From interface-limited to Auger-dominated carrier dynamics in $π$-SnS

TL;DR

This work investigates ultrafast carrier dynamics in metastable cubic π-SnS using attosecond XUV transient absorption at the Sn $4d$ edge, enabling element- and orbital-specific tracking of conduction-band filling, edge shifts from band-gap renormalization, and recombination. A two-temperature framework reveals a density-dependent crossover from phonon-limited cooling to Auger-assisted carrier–carrier cooling, with the slow recombination component transitioning from interface-limited at low density to Auger-dominated above $n\approx 1\times10^{20}$ cm$^{-3}$. Coherent phonon motion with a period of $188\pm6.8$ fs indicates strong electron–phonon coupling and ISRS-driven lattice dynamics. Overall, π-SnS serves as a model complex semiconductor for disentangling nonequilibrium carrier and lattice processes, and ATAS proves powerful for resolving fast, density-dependent mechanisms relevant to energy-conversion applications.

Abstract

Metastable cubic tin(II) sulfide ($π$-SnS) is an earth-abundant semiconductor whose three-dimensionally bonded chiral lattice may overcome the short minority-carrier lifetime of orthorhombic SnS while maintaining a near-ideal bandgap for tandem photovoltaics. Despite its promise, ultrafast carrier cooling and recombination mechanisms over illumination density remain poorly constrained. We use core-level extreme-ultraviolet attosecond transient absorption spectroscopy at the Sn $4d$ edge to track carrier injection, cooling, and recombination in $π$-SnS with element- and orbital-specific sensitivity. Following femtosecond near-infrared excitation, the Sn $4d\rightarrow$CB onset exhibits conduction-band state filling and a carrier-induced edge shift, enabling extraction of density-dependent kinetics. The transient response follows a biexponential decay with a fast hot-carrier cooling component and a slower recombination component. At low carrier densities, recombination is consistent with interface-limited processes, whereas above $\sim1\times10^{20}$ cm$^{-3}$ both cooling and recombination accelerate, indicating a crossover to carrier-carrier interaction-dominated dynamics. Coherent phonon oscillations with a period of $\sim188$ fs reveal coupling between electronic excitation and lattice motion. These results provide a comprehensive picture of nonequilibrium carrier and phonon dynamics in cubic SnS, reveal a change of mechanisms over a range of carrier densities, and establish the value of using attosecond transient absorption spectroscopy to study ultrafast processes in complex semiconductors that have optoelectronic and energy-conversion applications.

Figures (12)

• Figure 1: Crystal structure, excitation pathways, and electronic structure of cubic $\pi$-SnS. (a) Real-space crystal structure of cubic $\pi$-SnS, illustrating the three-dimensional network consisting of 64 Sn (grey) and S (yellow) atoms within the P3$_1$2 unit cell. (b) Schematic energy-level diagram summarizing the photoexcitation and relaxation processes probed in this work. Near-infrared excitation across the indirect band gap (red arrow) generates hot electron and hole populations in the conduction and valence bands, respectively. These carriers undergo rapid intraband cooling toward the band edges (1), followed by recombination mediated by interface or defect states within the band gap (discrete level), and subsequent electron–hole recombination (process 2). (c) Energy diagram for Auger cooling (1) and Auger recombination (2). The dashed parabolas in (b) and (d) show the shift of the bands induced by bandgap renormalization. (d) Density-functional-theory (DFT) calculated electronic band structure of cubic $\pi$-SnS along high-symmetry directions of the Brillouin zone, together with the projected density of states (DOS), highlighting the band gap and the orbital character of the valence and conduction bands relevant to the XUV transient absorption measurements. The crystal structure (a) and DFT calculated bandstructure (d) was adapted from Skelton2017_2.
• Figure 2: (a) Differential XUV absorbance of $\pi$-SnS across the Sn N$_{4,5}$ absorption edge. The differential absorbance is shown as function of XUV photon energy averaged over pump-probe delays between 0 and 100 fs (purple curve) and between 1 and 3 ps (blue curve). (b) Differential XUV absorbance as a function of the photon energy and pump-probe delay. The dashed vertical lines indicate the energies of the 4d$_{5/2}$$\rightarrow$CBM and 4d$_{3/2}$$\rightarrow$CBM transitions.
• Figure 3: Ultrafast build-up of the Sn $4d\rightarrow$CB onset response in $\pi$-SnS. (a) Short-timescale ATAS scan across the Sn $4d$ absorption onset recorded with 1 fs delay steps with an exciting pump energy of 9 $\mu$J. The indicated spectral windows highlight a state-filling window (dashed region at A$'$) and an edge-shift window (left dashed region). Both windows include contributions from pump-induced renormalization of the Sn $4d\rightarrow$CB onset (including band-gap and core-level shifts and core-exciton renormalization), while the green window additionally tracks conduction-band state filling. (b) Corresponding temporal responses illustrating an approximately instrument-response-limited rise of the state filling signal and the build-up of the edge-shift response, as well as a decay towards negative times for the state blocking signal. (c) Decomposition of state filling signal. The fitted A$'$ core-exciton and carrier injection response is shown as dashed gold and dashed purple curves respectively.
• Figure 4: (a) Charge carrier density-dependent temporal responses extracted from the state filling window centered at 26.7 eV (colored points) and corresponding fits (solid black curves). $z$-axis shows normalized differential absorption, $\Delta A$. Linear offset along density axis for clarity. (b,c) Decay rate fit constants as a function of charge carrier density. Blue cross-hatches: decay rates from 26.7 eV state filling window. Green circles: decay rates from 25.7 eV sate filling window Error bars indicate 1 standard deviation. (b) shows fast decay rate $k_\text{f}$. Solid curves show power law fits to the two cooling regimes. (c) shows slow decay rate $k_\text{s}$. Solid curve shows fit of the decay rates extracted from the 25.7 and 26.7 state filling windows using Eq. \ref{['eq:Gamma_def']}.
• Figure 5: Coherent phonon oscillations as function of delay averaged over the spectral region between 26.25 and 26.35 eV with strong lattice response. The data are shown in black while the magenta curve is the fit to the data using Eq. \ref{['eq:eq_ph']}.