Fig. 3: Late-time decay analysis of TDR signal of Y₂Ti₂O₅S₂ photocatalyst.

a TDR profile at pump fluence intensity \({P}_{{{{{{\rm{FL}}}}}}}=4.5\,{{\upmu }}{{{{{\rm{J}}}}}}\,\) and probe photon energy of 0.24 eV fitted with the power law: \(A\times {t}^{-\alpha }\). b, c Variation of estimated amplitude \(A\) and exponent \(\alpha\) with \({P}_{{{{{{\rm{FL}}}}}}}\). In b and c, the dashed lines correspond to the analytical solution from Eq. (2) at trap density \({N}_{{{{{{\rm{t}}}}}}}=5.1\times {10}^{17}\,{{{{{\rm{c}}}}}}{{{{{{\rm{m}}}}}}}^{-3}\) and energy dispersion parameter \(\alpha =0.19\) (\({E}_{0}=0.137\,{{{{{\rm{eV}}}}}}\)). d, Proposed model schematic showing exponential tail-states of VB (\({N}_{{{{{{\rm{t}}}}}}}g(E)\)) along with bimolecular band-to-band transition of mobile electrons and trapping/detrapping of holes. Here, \({k}_{{{{{{\rm{r}}}}}}}\), \({k}_{{{{{{\rm{t}}}}}}},\) and \({k}_{{{{{{\rm{d}}}}}}}\) are the corresponding rate constants, whereas \({p}_{{{{{{\rm{m}}}}}}}\left(t\right),{p}_{{{{{{\rm{t}}}}}}}\left(E,t\right),\) and \(n(t)\) are the density of mobile holes, trapped holes at energy \(E\), and electrons at time \(t\) after photoexcitation, respectively. Source data are provided as a Source Data file.