The Relativistic Heavy Ion Collider (RHIC) contributes fundamental advances to nuclear physics by colliding a wide range of ions. A novel electron cooling section, which is a key component of the proposed luminosity upgrade for RHIC, requires the acceleration of high-charge electron bunches with low emittance and energy spread. A promising candidate for the electron source is the recently developed concept of a high quantum efficiency photoinjector with a diamond amplifier. To assist in the development of such an electron source, we have implemented algorithms within the VORPAL particle-in-cell framework for modeling secondary electron and hole generation, and for charge transport in diamond. The algorithms include elastic, phonon, and impurity scattering processes over a wide range of charge carrier energies. Results from simulations using the implemented capabilities will be presented and discussed

Ben-Zvi, Ilan

Busby, R.

Cary, J. R.

Chang, X.

Dimitrov, D. A.

Keister, J.

Muller, E.

Rao, T.

Smedley, J.

Wu, Q.

UNT Digital Library

Pres. PAC'09 Conf., Vancouver, BC4-8 May (2009)BNL 90592-2009-CP3D SIMULATIONS OF SECONDARY ELECTRON GENERATIONAND TRANSPORT IN A DIAMOND ELECTRON BEAM AMPLIFIER*R. Busby, D.A. Dimitrov, and J.R. CaryTech-X CorporationBoulder, CO 80303I. Ben-Zvi, X. Chang, J. Keister, E. Muller, T. Rao, J. Smedley, and Q. WUBrookhaven National LaboratoryUpton, NY 11973-5000May,2009*This manuscript has been authored by Brookhaven Science Associates, LLC underContract No. DC-AC02-98CHI0886 with the U.S. Department of Energy. The UnitedStates Government retains, and the publisher, by accepting the article for publication,acknowledges, a world-wide license to publish or reproduce the published form of thismanuscript, or allow others to do so, for the United States Government purposes.DISCLAIMERThis work was prepared as an account of work sponsored by an agency of the UnitedStates Government. Neither the United States Government nor any agency thereof, norany of their employees, nor any of their contractors, subcontractors, or their employees,makes any warranty, express or implied, or assumes any legal liability or responsibilityfor the accuracy, completeness, or any third party's use or the results of such use of anyinformation, apparatus, product, or process disclosed, or represents that its use wouldnot infringe privately owned rights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark, manufacturer, or otherwise, doesnot necessarily constitute or imply its endorsement, recommendation, or favoring by theUnited States Government or any agency thereof or its contractors or subcontractors.The views and opinions of authors expressed herein do not necessarily state or reflectthose ofthe United States Government or any agency thereof3D SIMULATIONS OF SECONDARY ELECTRON GENERATION ANDTRANSPORT IN A DIAMOND ELECTRON BEAM AMPLIFIER *R.Busby, D. A. Dimitrovl, J. R. Cary, Tech-X Corp., Boulder, CO 80303, USAI. Ben-Zvi, X. Chang, J. Keister, E. Muller, T. Rao, J. Smedley, Q. Wu, BNL, Upton, NY 11973, USAAbstractThe Relativistic Heavy Ion Collider (RHIC) contributesfundamental advances to nuclear physics by colliding awide range of ions. A novel electron cooling section, whichis a key component of the proposed luminosity upgradefor RHIC, requires the acceleration of high-charge elec-tron bunches with low emittance and energy spread. Apromising candidate for the electron source is the recentlydeveloped concept of a high quantum efficiency photoin-jector with a diamond amplifier [1]. To assist in the devel-opment of such an electron source, we have implementedalgorithms within the VORPAL particle-in-cell frameworkfor modeling secondary electron and hole generation, andfor charge transport in diamond. The algorithms includeelastic, phonon, and impurity scattering processes over awide range ofcharge carrier energies. Results from simula-tions using the implemented capabilities will be presentedand discussed.INTRODUCTIONA new concept for a photo-cathode with a diamond am-plifier was recently proposed [1] and is currently under ac-tive development [2, 3]. The diamond amplified photo-cathode (DAP) has demonstrated the potential to addressthe need for high peak and average current, high brightnessand low thermal emittance electron beams in current andfuture accelerator-based systems. Moreover, the DAP hasnegligible contamination problems, requires two orders ofmagnitude less laser power, and is expected to have a longlifetime in comparison to existing photo-cathodes.The idea for the DAP operation consists of generatingfirst a beam of electrons using a conventional photocath-ode. These are the primary electrons that are acceleratedto energies of about 10 keY before impacting a diamondwindow. When these primary electrons enter into the dia-mond, they experience inelastic scattering processes lead-ing to the generation of secondary electrons and holes. Anysecondary electron or a hole that is produced with a suf-ficiently high energy can also participate in such inelasticprocesses, generating more electron-hole (e-h) pairs. Theseinelastic scattering processes continue until none ofthe freeelectrons and holes has sufficiently high energy to gener-ate additional e-h pairs. However, the total number of pro-duced secondary electrons is generally much larger than* We are grateful to the US DoE for supporting this work under theDE-FG02-06ER84509 grant.t dad@txcorp.comthe number of primary electrons. The free charged carriersalso experience inelastic scattering involving the emissionor absorption of phonons (lattice excitations). If an exter-nal field is applied in the diamond, the free electrons andholes will start drifting in opposite directions. Large num-bers of the secondary electrons are transported through thediamond and emitted from one of its surfaces. Diamondemission surfaces are prepared to have a negative electronaffinity (NEA) in order to increase the emission. The elec-trons are emitted into the accelerating cavio/ of an electrongun.To optimize the performance of the DAP concept, it is ofconsiderable interest to understand the generation of secon-daries and their transport in diamond samples with differentcharacteristics (thickness, concentration and type of impu-rities, surface effects at both metal coated and NEA sur-faces) and how a diamond amplifier couples to the overalloperation of the complete photoinjector system. To addressthis problem, we have been developing models, within theVORPAL [4] computational framework, for simulation ofsecondary electron generation and charge transport in dia-mond. Initially, we implemented models for the inelasticscattering leading to generation of secondary electrons andholes [5]. Here, we report on our work to enable the sim-ulation of charge transport in diamond. The ability to sim-ulate both secondary electron generation and charge trans-port allows us to investigate electron gain from diamond ina transmission mode setup (D. A. Dimitrov et al. in theseproceedings).MODELING SECONDARY ELECTRONGENERATION AND TRANSPORTThe short time scale (of the order of 100 fs) dynamics ofelectrons in diamond with medium range ofenergies (fromabout 50 eV to 10 keV) was treated by considering elasticand inelastic scattering processes, with the latter leadingto generation of secondary electrons and holes [6, 7, 8].For the inelastic scattering, we implemented first the Ash-ley model described by Ziaja et al. [6, 7] and consideredsecondary electron generation effects with it [5]. Recently,we also implemented the TPP-2 optical model for the in-elastic scattering that produces scattering rates in betteragreement [8] with the rates from band-structure calcula-tions [9] at low energies (f'.J 10 eV). For the elastic scat-tering in the medium energy range we used the rates givenin Ref. [8] but our implementation [5] is based on methodsfrom semiconductor device simulations [10]. The scatter-ing rates for the elastic and the inelastic (calculated withE(eV)'" ,.ELECTRON TRANSPORT SIMULATIONStic phonons and the three optical phonons considered areshown in the bottom plot of Fig. 1 at T = 300 K. The9 and f type rates are for transitions between parallel andperpendicular valleys, respectively. Decreasing the temper-ature ofdiamond reduces these rates [11]. For comparison,the rates for scattering of electrons from charged impuri-ties (using the model from Ref. [11]) at two concentrationsis also shown together with the electron-phonon scatteringrates. The data plotted in Fig. 1 shows that in the mediumelectron energy range, the rates for secondary electron gen-eration and for elastic scattering are several orders of mag-nitude larger than the electron-phonon and charged impu-rity scattering ones. However, at low electron energies (10eV and lower) the secondary electron generation rates arecomparable to the electron-phonon rates. Note that mod-eling of electron transport with energies close to the bot-tom of the conduction band does not include elastic scat-tering [9] from the periodic potential of the carbon ions asdone for the medium energy range [6].We have implemented a general Monte Carlo algorithmto handle all scattering processes (it also includes null col-lisions [10] to increase the efficiency). In between scatter-ing events, the particle-in-cell algorithms in VORPAL [4]provide the capability to self-consistently move particlesinteracting with electromagnetic fields.10Energy (eV)0.11~.01« •. imp. deDII. 8e2O•• , imp. deDII. 1.64e201014:.: :::::~t_. g3Abs_ g3Emit_. t3Ab.- f3Emitf2Ab.t2Emit1013L...----L--l-.-...L-....l-.L...J....L..JL...L----L.--L-~...L_l..J....L.I._____JI...._.__l.___L_.L...L..L..L_J...J1011015 r.======~----.-or------..,the TPP-2 model) processes are shown in the top plot ofFig. 1.Figure 1: The top plot shows the inelastic scattering ratesfor generation of secondary electrons and holes (calculatedfrom the TPP-2 model) together with the elastic rates in themedium energy range. The bottom plot shows the rates forelectron-phonon (low energy inelastic) and impurity (elas-tic) scattering processes.The free (conduction band) electrons in diamond also ex-perience low-energy inelastic scattering with phonons (lat-tice excitations) and elastic scattering from charged impuri-ties. Charge transport cannot be simulated accurately with-out including the electron-phonon scattering. These inelas-tic processes lead to additinal relaxation of the the electronenergies to reach the drift state in an applied field. At lowfields, free electrons have energies close to the bottom ofthe conduction band and drift with temperature effectivelyequal to the temperature of the diamond crystal (a highlydesirable property for generation of beams with low ther-mal emittance).For the low-energy inelastic scattering with optical andacoustic phonons we implemented Monte Carlo algorithmsbased on the models given by Jacoboni and Reggiani [11].In diamond, these models approximate the energy bandswith a parabolic dependence on the electron wave vectorand have ellipsoidal constant energy surfaces. Both in-tervalley and intravalley electron-phonon processes are in-cluded. The rates for the emission and absorption ofacous-In this Section, we discuss representative results fromsimulations with the implemented models on electron"transport after secondary electrons and holes are generatedusing one of the models for inelastic scattering. We usedthe Ashley model for the results here and primary electronenergy of 2.7 keY. We reported effects related to the sec-ondary electron generation with this model in a previousstudy [5] and present only new results from the transportsimulations here.The domain was split into a three-dimensional grid, typ-ically of 24 x 24 x 24 cells, with a cell edge size of 0.1J.1m. For the simulations described here, a small time step(usually 8 x 10-18 s) was used during the creation of thesecondary electrons (to resolve the mean free time for theseprocesses) which happens during the first few hundred fem-toseconds. Phonon scattering was not enabled during thistime interval. At the end of this interval, the VORPAL datawas dumped, the input file modified to increase the timestep (for faster simulation runs while still resolving themean free times of the low energy scattering processes),and to enable scattering of the free charged carriers withphonons. The total propagation time of these simulationswas approximately 20 ps.We specifically studied the dependence of the drift ve-locity obtained with the phonon scattering models on theapplied external field magnitudes' in a range values from0.05 to 10 MV/m. This is a range of interest for use indiamond amplified photo-cathodes. Our goal was to ver-ify that the models can describe the transport of electronclouds with drift velocities in agreement with experimentalmeasurements for this range of applied fields.0.8~'=0. 0.6~g.s~ 0.4~~ 0.2•6t Ips)10 12framework for simulation of secondary electron generationand transport in diamond. We presented results from trans-port simulations to determine the electron drift velocity de-pendence on the applied field. These simulations test theimplemented electron-phonon scattering models. The driftvelocity obtained from VORPAL agrees well with experi-mental data and more detailed band-structure calculationsfor the fields of interest. This gives us confidence thatthe electron-phonon models we implemented in VORPALare adequate to simulate electron transport in diamond forstudying DAP properites. In future developments, we willinvestigate how to incorporate models of electron emissionfrom diamond surfaces with negative electron affinities andeffects related to trapping of electrons in diamond.REFERENCESFigure 2: The drift velocity evolution at two applied fieldsindicate the rate of convergence to the (time) average values(given in the legend).The relaxation behavior of the drift velocity to steadystate from simulations at two field values is shown Fig. 2.The results show that it takes of the order of a few pi-coseconds to reach the steady state. The relaxation timedecreases when increasing the applied field.'.•105 •ii •0~~ ••0.1 1 10Electric Field Magnitude (MV/m)Figure 3: The obtained average electron drift velocity vsapplied field from VORPAL simulations of electron trans-port in diamond agrees well with experimental data.The dependence of the average electron drift velocityon the applied field magnitude obtained from the VOR-PAL simulations with the models we implemented for theelectron-phonon scattering is shown in Fig. 3. These val-ues agree well with experimental data and the more de-tailed, band-structure Monte Carlo simulation results givenby Watanabe et ale [9].SUMMARYWe described here the overall modeling capabilitieswe have implemented within the VORPAL computational[1] I. Ben-Zvi, X. Chang, P. D. Johnson, 1.Kewisch, and T. Rao.Secondary emission enhanced photoinjector. C-AD Acceler-ator Physics Report C-A/AP/149, BNL, 2004.[2] X. Chang, 1. Ben-Zvi, A. Burrill, S. Hulbert, P. D. Johnson,1. Kewisch, T. Rao, 1. Smedley, Z. Segalov, and Y. Zhao.Measurement of the secondary emission yield of a thin di-amond window in transmission mode. In C. Horak, editor,2005 Particle Accelerator Conference. IEEE, number 2251-3,2005.[3] X. Chang, I. Ben-Zvi, A. Burrill, J. Grimes, T. Rao,Z. Segalov, 1. Smedley, Q. WU Recent Progress on the Dia-mond Amplified Photo-cathode Experiment In 2007 ParticleAccelerator Conference. IEEE, pp. 2044-6, 2007.[4] C. Nieter and 1.R. Cary. VORPAL: a versatile plasma simu-lation code. 1. Comput. Phys., 196:448-473, 2004.[5] D. A. Dimitrov, R. Busby, D. L. Bruhwiler, J. R. Cary, 1.Ben-Zvi, T. Rao, X. Chang, 1. Smedley, Q. Wu 3D Simulations ofSecondary Electron Generation and Transport in a DiamondAmplifier for Photocathodes In 2007 Particle AcceleratorConference. IEEE, pp. 3555-7,2007.[6] B. Ziaja, D. van der Spoel, A. Szoke, and J. Hajdu. Auger-electron cascades in diamond and amorphous carbon. Phys.Rev. B, 64(214104-1/8), 2001.[7] B. Ziaja, A. Szoke, D. van der Spoel, and J. Hajdu. Space-time evolution ofelectron cascades in diamond. Phys. Rev. B,66:024116-1/9, 2002.[8] B. Ziaja, R. A. London, and 1. Hajdu. Unified model ofsecondary electron cascades in diamond. 1. Appl. Phys.,97:064905-1/9, 2005.[9] T. Watanabe, T. Teraji, T. Ito, Y. Kamakura, and K. TaniguchiMonte Carlo simulations of electron transport properties ofdiamond in high electric fields using full band structure 1.Appl. Phys. 95:4866-74, 2004.[10] M. Lundstrom. Fundamentals ofCarrier Transport. Cam-bridge University Press, second edition, 2000.[11] C. Jacoboni and L. Reggiani The Monte Carlo method forthe solution of charge transport in semiconductors with ap-plications to covalent materials Rev. Mod. Phys., 64:645-705,1983.

3D Simulations of Secondary Electron Generation and Transport in a Diamond Electron Beam Amplifier

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3D Simulations of Secondary Electron Generation and Transport in a Diamond Electron Beam Amplifier

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