Direct and simultaneous observation of ultrafast electron and hole dynamics in germanium

Abstract

Understanding excited carrier dynamics in semiconductors is crucial for the development of photovoltaics and efficient photonic devices. However, overlapping spectral features in optical pump-probe spectroscopy often render assignments of separate electron and hole carrier dynamics ambiguous. Here, ultrafast electron and hole dynamics in germanium nanocrystalline thin films are directly and simultaneously observed by ultrafast transient absorption spectroscopy in the extreme ultraviolet at the germanium M_4,5 edge. We decompose the spectra into contributions of electronic state blocking and photo-induced band shifts at a carrier density of 8 × 10²⁰ cm^-3. Separate electron and hole relaxation times are observed as a function of hot carrier energies. A first-order electron and hole decay of ∼1 ps suggests a Shockley-Read-Hall recombination mechanism. The simultaneous observation of electrons and holes with extreme ultraviolet transient absorption spectroscopy paves the way for investigating few- to sub-femtosecond dynamics of both holes and electrons in complex semiconductor materials and across junctions.

Figure 1. XUV ultrafast transient absorption spectroscopy in germanium.

(a) In the experiment a time-delayed broadband XUV pulse is used to probe the transient absorption of a nanocrystalline germanium thin film after excitation with a broadband VIS-NIR pump pulse. (b) Band diagram and projected density of states (DOS) for germanium, calculated here by density functional theory calculation (see Methods section). The VIS-NIR pump pulse initially promotes electrons (filled red circle) into the CB leaving behind a hole (open red circle) in the VB. (c) Transition probability P for the specific VIS-NIR pump pulse used in this experiment at different parts of the band diagram (see Supplementary Note 2). The large bandwidth of the pump pulse allows to generate holes at all slopes of the Γ valley in the light-hole band (yellow solid line in c) and heavy-hole band (red solid line in c) as well as the split-off band (brown solid line in c) by one-photon transitions without the assistance of phonons (that is, direct transitions). At the M_4,5 edge the XUV pulse probes the transient state in the VB and CB from a 3d core level as indicated by the purple lines and arrows in b,c; the 3d core level has a significant spin-orbit splitting in germanium of 0.58 eV (ref. 23), and transitions from both spin-orbit states are observed to those parts of the bands that are of 4p orbital character. The VB and CB in germanium are primarily of 4s and 4p orbital character. The orbital character is encoded by a red and green colour code, respectively, for 4s and 4p orbital character in b. (d) The spectrum of the broadband XUV probe pulse covers the M_4,5 edge of germanium (see absorbance in dotted blue line in d) around 30 eV.

Figure 2. Decomposition of the contributions from SB and broadening and band shifts.

(a) Raw transient absorption data. Using the measured static absorbance (b) the measured ΔA_meas trace (a) is decomposed into three major components: (c) SB, (d) broadening of the excited state and (e) a redshift of the ground state, via an iterative algorithm, see text for details. (f) Modifying the SB contribution with a subsequent spin-orbit separation allows quantitative visualization of the electron and hole contributions, referred to as carrier dynamics. (g) The amount of redshift ΔE_shift(τ) over the delay shows a constant non-zero shift for negative time delays, which is heat induced from previous laser pulses, and a time dependence for positive delays.

Figure 3. Differential absorption experiment in comparison to first-principles calculations.

(a) A carrier dynamics signal (I=2 × 10¹¹  W cm⁻²) features positive and negative differential absorption in the VB and CB, respectively. Positive time delays correspond to the VIS-NIR pump pulse arriving before the XUV probe pulse. Comparison with a calculated density of states (DOS) allows assigning characteristic valleys of the band structure to the measured energy axis (cf. Fig. 1c). (b) The absolute values of the rises of the two main transient features around 28.3 eV (VB) and 29.9 eV (CB) are associated with electrons (blue open circles) and holes (red open squares), respectively, exhibiting a rise time limited by the duration of the VIS-NIR pulse. The measured band shift ΔE_shift(τ) (black open diamonds) also follows the carrier excitation within the instrumental response time. The solid lines in b are moving averages to guide the eye. In (c) the differential absorption of the carrier dynamics directly after VB to CB excitation, that is, for positive time delays averaged over τ=8 to 12 fs (indicated by the black rectangle in a), is shown. The shaded error bar in (c) corresponds to the s.d. of individual data points within the averaging window. The dashed black line shows the differential absorption calculated from a TDDFT calculation assuming pulses with a peak intensity of 10¹¹ W cm⁻².

Figure 4. Electron kinetics in nanocrystalline germanium following ultrafast excitation.

(a) The measured change of absorbance in the carrier dynamics in the spectral region of the CB decomposed into two singular value components. (b,c) The spectrum and the time dynamics of these singular value components, respectively. (d) Calculating a transient signal from both components and their time dependence yields good agreement with the measurement. (a,d) Share the colour bar indicated in d. The temporal dependence of the stronger component can be best described by a single exponential decay with a time constant of Δτ_e,recomb=(1,140±50) fs associated with the carrier recombination. The weaker component has a time constant of τ_e,relax=(110±30) fs, suggesting a fast relaxation of hot electrons from higher energies to lower energies. (e) For a section of the CB near the band edge, a single exponential decay is fit to each energy slice of the data, which allows the construction of a map of the dynamics of hot electrons versus energy (f), which is in reasonable agreement with the data. (g) The obtained time constants versus energy (blue line with shaded error band (g)) indicate increased lifetimes of carriers at the CB valleys at several energies, with the longest lifetimes at the low-energy valleys, consistent with the SVD analysis. The shaded error bands correspond to the uncertainty of the retrieved fit parameters. See text discussion for further explanation and interpretation.

Figure 5. Hole kinetics in nanocrystalline germanium following ultrafast excitation.

(a) The measured change of absorbance in the spectral region of holes can be decomposed into two singular value components. (b,c) The signal distribution and time dynamics of the two largest singular value components, respectively. (d) Their addition reproduces the observed transient absorption trace. (a,d) Share the colour bar indicated in d. The stronger component (red data in (b,c)) can be associated with thermalized holes. The growth of this component for τ_{split-off,heavy hole}=(140±10) fs and subsequent decay in τ_h,recomb=(1,080±90) fs can be understood by holes scattering from the split-off band to the heavy-hole band and subsequent recombination with electrons. The weaker component (blue data in (b,c)) can be associated with hot holes, which exhibit a fast relaxation to lower hole energies within τ_relax=(170±10) fs. See text for further explanations.

Figure 6. Band shift depending on time delay and intensity.

Here the band shift ΔE_shift=(τ) for different excitation intensities is depicted. The temporal behaviour suggests that the observed shift is predominantly due to a redshift of the CB due to carrier-induced band shift , assuming a single exponential carrier decay with a time constant of 1.1 ps (red dotted line). In the inset the measured initial shifts (black squares) for different initial carrier densities is compared to an analytic calculation of the band shift. The calculated redshift of the CB (red dashed line, inset) due to bandgap renormalization (BGR) for different carrier densities is slightly larger than the measured band shifts. The vertical error bars in the inset correspond to the s.d. of the data points in the time delay segment. The horizontal error bars are derived by taking the uncertainties of the measured excitation fluence into account. See text for discussion.