Power-dependent spectral shift of photoluminescence from ensembles of silicon nanocrystals
© Timmerman and Gregorkiewicz; licensee Springer. 2012
Received: 18 April 2012
Accepted: 22 June 2012
Published: 12 July 2012
Nanocrystals are widely studied for their tunable optical properties, most importantly increased luminescence efficiency and emission energy. Quantum confinement effects are found for many different types of nanocrystals, and these introduce a relation between the emission wavelength and the size of nanocrystals. When ensembles of nanocrystals with a distribution of sizes are studied, this can have profound effects on their luminescence spectra. Here, we show how photoluminescence spectra of ensembles of silicon nanocrystals can shift under different excitation conditions, resulting from differences in absorption cross-section of the individual nanocrystal sizes. This effect, together with the fact that after a pulsed excitation a silicon nanocrystal can only emit a single photon, determines how the distribution of excited nanocrystals changes and leads to the spectral shift for different excitation powers. Next to this effect, the influence of different radiative rates in such ensembles is also addressed. These notions are important for the interpretation of photoluminescence data for silicon nanocrystals but can be extended to any nanoparticle system comprising size-distributed ensembles.
Nanoparticles of many different semiconductor materials are intensively studied for their interesting optical properties. Quantum confinement in these nanostructures leads to strong altering of radiative rates and energy structure. In general, stronger confinement in smaller particles gives rise to shorter emission wavelengths . Due to limitations in size selectivity on this scale, ensembles of nanoparticles always show a distribution of sizes and shapes. This results in inhomogeneously broadened photoluminescence (PL) spectra. For indirect band gap semiconductors, there is a special interest in the use of nanocrystals (NCs). In the bulk equivalent of these material, electron-hole radiative recombination has very low probability, since the difference in crystal momentum between the top of the valence band and bottom of conduction band can not be compensated by photon emission. In this case, optical transitions need to be accompanied by phonons, lowering their probability. For example, the radiative lifetime of excitons in bulk silicon is in the order of milliseconds. In Si NCs, the momentum conservation rule is relaxed, as k is not a good quantum number any more, and radiative phononless transitions become more probable. This leads to a substantial decrease of the radiative recombination time, which can be observed by photoluminescence lifetime measurements (from milliseconds to microseconds for the smallest Si NCs) [2, 3].
PL spectroscopy is a powerful tool that is often used to determine specific properties of NCs. Most importantly, once a relationship has been determined between the size and the associated photon energy, it can be used as a relatively simple experimental way to determine sizes and distributions hereof.
In this work, we study PL spectra of silicon NCs and their change for different excitation fluences. A combination of size-dependent absorption cross-section and saturation effects in these NCs has a profound effect on the measured PL spectrum. We show simulations of this effect and compare them with experimental data. The effect of excitation conditions on the spectral profile will be discussed. Next to this, the influence of different PL lifetimes present in an ensemble of NCs is also addressed.
A silicon-rich silicon oxide film with a thickness of 350 nm was deposited on a quartz substrate by a radio frequency co-sputtering technique. Subsequent annealing of the sample at a temperature of 1,150°C in nitrogen atmosphere for 30 min induced formation of Si NCs. The layer of Si NCs in amorphous SiO2 created in this way was characterized by an excess Si amount of 5 vol.% and contained NCs with an average diameter of approximately 3.5 nm.
PL experiments were performed under pulsed excitation provided by an optical parameter oscillator, pumped by the 3rd harmonic of a Nd:YAG laser, with a wavelength of 416 nm (3 eV) and pulse width of approximately 9 ns. Luminescence was dispersed by a monochromator (Solar M266, SOLAR Laser Systems, Minsk, Republic of Belarus) and detected by a linear detector (Hamamatsu S10141-1108s, Hamamatsu Photonics K.K., Shizuoka Pref., Japan). The entire system was calibrated for its spectral response with a calibration source. All measurements were taken at room temperature.
where ESi is the band gap of bulk Si, similar as the theoretical dependence determined in [6, 7]. When an intrinsic yield of PL of 100% is assumed for all sizes [8, 9], we can obtain a size distribution directly from PL spectrum, as the emission wavelength is related to the band gap. It is important to note that this is only valid for the optically active NCs in the entire distribution. Different effects can quench or enhance luminescence from Si NCs, which could introduce a size-dependent emission efficiency. For example, a single dangling bond on the surface will quench PL completely , and the chance of that will be strongly size-dependent. Other effects like exciton hopping [11, 12] and non-radiative radiation via defects  can change the wavelength-dependent quantum efficiencies and, thus, the final emission spectrum. If such effects are quantified for a certain system, this could be used in order to get information about the entire distribution from the determined PL spectra. For the rest of the analysis done here, however, we assume that all NCs are optically active.
The shift of PL spectra to shorter wavelengths when increasing the excitation power has been shown to occur in different types of NC ensembles. Different explanations have been suggested in order to account for this behavior [22–24], and the importance of the absorption cross-section has been noted as well [16, 25]. Although the above proposed framework does not necessarily fully explain the experimentally observed shifts of PL spectra, it is important to account for the strong influence of the discussed effects. It should be emphasized that the analysis and simulations done here are based on the condition that the system is excited by a short pulse, with respect to the PL lifetime, and that the emerging luminescence is decaying fully in between the subsequent pulses. In experimental practice, this means that the pulse repetition rate should be small enough to allow all excited NCs to return to the ground state. Under continuous excitation, typical for the majority of experimental reports, the PL characteristics change considerably, as equilibrium conditions are important in this case. The size-dependent decay time could substantially alter the excitation power-dependent emission, and an even larger blueshift can be expected as the shorter PL lifetime of small NCs allows for more radiative recombinations. Now, the question arises under which experimental conditions PL spectra should be collected in order to get reliable information about the physical parameters of the system. For NCs showing long decay times, like Si, it is possible to excite the entire distribution by a pulsed excitation. After this, all multiple carriers simultaneously present in the same NC undergo a fast Auger non-radiative recombination, and every NC can, in principle, emit a photon. This would then be the best way to obtain information about the entire ensemble. However, high pump fluences might be necessary to arrive to this situation, and non-linear and heating effects can appear and influence PL properties . Alternatively, at low powers where the average amount of absorbed photons per NC <<1, the shape of the PL spectrum will not change for varying power. This would be the best region to do comparative experiments, but the low intensity of PL signal might complicate the practical usability of this approach. It is also important to note that, in this case, PL will be dominated by contribution from large NCs. For more accurate information about smaller particles, a scaling based on absorption cross-section should be employed.
To sum up, it has been shown that PL spectra of typical Si NC ensembles show a relatively strong dependence on the excitation fluence. A shift of 30 nm in the maximum of PL intensity appears between spectra taken at a low power excitation and under saturation conditions. It has been demonstrated that this shift can be modeled fairly well by taking into account the differences in absorption cross-section for different sizes of NCs. This, and the notion that each Si NC can only emit a single photon after a pulsed excitation, determines the distribution of the ensemble that is excited and contributes to PL. The evolution of the excited state distribution with respect to excitation pump fluence can be modeled fairly well by these simulations. Additional simulations, taking into account also differences in PL lifetime in the ensemble, show spectral narrowing and red shift for peak intensity in time-dependent spectra. While the presented modeling demonstrates the importance of excitation conditions on the PL spectra of ensembles of Si NCs, this approach can be extended to all semiconductor NCs, where ensembles and size-dependent absorption are imminent.
DT and TG are post-doctoral researcher and full professor, respectively, at the van der Waals - Zeeman Institute at the University of Amsterdam.
The authors would like to thank The Netherlands Organisation for Scientific Research (NWO) for financial support. They also want to acknowledge Brent Huisman for the contribution in spectroscopic measurements.
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