Biexciton Emission as a Probe of Auger Recombination in Individual

Mar 13, 2015 - Material and Nano Physics Department, ICT School, KTH—Royal Institute of Technology, 16440 Kista, Sweden. J. Phys. Chem. C , 2015, 11...
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Biexciton Emission as a Probe of Auger Recombination in Individual Silicon Nanocrystals Federico Pevere, Ilya Sychugov,* Fatemeh Sangghaleh, Anna Fucikova,† and Jan Linnros Material and Nano Physics Department, ICT School, KTHRoyal Institute of Technology, 16440 Kista, Sweden S Supporting Information *

ABSTRACT: Biexciton emission from individual silicon nanocrystals was detected at room temperature by time-resolved, single-particle luminescence measurements. The efficiency of this process, however, was found to be very low, about 10−20 times less than the single exciton emission efficiency. It decreases even further at low temperature, explaining the lack of biexciton emission line observations in silicon nanocrystal single-dot spectroscopy under high excitation. The poor efficiency of the biexciton emission is attributed to the dominant nonradiative Auger process. Corresponding measured biexciton decay times then represent Auger lifetimes, and the values obtained here, from tens to hundreds of nanoseconds, reveal strong dot-to-dot variations, while the range compares well with recent calculations taking into account the resonant nature of the Auger process in semiconductor nanocrystals.

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kinetic form.9 Considering a single nanocrystal, if the Auger recombination rate is low, one would expect new emission peaks to emerge in the PL spectrum as soon as the corresponding exciton states start to be populated. For higher states, e.g., p-states, emission occurs at significantly higher energy while for the biexciton, the emission can occur at either slightly higher or slightly lower energy than the single exciton peak depending on Coulomb and exchange interaction. Indeed, this exciton energy-level structure has been reported for several direct band gap quantum dot systems, such as In0.6Ga0.4As and CdSe among others.10,11 The confirmation of a biexciton nature of these new peaks can then be obtained from powerdependent measurements: at low excitation the population rate equations predict that the PL intensity increases linearly for the exciton peak and quadratically for the biexciton one. The presence of the biexciton emission can also be detected by time-resolved single-dot techniques where it can be distinguished from the exciton signal. First, time-resolved single-dot PL decay measurements can allow distinction between a slow power-independent exciton lifetime and a fast power-dependent biexciton lifetime.12 Second, photon correlation measurements of the single dot autocorrelation function g(2) can detect the presence of biexciton emission as a “contamination” in the antibunching dip and allow estimation of the ratio between exciton and biexciton quantum yields.13 Regarding silicon nanocrystals, Auger recombination is believed to be responsible for the suppression of biexciton (as well as multiexciton) radiative recombination, which leads to PL saturation at high excitation pump fluxes.6,14,15 However, the characteristic lifetime of this nonradiative process (τA) is subject of intensive debates nowadays. In fact, theoretical

INTRODUCTION Although silicon is one of the most used semiconductors in electronic devices, it has always been regarded as a poor lightemitter, due to its indirect-bandgap nature. This is true if we consider bulk silicon, but at the nanoscale the electrical and optical properties can be strongly modified by the quantum confinement effect occurring for silicon nanocrystals (Si-NCs) of a size comparable to the exciton Bohr radius (∼5 nm).1,2 Indeed, at such low dimensions, not only the density of states becomes discrete but also the bandgap can be tuned by the size of the nanocrystal. Moreover, the carrier confinement, dictated by the uncertainty principle, spreads the electron and hole wave functions in k-space, leading to the so-called “breakdown” of the momentum-conservation law:3 the optical transition becomes quasi-direct and a no-phonon (NP) emission line can be detected in the photoluminescence (PL) spectrum of individual silicon nanocrystals.4 Compared to direct-bandgap semiconductor quantum dots, where the radiative exciton lifetimes are of the order of nanoseconds or even picoseconds, the reported values for Si-NCs embedded in a SiO2 matrix lie between 10 μs and 1 ms.2,5 If we consider also that their absorption cross-section can vary from 10−16 to 10−14 cm2 at ∼3 eV (corresponding to our pump laser) for the emission range 1.7−2.0 eV,6,7 then it appears relatively easy to create two excitons (or a biexciton) by a moderately high continuous-wave optical excitation (10−2−102 W/cm2). The generation of a biexciton in a quantum-dot system satisfies the condition of population inversion required for stimulated emission. For silicon nanocrystals dispersed in a silicon dioxide matrix, this phenomenon was reported for the first time by Pavesi et al. in both waveguide and transmission configurations, raising hope for the first silicon laser.8 In that work, a net optical gain was explained in terms of suppressed Auger recombination, a nonradiative process where the exciton energy is transferred to a third carrier (electron or hole) in a © XXXX American Chemical Society

Received: February 3, 2015 Revised: March 13, 2015

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DOI: 10.1021/acs.jpcc.5b01114 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C calculations of τA seem to vary considerably when different approaches are used.14−18 On the one hand, tight-binding calculations predict Auger lifetimes between 100 ps and 100 ns for Si-NCs emitting in the range 1.7−2.0 eV.14,15 On the other, pseudopotential,16 multiband effective mass approximation,17 and ab initio calculations18 seem to lower the upper limit to 10 ns. Furthermore, depending on the energy level broadening (i.e., electron−phonon coupling) considered, these bounds can vary significantly even within the same approximation method.15,16 Considering also fast transient photoluminescence and absorption (TA) measurements19−21 on ensembles of oxide-passivated Si-NCs, the range of τA widens even further to 4 orders of magnitude, from 10 ps to 100 ns. This broad interval can be partially explained by recent theoretical work, which shows that the Auger lifetime of a quantum-confined structure is strongly dependent on the confinement size and exhibits a resonant structure, where the minima correspond to “magic widths”.22−24 Indeed, calculations for Si/SiO2 nanocrystals predict the existence of such “magic-size” off-resonant particles that could feature long Auger lifetimes, up to 250 ns.24 Moreover, the effect of the shape of the nanocrystals has also been proved to be significant in Auger recombination.25,26 Obviously, ensemble measurements do not allow probing of such strong variations of τA between individual particles, yielding only a weighted average value. More importantly, other nonradiative mechanisms related to fast energy transfer in dense ensembles of nanocrystals can distort the estimated value of the intrinsic Auger process rate deduced from such ensemble measurements.27 In this work, we have directly probed Auger/biexciton processes in single silicon nanocrystals. While low temperature spectroscopy did not reveal any new emission lines under strong excitation, the luminescence intensity showed clear saturation behavior, suggesting an efficient Auger process. Time-resolved measurements, however, allowed detection of the biexciton emission signature as a fast (∼ns) initial transient under stronger excitation in the luminescence decay curve (typically ∼μs decay). The extracted values of the characteristic Auger lifetimes from the decay curves, indeed, appeared to be much shorter than the expected biexciton radiative decay times. In addition, the obtained temperature dependence of the biexciton quantum yield, not exceeding 0.1% below 10 K, provided explanation of the lack of specific lines in the lowtemperature spectra which we have actively searched for. The variation of Auger lifetimes from dot-to-dot in Si nanocrystals is experimentally demonstrated in this work, and their absolute values were found to be comparable with recent theoretical calculations.

surface was confirmed by Fourier transform infrared measurements, TEM, and optical characterization. In contrast with the standard chemical synthesis based on hydrogen silsesquioxane, where organic molecules are attached to NC surface in the postprocessing step,29 our fabrication route does not proceed further. Thus, formed Si-NCs were found to feature narrow homogeneous luminescence line width (∼200 μeV at 35 K), attributed to the weak coupling between electrons and acoustic phonons.28 The second sample (B) was fabricated from a low-doped silicon-on-insulator wafer. A plasma etching step reduced the top silicon layer, whose nonuniform thickness at the nanometer scale could randomly form silicon nanocrystals of different sizes.4 Rapid thermal annealing (10−30 s at 900 °C) was used to grow a few nanometer thick oxide shell, which passivates the NCs. Compared to the first sample, where thin shell nanocrystals are embedded in a porous film and can be considered matrix-free, here the passivation layer is thicker (several nanometers), which translates into a slightly broader homogeneous PL line width.28 Narrow individual nanocrystal line widths (∼200 μeV), however, could still be observed from this sample at lower temperature (10 K).28 In the third sample (C), silicon quantum dots were formed from a low-doped Si wafer by electron-beam lithography (EBL), plasma etching, and oxidation.30 EBL was executed using negative resist (HSQ) to reflect a pattern of undulating walls with different thicknesses on a silicon wafer. Subsequently, in order to transfer the mask pattern, reactive ion etching (HBr) was performed for 40 s leading to the creation of silicon walls approximately 300 nm in height. Finally, space-separated silicon nanocrystals were formed by shrinking the core size of the nanowalls via self-limiting oxidation31 at 900 °C for 5 h, forming a thick oxide shell (tens of nanometers). In contrast with the previous samples, the luminescence fwhm here was found to be broad, approximately 100−200 meV at room temperature and ∼1 meV at 10 K.32 Previously, all three samples were optically analyzed using standard techniques and the crystallinity of the silicon nanoparticles was confirmed by TEM.4,30 The insets in Figure 2 are typical TEM images of silicon nanocrystals from HSQ (left) and SOI (right) samples, where (111) plane lattice fringes of crystalline silicon and a few-nanometer thick amorphous oxide layer for the SOI sample are visible. Photoluminescence power dependence of single silicon quantum dots was measured at low temperature using a microphotoluminescence setup that consists of a Zeiss Observer.Z1m inverted microscope loaded with a 63× window-corrected objective lens (0.75 NA) and with two exit ports selectable by a rotating mirror. The first port was connected to an Andor-SR500 imaging spectrometer with two diffraction gratings, featuring resolutions of 0.9 and 0.08 nm (∼200 μeV at 700 nm), followed by a thermoelectrically cooled (−100 °C) CCD camera, Andor iXon3. For low temperature measurements (10 K), the samples were placed on the coldfinger of an Oxford Instruments liquid-helium flow cryostat, which was evacuated continuously (∼10−7−10−6 mbar) to ensure thermal insulation. The second port of the microscope was connected to an avalanche photodiode (Becker & Hickl, DPC-230) for single-dot, single-photon counting. The small active area of this detector (∼20 μm2) produces low dark counts (few per second), making possible detection of the weak single-dot signal (tens of counts per second). All PL experiments were carried out under laser excitation of λexc =

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EXPERIMENTAL AND THEORETICAL METHODS Three Si-NC samples, prepared via different techniques, were used in this study. The slight difference in their optical properties (e.g., luminescence line width, background luminescence) allowed us to select the most appropriate sample for a specific measurement. For the first sample (A), HSQ resist supplied by Dow Corning (XR-1541, 10 wt % solution in methyl isobutyl ketone) was spin-coated onto a clean piece of silicon wafer and left drying for 24 h. Subsequent annealing of the sample was performed at 1000 °C in 5% H2 and 95% Ar for 1 h. Cross-sectional transmission electron microscope (TEM) images revealed the porous structure of the resulting film, whose thickness was about 100 nm.28 In this layer, the formation of silicon nanocrystals with Si−O−RI bonds on the B

DOI: 10.1021/acs.jpcc.5b01114 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C 405 nm (Omicron PhoxX) in dark field (laser beam incident angle, ∼45°) or under bright field (excitation through the objective lens) configurations. In the case of time-resolved measurements, a pulsed laser beam with a repetition rate of ∼20 kHz and 50% duty cycle was used. Depending on the particular decay parameters of a probed single quantum dot, those values were varied accordingly. Note that only nonblinking Si-NCs without spectral diffusion were considered for spectral measurements, as detected by recorded, few-frames “movies”. Furthermore, since the NCs are spatially well separated and their emission energies (1.7−2.0 eV) are larger than ℏωexc/2 (1.5 eV), both one-site and two-site carrier multiplication processes typical for dense ensembles of such nanocrystals27 can be neglected. Analysis of the PL intensity data was carried out by using a model based on rate equations. In addition, since at high excitation power densities the statistical nature of the incoming photons can play a significant role, and in order to verify the validity of the model, a kinetic Monte Carlo (MC) simulator was developed in MATLAB. In this code the independent parameters were absorption cross section of the nanocrystal, exciton lifetime, biexciton lifetime, and respective quantum efficiencies. For each of them a range of physically acceptable values was set, taking into account our results as well as available literature.2 The dynamical evolution of the exciton states was simulated with both absorption and recombination processes as determined by Poisson statistics. At each excitation power density, the simulated time can be set equal to the corresponding experimental acquisition time used. Finally, in order to limit the computational time, an upper boundary of 107 absorbed photons was set per each excitation power density considered. In order to express the PL intensity in absolute units (photons/s), the system detectivity was estimated considering the sample emissivity, the optical losses of the system, and the CCD detectivity. For the HSQ sample (NCs in a thin film on Si substrate, 6% emissivity in the upper hemisphere33) the detectivity was 0.05 CCD counts/photon, whereas for the SOI sample (NCs on 1.1 μm buried oxide, 18% emissivity in the upper hemisphere33) it was 0.15 CCD counts/photon. Prior to the PL decay analysis, the background was first subtracted and binning was performed when possible to improve the signal-to-noise ratio. Because of the subnanosecond response function of our system, no deconvolution was carried out on the lifetimes which were extracted by a monoand biexponential fitting of the decay trace at low and high excitations, as described below.

Figure 1. Low-temperature PL spectra of a single silicon quantum dot, labeled as QDA4, fabricated from HSQ, taken under different continuous wave excitation power densities, from 70 (bottom) to 6200 W/cm2 (top). The excitation wavelength was 405 nm.

relationship is linear at low excitations whereas saturation starts at higher pumping (∼1021 (ph/cm2)/s here). A silicon nanocrystal can be modeled as a three-state system where the states ⟨0⟩, ⟨1⟩, and ⟨2⟩ correspond to the presence of 0, 1, and 2 excitons in the nanocrystal, respectively.6 Higher states are not considered here as will be justified later. The evolution of the states’ occupation probabilities can be described by rate equations, ⎧ dp p ⎪ 0 = −Φex σp0 + 1 τ1 ⎪ dt ⎪ p p ⎪ dp1 ⎨ = Φex σ(p0 − p1 ) − 1 + 2 τ1 τ2 ⎪ dt ⎪ p2 ⎪ dp2 ⎪ dt = Φex σp1 − τ ⎩ 2

(1)

where pi denotes the occupation probability of the ith state, Φex corresponds to the excitation photon flux, σ is the absorption cross section (i.e., σ is equal for both ⟨0⟩ → ⟨1⟩ and ⟨1⟩ → ⟨2⟩ transitions under nonresonant excitation used here), and τi represents the total lifetime of the transition ⟨i⟩ → ⟨i − 1⟩. It is important to note that eq 1 differs from the system of rate equations considered by Kovalev et al. First we consider the lifetime as τi−1 = τi,r−1 + τi,nr−1, where τi,r (τi,nr) is the radiative (nonradiative) lifetime, since we showed before that the quantum efficiency of an oxide-passivated single Si nanocrystal can be between 0 and 1.7 Second, the absorption cross section is dependent only on the excitation energy in our model and not on the emission energy, since the energy range probed is quite limited (1.7−2.0 eV). Last, we do not simply neglect emission from the biexciton, since this is exactly what we are looking for. In the case of continuous wave excitation and steady-state condition we have dpi/dt = 0. By substituting this into eq 1 and considering that the exciton and biexciton absolute PL intensities are respectively given by I1 = p1/τ1,r and I2 = p2/τ2,r, we have

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RESULTS AND DISCUSSION Figure 1 shows a series of low-temperature PL spectra of a single silicon nanocrystal (labeled as QDA4) from the HSQ sample, taken at different excitation power densities. This sample was found to contain nanocrystals with the narrowest line width28 and hence was most suitable for revealing biexciton line under strong pumping. A narrow single Lorentzian emission line located at 657−658 nm can be clearly resolved in all the spectra. Regarding its origin, we attribute it to NP radiative recombination of excitons in the nanocrystals.4 By increasing the excitation, however, no other emission lines can be resolved and the total PL intensity seems to saturate. This behavior is better shown in log scale in Figure 2a, where the PL intensity of QDA4 is plotted as a function of the excitation photon flux. As previously reported in other works,2,6 the

I1 =

η1Φex σ 1 + τ1Φex σ + τ1τ2 Φex 2σ 2

(2)

2 2

I2 = C

η2τ1Φex σ

1 + τ1Φex σ + τ1τ2 Φex 2σ 2

(3) DOI: 10.1021/acs.jpcc.5b01114 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 2. PL intensity as a function of the excitation photon flux for individual silicon nanocrystals in log−log scale. (a) Measured data for a quantum dot synthesized from HSQ, QDA4 (squares); rate equations fitting (red dashed line) yielding η1 = 36% and τ2 = 100 ns with fixed values σ = 10−16 cm2 and τ1 = 12 μs; MC simulations with the same parameters (blue dashed line). (b) Measured data for 13 Si-QDs fabricated from SOI (squares); dashed lines are guides for the eye. The error bars do not exceed data point size. The insets are representative TEM images of the nanocrystals; silicon (111) plane lattice fringes can be distinguished in both of them, and the oxide shell can be discerned in the right image.

where η1 and η2 are the respective quantum yields. Hence, in the case of high η2, one would be able to spectrally resolve at least two PL peaks, the exciton and the biexciton peak, assuming that their line width is narrow enough, where their PL integrated intensity would follow eqs 2 and 3, respectively.11,34,35 The data of Figure 2a can be fitted reasonably well with eq 2 (red dashed line) if we set σ = 10−16 cm2, in accordance with Kovalev et al.,6 and τ1 = 12 μs, which is well in the range of the reported lifetimes. The output parameters from the fitting are η1 = 36% and τ2= 100 ns. In addition, with these values, MC simulations give almost identical results (blue dashed line), thus confirming the validity of the rate equations in the studied excitation power range. According to the fitting, an average of one exciton in the nanocrystal (⟨NX⟩ = 1), corresponding to an excitation of ∼1022 (ph/cm2)/s, was reached and even surpassed during our experiments without any indication of biexciton emission in the recorded spectra (cf. Figure 1). Furthermore, for the same dot, using an approximation common for direct bandgap QDs,11,36,37 the biexciton radiative lifetime can be estimated as τ2,r = τ1,r/4 = τ1/4η1 ≈ 8.3 μs. The measured biexciton lifetime values τ2 appear to be almost 2 orders of magnitude shorter, suggesting nonradiative Auger process as a dominant one for the biexciton decay at this temperature. The PL power-dependence behavior is very similar between HSQ and SOI samples, as shown in Figure 2b representing the data from 14 single Si-NCs fabricated from SOI. For this sample also, no biexciton emission lines were detected and it is again possible to fit the data of each dot with eq 2 by setting the absorption cross section (fitting not shown here). So far, our preliminary rough estimates indicate that the biexciton lifetime (τ2) is limited by the Auger process lifetime (τA). In order to measure these lifetimes directly, it is necessary to perform single-dot PL decay measurements at different excitation powers, which require samples with very low background signal and traceable dot position for repetitive measurements. For this purpose, single Si-NCs from the nanowall sample were employed.32 Figure 3 shows normalized room-temperature PL decay curves in log scale for one of such nanodot, QDC1, taken at two different excitation power densities. At 20 W/cm2 (∼4 × 1019 (ph/cm2)/s), the decay trace has a monoexponential form,

Figure 3. Normalized PL decay curves (in log scale) of a single silicon quantum dot, QDC1, embedded in Si nanowalls, measured at two different excitation powers, 20 W/cm2 (black squares) and 60 W/cm2 (red squares) with an excitation wavelength of 405 nm. The inset is a zoomed-in plot of the first 0.5 μs. At low excitations the data can be fitted by a monoexponential with time constant τ1 = 5.8 ± 0.2 μs (black dashed line). An additional fast component, with τ2 = 0.11 ± 0.04 μs appears at high excitations (red dashed line). The error bars represent standard deviation of the measured data.

I(t ) = I1e(−t / τ1)

(4)

giving τ1 = 5.8 ± 0.2 μs, a reasonable value for this type of NC.5,7 However, when the excitation is increased to 60 W/cm2 (∼1020 (ph/cm2)/s), an additional fast component appears and the decay should be modeled as biexponential, I(t ) = I1e(−t / τ1) + I2e(−t / τ2)

(5)

where τ1 appears to be the same, τ1 = 5.9 ± 0.4 μs, and the fast component constant is τ2 = 0.11 ± 0.04 μs, with corresponding intensities I1 = 0.69 ± 0.02 and I2 = 0.33 ± 0.06. For this particular dot emitting at 1.70 eV, both σ = 1.46 × 10−14 cm2 and η1 = 9% were previously measured and reported,7 allowing us to extract the biexciton quantum yield value. From eqs 2 and 3, the ratio between biexciton and exciton QY is given by η2 η1

=

I2 1 I1 τ1σ Φexc

(6)

Then, by attributing the fast PL decay component to the biexciton recombination, we can use eq 6 to obtain η2/η1 = 4.3% and finally η2 = 0.4% for QDC1. Alternatively, biexciton quantum yield can be estimated directly from the measured decay constants as η2 ≡ τ2/τ2r = 4τ2/τ1r = 4τ2η1/τ1 = 0.7%. So D

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The Journal of Physical Chemistry C Table 1. Typical Range of Auger Lifetimes (ns) for Silicon Nanocrystals Emitting between 1.7 and 2.0 eV theoretical calculations

experimental results

tight-binding14,15

pseudopotential,16 multiband eff mass,17 ab initio18

envelope function24 (resonance structure)

ensemble TA and PL19−21

single-dot PL (this work)

0.1−100

0.1−10

20−120

0.01−0.1

30−300

to the theory,24 our emission range (1.7−2.0 eV) can reasonably correspond to a uniform distribution of NCs with a radius between 1.85 and 2.30 nm. Then, by use of theoretical results,24 the simulated distribution of τA for these NCs is indicated in Figure 4 by the red line. As can be seen, our data are in reasonably good agreement with the calculations that predict strong Auger suppression for some “magic-size” Si-NCs resulting in longer lifetimes. However, given that our nanocrystals are not perfect spheres,32 we must note that the distribution of Auger lifetimes can also result from the difference in shape of the nanocrystals.25,26 Finally, we can estimate the ratio of biexciton and exciton quantum yields as a function of temperature using temperaturedependent exciton decay lifetimes measured for single silicon nanocrystals, shown in Figure 5 (green circles). For 0D

the absolute value of the biexciton quantum yield is indeed quite low because of the strong nonradiative Auger process. This result, obtained from room temperature decay measurements, is similar to our rough estimations from the lowtemperature saturation curves above. In order to compare our experimental results on characteristic Auger lifetimes with the data available in literature,14−19,21,24 we have summarized the values for silicon nanocrystals (1.7−2.0 eV emission range) in Table 1. As one can see, the range found in this work, τA ∈ [30, 300] ns, is in accordance with calculations based on tight-binding and envelope function approximation.14,15,24 Although the lower values (picosecond range) obtained from TA measurements on ensembles of Si-NCs are supported by some other calculations,14−18 certain considerations should be made. First, those relaxation times could be influenced by the interaction between closely spaced Si-NCs.27 Second, dot-todot variations of the Auger lifetime cannot be detected by employing averaging ensemble techniques. As a result, singledot measurements on isolated NCs (as done in this work) seem to be more appropriate for a fair comparison with the theory on the intrinsic Auger recombination rate. In Figure 4 the distribution of measured Auger lifetimes for 10 single Si-NCs (nanowalls sample) at room temperature is

Figure 5. Temperature dependence of the measured exciton lifetime of a single Si-NC (green circles) and of the calculated ratio between biexciton and exciton quantum yields averaged over different Si-NCs (black squares). The nanocrystals were embedded in nanowalls. Both axes are in log scale, and the error bars represent standard deviation of the measured data (green) and width of the statistical distribution (black), respectively. For the calculation we assume that the Auger lifetime is constant with temperature and the biexciton radiative rate is 4 times larger than the exciton one: τ2,r = τ1,r/4.

systems, the Auger lifetime can be considered as temperatureindependent, as it was predicted by the theory and also confirmed experimentally.38−40 More precisely, regarding SiNCs, the breakdown of the k-conservation rule leads to a temperature independent biexciton Auger lifetime.20,41 If we assume again τ2,r = τ1,r/4, then η2/η1 = 4τ2/τ1 ≈ 4τA/τ1. Figure 5 (black squares) thus shows the obtained ratio η2/η1 as a function of the temperature. Notice that both quantum yields are average values from different NCs probed. Additionally, from noise equivalent power considerations, our minimum detectable biexciton quantum efficiency is ∼0.15%, thus η2/η1 ≈ 0.4%, in the case of QDA4 at Φex = 1022 (ph/s)/cm2. At room temperature, η2/η1 = 7.6%, which allows us to detect biexciton emission from the PL decay of single Si-QDs but not from the PL spectrum due to the broad homogeneous fwhm at room temperature (∼100 meV).30 With decreasing temperature the ratio rapidly drops to 0.2% at 10 K, below the detection limit of our system, explaining the lack of any biexciton emission lines in the low-temperature spectra (cf. Figure 1).

Figure 4. Distribution of measured Auger lifetimes from single Si-QDs embedded in Si nanowalls (gray bars). For comparison, the red line is a log-normal fit extracted from theory considering our emission range, 1.7−2.0 eV.24 The inset shows the PL decay traces of two quantum dots having different τ2: the squares represent measured data, and the solid lines are biexponential fittings. The error bars indicate standard deviation of the measured data.

shown. Notice that for one Si-NC (QDC3) we could not resolve τA, which is then lower than the corresponding time resolution used (40 ns). The measured values vary within an order of magnitude, and two decay curves of quantum dots QDC5 and QDC13 are plotted in the inset as an example. For the first one we have τA = 80 ± 30 ns, less than 150 ns as for most other NCs probed; for the second one we get τA = 300 ± 120 ns, which is the longest measured from this set. According E

DOI: 10.1021/acs.jpcc.5b01114 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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CONCLUSIONS In this work, we have studied the Auger process and biexciton emission in single, differently fabricated silicon nanocrystals: chemically synthesized from HSQ and produced by thermal oxidation from thin SOI wafers and nanowalls. The evolution of the low-temperature PL spectrum of narrow-line width Si-NCs as a function of the continuous-wave excitation power revealed no biexciton emission lines (nor any multiexciton lines). At the same time the total PL intensity showed clear saturation behavior with increasing excitation, indicating a low biexciton quantum yield. Saturation curves for each dot could be fitted by rate equations considering exciton emission only, as confirmed by our kinetic Monte Carlo simulator. To verify these results, single Si-NCs were probed by time-resolved measurements at room temperature. At low excitations, only the exciton (∼μs) decay component was found, whereas at high excitations a considerably weaker fast (∼ns) decay component appeared. The latter was assigned to biexciton emission, and its quantum efficiency was estimated to be ∼0.5%. Extracted Auger lifetime τA varies from 30 to 300 ns depending on the dot considered, well in the range suggested by recent theoretical calculations. Our experimental results were also confirmed by the calculated temperature-dependence of the ratio between biexciton and exciton quantum yields. At room temperature, a weak biexciton emission (η2/η1 = 7.6%) can be detected from the PL decay curves, but it is not resolved in the PL spectra given the broad homogeneous fwhm (∼100 meV). Conversely, at low temperatures, the biexciton quantum yield is extremely low (η2/η1 = 0.2%); thus, it is not possible to detect any biexciton emission, although the homogeneous fwhm is very narrow (∼200 μeV). Consistently low biexciton quantum yield values obtained by these two methods at different temperatures indicate that Auger nonradiative recombination is quite efficient in reducing the PL quantum yield of Si-NCs at high excitation powers. However, considering the Auger lifetime variations, enhanced biexciton quantum yield can be expected for some NCs because of the theoretically predicted resonance nature of the Auger process.22−24 Our large variations in the Auger rate indeed confirm the existence of such resonances also for silicon nanocrystals.

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AUTHOR INFORMATION

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ACKNOWLEDGMENTS Financial support from the Swedish Research Council (VR) through an individual contract and through a Linnaeus grant (ADOPT) is gratefully acknowledged. A.F. thanks the Carl Tryggers Foundation for the postdoc scholarship. The authors acknowledge Benjamin Bruhn for the preparation of the nanowalls sample.

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ABBREVIATIONS USED NC, nanocrystal; QD, quantum dot; Si-NC, silicon nanocrystal; Si-QD, silicon quantum dot; PL, photoluminescence; fwhm, full-width at half-maximum; TA, transient induced absorption

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REFERENCES

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S Supporting Information *

MATLAB source file containing the kinetic Monte Carlo simulator used to confirm the validity of rate equations at high excitation power densities. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author

*E-mail: [email protected]. Present Address †

A.F.: Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Prague 2, CZ-121 16, Czech Republic. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest. F

DOI: 10.1021/acs.jpcc.5b01114 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.5b01114 J. Phys. Chem. C XXXX, XXX, XXX−XXX