Femtosecond tracking of carrier relaxation in germanium with extreme ultraviolet transient reflectivity

Christopher J. Kaplan, Peter M. Kraus, Andrew D. Ross, Michael Zürch, Scott K. Cushing, Marieke F. Jager, Hung-Tzu Chang, Eric M. Gullikson, Daniel M. Neumark, and Stephen R. Leone

Phys. Rev. B 97, 205202 – Published 8 May 2018

Abstract

Extreme ultraviolet (XUV) transient reflectivity around the germanium $M_{4, 5}$ edge ( $3 d$ core-level to valence transition) at 30 eV is advanced to obtain the transient dielectric function of crystalline germanium [100] on femtosecond to picosecond time scales following photoexcitation by broadband visible-to-infrared (VIS/NIR) pulses. By fitting the transient dielectric function, carrier-phonon induced relaxations are extracted for the excited carrier distribution. The measurements reveal a hot electron relaxation rate of $3.2 \pm 0.2 ps$ attributed to the $X − L$ intervalley scattering and a hot hole relaxation rate of $600 \pm 300 fs$ ascribed to intravalley scattering within the heavy hole (HH) band, both in good agreement with previous work. An overall energy shift of the XUV dielectric function is assigned to a thermally induced band gap shrinkage by formation of acoustic phonons, which is observed to be on a timescale of 4–5 ps, in agreement with previously measured optical phonon lifetimes. The results reveal that the transient reflectivity signal at an angle of $66^{\circ}$ with respect to the surface normal is dominated by changes to the real part of the dielectric function, due to the near critical angle of incidence of the experiment $(66^{\circ} – 70^{\circ})$ for the range of XUV energies used. This work provides a methodology for interpreting XUV transient reflectivity near core-level transitions, and it demonstrates the power of the XUV spectral region for measuring ultrafast excitation dynamics in solids.

Received 21 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.205202

Physics Subject Headings (PhySH)

Light-matter interaction Optical conductivity

Elemental semiconductors

Reflectivity

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Christopher J. Kaplan¹, Peter M. Kraus¹, Andrew D. Ross¹, Michael Zürch¹, Scott K. Cushing¹, Marieke F. Jager¹, Hung-Tzu Chang¹, Eric M. Gullikson², Daniel M. Neumark^1,3, and Stephen R. Leone^1,3,4

¹Department of Chemistry, University of California, Berkeley, California 94720, USA
²Center for X-ray Optics, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Chemical Sciences Division, Lawrence Berkeley National Laboratory, USA
⁴Department of Physics, University of California, Berkeley, California 94720, USA

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Issue

Vol. 97, Iss. 20 — 15 May 2018

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Images

Figure 1
Femtosecond transient reflectivity in germanium. (a) A time delayed XUV pulse probe transient reflectivity in single-crystal germanium, after excitation with a few cycle NIR pump pulse. (b). The NIR pump promotes electrons from the valence band (red) to the conduction band (green). Subsequently, reflectivity of the XUV probes the excited carrier distribution via transitions from $3 d$ core states to the valence and conduction bands at the $M_{4, 5}$ edge. (c) Static reflectivity of germanium at $66^{\circ}$ angle of incidence, $s$ polarization. (d). Raw transient reflectivity data measured, with marked reflectivity features 1, 2, and 3 as described in text.
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Figure 2
Transient reflectivity modeling and decomposition. (a) Electron contribution to $Δ R / R$ computed from dielectric function fit in Eq. (1). (b) Hole contribution to $Δ R / R$ computed from dielectric function fit. (c) Shift contribution to $Δ R / R$ computed from the dielectric function fit. (d) Total recovered $Δ R / R$ computed from the dielectric function fit.
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Figure 3
Recovered time-resolved dielectric function. (a) Transient dispersive $Δ ɛ_{1}$ retrieved from model. (b) Transient absorptive $Δ ɛ_{2}$ retrieved from model. (c) Carrier contribution to $Δ ɛ_{1}$ retrieved from model. (d) Carrier contribution to $Δ ɛ_{2}$ retrieved from model, showing carrier center energies of electrons (red line), and holes (blue line), respectively.
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Figure 4
Sensitivity of transient reflectivity to $ɛ_{1}$ : (a) $Δ R / R$ computed with static $ɛ_{1}$ and transient $ɛ_{2}$ retrieved with model. (b) $Δ R / R$ computed with static $ɛ_{1}$ and transient $ɛ_{2}$ . (c) Red, $\partial R / \partial ɛ_{2}$ at experimental angle of incidence (66), computed from static dielectric function, showing zero at 29.8 eV. Grey, $\partial R / \partial ɛ_{1}$ at experimental angle of incidence (66), computed from static dielectric function, showing no zero. (d) Heatmap: $\partial R / \partial ɛ_{2}$ as a function of angle of angle of incidence, computed from static dielectric function. Red line: critical angle for XUV computed from static dielectric function, clearly tracking the zero of $\partial R / \partial ɛ_{2}$ .
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Figure 5
Kinetics extracted from dielectric fit. (a) Electron (red) and hole (blue) positions (central energies) obtained from Eq. (3) with biexponential fits. The electron position stops at 4 ps due to depletion of electron signal. (b) $Δ ɛ_{2}$ obtained for electrons (red) and holes (blue) with fits from model (see text). (c) Redshift extracted from modeled dielectric function, along with biexponential fit.
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