Supplementary Materials Sample characterization The presence of Si-QDs is established by Transmission Electron Microscopy (TEM), by which the average QD diameter of d QD 2.2 ± 0.5 nm has been determined (Fig. S1 and Fig. 3a in the manuscript). It should be noted that the detection resolution can be limited due to insufficient number of detected Si-QDs and weak contrast of TEM signal for small (d QD < 2 nm) Si-QDs, possibly having disordered non-crystalline core. Therefore, the determined average diameter can be interpreted as an upper limit. Figure S1. TEM image of butyl-capped Si-QDs.
Nuclear Magnetic Resonance (NMR) analysis shows no signal from Si-O-CH 2, which confirms that Si-QDs were originally butyl-terminated: from 1 H NMR we can see that there is no signal in the range 3-4 ppm related to CH 2 -O (Figs. S2a,c), which is confirmed also by the 13 C NMR, where no signal at ~70-72 ppm has been observed (Fig. S2b). a b c Fig S2: NMR spectroscopy of butyl-terminated Si-QDs. (a) 1 H NMR spectrum and (b) 13 C NMR, showing all four carbon atoms of the butyl chain; (c) DOSY NMR spectrum of butyl-terminated Si-QDs. The passivation of the QD surface by butyl-chains is confirmed by Fourier Transform Infrared technique (FTIR) (Fig. S3). FTIR spectrum shows several characteristic vibrational modes related to Si-C, CH 2 or CH 3 bonds. Strong signals corresponding to C-H stretching vibrations were observed, with the symmetric CH 2 stretching located at 2874 cm -1, the asymmetric CH 2 stretching at 2928 cm -1 and the asymmetric CH 3 stretching at 2963 cm -1. The Si-C scissoring and stretching vibrations are visible at 1459 cm -1 and 1261 cm -1, respectively, in agreement with the covalent Si-C attachment of the butyl to the Si-QDs surface. Peak at 1024 cm -1 corresponds to CH 2 rocking/wagging vibration mode. The signal at 1096 cm -1 corresponds to Si-O-Si or Si-O-C vibrations, occurring due to inevitable oxidation during sample processing for FTIR spectroscopy, when sample has been extensively dried to eliminate signal from organic solvents.
Fig. S3 FTIR spectrum of butyl-capped Si-QDs. Single-QD spectroscopy Single QD spectra were measured at room temperature using back-illuminated CCD camera and Olympus IX-71 microscope (air objective, magnification 100, working distance 3-6 mm). Sample was excited by a cw diode laser at 405 nm (~50 µw). A typical set of PL emission spectra of a single Si-QD are plotted in Fig. S4a. Spectra were measured at room temperature and integrated for 10 min. Spectra show multiplepeak structure, assigned to phonon replicas. The average FWHM (Full Width at Half Maximum) of replicas is ~110 mev and their energy (splitting of peaks) ~160 mev. This energy correlates with a strong absorption peak in FTIR spectra (Fig. S3) at ~1261 cm -1 related to Si-C covalent bond stretching vibration mode. a b Fig. S4 Single QD spectroscopy. (a) A set of typical single Si-QD (normalized) PL spectra with typical phonon replicas, compared to an Si-QDs ensemble PL spectrum (gray), excited at the same photon energy (normalized for the sake of comparison). (b) PL lifetime of randomly selected single Si-QD, measured spectrally unresolved in confocal regime.
PL lifetime of a single Si-QD was measured using MicroTime 200 inverted confocal microscope (PicoQuant). The sample was excited by a pulsed diode laser at 405 nm (40 MHz repetition rate, 60 ps pulses, 0.43 mw). The PL decay has two components, a fast one of ~969±22 ps and a slow one of ~5.0±0.2 ns (Fig. S4b). More details on single QD spectroscopy from this sample can be found in Ref. 22. Tight-binding calculations CH 3 -terminated Si-QD is modelled as a spherical silicon nanocrystal covered by an atomic shell of carbon, followed by a shell of hydrogen atoms. sp3d5s* empirical tight binding (TB) technique with the nearest neighbour interactions (Ref. S1) has been used to calculate electron spectra and wave functions. The parameters for the Si- H bond are taken from Ref. S2. Contrary to oxygen, carbon has sp3 hybridization, so it does not change energy spectrum of the Si-QD dramatically (see Fig. 3b in the manuscript). Although there is no data on carbon parameters for sp3d5s* tightbinding model, Ref. S3 suggests those for sp3s* model, fitting to ab-initio results. To simulate the carbon layer, we modified surface silicon atoms by lowering the s- and p- orbitals diagonal (on-site) energies by 3 ev. Hole and electron density in k-space Ψ(k) 2 for CH 3 -terminated Si-QD of 2.5 nm in diameter (Fig. S5, black and red) were calculated by making the Fourier transformation from the expansion coefficients Ψ ν (R) over the tight-binding basis Ψ ν (r-r), where index ν labels orbital symmetry and R is the atom origin. Obtained densities Ψ ν (k) 2 were summed over ν. Data from Fig. S5 (black) are plotted in Fig. 4 (right upper panel) in the manuscript. In Fig. 4 (left upper panel) is shown similar result obtained for H-terminated Si-QD. Fig. 4 (middle upper panel) is a sketch, following model in Ref. 5. The real space densities Ψ ν (R) 2 (Fig. S5 gray) are calculated summing Ψ ν (R) 2 over index ν. For better presentation, the results were convoluted with the Gaussian with dispersion equal to 0.3a, where a is the lattice constant. Data from Fig. S5 (gray, LUMO) are illustratively sketched in Fig. 4 (right lower panel). Similar illustrations are done also for H- and O-terminated Si-QDs.. Fig. S5 Electron and hole density Ψ 2 in the HOMO and LUMO states in the real (gray) and k-space in Γ-X (black) and Γ -L (red) directions.
Wave functions obtained in TB model are used to calculate absorption cross-section in Fig. S6 and the radiative rates in Fig. 3d (gray and green circles) in the manuscript, following the procedure described in Ref. S4 for Si-QDs in SiO 2. Fig. S6 Comparison of theoretical simulations of the absorption cross-section for 1.8 nm (red), 2.5 nm (green) and 3 nm (blue) Si-QDs terminated by -H (dotted lines) and -CH 3 (full lines). One can notice that the near-band-edge part of the absorption spectrum in Fig. 1c and absorption cross-section in Fig. S6 do not show any strong size-dependent features, characteristic for typical direct bandgap QDs, like CdSe or PbSe. To understand the main difference between such typical direct bandgap material and these directbandgap-like Si-QDs, we plot calculated electron-hole states energies together with their radiative rates in a 2D graph in Fig. S7 for both, H- (black) and CH 3 -terminated (red) Si-QDs of diameter 2.5 nm. The blue-shaded area depicts the range of radiative rates typical for direct bandgap materials. From Fig. S7 we can see that density of states with high radiative rate, i.e. direct-bandgap-like states, is quite low, compared to typical direct bandgap materials. Actually, vast majority of states stays in the low radiative rate region, characteristic for the phonon-assisted indirect or so called quasi-direct transitions (see Refs. 2 and 3 in the manuscript). Nevertheless, the crucially important low energy states, contributing to steady-state PL and band-edge absorption cross-section, are direct-bandgap-like. The lowest energy states are marked in Fig. S7 by a blue circle.
Fig. S7 2D graph of calculated e-h states positioned according to their energy and radiative transition rate for H- (black) and CH 3 -terminated (red) Si-QDs of diameter 2.5 nm. The blue-shaded area depicts range of transition probabilities, usual for direct bandgap semiconductors. The blue circles depict the states with the lowest energy. Experimental evaluation of the radiative rates The radiative rate values k rad (d QD ), where d QD is diameter of Si-QD, were estimated from k rad (d QD ) η ext /τ eff (d QD ), where τ eff is PL lifetime and η ext is the absolute external quantum efficiency (eqe). k rad estimated in this way represent the lower limit of radiative rates, because k rad η int /τ eff, and η ext η int, where η int is the internal quantum efficiency (iqe). PL lifetimes τ eff were measured using pulsed laser excitation (370 nm, 140 fs pulse duration, 4 MHz repetition rate) in a single photon counting regime by Photomultiplier (PMT) detector with response time of 26 ps. PL lifetime features two components (Fig. S8a): a fast one (black dots) of 600-900 ps and a slower one (red dots) between 3 and 4 ns. Both components show weak linear dependence on emission photon energy, i.e. size of the Si-QDs. To check for possible slow decaying components, PL dynamics was investigated in the whole spectral range (1.8 ev 3.2 ev) also under ns pulsed laser excitation in the single photon counting regime using PMT, however, no signal decaying slower than ~7 ns (ns-laser pulse duration) was detected. For estimation of the radiative rates k rad, the slower component of ~3-4 ns in PL decay is taken as the effective lifetime τ eff.
a b Fig. S8 PL lifetime and external quantum efficiency. (at) Fast (black) and slow (red) components of the PL lifetime from Si-QDs ensemble. (b) External quantum efficiency (eqe) measured for different excitation photon energies. For the measurements of the η ext, we used integration sphere technique (for more details see Refs. 27 and 28). Emission and absorption of a sample and a reference were evaluated. The sample contains butyl-terminated Si-QDs in UV-grade ethanol in quartz cuvette, and the reference contains only the UV-grade ethanol in quartz cuvette of the same type. η ext at various excitation wavelengths is determined as the ratio of the number of emitted photons (equal to subtracted integrated PL signal of the sample and reference in the spectral range of the emission) and the number of absorbed photons (subtracted integrated excitation peak measured with reference and sample in the spectral range of the excitation) (Refs. 27, 28 in the manuscript). In both, PL and excitation peak intensity is divided by the appropriate photon energy: where I em and I exc are the measured emission and excitation intensities for the sample and reference denoted by subscripts sample and ref ). C(E) is the correction for the detection system spectral sensitivity, which was separately determined with absolutely calibrated lamp, and E em and E exc are the emission and excitation photon energies. In Fig. S8b are plotted resulting η ext for different excitation energies. For excitation wavelength of 370 nm, under which the τ eff were measured, η ext of ~4 % was estimated. Resulting k rad (d QD ) are therefore of values ~10 7 s -1 and are depicted in Fig. 3d (green triangles) for each τ eff (d QD ) detected at various emission energies.,
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