Size-Dependent Intrinsic Radiative Decay Rates of Silicon Nanocrystals at Large Confinement Energies

We study ultrafast photoluminescence (PL) dynamics of Si nanocrystals (NCs). The early-time PL spectra ($<1\mathrm{ns}$), which show strong dependence on NC size, are attributed to emission involving NC quantized states. The PL spectra recorded for long delays ($>10\mathrm{ns}$) are almost independent of NC size and are likely due to surface-related recombination. Based on instantaneous PL intensities measured 2 ps after excitation, we determine intrinsic radiative rate constants for NCs of different sizes. These constants sharply increase for confinement energies greater than $\sim 1\mathrm{eV}$ indicating a fast, exponential growth of the oscillator strength of zero-phonon, pseudodirect transitions.

Figure 1

(a) SSPL (solid lines), UPL (symbols; $t=2\mathrm{ps}$, pump fluence $j_p=0.5\mathrm{mJ}{\mathrm{cm}}^{-2}$), and absorption (dashed line) spectra for a series-A Si NC sample. The arrow marks the energy gap of bulk Si. (b) The UPL spectral maximum versus the SSPL maximum for all of the series-A and series-B samples studied here (symbols); the dashed line corresponds to the situation where UPL and SSPL have the same emission maxima.

Figure 2

(a) Time-resolved PL (lines; TCSPC, $j_p=0.38\mu \mathrm{J}{\mathrm{cm}}^{-2}$) and SSPL (gray shading) spectra of Si NCs (series-B sample); the TCSPC spectra are normalized to the same area. (b) Time transients (symbols) measured for three spectral energies indicated by arrows in panel (a); lines are single-exponential fits. (c) The PL spectra of a series-A sample generated by integrating spectrally resolved PL dynamics for time intervals $t=0–5\mathrm{ns}$ (blue line) and $t>5\mathrm{ns}$ (red line) and the sum spectrum (green line) in comparison to the measured SSPL (gray shading). (d) The dependence of the maxima of the short-lived (blue diamonds) and the long-lived (red squares) PL bands on the SSPL maximum (shown also along the vertical axes by crosses). (e) Early-time PL dynamics for a series-A sample monitored at 1.91 eV (solid circles) and 2.48 eV (open squares). The signal buildup at the lower energy (${\tau }_b=0.61\mathrm{ps}$) is complimentary to the hot PL decay at the higher energy (${\tau }_d=0.38\mathrm{ps}$). (f) Schematics of relaxation processes in Si NCs. Following photoexcitation, an exciton relaxes into the lowest energy quantized state, $|1⟩$, from which it can either recombine radiatively (“fast,” high-energy PL feature, ${\tau }_r$) or nonradiatively (${\tau }_{\mathrm{nr}}$) or get trapped at the surface (${\tau }_{\mathrm{tr}}$) and then recombine through the surface site (“slow,” low-energy PL feature, ${\tau }_s$). Energies of the NC-core states are size dependent, while the energy of the surface state is virtually NC-size independent.

Figure 3

(a) The radiative rate constant versus the UPL peak position for series-A (diamonds) and series-B (squares) Si NC samples. These data were derived from spectrally integrated UPL spectra measured at 2 ps for Si NCs (lines in the inset; series-A samples) and the reference CdSe NC sample (gray shading in the inset). All samples had approximately the same optical density at the pump wavelength and were excited with the same pump fluences. (b) The dependence of the radiative rate constant on the NC confinement energy (solid squares and open diamonds; this work) in comparison to pseudodirect transition rates derived from the experimental data of Ref. 20 (open squares) and calculated phonon-assisted decay rates (dashed line) from Ref. 21. The rates of pseudodirect recombination can be closely described by an exponential dependence (solid line).