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Hot electron cooling in InSb probed by ultrafast time-resolved terahertz cyclotron resonance

Chelsea Q. Xia, Maurizio Monti, Jessica L. Boland, Laura M. Herz, James Lloyd-Hughes, Marina R. Filip, and Michael B. Johnston
Phys. Rev. B 103, 245205 – Published 28 June 2021
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Abstract
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Article Text
  • INTRODUCTION
  • TIME-RESOLVED MAGNETOTERAHERTZ…
  • CYCLOTRON RESONANCE IN PHOTOEXCITED InSb
  • HOT ELECTRON COOLING IN InSb
  • CONDUCTION BAND NONPARABOLICITY PROBED…
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Measuring terahertz (THz) conductivity on an ultrafast timescale is an excellent way to observe charge-carrier dynamics in semiconductors as a function of time after photoexcitation. However, a conductivity measurement alone cannot separate the effects of charge-carrier recombination from effective mass changes as charges cool and experience different regions of the electronic band structure. Here we present a form of time-resolved magneto-THz spectroscopy that allows us to measure cyclotron effective mass on a picosecond timescale. We demonstrate this technique by observing electron cooling in the technologically significant narrow-bandgap semiconductor indium antimonide. A significant reduction of electron effective mass from 0.032 to 0.017 me is observed in the first 200 ps after injecting hot electrons. The measured electron effective mass in InSb as a function of photoinjected electron density agrees well with conduction band nonparabolicity predictions from ab initio calculations of the quasiparticle band structure.

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    • Received 10 February 2021
    • Revised 7 June 2021
    • Accepted 8 June 2021

    DOI:https://doi.org/10.1103/PhysRevB.103.245205

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Carrier dynamicsLandau levelsOptical conductivityPhotoconductivity
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Chelsea Q. Xia1, Maurizio Monti2, Jessica L. Boland1,3, Laura M. Herz1, James Lloyd-Hughes2, Marina R. Filip1, and Michael B. Johnston1,*

    • 1Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, OX1 3PU Oxford, United Kingdom
    • 2Department of Physics, University of Warwick, Gibbet Hill Road, CV4 7AL Coventry, United Kingdom
    • 3Photon Science Institute, Department of Electrical and Electronic Engineering, University of Manchester, Oxford Road, M13 9PL Manchester, United Kingdom

    • *michael.johnston@physics.ox.ac.uk

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    Vol. 103, Iss. 24 — 15 June 2021

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    • Figure 1
      Figure 1

      (a) A schematic diagram of the time-resolved magneto-THz spectroscopy experiment of an undoped InSb sample. The magnetic field vector B and the k-vector of the THz pulse are in the same direction and perpendicular to the sample surface. The linearly polarized incident THz pulse is a superposition of right-handed and left-handed circular polarization components. (b) Electric field of the transmitted THz pulse without photoexcitation, Edark(t,tdelay,B), measured at a magnetic field B=0.6 T. (c) The change of THz transmission ΔE(t,tdelay,B) measured at 200 ps after photoexcitation with a fluence at 5.4nJcm−2 under a magnetic field B=0.6 T. The x component and the y component of the recorded THz signal are represented by the light blue and dark blue curves, respectively, and the pink curve represents the resultant THz signal. The small feature seen in the THz signal at 7.5 ps is an experimental artefact caused by a weak reflection from an optical element along the THz beam path.

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    • Figure 2
      Figure 2

      (a) THz transmission spectra of InSb measured at 200 ps after photoexcitation at fluence 5.4 nJcm−2 with magnetic field ranging from 0.1 to 1 T at a tempertaure of 4 K. The small shoulders shown at high frequency (1.5–2 THz) are experimental artefacts associated with the reduced spectral response of the measurement system over this range. (b) Cyclotron resonance frequency as a function of magnetic field, where the cyclotron resonance frequency corresponds to the minima of the transmission spectra shown in panel (a). The dotted line corresponds to a linear fit of the cyclotron frequency as a function of magnetic field. (c) InSb electron effective mass at 4 K extracted from the cyclotron resonance frequency according to ωc=eB/m*. The dotted line corresponds to the effective mass obtained from the slope of the linear fit determined in panel (b).

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    • Figure 3
      Figure 3

      (a) Frequency-averaged photoconductivity 〈σxx〉 of InSb measured at 4 K as a function of time after photoexcitation by a 35 fs, 335nJcm−2 pulse of 1.55 eV photons. The pink triangles represent the pump-probe delay times when the cyclotron resonance measurements were recorded. (b) Electron effective masses (red diamonds) calculated from the cyclotron resonance measurements which were performed at 13, 20, 27, 47, and 200 ps after photoexcitation. The blue squares represent the product of charge-carrier density and relaxation time, nτ. (c) Quasiparticle band structure of InSb, calculated within the G0W0 approximation (see Appendices pp5 and pp6 for details). The dark blue lines represent the conduction band (CB) and the light blue lines represent the valence band (VB), including the heavy hole (HH), light hole (LH), and split-off (SO) bands. The bottom panel is a zoom-in of the area near the Γ valley. The pink dashed line represents a parabolic CB for comparison which overlaps with the nonparabolic CB near the Γ minimum. The solid and open red circles represent an electron-hole pair generated by photoexcitation. The black arrows represent the hot electron cooling process. (d) Photoconductivity measured at 200 ps after photoexcitation. The top panel shows Δσxx measured without magnetic field, which is fitted with the Drude model given by Eq. (1). The middle and bottom panels show Δσxx measured at magnetic field B=0.4 T under fluence 468 and 54nJcm−2, respectively, fitted with the theoretical magnetoconductivity given by Eq. (4).

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    • Figure 4
      Figure 4

      (a) Experimental cyclotron resonance spectra (solid circles) of InSb at a temperature of 4 K measured 200 ps after photoexcitation with electron densities of 1.1×1014, 1.1×1015, 1.0×1016, and 2.0×1016cm−3 under a magnetic field B=0.4 T. The uncertainties in Re(Δσxx) are obtained from the THz spectral response (see Appendix pp4). The solid lines represent the theoretical magnetoconductivity spectra which were obtained from Eq. (5) and normalized to the experimental data. (b) Cyclotron resonance frequency, fc=ωc/2π (solid blue circles), and momentum scattering time, τ (open red circles), as a function of electron density.

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    • Figure 5
      Figure 5

      InSb electron effective mass as a function of electron density. The red solid circles with error bars represent the experimental effective mass measured in a cryostat held at 4 K for photoinjected electron densities 1.1×1014, 1.1×1015, 1.0×1016, and 2.0×1016cm−3. The blue-purple colored solid circles represent the theoretically calculated effective masses, with the electron temperature indicated by the color scale on the right. The open circles and solid triangles represent previously reported effective masses measured in n-type InSb with various doping densities [27, 28]. The inset shows the estimated electronic temperature as a function of electron density, obtained by equating theoretical and experimental effective masses for each carrier concentration.

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    • Figure 6
      Figure 6

      Schematic for magneto-THz spectroscopy setup. The cartoon on the righthand side shows the configuration of the superconducting magnet along with two pairs of off-axis parabolic mirrors which are used for focusing the THz pulse onto the sample and the (111) ZnTe detection crystal, respectively.

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    • Figure 7
      Figure 7

      Cyclotron resonance spectra of InSb measured at B=0.4 T at (a) 13 ps, (b) 20 ps, (c) 27 ps, (d) 47 ps, and (e) 200 ps after photoexcitation under fluence 335nJcm−2. The blue solid circles represent the experimental data, whereas the red curves are magnetoconductivity fits given by the real part of Δσxx component of Eq. (4).

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    • Figure 8
      Figure 8

      Electron distribution profiles as a function of depth in InSb calculated at 0, 50, 100, 150, and 200 ps after photoexcitation. The initial photoexcitation fluence is 5.4nJcm−2. The dashed lines represent the absorption depth 1/α and effective absorption depth 1/α′ at 200 ps.

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    • Figure 9
      Figure 9

      Normalized raw spectrum of the THz electric field for the THz spectroscopy system used in this study without the application of a spectral response correction. The shaded regions indicate the frequencies at which the spectral amplitude falls to less than 40% of the spectrometer's peak spectral response. The signal-to-noise ratio and random errors are expected to be more significant in these regions.

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    • Figure 10
      Figure 10

      (a) G0W0 conduction band energy of InSb as a function of wave vector along several high symmetry directions in the Brillouin zone. (b) Fit of the conduction band energy calculated within the G0W0 approximation (red dots) using the Kane model (black line) along the Γ-X direction.

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    • Figure 11
      Figure 11

      Calculated effective masses of InSb as a function of electronic temperature at different electron densities.

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    • Figure 12
      Figure 12

      Evolution of electron distribution in InSb conduction band before and after thermalization. Panels (a–c) show the nonthermal electron distribution with increasing time delays after photoexcitation on a femtosecond timescale. HH, LH, and SO represent transitions from heavy-hole, light-hole and split-off bands, respectively. Panels (d, e) show the thermalized electron distribution at high and low temperatures, respectively, which follows the Fermi-Dirac distribution and happens on a much slower timescale (picosecond) than the nonthermal distribution.

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