2018;25:32. doi: 10.1107/S1600577517015612. PubMed DOI

Bencivenga F, et al. Four-wave-mixing experiments with seeded free electron lasers. Far. Disc. 2016;194:283. doi: 10.1039/C6FD00089D. PubMed DOI

Foglia L, et al. First evidence of purely extreme-ultraviolet four-wave mixing. Phys. Rev. Lett. 2018;120:263901. doi: 10.1103/PhysRevLett.120.263901. PubMed DOI

Bencivenga F, et al. Nanoscale transient gratings excited and probed by extreme ultraviolet femtosecond pulses. Sci. Adv. 2019;5:eaaw5805. doi: 10.1126/sciadv.aaw5805. PubMed DOI PMC

Tkachenko, V. et al. Time-resolved ionization measurements with intense ultrashort XUV and X-ray free-electron laser pulses. Laser Particle Beams1–7 (2019).

Lipp V, Medvedev N, Ziaja B. Classical Monte-Carlo simulations of X-ray induced electron cascades in various materials. Proc. SPIE. 2017;10239:102360H.

Medvedev N. Femtosecond X-ray induced electron kinetics in dielectrics: Application for FEL-pulse-duration monitor. Appl. Phys. B. 2015;118:417. doi: 10.1007/s00340-015-6005-4. DOI

Keski-Rahkonen O, Krause MO. Total and partial atomic-level widths. Atom. Data Nucl. Data Tables. 1974;14:139–146. doi: 10.1016/S0092-640X(74)80020-3. DOI

Okhrimovskyy A, Bogaerts A, Gijbels R. Electron anisotropic scattering in gases: A formula for Monte Carlo simulations. Phys. Rev. E. 2002;65:037402. doi: 10.1103/PhysRevE.65.037402. PubMed DOI

Cullen, D. A survey of atomic binding energies for use in EPICS2017. in Technical Reports, Vienna. https://www-nds.iaea.org/epics/ (2018).

Kim Y-K, Rudd EM. Binary-encounter-dipole model for electron-impact ionization. Phys. Rev. A. 1994;50:3954. doi: 10.1103/PhysRevA.50.3954. PubMed DOI

Medvedev N. Femtosecond x-ray induced electron kinetics in dielectrics: application for fel-pulse-duration monitor. Appl. Phys. B. 2015;118:417–429. doi: 10.1007/s00340-015-6005-4. DOI

Plante I, Cucinotta FA. Cross sections for the interactions of 1 eV-100 MeV electrons in liquid water and application to Monte-Carlo simulation of HZE radiation tracks. New J. Phys. 2009;11:063047. doi: 10.1088/1367-2630/11/6/063047. DOI

Mecseki K, et al. Hard X-ray induced fast secondary electron cascading processes in solids. Appl. Phys. Lett. 2018;113:114102. doi: 10.1063/1.5046070. DOI

Ashley J. Interaction of low-energy electrons with condensed matter: Stopping powers and inelastic mean free paths from optical data. J. Electr. Spec. Rel. Phenom. 1988;46:199. doi: 10.1016/0368-2048(88)80019-7. DOI

Tanuma S, Powell C, Penn D. Calculations of electron inelastic mean free paths. II. Data for 27 elements over the 50–2000 eV range. Surf. Interf. Anal. 1991;17:911. doi: 10.1002/sia.740171304. DOI

Fernández-Varea J, Liljequist D, Csillag S, Raety R, Salvat F. Monte Carlo simulation of 0.1 - 100 keV electron and positron transport in solids using optical data and partial wave methods. Nucl. Inst. Methods Phys. Res. B. 1996;108:35–50. doi: 10.1016/0168-583X(95)01055-6. DOI

Ziaja B, London RA, Hajdu J. Unified model of secondary electron cascades in diamond. J. Appl. Phys. 2005;97:064905. doi: 10.1063/1.1853494. DOI

Ashcroft, N. & Mermin, N. Solid State Physics. (Harcourt, Inc., 1976).

Yeh P. Optical Waves in Layered Media. Wiley; 2005.

Ziaja B, Medvedev N, Tkachenko V, Maltezopoulos T, Wurth W. Time-resolved observation of band-gap shrinking and electron-lattice thermalization within X-ray excited gallium arsenide. Sci. Rep. 2015;5:18068. doi: 10.1038/srep18068. PubMed DOI PMC

Milov I, et al. Mechanism of single-shot damage of Ru thin films irradiated by femtosecond extreme UV free-electron laser. Opt. Exp. 2018;26:19665. doi: 10.1364/OE.26.019665. PubMed DOI

Meyaard, D. S., Lin, G.-B., Cho, J. & Schubert, E. F. Efficiency droop in gallium indium nitride (GaInN)/gallium nitride (GaN) LEDs. in Nitride Semiconductor Light-Emitting Diodes, Vol. 279 (2014).

Svantesson KG, Nilsson NG. The temperature dependence of the Auger recombination coefficient of undoped silicon. J. Phys. C: Solid State Phys. 1979;12:5111. doi: 10.1088/0022-3719/12/23/019. DOI

MacArthur, J., Duris, J., Huang, Z. & Marinelli, A. High power sub-femtosecond X-ray pulse study for the LCLS. in Proceedings of IPAC2017, Copenhagen, Denmark. 10.18429/JACoW-IPAC2017-WEPAB118 (2017).

Quantifying electron cascade size in various irradiated materials for free-electron laser applications