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Ultrafast electron intervalley scattering and hole dynamics in amorphous and crystalline Ge

Antónia Gera1, Zsolt Tóth2, Zsuzsanna Márton1, Péter Dombi3, Zsuzsanna Pápa1,*, and Judit Budai1,4,†

  • *Contact author: zsuzsanna.papa@eli-alps.hu
  • †Contact author: judit.budai@eli-alps.hu

Phys. Rev. B 113, 205204 – Published 21 May, 2026

DOI: https://doi.org/10.1103/qkbh-bb3f

Abstract

Understanding the role of holes in energy transport mechanisms and determining electron intervalley scattering times is crucial for optimising Ge-based optoelectronic devices such as transistors, photodetectors, power devices, and light emitters. By employing our recently developed, ultrafast 20-fs resolution ellipsometer, we demonstrate that the absorption (ɛ2) in various types of Ge continues to decrease in the first picosecond after optical excitation, proving that the revival of the absorption is limited by the intrabandlike relaxation of holes (near the Γ point), instead of the intervalley scattering of the electrons. The observed decay times depend on the probing photon energies attributed to the different lifetimes of the holes in the light, split-off and heavy-hole bands. With gradually decreasing degree of crystallinity of our single crystalline, semicrystalline and amorphous Ge samples, the recovery times also decrease, which is related to the appearance and intensification of real-space scattering events over reciprocal space scattering. There is excellent correspondence for electron relaxation times for different samples with our two-temperature model, which is thoroughly analyzed via band-structure calculations. Our results contribute to the understanding of the excitation and decay processes in not only crystalline semiconductors, but also semicrystalline and amorphous semiconductors, resolving corresponding debates.

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References (35)

  1. B. Liao, E. Najafi, H. Li, A. J. Minnich, and A. H. Zewail, Photo-excited hot carrier dynamics in hydrogenated amorphous silicon imaged by 4D electron microscopy, Nat. Nanotechnol. 12, 871 (2017).
  2. S. Espinoza, S. Richter, M. Rebarz, O. Herrfurth, R. Schmidt-Grund, J. Andreasson, and S. Zollner, Transient dielectric functions of Ge, Si, and InP from femtosecond pump-probe ellipsometry, Appl. Phys. Lett. 115, 052105 (2019).
  3. S. Richter, O. Herrfurth, S. Espinoza, M. Rebarz, M. Kloz, J. A. Leveillee, A. Schleife, S. Zollner, M. Grundmann, and J. Andreasson, Ultrafast dynamics of hot charge carriers in an oxide semiconductor probed by femtosecond spectroscopic ellipsometry, New J. Phys. 22, 083066 (2020).
  4. J. Budai, Zs. Pápa, P. Petrik, and P. Dombi, Ultrasensitive probing of plasmonic hot electron occupancies, Nat. Commun. 13, 6695 (2022).
  5. P. Sándor, B. Lovász, J. Budai, Z. Pápa, and P. Dombi, Ultrafast surface plasmon probing of interband and intraband hot electron excitations, Nano Lett. 24, 8024 (2024).
  6. L. G. Oldal, B. Gilicze, T. Bartyik, D. Kiss, M. Devetta, G. Zeni, F. Frassetto, L. Poletto, T. Csizmadia, and B. Major, Combined, table-top extreme-ultraviolet ellipsometry and polarimetry for studying ultrafast processes in matter, J. Phys. Photon. 8, 01LT01 (2026).
  7. V. C. Agulto, T. Iwamoto, Z. Zhao, S. Liu, K. Kato, and M. Nakajima, Wafer-scale mapping of carrier density and mobility with terahertz time-domain ellipsometry, Opt. Lett. 50, 948 (2025).
  8. J. Csontos, Z. Tóth, Z. Pápa, B. Gábor, M. Füle, B. Gilicze, and J. Budai, Ultrafast in-situ null-ellipsometry for studying pulsed laser—Silicon surface interactions, Appl. Surf. Sci. 421, Part B, 325 (2017).
  9. S. Zollner, K. D. Myers, J. M. Dolan, D. W. Bailey, and C. J. Stanton, Theory of femtosecond ellipsometry in Ge at 1.5 eV, Thin Solid Films 313–314, 568 (1998).
  10. G. Mak and W. W. Rühle, Femtosecond carrier dynamics in Ge measured by a luminescence up-conversion technique and near-band-edge infrared excitation, Phys. Rev. B 52, R11584(R) (1995).
  11. X. Q. Zhou, H. M. van Driel, and G. Mak, Femtosecond kinetics of photoexcited carriers in germanium, Phys. Rev. B 50, 5226 (1994).
  12. G. Mak and H. M. van Driel, Femtosecond transmission spectroscopy at the direct band edge of germanium, Phys. Rev. B 49, 16817(R) (1994).
  13. C. A. Armenta, M. Zahradník, M. Rebarz, C. Emminger, S. Espinoza, S. Vazquez-Miranda, J. Andreasson, and S. Zollner, Band-filling and relaxation effects in the transient dielectric function of Ge, J. Appl. Phys. 138, 205702 (2025).
  14. E. J. Loren, J. Rioux, C. Lange, J. E. Sipe, H. M. van Driel, and Arthur L. Smirl, Hole spin relaxation and intervalley electron scattering in germanium, Phys. Rev. B 84, 214307 (2011).
  15. Z. Liu, M. O. Nestoklon, J. L. Cheng, E. L. Ivchenko, and M. W. Wu, Spin-dependent intravalley and intervalley electron–phonon scatterings in germanium, Phys. Solid State 55, 1619 (2013).
  16. A. Giorgioni, E. Vitiello, E. Grilli, M. Guzzi, and F. Pezzoli, Valley-dependent spin polarization and long-lived electron spins in germanium, Appl. Phys. Lett. 105, 152404 (2014).
  17. S. Zollner, K. D. Myers, K. G. Jensen, J. M. Dolan, D. W. Bailey, and C. J. Stanton, Femtosecond interband hole scattering in Ge studied by pump-probe reflectivity, Solid State Commun. 104, 51 (1997).
  18. M. Zürch, H.-T. Chang, L. J. Borja, P. M. Kraus, S. K. Cushing, A. Gandman, C. J. Kaplan, M. H. Oh, J. S. Prell, D. Prendergast, C. D. Pemmaraju, D. M. Neumark, and S. R. Leone, Direct and simultaneous observation of ultrafast electron and hole dynamics in germanium, Nat. Commun. 8, 15734 (2017).
  19. T. T. Tran, J. Wong-Leung, L. A. Smillie, A. Hallén, M. G. Grimaldi, and J. S. Williams, High hole mobility and non-localized states in amorphous germanium, APL Mater. 11, 041115 (2023).
  20. V. A. Volodin, G. K. Krivyakin, G. D. Ivlev, S. L. Prokopyev, S. V. Gusakova, and A. A. Popov, Crystallization of amorphous germanium films and multilayer a-Ge/a-Si structures upon exposure to nanosecond laser radiation, Semiconductors 53, 400 (2019).
  21. J. Budai, B. Farkas, Z. L. Horváth, and Zs. Geretovszky, On determining the optical properties and layer structure from spectroscopic ellipsometric data using automated artifact minimization method, Thin Solid Films 567, 14 (2014).
  22. See Supplemental Material at http://link.aps.org/supplemental/10.1103/qkbh-bb3f for a detailed discussion of transient ε1, ellipsometric modelling, two-temperature model, and estimation of charge carrier density, electron temperatures, and band-gap renormalization, which includes Refs. [22, 23, 24, 25, 26, 27].
  23. R. R. Alfano, Semiconductors Probed by Ultrafast Laser Spectroscopy (Academic Press, New York, 1984), Vol. 1.
  24. L. L. Taylor, J. Xu, M. Pomerantz, T. R. Smith, J. C. Lambropoulos, and J. Qiao, Femtosecond laser polishing of germanium, Opt. Mater. Express 9, 4165 (2019).
  25. A. Abdelmalek, L. Kotsedi, Z. Bedrane, E.-H. Amara, M. Girolami, and M. Maaza, Optical and thermal behavior of germanium thin films under femtosecond laser irradiation, Nanomater. 12, 3786 (2022).
  26. S.-M. Lee, D. G. Cahill, and R. Venkatasubramanian, Thermal conductivity of Si–Ge superlattices, Appl. Phys. Lett. 70, 2957 (1997).
  27. M. Beekman, S. Stefanoski, W. Wong-Ng, J. A. Kaduk, Q. Huang, C. Reeg, C. R. Bowers, and G. S. Nolas, Structure and thermal conductivity of Na1−xGe3+z, J. Solid State Chem. 183, 1272 (2010).
  28. J. Tauc, R. Grigorovic, and A. Vancu, Optical properties and electronic structure of amorphous germanium, Phys. Status Solidi 15, 627 (1966).
  29. L. Viña, S. Logothetidis, and M. Cardona, Temperature dependence of the dielectric function of germanium, Phys. Rev. B 30, 1979 (1984).
  30. H. Rafla-Yuan, J. D. Rancourt, and M. J. Cumbo, Ellipsometric study of thermally evaporated germanium thin film, Appl. Opt. 36, 6360 (1997).
  31. J. R. Blanco, R. Messier, K. Vedam, and P. J. McMarr, Spectroscopic ellipsometry study of rf-sputtered a-Ge films, MRS Online Proceedings Library 38, 301 (1984).
  32. M. Miranda, T. Fordell, C. Arnold, A. L'Huillier, and H. Crespo, Simultaneous compression and characterization of ultrashort laser pulses using chirped mirrors and glass wedges, Opt. Express 20, 688 (2012).
  33. M. Miranda, P. Rudawski, C. Guo, F. Silva, C. L. Arnold, T. Binhammer, H. Crespo, and A. L'Huillier, Ultrashort laser pulse characterization from dispersion scans: A comparison with SPIDER, in CLEO: 2013, OSA Technical Digest (online) (Optica Publishing Group, 2013), paper JTh2A.31.
  34. S. Richter, M. Rebarz, O. Herrfurth, S. Espinoza, R. Schmidt-Grund, and J. Andreasson, Broadband femtosecond spectroscopic ellipsometry, Rev. Sci. Instrum. 92, 033104 (2021).
  35. D. W. Bailey and C. J. Stanton, Calculations of femtosecond differential optical transmission in Ge, J. Appl. Phys. 77, 2107 (1995).

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