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Secondary Electron Emission and Yield Spectra of Metals from Monte IOP Journal of Physics: Condensed Matter Journal of Physics: Condensed Matter J. Phys.: Condens. Matter J. Phys.: Condens. Matter 31 (2019) 055901 (11pp) https://doi.org/10.1088/1361-648X/aaf363 31 Secondary electron emission and yield 2019 spectra of metals from Monte Carlo © 2018 IOP Publishing Ltd simulations and experiments JCOMEL Martina Azzolini1,2, Marco Angelucci3, Roberto Cimino3 , Rosanna Larciprete3,4, Nicola M Pugno2,5,6 , Simone Taioli1,7 055901 and Maurizio Dapor1 1 European Centre for Theoretical Studies in Nuclear Physics and Related Areas (*ECT*­FBK) and Trento M Azzolini et al Institute for Fundamental Physics and Applications (TIFPA­INFN), Trento, Italy 2 Laboratory of Bio­Inspired and Graphene Nanomechanics—Department of Civil, Environmental Secondary electron emission and yield spectra of metals from Monte Carlo simulations and experiments and Mechanical Engineering, University of Trento, Trento, Italy 3 Laboratori Nazionali di Frascati (INFN), Frascati (RM), Italy 4 Institute for Complex System (CNR), Rome, Italy Printed in the UK 5 School of Engineering and Materials Science, Materials Research Institute, Queen Mary University of London, London, United Kingdom 6 Ket Lab, Edoardi Amaldi Foundation, c/o Italian Space Agency, Rome, Italy CM 7 Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic E­mail: [email protected], [email protected] and [email protected] 10.1088/1361-648X/aaf363 Received 12 September 2018, revised 16 November 2018 Accepted for publication 23 November 2018 Paper Published 19 December 2018 Abstract 1361-648X In this work, we present a computational method, based on the Monte Carlo statistical approach, for calculating electron energy emission and yield spectra of metals, such as copper, silver and gold. The calculation of these observables proceeds via the Mott theory with a Dirac Hartree Fock spherical potential to deal with the elastic scattering processes, and by 5 – – using the Ritchie dielectric approach to model the electron inelastic scattering events. In the latter case, the dielectric function, which represents the starting point for the evaluation of the energy loss, is obtained from experimental reflection electron energy loss spectra. The generation of secondary electrons upon ionization of the samples is also implemented in the calculation. A remarkable agreement is obtained between both theoretical and experimental electron emission spectra and yield curves. Keywords: secondary electron emission, Monte Carlo method, noble metals, yield (Some figures may appear in colour only in the online journal) 1. Introduction with low work function photocathode or by increasing the local curvature of the surface by steep edges. The emission of secondary electrons plays a fundamental role On the other hand, in other applications the emission of in materials characterization techniques [1, 2], such as scan­ secondary electrons must be suppressed, e.g. in particle accel­ ning electron microscopy [3, 4], and in affecting the perfor­ erators. Indeed, detrimental effects on the machine stability, mance of a variety of electron devices, such as the detectors which might result in beam loss [7–12], can be caused by the based on electron multipliers [5, 6]. These techniques in par­ so­called multipactor effect. This phenomenon appears when ticular seek a high value of the electron yield to reach a low the current of re­emitted electrons grows uncontrollably due noise­to­signal ratio for enhancing the image quality. High to presence of electronic charges in proximity of the vacuum electron yield can be achieved by coating the photomultiplier tube walls. The latter are accelerated by the primary beam, 1361-648X/19/055901+11$33.00 1 © 2018 IOP Publishing Ltd Printed in the UK J. Phys.: Condens. Matter 31 (2019) 055901 M Azzolini et al producing an avalanche of secondary electrons. In this regard, curves from very low primary energies to about 1000 eV chemical treatment, coating [13, 14] and patterning of the [9–12, 29, 30]. The SEY, i.e. the ratio of the number of elec­ target surface [15–18] were used to overcome the harmful trons leaving the sample surface (Is) to the number of incident effects brought about by this phenomenon. Analogous criti­ electrons (Ip) per unit area, was determined experimentally cality concerns microwave and RF components for space by measuring I and the total sample current I = I I , so p t p − s applications that find one of their most important functional that δ = 1 It/Ip. For the SEY measurements, the electron limitations in the multipactor and corona breakdown dis­ beam was set− to be smaller than 1 mm2 in transverse cross­ charges [19]. sectional area at the sample surface. To measure the current Despite these remarkable attempts, several issues could of the impinging primary electrons, a negative bias voltage be bypassed by developing an efficient and accurate method ( 75 V) was applied to the sample. The SEY measurements to calculate the electron yield of the investigated material, in were− performed at normal incidence, by using electron beam order to predict the secondary emission and thus to tailor the currents of a few nA. A SpectraLEED Omicron LEED/Auger solution according to the application sought for. In this regard, retarding field (RF) analyser system was specially modified analytic descriptions of the secondary electron energy yield to be able to collect angle integrated EDC with RF filtering have been developed over the years [20–24]. and computer control while using the gun in LEED mode, In this work, we present an accurate computational i.e. with a low­energy focused beam. The e− gun provided approach, based on the Monte Carlo method [25], to simu­ a small and stable (both in current and position) beam spot late electron trajectories leading to secondary electron on the sample, in the energy range from 30 to 1000 eV. This emission and we compare theoretical lineshapes with our set­up can measure angle integrated EDC with the limitation recorded experimental yield spectra. Within this approach, typical of any RF analyzers. While the secondaries are consis­ elastic col lision and inelastic scattering processes are care­ tently measured at all primary energies, elastic peaks broaden fully evaluated. In the former case this means to assess the due to increasingly poor resolution at higher primary energies, angular deviation along the path of the electrons in their way showing an additional strong asymmetry on the low energy out of the solid, while in the latter the electron energy loss. side due to the integration of the background [31, 32]. Despite In particular, the elastic scattering is treated within the Mott those known limitations, the data can be used in this work to theory [26] using a Dirac–Hartree–Fock spherical potential, extract the relevant information needed. The sample can be while the inelastic scattering events are dealt with the Ritchie transferred from air into UHV conditions and can be cooled di electric theory [27]. The Monte Carlo method is used to down to 10 K, exposed to various types of gases and cleaned simulate the secondary spectra of three metallic targets, that by subsequent cycles of Ar sputtering. All the polycrystalline + is copper, silver and gold. The dielectric functions used in the metallic samples here studied were cleaned by repeated Ar 6 assessment of the energy loss of these materials are obtained sputtering cycles at 1.5 KeV in Ar pressure of 5 10− mbar from reflection electron energy loss (REEL) experiments [28]. until no signal of C and O was observed in the XPS× spectrum. This treatment thus takes into account the contribution to the secondary emission spectra of both bulk and surface plasmon 3. Computational details excitations, increasing the accuracy of the computed data. This paper is structured as follows: in the following sec­ 3.1. Monte Carlo tion 2 the experimental procedures used in the measurements of the secondary emission and yield spectra of all metals are The Monte Carlo approach models the spectral distribution of described. Afterwards, a detailed discussion of the computa­ energy transferred to a specimen bombarded with a perpend­ tional Monte Carlo approach is presented in section 3. Finally, icularly incident electron beam by following the electron in section 4 we present a thorough comparison between simu­ trajectories within the target. The electron trajectories result lated and experimental data of secondary emission and yield from the elastic and inelastic interactions undergone by the spectra. electrons scattered by the nuclei and the electron clouds of target atoms, respectively. Secondary electrons are generated via inelastic interac­ 2. Experimental details tions through the ionization of the target’s atomic centers. In the latter process, by measuring the kinetic energies of the The experimental apparatus used to study the secondary escaping charges, the electron emission energy spectra can electron yield (SEY) and angle integrated energy distribu­ be recorded. In the Monte Carlo simulation of this emission tion curves (EDC) is hosted in the ‘Material Science’ labo­ mechanism the trajectories of secondary electrons, similarly ratory of LNF­INFN, Frascati (Rome). For our experiments to those generated by elastic and non­ionizing inelastic scat­ we used a specially built UHV µ­metal chamber with less tering, are followed by using a statistical algorithm. At vari­ than 5 mGauss residual magnetic field at the sample position, ance, the path of electrons with kinetic energies below the pumped by a CTI8 cryopump to ensure a vacuum better than value of the work function or of electrons emitted by the spec­ 10 10− mbar. The set­up has been designed to limit the residual imen is considered terminated. magnetic field near the sample, which can deviate low­energy In Monte Carlo simulations, the probability of elastic and electrons. Ion pumps are not used due to their detrimental inelastic scattering events is assessed by comparing random stray magnetic field.
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