Optical transitions from the lower triplet and the upper singlet states are forbidden and allowed respectively, due to spin selection rules [1, GSK3326595 2, 39, 40, 53]. However, the lifetime
of the triplet state becomes weakly allowed due to spin-orbit interaction [39, 40, 53]. Hence, the triplet lifetime is expected to be considerably longer than the singlet lifetime. At low temperatures (where kT < < Δ, and Δ is the singlet-triplet splitting energy; see inset to Figure 3b), only the triplet level is populated and therefore, the PL decay time is dominated by the triplet lifetime and is relatively long (the low-temperature plateau regions in Figure 3a). As the temperature increases (above approximately 30 K), the upper singlet
level becomes thermally populated and the overall lifetime shortens according to the following expression: (2) where τ R stands for the radiative decay time and τ L and τ U are the lower triplet and the upper singlet lifetimes respectively (g = 3 is the levels degeneracy ratio) [1, 39, 40, 53]. At high temperatures, the decay time is dominated by the much faster upper singlet lifetime. Figure 2 PL decay curves. The PL decay curves of H-PSi measured VX-809 order at a photon energy of 2.03 eV (610 nm) and at various temperatures. The solid lines present the best fit to a stretched exponential function (Equation 1). Inset shows the PL spectrum of H-PSi measured at room
temperature. Figure 3 PL lifetime and integrated PL. (a) Arrhenius 5-Fluoracil plot of the PL lifetime (on a semi-logarithmic scale) as a function of 1/T, at a photon energy of 2.03 eV (610 nm) for H-PSi (red Selleck JQEZ5 circles) and O-PSi (black squares). The solid lines represent the best fit to the singlet-triplet model of Eq.2. (b) Arrhenius plot of the integrated PL. Inset shows the schematics of the excitonic two-level model with the upper excitonic singlet-triplet state and the ground (no exciton) state. The arrows represent the allowed (from the singlet) and the forbidden (from the triplet) optical transitions. From Figure 3a we found that within the experimental errors, the upper singlet decay times of H- and O- PSi (at photon energy of 2.03 eV) are essentially the same (1.0 ± 0.2 μs and 1.3 ± 0.2 μs for H-PSi and O-PSi, respectively). However, at low temperatures the H-PSi decay time is faster than that of the O-PSi (200 ± 50 μs relative to 480 ± 50 μs, respectively). To further explore the differences between H- and O- PSi decay times, the singlet and the triplet lifetimes as well as the energy splitting were extracted over the measurement’s range of photon energies and are plotted in Figure 4. As expected, the upper singlet lifetime (τ U) is significantly shorter (by about one to two orders of magnitude) than the lower triplet lifetime (τ L) over this range of photon energies.
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