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Scattering of e\(^\pm \) by silicon atoms and transport coefficients in mixtures of inert gas with silicon vapor

  • Regular Article – Atomic and Molecular Collisions
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Abstract

This work reports on the differential and various angle integrated cross sections for the scattering of electrons and positrons by silicon atoms. Moreover, the Sherman function \(S(\theta )\) and two other spin asymmetry parameters \(U(\theta )\) and \(T(\theta )\) have been calculated. Critical minima in the elastic differential cross sections and maximum spin polarization points were identified for this element. Dirac partial wave method with a complex optical model potential is used to carry out these investigations. Transport characteristics of electrons in silicon vapors and mixtures of inert gases (helium, argon) with silicon vapor were calculated using the Monte Carlo method. For electric field strengths ranging from 1 to 100 Td, drift velocity, average electron energy, diffusion and mobility coefficients, and electron energy distribution function are studied. We have shown that impurities of silicon vapor significantly affect electron transport in noble gases.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All the data of this study presented in graphical form. The datasets are available from the corresponding author on reasonable request.]

References

  1. R. Jansen, Silicon spintronics. Nat. Mater. 11, 400–408 (2012)

    ADS  Google Scholar 

  2. G. Cunge, D. Vempaire, R. Ramos, M. Touzeau, O. Joubert, P. Bodard, N. Sadeghi, Radical surface interactions in industrial silicon plasma etch reactors. Plasma Sources Sci. Technol. 19, 034017 (2010)

    ADS  Google Scholar 

  3. T.S. Pedersen, J.R. Danielson, C. Hugenschmidt, G. Marx, X. Sarasola, F. Schauer, L. Schweikhard, C.M. Surko, E. Winkler, Plans for the creation and studies of electron–positron plasmas in a stellarator. New J. Phys. 14, 035010 (2012)

    ADS  Google Scholar 

  4. R. Juhasz, N. Elfström, J. Linnros, Controlled fabrication of silicon nanowires by electron beam lithography and electrochemical size reduction. Nano Lett. 5, 275–280 (2004)

    ADS  Google Scholar 

  5. A. Jablonski, I. Tilinin, Towards a universal description of elastic scattering effects in X-ray photoelectron spectroscopy. J. Electron Spectrosc. Relat. Phenom. 74, 207–229 (1995)

    Google Scholar 

  6. A. Jablonski, F. Salvat, C.J. Powell, Comparison of electron elastic-scattering cross sections calculated from two commonly used atomic potentials. J. Phys. Chem. Ref. Data 33, 409–451 (2004)

    ADS  Google Scholar 

  7. N. Sherman, Coulomb scattering of relativistic electrons by point nuclei. Phys. Rev. 103, 1601–1607 (1956)

    MATH  ADS  Google Scholar 

  8. A.K.F. Haque, M.M. Haque, P.P. Bhattacharjee, M.A. Uddin, M.A.R. Patoary, M.I. Hossain, A.K. Basak, M.S. Mahbub, M. Maaza, B.C. Saha, Relativistic calculations for spin-polarization of elastic electron—mercury scattering. J. Phys. Commun. 1, 035014 (2017)

    Google Scholar 

  9. G. Rufa, Parity-violating asymmetry in elastic electron scattering on nuclei: partial-wave analysis. Nucl. Phys. A 384, 273–286 (1982)

  10. O. Moreno, E.M. de Guerra, P. Sarriguren, J.M. Udías, Parity-violating elastic electron scattering and nuclear structure. J. Phys. G Nucl. Part. Phys. 37, 064019 (2010)

    ADS  Google Scholar 

  11. B. Jalali, S. Fathpour, Silicon photonics. J. Lightwave Technol. 24, 4600–4615 (2006)

    ADS  Google Scholar 

  12. D. Liang, J.E. Bowers, Recent progress in lasers on silicon. Nat. Photonics 4, 511–517 (2010)

    ADS  Google Scholar 

  13. J. Ballato, T. Hawkins, P. Foy, R. Stolen, B. Kokuoz, M. Ellison, C. McMillen, J. Reppert, A.M. Rao, M. Daw, S.R. Sharma, R. Shori, O. Stafsudd, R.R. Rice, D.R. Powers, Silicon optical fiber. Opt. Express 16, 18675 (2008)

    ADS  Google Scholar 

  14. S. Liu, A. Khope, Latest advances in high-performance light sources and optical amplifiers on silicon. J. Semicond. 42, 041307 (2021)

    ADS  Google Scholar 

  15. J.J. Saarinen, S.M. Weiss, P.M. Fauchet, J.E. Sipe, Optical sensor based on resonant porous silicon structures. Opt. Express 13, 3754 (2005)

  16. S. Seidel, Silicon strip and pixel detectors for particle physics experiments. Phys. Rep. 828, 1–34 (2019)

    ADS  Google Scholar 

  17. H.-G. Moser, Silicon detector systems in high energy physics. Prog. Part. Nucl. Phys. 63, 186–237 (2009)

    ADS  Google Scholar 

  18. Dr.D.A. Bauer, Dark matter detection with cryogenic detectors. J. Phys. Conf. Ser. 120, 042002 (2008)

  19. J. Shieh, S. Ravipati, F.-H. Ko, K.K. Ostrikov, Plasma-made silicon nanograss and related nanostructures. J. Phys. D Appl. Phys. 44, 174010 (2011)

    ADS  Google Scholar 

  20. M. Engelhardt, R. Pothiraja, K. Kartaschew, N. Bibinov, M. Havenith, P. Awakowicz, Interaction of an argon plasma jet with a silicon wafer. J. Phys. D Appl. Phys. 49, 145201 (2016)

    ADS  Google Scholar 

  21. A.A. Masyanov, Application of plasma methods for the synthesis of nanostructures. J. Phys. Conf. Ser. 2270, 012051 (2022)

    Google Scholar 

  22. M.E. Riley, C.J. MacCallum, F. Biggs, Theoretical electron–atom elastic scattering cross sections. Atom. Data Nucl. Data Tables 15, 443–476 (1975)

    ADS  Google Scholar 

  23. R. Mayol, F. Salvat, Total and transport cross sections for elastic scattering of electrons by atom. Atom. Data Nucl. Data Tables 65, 55–154 (1997)

    ADS  Google Scholar 

  24. 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, (United States, 1991) (1991)

  25. R.J. Meredith, W. Williamson, V.J. Montemayor, N. Öztürk, A.J. Antolak, Low-energy elastic scattering of electrons by bound silicon and germanium atoms. J. Appl. Phys. 68, 4937–4941 (1990)

    ADS  Google Scholar 

  26. E.J. Robinson, S. Geltman, Single- and double-quantum photodetachment of negative ions. Phys. Rev. 153, 4–8 (1967)

    ADS  Google Scholar 

  27. P.L. Bartlett, A.T. Stelbovics, Calculation of electron-impact total-ionization cross sections. Phys. Rev. A 66, 012707 (2002)

    ADS  Google Scholar 

  28. Y.-K. Kim, P.M. Stone, Ionization of silicon, germanium, tin and lead by electron impact. J. Phys. B Atom. Mol. Opt. Phys. 40, 1597–1611 (2007)

    Google Scholar 

  29. J. Kaur, D. Gupta, R. Naghma, D. Ghoshal, B. Antony, Electron impact ionization cross sections of atoms. Can. J. Phys. 93, 617–625 (2015)

    ADS  Google Scholar 

  30. M. Dapor, A. Miotello, Differential, total, and transport cross sections for elastic scattering of low energy positrons by neutral atoms (Z = 1–92, E = 500–4000 eV). Atom. Data Nucl. Data 69, 1–100 (1998)

    ADS  Google Scholar 

  31. A.J. Antolak, W. Williamson, Elastic scattering of low-energy positrons by bound silicon and germanium. J. Appl. Phys. 69, 3760–3762 (1991)

    ADS  Google Scholar 

  32. R.S. Freund, R.C. Wetzel, R.J. Shul, T.R. Hayes, Cross-section measurements for electron-impact ionization of atoms. Phys. Rev. A 41, 3575–3595 (1990)

    ADS  Google Scholar 

  33. I.E. McCarthy, C.J. Noble, B.A. Phillips, A.D. Turnbull, Optical model for electron scattering from inert gases. Phys. Rev. A 15, 2173–2185 (1977)

    ADS  Google Scholar 

  34. W. Bühring, Polarization of slow electrons (100–2000 eV) elastically scattered from heavy atoms. Zeitschrift für Physik 208, 286–298 (1968)

  35. M. Shorifuddoza, M.A.R. Patoary, D.H. Jakubassa-Amundsen, A.K.F. Haque, M.A. Uddin, Scattering of e\(^\mp \) from ytterbium atoms. Eur. Phys. J. D 73, 66 (2019)

    Google Scholar 

  36. D.H. Jakubassa-Amundsen, A.K.F. Haque, M.M. Haque, M.M. Billah, A.K. Basak, B.C. Saha, M.A. Uddin, Electron and positron scattering from precious metal atoms in the eV to MeV energy range. Atoms 10, 82 (2022)

    ADS  Google Scholar 

  37. M. Shorifuddoza, P.K. Das, R. Kabir, A.K.F. Haque, M.A. Uddin, Angular distributions and critical minima in the elastic scattering of electrons by atomic copper. Int. J. Quantum Chem. 121, 66 (2020)

    Google Scholar 

  38. M.M. Khatun, M.M. Haque, M.A.R. Patoary, M. Shorifuddoza, M.H. Khandker, A.K.F. Haque, H. Watabe, M.A. Uddin, Theoretical study of e\(^\pm \) scattering by the Au atom. Results Phys. 29, 104742 (2021)

  39. R. Hassan, M.N.A. Abdullah, M. Shorifuddoza, M.H. Khandker, M.A.R. Patoary, M.M. Haque, P.K. Das, M. Maaza, M.M. Billah, A.K.F. Haque, M.A. Uddin, Scattering of e\(^{\pm }\) off silver atom over the energy range 1 eV–1 MeV. Eur. Phys. J. D 75, 66 (2021)

    Google Scholar 

  40. R. Hassan, M.M. Haque, A. K. F. Haque, M. Shorifuddoza, M.H. Khandker, M.A.R. Patoary, A.K. Basak, M. Maaza, B.C. Saha, M.A. Uddin, Relativistic study on the scattering of electrons and positrons from atomic iron at energies 1 eV–10 keV. Mol. Phys. 119, e1849838 (2020)

  41. H. Watabe, M.M. Haque, M.M. Billah, M.H. Khandker, M. Shorifuddoza, M.N.A. Abdullah, A.K.F. Haque, M. Maaza, B.C. Saha, A.K. Basak, M.A. Uddin, Scattering of e\(^\pm \) with Al, Ni, Cu, Ag, Pt and Au atoms including the relativistic effect at 1 eV \(\le \)\(E_i\)\(\le \)1 MeV. Adv. Quantum Chem. 89, 66 (2023)

    Google Scholar 

  42. S.A. Mayorov, Calculation of characteristics of electron drift in neon under a DC electric field. Bull. Lebedev Phys. Inst. 36, 299–304 (2009)

    ADS  Google Scholar 

  43. V.S. Kurbanismailov, S.A. Maiorov, O.A. Omarov, G.B. Ragimkhanov, Optical and kinetic characteristics of an atmospheric pressure pulsed discharge in helium with iron vapor. Techn. Phys. 64, 348–351 (2019)

    ADS  Google Scholar 

  44. S.M. Ri Golyatina, Characteristics of electron drift in a constant electric field for inert gases. Appl. Phys. 5, 22 (2011)

    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. Comput. Phys. Commun. 165, 157–190 (2005)

    MATH  ADS  Google Scholar 

  46. J. Desclaux, A multiconfiguration relativistic Dirac–Fock program. Comput. Phys. Commun. 9, 31–45 (1975)

    ADS  Google Scholar 

  47. B. Hahn, D.G. Ravenhall, R. Hofstadter, High-energy electron scattering and the charge distributions of selected nuclei. Phys. Rev. 101, 1131–1142 (1956)

    ADS  Google Scholar 

  48. J.B. Furness, I.E. McCarthy, Semiphenomenological optical model for electron scattering on atoms. J. Phys. B Atom. Mol. Phys. 6, 2280–2291 (1973)

    ADS  Google Scholar 

  49. F. Salvat, Optical-model potential for electron and positron elastic scattering by atoms. Phys. Rev. A 68, 012708 (2003)

    ADS  Google Scholar 

  50. J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048–5079 (1981)

    ADS  Google Scholar 

  51. A. Jain, Low-energy positron–argon collisions by using parameter-free positron correlation polarization potentials. Phys. Rev. A 41, 2437–2444 (1990)

    ADS  Google Scholar 

  52. D.R. Lide, CRC Handbook of Chemistry and Physics, 79th edn. (CRC Press, Boca Raton, 1999)

    Google Scholar 

  53. N.F. Mott, H.S.W. Massey, The Theory of Atomic Collisions, 3rd edn. (Oxford University Press, London, 1965)

  54. E.P.L. Berestetskii, V.B. Lifshitz, Quantum Electrodynamics, vol. 8 (Elsevier, Oxford, 1982)

    Google Scholar 

  55. F. Salvat, J. Fernández-Varea, W. Williamson, Accurate numerical solution of the radial Schrödinger and Dirac wave equations. Comput. Phys. Commun. 90, 151–168 (1995)

    MATH  ADS  Google Scholar 

  56. K. Joshipura, C.G. Limbachiya, Theoretical total ionization cross-sections for electron impact on atomic and molecular halogens. Int. J. Mass Spectrom. 216, 239–247 (2002)

  57. K. Joshipura, M. Vinodkumar, B. Antony, N. Mason, Theoretical total ionization cross-sections of CH\(_x\), CF\(_x\), SiH\(_x\), SiF\(_x\) (x = 1–4) and CCl\(_4\) targets by electron impact. Eur. Phys. J. D Atom. Mol. Opt. Phys. 23, 81–90 (2003)

    ADS  Google Scholar 

  58. J. Kessler, Polarized Electrons (Springer, Berlin, 1976)

    Google Scholar 

  59. Y.-K. Kim, M.E. Rudd, Binary-encounter-dipole model for electron-impact ionization. Phys. Rev. A 50, 3954–3967 (1994)

    ADS  Google Scholar 

  60. Phelps, Database. www.lxcat.net/Phelps, retrieved on June 17, 2020

  61. Puech, Database. www.lxcat.net/Puech, retrieved on February 20, 2020

  62. N. Bohr, XXXVII. On the constitution of atoms and molecules. Lond. Edinb. Dublin Philos. Mag. J. Sci. 26, 476–502 (1913)

    Google Scholar 

  63. C. Ramsauer, Über den wirkungsquerschnitt der gasmoleküle gegenüber langsamen elektronen. i. fortsetzung. Annalen der Physik 371(24), 546–558 (1922)

    ADS  Google Scholar 

  64. J. Townsend, V. Bailey, The motion of electrons in argon. Lond. Edinb. Dublin Philos. Mag. J. Sci. 43, 593–600 (1922)

    Google Scholar 

  65. D. Walker, Relativistic effects in low energy electron scattering from atoms. Adv. Phys. 20, 257–323 (1971)

    ADS  Google Scholar 

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Acknowledgements

Authors are thankful for the partial funding of the MEXT KAKENHI through the Project Number (B) H20H03615.

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Das, P.K., Ragimkhanov, G.B., Khalikova, Z.R. et al. Scattering of e\(^\pm \) by silicon atoms and transport coefficients in mixtures of inert gas with silicon vapor. Eur. Phys. J. D 77, 173 (2023). https://doi.org/10.1140/epjd/s10053-023-00746-x

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