Resolving Transient Electron-Phonon Coupling with Time-Resolved Spontaneous Raman Spectroscopy

Abstract

Understanding the interaction of charge carriers with lattice vibrations in the quasi-equilibrium regime is crucial for semiconductor functionality. However, the structural signatures of these interactions are often too subtle for conventional ultrafast techniques to detect. We developed a time-resolved spontaneous Raman technique based on time-correlated single-photon counting to track the spectral response following photoexcitation, providing sub-wavenumber spectral resolution and a few-hundred-picosecond temporal resolution. Unlike traditional pump-probe schemes, our method utilizes a modulated continuous-wave probe to maintain high spectral resolution, enabling detection of low-frequency Raman shifts down to 10 cm$^{-1}$. Applied to lightly boron-doped silicon, we resolve intra-valence band and inter-valence band electronic transitions. A coupled-mode analysis of transient phonon asymmetry, resulting from interference with the inter-valence band transitions, reveals electron-phonon coupling parameters that directly relate to carrier recombination. By capturing these subtle dynamical shifts, we demonstrate that this platform offers a powerful probe for investigating electron-phonon interactions in long-lived excited states.

Figures (11)

• Figure 1: (a) Schematic of the time-resolved spontaneous Raman spectroscopy apparatus utilizing time-correlated single-photon counting. A modulated continuous-wave probe at 785 nm and a pulsed pump at 515 nm are co-aligned onto the sample. (b) Normalized probe-only Raman spectra of the silicon optical phonon at 10 K are recorded using a CCD detector (black) and reconstructed from a single 50 ps time bin using the single-photon avalanche photodiode with TCSPC (red). The overlap demonstrates that introducing picosecond time resolution does not compromise spectral resolution.
• Figure 2: Time-resolved spontaneous Raman response of lightly boron-doped silicon at $280~\mathrm{K}$. (a) Top panel: Raman spectrum of low-doped silicon pre-excitation (red) and post-excitation (green). Bottom panel: Differential spectra $\Delta I(\omega,t)$ obtained by subtracting the pre-excitation spectrum from each transient spectrum. The bold spectrum at $t = 2.35~\mathrm{ns}$ represents the maximum distortion. Differential spectra are offset for clarity, with gray axes indicating the zero level and gray scale bars representing the $\Delta I$ magnitude for each spectral range. The data reveal a transient amplification of the low-frequency intra-valence-band (intra-VB) signal and a time-dependent modification of the optical phonon near $521~\mathrm{cm^{-1}}$ due to the inter-valence-band (inter-VB) transitions. (b) Time-dependent anti-Stokes/Stokes amplitude ratio. The constant ratio verifies that no significant lattice heating occurs during the measurement. (c) Temporal evolution of the normalized integrated absolute differential intensity $\sum_{\omega} |\Delta I|$, integrated over the intra-VB ($10$--$200~\mathrm{cm^{-1}}$, blue) and phonon ($510$--$560~\mathrm{cm^{-1}}$, black) spectral ranges, shown with bi-exponential fits.
• Figure 3: Time-resolved lineshape analysis of the optical phonon and the inter-valence-band (inter-VB) spectral region in lightly boron-doped silicon at $280~\mathrm{K}$. (a) Raman spectrum $2.35~\mathrm{ns}$ after photoexcitation. Gray circles indicate the time-averaged spectrum integrated over $2.35$--$2.85~\mathrm{ns}$, shown alongside the two-coupled-modes fit (black). The asymmetry of the peak is apparent compared to the purely phononic contribution (blue), with most of the asymmetry originating from the cross terms (red) between the inter-VB transitions and the phonon. The direct contribution from the inter-VB electronic transitions (green) is negligible. (b) Statistical $R^{2}$ for the coupled-mode fit (black), compared with a single Lorentz oscillator fit (brown). (c) Temporal evolution of the absolute real ($|\delta|$, blue) and imaginary ($|\gamma|$, red) coupling parameters. The dashed curves in (b) and (c) represent bi-exponential fits to the transients.
• Figure S1: Time-resolved Raman measurement scheme demonstrates the efficiency of the photoluminescence and background subtraction. Raw data at 280 K are presented as false-color heatmaps, with brighter colors indicating higher intensity. The time-resolved Raman data is collected under (a) simultaneous illumination of the pump and probe lasers and (b) under pump laser only, when the probe laser amplitude was off-modulated at the AOM. (c) The subtraction of the pump-only matrix from the pump+probe matrix yields the time-resolved Raman matrix that is used as the starting point for all subsequent analyses in this paper. Top panels - single Raman spectra reconstructed at the 2.00 ns time bin, marked with blue arrows on the heatmaps.
• Figure S2: Time-resolved spontaneous Raman response of lightly boron-doped silicon. Heatmap of the Stokes differential Raman intensity $\Delta I(\omega,t)$ at 280 K, defined relative to the pre-excitation spectrum (top), showing a transient low-frequency electronic continuum and a time-dependent modification of the optical phonon near 521 cm$^{-1}$.