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Size Dependent Exciton Formation Dynamics in Colloidal Silicon Quantum Dots Matthew R Bergren, Peter K. B. Palomaki, Nathan R. Neale, Thomas E. Furtak, and Matthew C. Beard ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b07073 • Publication Date (Web): 26 Jan 2016 Downloaded from http://pubs.acs.org on January 29, 2016
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Size Dependent Exciton Formation Dynamics in Colloidal Silicon Quantum Dots Matthew R. Bergren,1,2 Peter K. B. Palomaki,1 Nathan R. Neale,1 Thomas E. Furtak,2 and Matthew C. Beard1,2 1. National Renewable Energy Laboratory, Golden, CO 2. Physics Department, Colorado School of Mines, Golden, CO Abstract We report size-dependent exciton formation dynamics within colloidal silicon quantum dots (Si QDs) using time-resolved terahertz (THz) spectroscopy measurements. THz photoconductivity measurements are used to distinguish the initially created hot-carriers from excitons that form at later times. At early pump/probe delays, the exciton formation dynamics are revealed by the temporal evolution of the THz transmission. We find an increase in the exciton formation time, from ~500 fs to ~900 fs, as the Si QD diameter is reduced from 7.3 to 3.4 nm and all sizes exhibit slower hot-carrier relaxation times compared to bulk Si. In addition, we determine the THz absorption cross section at early delay times is proportional to the carrier mobility, while at later delays is proportional to the exciton polarizability, . We extract a sizedependent and find an ~ dependence, consistent with previous reports for quantum-
confined excitons in CdSe, InAs, and PbSe QDs. The observed slowing in exciton formation time for smaller Si QDs is attributed to decreased electron-phonon coupling due to increased quantum confinement. These results experimentally verify the modification of hot-carrier relaxation rates by quantum confinement in Si QDs, which likely plays a significant role in the high carrier multiplication efficiency observed in these nanomaterials. Keywords: Silicon Quantum Dots; Time-resolved THz spectroscopy; Carrier Dynamics Boosting solar energy conversion efficiencies above the 1-sun Shockley-Queisser limit (33%) that limits existing single-junction solar converter systems towards the 1-sun Ross-Nozik limit (66%)1 is only possible if the excess kinetic energy of hot-carriers can be harvested. Typically, optical excitation with photon energies exceeding the semiconductor band gap (Eg) results in excited “hot-carriers” that quickly relax to the conduction band edge by losing excess kinetic energy to the crystal lattice in the form of heat. Several strategies have been proposed to mitigate this energy loss mechanism including space separated quantum cutting,2 optical downconversion,3 hot-carrier extraction through energy selective contacts,4,
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generation (MEG),6-10 and intermediate band solar cells.11 Though hot-carrier relaxation
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mechanisms have been identified in quantum-confined systems, such as quantum dots (QDs), nanorods (NRs), quantum platelets, quantum films, etc.,12-18 experimental verification of modifying hot-carrier relaxation rates have been elusive.19 Several groups have suggested that the discrete energy levels present in nanostructures should reduce phonon-mediated relaxation pathways if the energy level spacing exceeds the optical phonon energies.20-23 Such slowed cooling has been observed when other hot-carrier relaxation pathways are eliminated, for example, slowed hot-carrier cooling in alkylthiol surface-passivated CdSe/ZnSe core-shell QDs measured by transient absorption spectroscopy.22 Several methods exist to observe hot carrier relaxation, including ultrafast transient absorption (TA), time-resolved photoluminescence (TRPL) and time-resolved THz spectroscopy (TRTS).6,
15, 22, 24-27
Whereas TA and TRPL have the ability to measure ultrafast carrier
dynamics, only TRTS can obtain the frequency-resolved complex photoconductivity, ∆ ; of the sample. The complex-photoconductivity spectra can then be used to extract fundamental electrical properties such as carrier scattering times and photoinduced carrier densities. These parameters can be extracted for multiple pump-probe delays, , and thus can be monitored as a function of time.28 In addition, for indirect bandgap semiconductors such as silicon, there are no spectroscopic signatures in TA spectra. TRPL measurements are also difficult to perform on indirect semiconductors like Si, since the emission rate is low (even when the PLQY is high), which further complicates the study of carrier dynamics in these systems. Here, we employ TRTS to investigate the exciton and carrier dynamics of silicon quantum dots (Si QDs) by analyzing their size-dependent ultrafast carrier dynamics and their accompanying photoconductivity spectra. We utilize TRTS to distinguish between ∆ spectra that show clear signatures between signals stemming from excitons, localized carriers, and free carriers29-33 and clearly show slowed hot-carrier relaxation times for smaller Si QDs.
Results/Discussion We studied four Si QD samples which were synthesized by the decomposition of silane gas in an RF-enhanced non-thermal plasma reactor, as described previously34 (full details in supplemental information). We recently developed a sizing curve as a convenient method for determining the average Si QD diameter from the peak photoluminescence energy and used that relationship to determine the average QD diameter of the samples studied here.35 The Si QD sizes used in this study were determined to be 3.4, 4.7, 6.2, and 7.3 nm. The size distribution (~20%) was estimated from the FWHM of the PL emission spectra. Representative
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TEM images are provided in the supplemental information (Fig. S1) and show crystalline cores surrounded by passivating dodecyl ligands. A thermally initiated reaction between 1-dodecene and as-prepared, hydride-terminated Si QDs was used to functionalize QD surfaces with dodecyl ligands that we previously extensively studied and characterized.35 In this prior work, detailed FTIR analysis found an amorphous or disordered surface for the smaller QDs (3.4 and 4.7 nm), whereas the larger QDs (7.3 nm) exhibited homogeneous line-broadening associated with an ordered, crystalline surface (the cores of all Si QDs were crystalline). We revealed two distinct ligand attachment modes via either the alpha- or beta-carbon of the dodecyl ligand and we quantified the ratio of alpha/beta attachment and found that smaller Si QDs had a ratio of ~1:1, whereas larger Si QDs favored beta attachment by a ratio of ~1:9.
Figure 1. (a) Representative TRTS dynamics for the 4.7 nm Si QD sample (red circles) are compared to transient absorption dynamics (blue circles). The inset shows a schematic of the TRTS experiment. A THz probe pulse follows a 400 nm excitation pulse at variable delays. The change in the peak value of the transmitted THz electric field is monitored while varying the pump-probe delay. (b) The frequencyresolved photoconductivity measured at 0.5 ps and (c) 100 ps. The spectra at early times and late times show distinct features indicating that the THz signal is sensitive to hot-carriers at early delays and excitons at late delays. The decay of the THz transient thus follows the formation time of excitons.
In Figure 1a we compare the carrier dynamics measured by TRTS, ∆⁄ (red circles), to the dynamics obtained by TA, ∆⁄ (blue circles). A typical TRTS experiment schematic for the 4.7 nm sample is shown in the inset of Figure 1a. For both measurements, the excitation wavelength was 400 nm and the photon fluence was set so the average electron-hole (e-h) pair occupation,24 〈 〉 = ~1.5, where is the input fluence and is the per QD absorption cross section (taken from literature reports).24 In the TRTS dynamics we observe an initial sub-ps decay, while both techniques show similar long-lived dynamics after ~5-10 ps.
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Since the TA dynamics track the population statistics of the total e-h pair produced for each pump-probe delay,24 following our earlier report where we compared the THz dynamics of Si QDs to Si nanorods and bulk Si29, we hypothesize that the initial decay of the THz signal for the Si QDs is not associated with population decay but is instead associated with the transition of hot-carriers to excitons. We will later show in our analysis of the TRTS spectra (Fig. 1b and c) that this is indeed the case. The intermediate decay of 50 – 100 ps, which varies with QD size and is assigned to Auger recombination channels, is subsequently followed by a long-lived single-exciton decay29 (not studied here). Therefore, once excitons are formed, the TRTS and TA experiments yield similar results. The photomodulation of the THz transmitted field, ∆, is sensitive to changes in the susceptibility, ∆ , upon photoexcitation of the sample.36, 37 In the frequency domain, this can be expressed as,29
ΔE ; " 〈∆ ; 〉#$% &'(
(1)
where 〈 〉 indicates an average over all orientations of the photoexcited Si QDs, & is the speed of light, # is the optical penetration d epth, $% is the volume fraction of the Si QDs (see Methods section), and ∆ ; denotes the complex, frequency-dependent change in susceptibility, /
where is the THz probe frequency. The parameter ' *+, + *. /12*+, 1 4 56/7 8 takes into account the transmission of the THz pulse through a thick sample with bulk-like absorption,8 where 9 is the thickness of the cuvette and *. (*+, ) is the THz refractive index of the quartz / cuvette (host solvent). The parameter ( 2:+, + :;< >3:;< stems from effective media
theory where :+, is the permittivity of hexane and :;< is the permittivity of the embedded Si QDs.29 Equation 1 is strictly valid only in the linear excitation regime38 when ∆⁄ < 0.1 and for this study, all the measurements are made for values of ∆⁄ < 0.005. The values for $% , #, and :;< are tabulated in the methods section for each sample. Equation 1 can also be expressed in terms of the complex, frequency-dependent D E ∆C D E; FG through ∆H D E⁄IEJK yielding, photoconductivity ∆C
ΔE ; 〈∆ ; 〉#$% &: '(
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In Figure 1b and 1c, we display ∆ ; , at early ( = 0.5 ps) and late ( = 100 ps) delays, respectively. The spectra exhibit distinctive features that can be distinguished by the presence or absence of a real component to ∆ ; . The early time spectra exhibits a non-zero real component and thus can be assigned to hot-carriers while the spectra measured at late delays displays L4M N 0 and is attributed to excitons.29 The THz spectral differences between excitons and free-carriers have been previously observed for semiconductor QDs31-33 and polymer systems.39 The justification for why L4M N 0 when strongly bound excitons are present is the 0.1 - 2 THz bandwidth probe (1 THz = 4 meV) does not have sufficient energy to resonantly drive either excitonic or intraband transitions, where intraband energy level spacing is >10 meV in quantum-confined systems and thus, no L4MN is observed. Furthermore, carriers do not couple to acoustic phonons and thus phonon-assisted transitions (free-carrier transitions) are less probable.
Figure 2. a) The real and imaginary components of the change in the susceptibility for the 4.7 nm Si QDs. The dashed line represents the average of the the real component of the frequency-independent change in susceptibility. b) Size dependent exciton polarizability comparison between Si QDs and InAs QDs. An ~ scaling of the data is shown as a dashed line.
The concept of photoconductivity implies that charge carriers are free to move under the influence of an applied field. However, in the case where the QD dimensions are smaller than the natural carrier wavefunction, the concept of photoconductivity is not meaningful since the charge carrier wavefunction is delocalized over the nanostructure. In this regard, a useful common length scale is the exciton Bohr radius, OP , which can also be defined for electron and hole wavefunctions. In the case for Si, the exciton Bohr radius is ~5 nm. When the nanostructure dimensions are smaller than OP , ∆ is a more relevant property, but in general, ∆
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and ∆ can be used interchangeably. Converting ∆ (Fig. 1c) to ∆ (Fig. 2a) alters the spectrum from a negative, linearly increasing imaginary photoconductivity to a frequency-independent susceptibility spectrum, containing only a nonzero real component. The polarizability is related to the susceptibility through, Q 3∆ , /3 + ∆ , ,40 and in the limit where ∆ , is small, ∆ , Q ( = carrier density). One can immediately see that is proportional to an exciton absorption cross-section in the THz frequency regime. In the case of free charge carriers, ∆ 4R, and the mobility is proportional to the absorption cross-section. To further confirm the THz signal at 100 ps originates from excitons, we plot the size dependent Q in Figure 2b. For Si QDs, we find that Q scales as ~ (black circles and dashed-line), similar to the scaling reported for the direct bandgap semiconductor QDs
CdSe,27, 32, 33 CdTe,41 InAs (Fig. 2b, teal circles and dashed-line),31 and PbSe.33 As discussed by Wang et al., the exciton polarizability depends on both the transition dipole moment 4 ∙ and the transition energy level spacing (Δ;< ) of the QD, generally expressed as: Q ≈ |4 ∙ |/ / Δ;< .32 For a quantum-confined structure, the energy level spacing typically scales as Δ;< ~ℎ/ /X / , and thus an dependence is predicted. Despite the similar scaling, we find a smaller in Si QDs compared to InAs (Fig. 2b). According to Pijpers et al., there are two factors that are associated with the magnitude of Q ; the relative permittivity and the carrier effective masses.31 First, the relative permittivity, which indicates the ability of the nanostructure to screen applied fields, is : ≈ 12.4 for bulk InAs, which is similar to bulk Si ( : ≈ 11.7). Therefore, differences from screening of the electric field are discounted. Next, the carrier effective masses can be related to the conduction and valence intraband transition energies. In InAs QDs, the hole effective mass is much larger than the electron effective mass (X+ =0.4, X, =0.03) making the THz probe more sensitive to holes. In contrast, TA measurements are more sensitive to the carrier with the smaller effective mass, or electrons in the case of InAs QDs. Since a smaller effective mass results in a more delocalized wavefunction, the InAs electron wavefunction is more delocalized than the hole wavefunction, which results in an asymmetric exciton wavefunction that is more easily polarized than that for semiconductors with similar electron and hole effective masses such as Si ( X+ =0.4, X, =0.26). Therefore, the electron and hole in Si QDs can more easily screen one another than in InAs QDs, leading to an enhanced depolarization field inside the QD and decreased exciton polarizability. Based on these arguments, the overall magnitude of Q is expected to be smaller for Si QDs compared to InAs QDs. A similar argument can be made for Pb-chalcogenide QDs since the effective masses of electrons and holes are similar to one another, while in CdSe they are quite different.
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In accordance, Dakovski et al. compared Q for PbSe to CdSe and found much smaller values for PbSe QDs.33 Overall, the Si QDs studied in this research exhibit excitonic characteristics at later pump-probe delays that are consistent with results observed for other semiconductor QDs.
Figure 3. a) Early-time carrier dynamics for Si QDs of different diameters. The data have been offset for clarity. Samples excited with a 400 nm pump using an equivalent average number of photons absorbed per dot (〈 〉 < 1). b) Size dependent carrier dynamics exhibiting the formation of excitons from hotcarriers. Dashed lines represent the model described in the text which is globally fit to the data.
Carrier dynamics The size-dependent ultrafast carrier dynamics are shown in Figure 3, where we show data with 〈 〉 ~0.4-0.5, so as to compare the carrier dynamics under conditions where the response arises from QDs with only single generated electron-hole pairs. We observe smaller THz peak amplitudes associated with hot carriers ( ≅500 fs) for larger QD diameters (inset Fig. 3b, closed-circles), whereas the THz amplitude associated with excitons ( 100 ps) increases as the size of the Si QD increases (inset Fig. 3b, open-circles), which correlates with the size-dependent argument for discussed above. We attributed the apparent decrease in THz amplitude measured at ≅ 500 fs to a size-dependent change in hot-carrier relaxation, as the measured signal is a convolution of the system response with a fast decay processes. Thus, a faster hot-carrier relaxation results in reduced peak amplitudes (see Fig. S3 in supplemental information for more details). In our experiment the system response function (SRF) is ~200 fs, which is on the same time scale as hot-carrier relaxation measured for bulk Si (240-260 fs).7, 10, 42
In order to extract the exciton formation time for each QD size, we deconvolve the instrument
response in the modeling described below.
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We developed a model based on the time-dependent populations of hot-carriers and excitons. In our model, we consider the time-dependent fraction of excited carriers in four different states: (i) Singly excited hot-carriers, denoted by Z[\ , (ii) multi-excited hot-carriers,
[\ /] , (iii) multiple excitons existing in a single QD, QQ , and (iv) single excitons, Q . At
sufficiently high pump-fluences, a QD can absorb multiple photons sequentially, and subsequently produce multiple excitations. In the experiments reported here, we do not resolve differences in the early time dynamics (1e3
110*
>1e3
65*
>1e3
30*
>1e3
* Parameters held constant during fit (not shown: Gaussian – FWHM (SRF) = 400fs). Standard deviation values from the linear least-squares fits are in parenthesis.
Figure 4. Hot-carrier lifetime as a function of QD diameter.
In Fig. 3, we show the least squares best fit for selected data of the four Si QD sizes, where each sample has a similar average number of photons absorbed (〈 〉 < 0.4). The best fit
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parameters are provided in Table 1. We find that _[\ varies from ~500 fs to ~900 fs, where hotcarrier relaxation is slower in the small Si QDs (Fig. 4). For all Si QDs measured, the hot-carrier relaxation lifetimes obtained are 2 – 3.6x slower than has been measured previously in bulk Si. 7, 10, 42
We plot the values of the THz response at ~1ps and 100 ps in the inset to Fig. 3b.
Figure 5. Fluence dependent TRTS results for (a) 3.4 nm, (b) 4.7 nm, (c) 6.2 nm, and (d) 7.3 nm diameter samples. The dashed lines are the global fits our the model discussed in the text to the data. The data are offset vertically and horizontally for clarity. The data for 0-10 ps has been expanded so that the quality of the fits can be ascertained.
To confirm our model we performed fluence-dependent TRTS measurements on each Si QD size. The fluence-dependent response of the four samples is shown in Figure 5. The dashed lines are the global non-linear least squares best fit or our model to the data. All parameters were held constant to those determined above expect for the value of 〈 〉 for each trace. There is good agreement between our data and the model that provides confidence in our dynamical assignments.
However, while the model captures the majority of our data, the
agreement is not perfect. In particular, the model tends to underestimate the data in 1 to 10 ps
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temporal window, where the data tends to exhibit an additional decay component that is not consistent with known biexciton lifetimes. fluence and decreasing QD size.
The deviation tends to increase with increasing
In accordance with these observations, the conductivity
spectra in this regime exhibits some residual free-carrier like characteristics (See Fig. S5). One possible reason for this discrepancy could be that Auger recombination of two cold excitons produces hot-carriers that would exhibit free-carrier characteristics and is not captured in our model. A recent theoretical study of Si QDs found that an efficient Auger recycling mechanism controls the biexciton lifetimes.44 In that model, when biexcitons recombine they produce a single hot-carrier with energy twice that of the cooled carriers. The hot-carrier can then undergo multiexciton generation to produce two cold carriers that are then recycled to produce a hotcarrier and so forth. The recycling can be maintained as long as the hot-carriers do not lose energy such that they no longer can undergo the multiplication process. The decay of the multiexciton state is then a combination of the relative rates of Auger recombination, multiplication, and carrier cooling. In that model, the biexciton lifetimes that are experimentally measured using TA or THz reflect the decay of this recycling phenomenon as the multiexciton generation is shut off when the hot-carriers loose energy. While our data does suggest that hotcarriers are present during the biexciton decay, we could not reproduce our data assuming the Auger recycling model. More work is needed to fully map out these carrier dynamics and will be the subject of future work. Since the band gap of the nanocrystals increases with smaller QD size and the energy of the excitation remains fixed for each measurement, the excess energy produced by hotcarriers will differ with nanocrystal size. A more direct comparison is to calculate the cooling rates in terms of relaxed energy per unit time. To calculate these rates, we simply take the hotcarrier’s excess energy (pump energy – Eg) and divide it by the relaxation time (_[\ ). Using the PL peak emission of each QD sample (Table S1) for Eg, we calculate the energy relaxed per femtosecond to be 3.7(+/-0.2), 2.8(+/-0.1), 1.9(+/-0.1), and 2.1(+/-0.2) meV/fs for the 7.3, 6.2, 4.7, and 3.4 nm Si QDs, respectively. This direct comparison clearly shows a slowed hot-carrier relaxation as the size of the QD decreases. Indirect evidence of slowed hot carrier relaxation has previously been measured using PL for Si QDs embedded in SiO2, where an enhancement compared to bulk Si of phonon-less radiative recombination of hot-carriers was observed.12 The enhancement was attributed to a slowing of hot-carrier relaxation due to quantum confinement effects within the Si QDs, with carrier cooling times estimated at ~1-10 ps. A theoretical investigation of small Si QDs (2.5 nm) embedded in an SiO2 matrix also predicted hot-carrier relaxation times on the order of 1-10 ps,
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where the slow relaxation was attributed to fast recycling of optical phonons.21 In contrast to the PL measurements, TRTS is a direct measurement of hot-carrier lifetimes in Si QDs. Here, we observe the majority of hot-carrier relaxation occurs on a timescale
