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A refined Monte Carlo code for low-energy electron emission from gold material irradiated with sub-keV electrons

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Abstract

Considering the significance of low-energy electrons (LEEs; 0–20 eV) in radiobiology, the sensitization potential of gold nanoparticles (AuNPs) as high-flux LEE emitters when irradiated with sub-keV electrons has been suggested. In this study, a track-structure Monte Carlo simulation code using the dielectric theory was developed to simulate the transport of electrons below 50 keV in gold. In this code, modifications, particularly for elastic scattering, are implemented for a more precise description of the LEE emission in secondary electron emission. This code was validated using the secondary electron yield and backscattering coefficient. To ensure dosimetry accuracy, we further verified the code for energy deposition calculations using the Monte Carlo toolkit, Geant4. The development of this code provides a basis for future studies regarding the role of AuNPs in targeted radionuclide radiotherapy.

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Data availability

The data that support the findings of this study are openly available in Science Data Bank at https://www.doi.org/10.57760/sciencedb.j00186.00062 and http://resolve.pid21.cn/31253.11.sciencedb.j00186.00062.

References

  1. J.G. Kereiakes, D.V. Rao, Auger electron dosimetry: report of AAPM Nuclear Medicine Committee Task Group No. 6. Med. Phys. 19(6), 1359 (1992). https://doi.org/10.1118/1.596925

    Article  Google Scholar 

  2. A.I. Kassis, Therapeutic radionuclides: biophysical and radiobiologic principles. Semin. Nucl. Med. 38(5), 358–366 (2008). https://doi.org/10.1053/j.semnuclmed.2008.05.002

    Article  Google Scholar 

  3. I. Kyriakou, I. Tremi, A.G. Georgakilas et al., Microdosimetric investigation of the radiation quality of low-medium energy electrons using Geant4-DNA. Appl. Radiat. Isot. 172, 109654 (2021). https://doi.org/10.1016/j.apradiso.2021.109654

    Article  Google Scholar 

  4. J.A. O’Donoghue, T.E. Wheldon, Targeted radiotherapy using Auger electron emitters. Phys. Med. Biol. 41(10), 1973–1992 (1996). https://doi.org/10.1088/0031-9155/41/10/009

    Article  Google Scholar 

  5. A. Mozumder, Ionization and excitation yields in liquid water due to the primary irradiation: Relationship of radiolysis with far UV-photolysisPresented at the Symposium on Recent Trends in Photochemical Sciences, Trivandrum, January 8–10, 2000. Phys. Chem. Chem. Phys. 4(8), 1451–1456 (2002). https://doi.org/10.1039/b106017c

    Article  Google Scholar 

  6. L. Sanche, Low energy electron-driven damage in biomolecules. Eur. Phys. J. D 35(2), 367–390 (2005). https://doi.org/10.1140/epjd/e2005-00206-6

    Article  ADS  Google Scholar 

  7. B. Boudaiffa, P. Cloutier, D. Hunting et al., Resonant formation of DNA strand breaks by low-energy (3 to 20 eV) electrons. Science 287(5458), 1658–1660 (2000). https://doi.org/10.1126/science.287.5458.1658

    Article  ADS  Google Scholar 

  8. R. Barrios, P. Skurski, J. Simons, Mechanism for damage to DNA by low-energy electrons. J. Phys. Chem. B 106(33), 7991–7994 (2002). https://doi.org/10.1021/jp013861i

    Article  Google Scholar 

  9. W. Chen, S. Chen, Y. Dong et al., Absolute cross-sections for DNA strand breaks and crosslinks induced by low energy electrons. Phys. Chem. Chem. Phys. 18(48), 32762–32771 (2016). https://doi.org/10.1039/c6cp05201k

    Article  ADS  Google Scholar 

  10. Nanoparticle Enhanced Radiation Therapy. (IOP Publishing: 2020)

  11. P.-Y. Qi, Z.-T. Dai, J. Zhang et al., Investigation of the radiosensitization effect in FePt nanopaticle clusters with Monte Carlo simulation. Nucl. Sci. Tech. 29(11), 167 (2018). https://doi.org/10.1007/s41365-018-0495-9

    Article  Google Scholar 

  12. M.Y. Chang, A.L. Shiau, Y.H. Chen et al., Increased apoptotic potential and dose-enhancing effect of gold nanoparticles in combination with single-dose clinical electron beams on tumor-bearing mice. Cancer Sci. 99(7), 1479–1484 (2008). https://doi.org/10.1111/j.1349-7006.2008.00827.x

    Article  Google Scholar 

  13. J.F. Hainfeld, D.N. Slatkin, H.M. Smilowitz, The use of gold nanoparticles to enhance radiotherapy in mice. 49 (18), N309–N315 (2004). https://doi.org/10.1088/0031-9155/49/18/n03

  14. H. Nikjoo, L. Lindborg, RBE of low energy electrons and photons. Phys. Med. Biol. 55(10), R65 (2010). https://doi.org/10.1088/0031-9155/55/10/R01

    Article  ADS  Google Scholar 

  15. S.M. Pimblott, J.A. LaVerne, A. Mozumder, Monte Carlo simulation of range and energy deposition by electrons in gaseous and liquid Water. J. Phys. Chem. 100(20), 8595–8606 (1996). https://doi.org/10.1021/jp9536559

    Article  Google Scholar 

  16. L. Sanche, Cancer treatment: low-energy electron therapy. Nat. Mater. 14(9), 861–863 (2015). https://doi.org/10.1038/nmat4333

    Article  ADS  Google Scholar 

  17. E. Alizadeh, L. Sanche, Precursors of solvated electrons in radiobiological physics and chemistry. Chem. Rev. 112(11), 5578–5602 (2012). https://doi.org/10.1021/cr300063r

    Article  Google Scholar 

  18. J. Meesungnoen, J.-P. Jay-Gerin, A. Filali-Mouhim et al., Low-energy electron penetration range in liquid water. Radiat. Res. 158(5), 657–660 (2002). https://doi.org/10.1667/0033-7587(2002)158[0657:Leepri]2.0.Co;2

    Article  ADS  Google Scholar 

  19. A. Pronschinske, P. Pedevilla, C.J. Murphy et al., Enhancement of low-energy electron emission in 2D radioactive films. Nat. Mater. 14(9), 904–907 (2015). https://doi.org/10.1038/nmat4323

    Article  ADS  Google Scholar 

  20. A. Ku, V.J. Facca, Z. Cai et al., Auger electrons for cancer therapy - a review. EJNMMI Radiopharm. Chem. 4(1), 27 (2019). https://doi.org/10.1186/s41181-019-0075-2

    Article  Google Scholar 

  21. H. Seiler, Secondary electron emission in the scanning electron microscope. J. Appl. Phys. 54(11), R1–R18 (1983). https://doi.org/10.1063/1.332840

    Article  ADS  Google Scholar 

  22. Y. Lin, D.C. Joy, A new examination of secondary electron yield data. Surf. Interface Anal. 37(11), 895–900 (2005). https://doi.org/10.1002/sia.2107

    Article  Google Scholar 

  23. L.A. Gonzalez, M. Angelucci, R. Larciprete et al., The secondary electron yield of noble metal surfaces. AIP Adv. 7(11), 115203 (2017). https://doi.org/10.1063/1.5000118

    Article  ADS  Google Scholar 

  24. M. Dapor, Transport of Energetic Electrons in Solids. Computer Simulation with Applications to Materials Analysis and Characteriza-tion. 3 ed. (Springer International Publishing AG, Cham: 2020)

  25. D. Emfietzoglou, G. Papamichael, K. Kostarelos et al., A Monte Carlo track structure code for electrons (~10 eV–10 keV) and protons (~0.3–10 MeV) in water: partitioning of energy and collision events. Phys. Med. Biol. 45(11), 3171–3194 (2000). https://doi.org/10.1088/0031-9155/45/11/305

    Article  Google Scholar 

  26. S. Agostinelli, J. Allison, K. Amako et al., Geant4—a simulation toolkit. Nucl. Instrum. Methods. Phys. Res. B 506(3), 250–303 (2003). https://doi.org/10.1016/s0168-9002(03)01368-8

    Article  Google Scholar 

  27. R.A. Forster, L.J. Cox, R.F. Barrett et al., MCNP™ Version 5. 213, 82–86 (2004). https://doi.org/10.1016/s0168-583x(03)01538-6

  28. L. Deng, G. Li, B.-Y. Zhang et al., A high fidelity general purpose 3-D Monte Carlo particle transport program JMCT3.0. Nucl. Sci. Tech. 33(8), 108 (2022). https://doi.org/10.1007/s41365-022-01092-0

    Article  Google Scholar 

  29. Y. Wu, J. Song, H. Zheng et al., CAD-based Monte Carlo program for integrated simulation of nuclear system SuperMC. Ann. Nucl. Energy 82, 161–168 (2015). https://doi.org/10.1016/j.anucene.2014.08.058

    Article  Google Scholar 

  30. I. Kawrakow, Accurate condensed history Monte Carlo simulation of electron transport. I. EGSnrc, the new EGS4 version. Med. Phys. 27(3), 485–498 (2000). https://doi.org/10.1118/1.598917

    Article  Google Scholar 

  31. S. Incerti, G. Baldacchino, M. Bernal et al., The Geant4-DNA project. Int. J. Model. Simul. Sci. Comput. 01(02), 157–178 (2012). https://doi.org/10.1142/S1793962310000122

    Article  Google Scholar 

  32. M.A. Bernal, M.C. Bordage, J.M.C. Brown et al., Track structure modeling in liquid water: a review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit. Phys. Med. 31(8), 861–874 (2015). https://doi.org/10.1016/j.ejmp.2015.10.087

    Article  Google Scholar 

  33. S. Incerti, A. Ivanchenko, M. Karamitros et al., Comparison of GEANT4 very low energy cross section models with experimental data in water. Med. Phys. 37(9), 4692–4708 (2010). https://doi.org/10.1118/1.3476457

    Article  Google Scholar 

  34. S. Incerti, I. Kyriakou, M.A. Bernal et al., Geant4-DNA example applications for track structure simulations in liquid water: a report from the Geant4-DNA project. Med. Phys. 45(8), e722–e739 (2018). https://doi.org/10.1002/mp.13048

    Article  Google Scholar 

  35. V.A. Semenenko, J.E. Turner, T.B. Borak, NOREC, a Monte Carlo code for simulating electron tracks in liquid water. Radiat. Environ. Biophys. 42(3), 213–217 (2003). https://doi.org/10.1007/s00411-003-0201-z

    Article  Google Scholar 

  36. T. Liamsuwan, D. Emfietzoglou, S. Uehara et al., Microdosimetry of low-energy electrons. Int. J. Radiat. Biol. 88(12), 899–907 (2012). https://doi.org/10.3109/09553002.2012.699136

    Article  Google Scholar 

  37. D. Alloni, A. Campa, W. Friedland et al., Track structure, radiation quality and initial radiobiological events: considerations based on the PARTRAC code experience. Int. J. Radiat. Biol. 88(1–2), 77–86 (2012). https://doi.org/10.3109/09553002.2011.627976

    Article  Google Scholar 

  38. D. Sakata, S. Incerti, M.C. Bordage et al., An implementation of discrete electron transport models for gold in the Geant4 simulation toolkit. J. Appl. Phys. 120(24), 244901 (2016). https://doi.org/10.1063/1.4972191

    Article  ADS  Google Scholar 

  39. D. Sakata, I. Kyriakou, H.N. Tran et al., Electron track structure simulations in a gold nanoparticle using Geant4-DNA. Phys. Med. 63, 98–104 (2019). https://doi.org/10.1016/j.ejmp.2019.05.023

    Article  Google Scholar 

  40. Q. Gibaru, C. Inguimbert, P. Caron et al., Geant4 physics processes for microdosimetry and secondary electron emission simulation: Extension of MicroElec to very low energies and 11 materials (C, Al, Si, Ti, Ni, Cu, Ge, Ag, W, Kapton and SiO2). Nucl. Instrum. Methods Phys. Res. B 487, 66–77 (2021). https://doi.org/10.1016/j.nimb.2020.11.016

    Article  ADS  Google Scholar 

  41. T.-L. He, H.-L. Xu, K.-T. Huang et al., Monte Carlo simulation of incident electrons passing through thin metal layer. Nucl. Sci. Tech. 29(7), 103 (2018). https://doi.org/10.1007/s41365-018-0429-6

    Article  Google Scholar 

  42. M.-T. Tang, L.-J. Mao, H.-J. Lu et al., Design of an efficient collector for the HIAF electron cooling system. Nucl. Sci. Tech. 32(10), 116 (2021). https://doi.org/10.1007/s41365-021-00949-0

    Article  Google Scholar 

  43. N.F. Mott, N.H.D. Bohr, The scattering of fast electrons by atomic nuclei. Proc. Math. Phys. Eng. Sci. 124(794), 425–442 (1929). https://doi.org/10.1098/rspa.1929.0127

    Article  MATH  Google Scholar 

  44. F. Salvat, A. Jablonski, C.J. Powell, elsepa—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules. Comput. Phys. Commun. 165(2), 157–190 (2005). https://doi.org/10.1016/j.cpc.2004.09.006

    Article  ADS  Google Scholar 

  45. F. Salvat, A. Jablonski, C.J. Powell, elsepa—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules (New Version Announcement). Comput. Phys. Commun. 261, 107704 (2021). https://doi.org/10.1016/j.cpc.2020.107704

    Article  Google Scholar 

  46. J.W. Lynn, H.G. Smith, R.M. Nicklow, Lattice dynamics of gold. Phys. Rev. B 8(8), 3493–3499 (1973). https://doi.org/10.1103/PhysRevB.8.3493

    Article  ADS  Google Scholar 

  47. E. Schreiber, H.J. Fitting, Monte Carlo simulation of secondary electron emission from the insulator SiO2. J. Electron. Spectrosc. Relat. Phenom. 124(1), 25–37 (2002). https://doi.org/10.1016/s0368-2048(01)00368-1

    Article  Google Scholar 

  48. H.J. Fitting, E. Schreiber, J.C. Kuhr et al., Attenuation and escape depths of low-energy electron emission. J. Electron. Spectrosc. Relat. Phenom. 119(1), 35–47 (2001). https://doi.org/10.1016/s0368-2048(01)00232-8

    Article  Google Scholar 

  49. T. Verduin, Quantum noise effects in e Beam lithography and metrology. (Delft University of Technology, 2017)

  50. A.M.M.G. Theulings, Optimisation of photon detector tynode membranes using electron matter scattering simulations (Faculty of Applied Sciences, Delft University of Technology, Department of Imaging Physics, 2020)

    Google Scholar 

  51. J.N. Bradford, S. Woolf, Electron-acoustic phonon scattering in SiO2 determined from a pseudo-potential for energies of E≳EBZ. J. Appl. Phys. 70(1), 490–492 (1991). https://doi.org/10.1063/1.350254

    Article  ADS  Google Scholar 

  52. E. Kieft, E. Bosch, Refinement of Monte Carlo simulations of electron–specimen interaction in low-voltage SEM. J. Phys. D 41(21), 215310 (2008). https://doi.org/10.1088/0022-3727/41/21/215310

    Article  ADS  Google Scholar 

  53. R.H. Ritchie, Plasma losses by fast electrons in thin films. Phys. Rev. 106(5), 874–881 (1957). https://doi.org/10.1103/PhysRev.106.874

    Article  ADS  MathSciNet  Google Scholar 

  54. M. Vos, P.L. Grande, Extracting the dielectric function from high-energy REELS measurements. Surf. Interface Anal. 49(9), 809–821 (2017). https://doi.org/10.1002/sia.6227

    Article  Google Scholar 

  55. W.S.M. Werner, K. Glantschnig, C. Ambrosch-Draxl, Optical constants and inelastic electron-scattering data for 17 elemental metals. J. Phys. Chem. Ref. Data 38(4), 1013–1092 (2009). https://doi.org/10.1063/1.3243762

    Article  ADS  Google Scholar 

  56. R.H. Ritchie, A. Howie, Electron excitation and the optical potential in electron microscopy. Philos. Mag. J. Theoret. Exp. Appl. Phys. 36(2), 463–481 (1977). https://doi.org/10.1080/14786437708244948

    Article  Google Scholar 

  57. I. Abril, R. Garcia-Molina, C.D. Denton et al., Dielectric description of wakes and stopping powers in solids. Phys. Rev. A 58(1), 357–366 (1998). https://doi.org/10.1103/PhysRevA.58.357

    Article  ADS  Google Scholar 

  58. M. Vos, A model dielectric function for low and very high momentum transfer. Nucl. Instrum. Methods Phys. Res. B 366, 6–12 (2016). https://doi.org/10.1016/j.nimb.2015.09.091

    Article  ADS  Google Scholar 

  59. Y. Sun, H. Xu, B. Da et al., Calculations of energy-loss function for 26 materials. Chinese J. Chem. Phys. 29(6), 663–670 (2016). https://doi.org/10.1063/1674-0068/29/cjcp1605110

    Article  ADS  Google Scholar 

  60. A. Valentin, M. Raine, J.E. Sauvestre et al., Geant4 physics processes for microdosimetry simulation: very low energy electromagnetic models for electrons in silicon. Nucl. Instrum. Methods Phys. Res. B 288, 66–73 (2012). https://doi.org/10.1016/j.nimb.2012.07.028

    Article  ADS  Google Scholar 

  61. P. de Vera, R. Garcia-Molina, Electron inelastic mean free paths in condensed matter down to a few electronvolts. J. Phys. Chem. C 123(4), 2075–2083 (2019). https://doi.org/10.1021/acs.jpcc.8b10832

    Article  Google Scholar 

  62. E. D. Palik, Handbook Optical Constants of Solids 3rd ed. (Academic Press: 1998)

  63. D.L. Windt, W.C. Cash, Jr. M. Scott et al., Optical constants for thin films of Ti, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Ir, Os, Pt, and Au from 24 A to 1216 A. Appl. Opt. 27 (2), 246–278 (1988). https://doi.org/10.1364/ao.27.000246

  64. D.E. Cullen, J.H. Hubbell, L. Kissel EPDL97: the evaluated photo data library `97 version; United States, 1997.

  65. U. Fano, J.W. Cooper, Spectral distribution of atomic oscillator strengths. Rev. Mod. Phys. 40(3), 441–507 (1968). https://doi.org/10.1103/RevModPhys.40.441

    Article  ADS  Google Scholar 

  66. R.F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope (Springer, New York, 2011)

    Book  Google Scholar 

  67. D. Emfietzoglou, I. Kyriakou, R. Garcia-Molina et al., The effect of static many-body local-field corrections to inelastic electron scattering in condensed media. J. Appl. Phys. 114(14), 144907 (2013). https://doi.org/10.1063/1.4824541

    Article  ADS  Google Scholar 

  68. L.H. Yang, K. Tőkési, J. Tóth et al., Optical properties of silicon and germanium determined by high-precision analysis of reflection electron energy loss spectroscopy spectra. Phys. Rev. B 100(24), 245209 (2019). https://doi.org/10.1103/PhysRevB.100.245209

    Article  ADS  Google Scholar 

  69. R.A. Ferrell, Characteristic energy loss of electrons passing through metal foils II Dispersion relation and short wavelength cutoff for plasma oscillations. Phys. Rev. 107(2), 450–462 (1957). https://doi.org/10.1103/PhysRev.107.450

    Article  ADS  MATH  Google Scholar 

  70. N.D. Mermin, Lindhard dielectric function in the relaxation-time approximation. Phys. Rev. B 1(5), 2362–2363 (1970). https://doi.org/10.1103/PhysRevB.1.2362

    Article  ADS  Google Scholar 

  71. J. Lindhard, On the properties of a gas of charged particles. Kgl. Danske Videnskab. Selskab Mat.-fys. Medd. 28 (8), 1–57 (1954).

  72. V. Ochkur, The Born-Oppenheimer method in the theory of atomic collisions. J. Sov. Phys. JETP 18(2), 503–508 (1964)

    Google Scholar 

  73. C.T. Chantler, Detailed tabulation of atomic form factors. Photoelectric absorption and scattering cross section, and mass attenuation coefficients in the vicinity of absorption edges in the soft X-ray (Z=30–36, Z=60–89, E=0.1 keV–10 keV), addressing convergence issues of earlier work. J. Phys. Chem. Ref. Data 29(4), 597–1056 (2000). https://doi.org/10.1063/1.1321055

  74. S. Tanuma, S. Ichimura, K. Goto et al., Experimental determinations of electron inelastic mean free paths in silver, gold, copper and silicon from electron elastic peak intensity ratios. J. Surf. Anal. 9(3), 285–290 (2002). https://doi.org/10.1384/jsa.9.285

    Article  Google Scholar 

  75. H. Kanter, Slow-electron mean free paths in aluminum, silver, and gold. Phys. Rev. B 1(2), 522–536 (1970). https://doi.org/10.1103/PhysRevB.1.522

    Article  ADS  Google Scholar 

  76. S.M. Sze, J.L. Moll, T. Sugano, Range-energy relation of hot electrons in gold. Solid State Electron. 7(7), 509–523 (1964). https://doi.org/10.1016/0038-1101(64)90088-7

    Article  ADS  Google Scholar 

  77. H. Shinotsuka, S. Tanuma, C.J. Powell et al., Calculations of electron inelastic mean free paths. X. Data for 41 elemental solids over the 50 eV to 200 keV range with the relativistic full Penn algorithm. Surf. Interface Anal. 47(9), 871–888 (2015). https://doi.org/10.1002/sia.5789

  78. D.R. Penn, Electron mean-free-path calculations using a model dielectric function. Phys. Rev. B 35(2), 482–486 (1987). https://doi.org/10.1103/physrevb.35.482

    Article  ADS  MathSciNet  Google Scholar 

  79. J.C. Ashley, Interaction of low-energy electrons with condensed matter: stopping powers and inelastic mean free paths from optical data. J. Electron. Spectrosc. Relat. Phenom. 46(1), 199–214 (1988). https://doi.org/10.1016/0368-2048(88)80019-7

    Article  Google Scholar 

  80. S. Tanuma, C.J. Powell, D.R. Penn, Calculations of electron inelastic mean free paths for 31 materials. Surf. Interface Anal. 11(11), 577–589 (1988). https://doi.org/10.1002/sia.740111107

    Article  Google Scholar 

  81. S. T. Perkins, D. E. Cullen, S. M. Seltzer Tables and graphs of electron-interaction cross sections from 10 eV to 100 GeV derived from the LLNL Evaluated Electron Data Library (EEDL), Z = 1--100; UCRL-50400-Vol.31; 1991.

  82. S. Tanuma, C.J. Powell, D.R. Penn, Calculations of electron inelastic mean free paths. Surf. Interface Anal. 37(1), 1–14 (2005). https://doi.org/10.1002/sia.1997

    Article  Google Scholar 

  83. S. Tanuma, C.J. Powell, D.R. Penn, Calculations of electron inelastic mean free paths. IX. Data for 41 elemental solids over the 50 eV to 30 keV range. Surf. Interface Anal. 43(3), 689–713 (2011). https://doi.org/10.1002/sia.3522

  84. V. P. Zhukov, E.V. Chulkov, P.M. Echenique, Lifetimes and inelastic mean free path of low-energy excited electrons in Fe, Ni, Pt, and Au:Ab initio GW+T calculations. Phys. Rev. B 73, 125105 (2006). https://doi.org/10.1103/PhysRevB.73.125105

  85. M. Berger, J. Coursey, M. Zucker, ESTAR, PSTAR, and ASTAR: Computer programs for calculating stopping-power and range tables for Electrons, Protons, and Helium Ions (version 1.21),(1999). http://physics.nist.gov/Star, http://physics.nist.gov/Star (Accessed March 31, 2023).

  86. H.T. Nguyen-Truong, Electron inelastic mean free path at energies below 100 eV. J. Phys. Condens. Matter 29(21), 215501 (2017). https://doi.org/10.1088/1361-648X/aa6b9d

  87. M. Gryziński, Classical theory of atomic collisions. I. Theory of inelastic collisions. Phys. Rev. 138(2A), A336–A358 (1965). https://doi.org/10.1103/PhysRev.138.A336

  88. M. Gryziński, Two-particle collisions. II. Coulomb collisions in the laboratory system of coordinates. Phys. Rev. 138(2A), A322–A335 (1965). https://doi.org/10.1103/PhysRev.138.A322

  89. Z.J. Ding, X.D. Tang, R. Shimizu, Monte Carlo study of secondary electron emission. J. Appl. Phys. 89(1), 718–726 (2001). https://doi.org/10.1063/1.1331645

    Article  ADS  Google Scholar 

  90. Z.J. Ding, H.M. Li, X.D. Tang et al., Monte Carlo simulation of absolute secondary electron yield of Cu. Appl. Phys. A 78(4), 585–587 (2004). https://doi.org/10.1007/s00339-002-1994-3

    Article  ADS  Google Scholar 

  91. M. Azzolini, M. Angelucci, R. Cimino et al., Secondary electron emission and yield spectra of metals from Monte Carlo simulations and experiments. J. Phys. Condens. Matter 31(5), 055901 (2018). https://doi.org/10.1088/1361-648x/aaf363

  92. D.C. Joy, A database on electron-solid interactions. Scanning 17(5), 270–275 (1995). https://doi.org/10.1002/sca.4950170501

    Article  Google Scholar 

  93. D. Hasselkamp, S. Hippler, A. Scharmann, Ion-induced secondary electron spectra from clean metal surfaces. Nucl. Instrum. Methods Phys. Res. B 18(1–6), 561–565 (1986). https://doi.org/10.1016/s0168-583x(86)80088-x

    Article  ADS  Google Scholar 

  94. S. Tanuma, C.J. Powell, D.R. Penn, Calculations of stopping powers of 100 eV to 30 keV electrons in 10 elemental solids. Surf. Interface Anal. 37(11), 978–988 (2005). https://doi.org/10.1002/sia.2092

    Article  Google Scholar 

  95. H. Gümüş, Ö. Kabadayi, Practical calculations of stopping powers for intermediate energy electrons in some elemental solids. Vacuum 85(2), 245–252 (2010). https://doi.org/10.1016/j.vacuum.2010.06.004

    Article  ADS  Google Scholar 

  96. H. Shinotsuka, S. Tanuma, C.J. Powell et al., Calculations of electron stopping powers for 41 elemental solids over the 50 eV to 30 keV range with the full Penn algorithm. Nucl. Instrum. Methods Phys. Res. B 270, 75–92 (2012). https://doi.org/10.1016/j.nimb.2011.09.016

    Article  ADS  Google Scholar 

  97. H.T. Nguyen-Truong, Determination of the maximum energy loss for electron stopping power calculations and its effect on backscattering electron yield in Monte-Carlo simulations applying continuous slowing-down approximation. J. Appl. Phys. 114(16), 163513 (2013). https://doi.org/10.1063/1.4827843

  98. D.C. Joy, S. Luo, R. Gauvin et al., Experimental measurements of electron stopping power at low energies. Scanning Microscopy 10(3), 653–666 (1996). https://digitalcommons.usu.edu/microscopy/vol10/iss3/4

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Li-Heng Zhou, Shui-Yan Cao, Tao Sun, Yun-Long Wang, Jun Ma. The first draft of the manuscript was written by Li-Heng Zhou and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding authors

Correspondence to Shui-Yan Cao or Jun Ma.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 12004180, 21906083, 11975122, and 22006067), the Natural Science Foundation of Jiangsu Province (No. BK20190384), and the Fundamental Research Funds for the Central Universities (Nos. NE2020006, NS2022095).

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Zhou, LH., Cao, SY., Sun, T. et al. A refined Monte Carlo code for low-energy electron emission from gold material irradiated with sub-keV electrons. NUCL SCI TECH 34, 54 (2023). https://doi.org/10.1007/s41365-023-01204-4

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  • DOI: https://doi.org/10.1007/s41365-023-01204-4

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