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Efficient Carrier Multiplication in Colloidal Silicon Nanorods Carl Jackson Stolle, Xiaotang Lu, Yixuan Yu, Richard D. Schaller, and Brian A. Korgel Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b02386 • Publication Date (Web): 01 Aug 2017 Downloaded from http://pubs.acs.org on August 1, 2017

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Efficient Carrier Multiplication in Colloidal Silicon Nanorods Carl Jackson Stolle,† Xiaotang Lu, † Yixuan Yu, † Richard D. Schaller, ‡,§ Brian A. Korgel,†,* †

McKetta Department of Chemical Engineering, Texas Materials Institute, Center for Nano- and Molecular Science and Technology, The University of Texas at Austin, Austin, Texas 78712, USA ‡ Department of Chemistry, Northwestern University, Evanston, IL 60439, USA § Center for Nanoscale Materials, Argonne National Laboratories, Argonne, IL 60439, USA * Corresponding author: [email protected]; (T) +1-512-471-5633; (F) +1-512-471-7060

Abstract: Auger recombination lifetimes, absorption cross-sections and the quantum yields of carrier multiplication (CM), or multiexciton generation (MEG), were determined for solventdispersed silicon (Si) nanorods using transient absorption spectroscopy (TAS). Nanorods with an average diameter of 7.5 nm and aspect ratios of 6.1, 19.3, and 33.2 were examined. Colloidal Si nanocrystals of similar diameter were also studied for comparison. The nanocrystals and nanorods were passivated with organic ligands by hydrosilylation to prevent surface oxidation and limit the effects of surface trapping of photoexcited carriers. All samples used in the study exhibited relatively efficient photoluminescence. The Auger lifetimes increased with nanorod length and the nanorods exhibited higher CM quantum yield and efficiency than the nanocrystals with similar band gap energy Eg. Beyond a critical length, the CM quantum yield decreases. Nanorods with the aspect ratio of 19.3 had the highest CM quantum yield of 1.6 ± 0.2 at 2.9Eg, which corresponded to a multiexciton yield that was twice as high as observed for the spherical nanocrystals. Keywords: carrier multiplications, silicon nanocrystals, nanorods, multiple exciton generation, Auger recombination, quantum confinement

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When a semiconductor absorbs a photon with energy at least twice as large as the energy gap, h  2 E g , more than one electron-hole pair can be created through a process of carrier multiplication (CM), or multiple exciton generation (MEG).1 This process is very inefficient in bulk semiconductors because of selection rules due to momentum conservation and rapid nonradiative decay pathways: the threshold photon energy for CM in bulk semiconductors is typically >5Eg, with exceedingly high photon energies required to create additional excitons.2 Semiconductor quantum dots on the other hand can exhibit highly efficient CM, with CM threshold photon energies that can approach the energy conservation limit of 2Eg.2-14 Highly efficient CM has been observed from many different kinds of nanocrystals, including PbS,15,16 PbSe,15-19 PbSxSe1-x,16 PbTe,20 CdSe,21,22 InP,23,24 InAs,22,25,26 Ag2S,27 CuInSe2,28 Ge,29 and Si.3032

Significant interest in CM in quantum dots has largely stemmed from the fact that the

production of more than one exciton per absorbed photon offers a route to overcome the Shockley-Queisser efficiency limit for photovoltaic devices (PVs).33-42 It could also enhance quantum efficiencies of nanocrystal photocatalysts.38,43 Photocurrents consistent with the extraction of more than one electron-hole pair per absorbed photon have been observed in nanocrystal quantum dot PVs of PbS (internal quantum efficiency>100%),44 PbSe45 and CuInSe2 (external quantum efficiency>100%).46 However, significant enhancements in PV efficiency using CM require even higher CM efficiency. CM efficiency can be enhanced by changing the shape of quantum dots from spheres to rods or disks.47-53 PbSe nanorods have exhibited multiexciton yields that are nearly twice as high as those observed from PbSe nanocrystals with similar Eg (and diameter).47,54 The significantly stronger electron-hole Coulomb interactions in asymmetric nanostructures greatly enhances exciton binding energy and most likely is responsible for the higher CM efficiency.5,55 Nanorods


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also exhibit longer Auger (and correspondingly, biexciton) lifetimes than spherical nanocrystals of similar diameter because of their larger volume,56-58 which should further facilitate the extraction of multiexcitons in PVs. PbSe nanorod PVs recently demonstrated very high EQEs of up to 120%.59 Of the semiconductor nanocrystal materials studied to date, Si is perhaps the most relevant to the PV industry.60 Si solar cells dominate the commercial market and it makes sense to explore CM in nanoscale Si. Si is also not toxic and biocompatible.61,62 Fundamentally, Si is also different from most other semiconductor materials that have been studied, as it has an indirect band gap, making it a relatively weak light absorber, but with photoexcited electron-hole pairs that are especially long-lived.63 Si nanocrystals, however, exhibit a blue-shifted absorption edge due to quantum confinement effects and can be bright light emitters since crystal momentum is no longer conserved.64 Calculations have shown that Si is one of the more promising materials for high CM efficiency.6,9 One of the early ground-breaking studies to show that CM could be especially efficient in quantum dots was carried out using colloidal Si nanocrystals.30 Subsequent reports have appeared of efficient CM in Si nanocrystals embedded in SiO2,31,32 and a recent study proposing that CM can enhance PL quantum yield in Si nanocrystals,65,66 but there have been no other measurements of CM in colloidal solventdispersed Si nanocrystals reported since Ref. 30 in 2007. There have been no studies of CM in Si nanorods. In fact, there are only three experimental reports of CM in nanorods that we know of, in PbSe.47,50,52 All three studies showed enhanced CM efficiency in nanorods compared to nanocrystals. Here we report a comparative study of CM in Si nanorods and nanocrystals of similar diameter.


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The Auger lifetimes, absorption cross-sections and CM quantum yields were measured for solvent-dispersed Si nanorods with three different aspect ratios using transient absorption spectroscopy (TAS).

This study was enabled by synthetic methods recently developed to

produce light-emitting, organic ligand-passivated Si nanorods with tunable length.67,68

For

comparison, colloidal Si nanocrystals of similar size and Eg were also examined. The nanorods exhibited longer Auger lifetimes and higher CM quantum yield. Figure 1 shows transmission electron microscopy (TEM) images of the nanocrystal and nanorod samples that were used for the TAS studies. The Si nanocrystals were prepared using a well-developed synthetic route that relies on the thermal decomposition of hydrogen silsequioxane (HSQ) and surface passivation with organic ligands by thermal hydrosilylation with dodecene.69 (See Supporting Information for Experimental Details). Nanocrystals produced using this approach have relatively uniform size distributions, exhibit size-tunable luminescence with high quantum yield, clearly exhibit diamond cubic crystal structure in X-ray diffraction (XRD) and have very little surface oxidation, as measured by X-ray photoelectron spectroscopy (XPS) (see Supporting Information Fig. S1).69,70 The nanocrystals used for this study had an average diameter of 6.6 ± 0.4 nm based on TEM. The Si nanorods were produced by a colloidal solution-liquid-solid (SLS) growth method using tin (Sn) nanoparticles as seeds to obtain samples with similar diameter and different aspect ratios.67,68 The use of tin seeds, as opposed to the more commonly used gold, is important for the CM measurements. Gold seeds for Si nanorods have been shown to leave residual impurities—even after removing the gold seeds by etching—that serve as electron-hole traps and quench photoluminescence.71,72 These impurity traps could negatively affect the CM efficiency. As-synthesized Sn-seeded nanorods are also not fluorescent. But after removing the tin seeds by etching, followed by surface passivation via


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thermally-promoted hydrosilylation with octadecene similar to Si nanocrystals, the Si nanorods recover their fluorescence.73 Similar to the Si nanocrystals used here, the nanorods produced using these methods have also been extensively characterized in the literature by XRD, XPS and absorbance and photoluminescence spectroscopy.67,68

For the CM studies, nanorods were

produced with average diameters of ~7.5 nm and average lengths of ~50 nm, ~150 nm, and ~250 nm determined by TEM.

Figure 1. TEM images and size histograms of Si nanocrystals and nanorods studied by TAS: (a) Si nanocrystals with average diameter of 6.6 ± 0.4 nm (6.5 nm nanocrystals), (b) Si nanorods with average diameter 7.6 ± 1.3 nm and length of 46.5 ± 3.5 nm (7.5x50 nm nanorods), (c) Si nanorods with average diameter of 7.6 ± 1.3 nm and length of 146.5 ± 19.1 nm (7.5x150 nm nanorods), and (d) Si nanorods with average dameter of 7.6 ± 1.3 nm and length of 252.1 ± 31.7 nm (7.5x250 nm nanorods).


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The nanocrystal and nanorod energy gaps Eg, were taken as the photoluminescence (PL) emission peak energies shown in Figure 2.

Because of the indirect band gap of Si, Si

nanocrystals and nanorods exhibit the featureless absorbance spectra shown in Figure 2 and the low density of states near the band edge make the light absorption too weak for an accurate determination of Eg from the optical absorption edge. The Stokes shift between the PL and the optical absorption is small, and the PL peak emission can be used as a reasonable estimate of Eg.30,70,74 The PL peak energies (i.e., Eg) for the nanorods and nanocrystals are 1.33 eV (~930 nm) and 1.27 eV (980 nm), respectively.

Figure 2. UV-vis-NIR absorbance and PL emission (405 nm excitation) spectra of the Si nanocrystals and nanorods that were used in this study (nanocrystals and nanorods are dispersed in toluene). PL quantum yields determined relative to a dye standard (IR-140) were 0.094% for the nanocrystals, and 0.047%, 0.003% and 0.005% for the 7.5x50 nm, 7.5x150 nm and 7.5x250 nm nanorods, respectively.


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TAS was used to study CM of colloidal dispersions of Si nanocrystals and nanorods in toluene. All TAS measurements were carried out using magnetic stirring to eliminate any effects of photocharging during the measurements.75 (See Experimental Details in Supporting Information).

Because Si has an indirect band gap, the state-filling-induced bleach at the

absorption edge typically used to monitor exciton population dynamics is too weak to observe and instead the characteristic longer wavelength photon-induced absorption of Si is utilized.30,63 Figure 3 shows a TA spectrum that is typical of the samples used in the study. The TA spectra for all of the samples exhibited similar spectral line shape and the induced absorption ∆ , was monitored at 1200 nm throughout (see Supporting Information Fig. S2 for TA spectra of all samples).

Figure 3. TA spectrum for 7.5x50 nm diameter Si nanorods dispersed in toluene using a 600 nm pump laser taken at 1 ps delay time.

Figure 4 shows TA kinetics of the Si nanocrystals and nanorods using a 600 nm pump wavelength. One absorbed photon at this pump wavelength cannot generate more than one


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exciton, because h  2 E g , and the TA kinetics at low photon flux, or pump fluence J, derive from the dynamics of single excitons. Even at relatively low J, some nanocrystals will absorb an additional photon before an existing photoexcited electron-hole pair has time to decay, resulting in more than one exciton in a single nanocrystal even though h  2 E g . The larger early-time TA signal and faster decay kinetics under high J reflects non-radiative Auger recombination of multiple excitons.17 In Figure 4, the average number of photons absorbed by the nanocrystals N , is shown. N  J .

As

N N

depends on J and the absorption cross-section  , of the nanocrystals: is increased, the amount of Auger recombination is increased.

The

instantaneous number of excitons per nanocrystal follows a Poisson distribution and it is not necessary for N  1 to have multiple excitons in the system.3,10 In fact, N must be relatively low to ensure that there are not a significant number of multiexcitons created by multiphoton absorption. These TA data are used to determine the rate of single exciton decay and Auger recombination.

Figure 4. Transient absorption (TA) kinetics of (A) 6.5 nm nanocrystals, (B) 7.5x50 nm nanorods, (C) 7.5x150 nm nanorods, and (D) 7.5x250 nm nanorods dispersed in toluene 8 ACS Paragon Plus Environment

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measured using a 600 nm pump wavelength. All curves are normalized to the signal at long delay times, at least 3 times the Auger lifetime (2 ns for the nanocrystals and 4 ns for the nanorods), at which only single excitons are present in the nanocrystals. The kinetics are taken from the induced absorption signal at 1200 nm.

N

was determined using values of 

determined by fitting Eqn. (1) to the data in Figure 6.

Figure 5 plots the biexciton Auger lifetimes for Si nanocrystals and Si nanorods. The biexciton lifetimes were determined by subtracting the single exciton baseline TA kinetics (low fluence, 600 nm pump wavelength, normalized at long pump-probe delay time) and fitting the difference signal to a biexponential decay. The slow time constant of the biexponential decay corresponds to Auger recombination while the fast decay corresponds to faster decay component arising from three photon absorption.34 The measured biexciton Auger lifetimes are provided in Table 1 and plotted in Figure 7A. Biexciton decay occurs on the 100 ps time scale, with Auger lifetimes increasing with length for nanorods of similar Eg.

Auger recombination in bulk

semiconductors depends on the carrier density, so this is consistent with the reduced exciton density in the larger volume nanorods.58 As shown in Figure 7A, the biexciton Auger lifetime increases with increasing aspect ratio and nanorod volume, in agreement with prior measurements for CdSe and PbSe.38,54


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Figure 5. High fluence TA kinetics differenced from the low fluence, single-exciton baseline (normalized at long delay time) for (A) 6.5 nm nanocrystals, (B) 7.5x50 nm nanorods, (C) 7.5x150 nm nanorods, and (D) 7.5x250 nm nanorods. The kinetics are fit to a biexponential decay with the longer decay component corresponding to the biexcitonic Auger lifetime, and the faster component relating to triexcitonic decay.

A 320 nm pump wavelength was used to determine if CM occurs in the nanocrystals and nanorods. The absorption cross section for 320 nm photons is about 50-100 times greater than for 600 nm photons based on both static and fluence dependent TAS (see Figures 2 and 6, respectively). Therefore, to ensure that excitation was in the single photon limit, very low pump fluences are required. For this reason, TA signal was collected only for three time points; negative time delay, relatively short time delay of 5 ps, at which multiexcitons can be present, and a long time delay of 2 ns for the nanocrystals and 4 ns for the nanorods) where only single excitons are present owing to Auger recombination. Figure 6 shows the ratio of the short time delay TA signal to the long time TA signal, Rpop, as a function of J measured using 600 nm and 320 nm pump wavelengths. The plots of Rpop 10 ACS Paragon Plus Environment

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versus J are used to determine the average number of excitons generated per absorbed photon, or CM quantum yield QY, and  :35 R pop 

J  QY 1  e J

(1)

 is the absorption cross section at the pump wavelength. QY and  for each sample in Table 1 were determined by fitting Eqn (1) to the data in Figure 6. The values of  in Table 1 were used to calculate the values of N shown in Figure 4. The values of  agree with those previously reported for Si nanocrystals30,68 and the ratios of the absorption cross sections at 600 nm and 320 nm agree well with the optical absorption data in Figure 2 (See Supporting Information Table S1).

Figure 6. The ratio of the TA signal measured at short times and long times (Rpop) as a function of pump laser fluence J, for A) 6.5 nm nanocrystals, B) 7.5x50 nm nanorods, C) 7.5x150 nm nanorods, and D) 7.5x250 nm nanorods at 600 nm and 320 nm pump wavelengths. The data are fit to Eqn. (1) to obtain the CM quantum yield (QY) and the absorption cross sections at 600 nm (σ600) and 320 nm (σ320) for each sample.


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Table 1. Summary of the dimensions of the Si nanocrystals and nanorods used in the study and the absorption cross sections at 320 nm and 600 nm (  320 and  600 ) and the QY determined by fitting Eqn (1) to the data in Figure 6. The Auger lifetimes were determined from the TA kinetics in Figure 5. Shape

Diameter (nm)

Length (nm)

Aspect Ratio (L/D)

Sphere

6.6 ± 0.4

N/A

Rod

7.6 ± 1.3

Rod Rod

 320

 600

cm )

( 1016 cm2)

QY

Auger lifetime (ps)

1

1.44 ± 0.17

1.16 ± 0.09

1.28 ± 0.05

210

46.5 ± 3.5

6.1

1.67 ± 0.47

6.61 ± 0.54

1.28 ± 0.14

480

7.6 ± 1.3

146.5 ± 19.1

19.3

2.78 ± 0.57

11.4 ± 3.7

1.61 ± 0.19

750

7.6 ± 1.3

252.1 ± 31.7

33.2

3.99 ± 0.62

17.5 ± 2.8

1.37 ± 0.14

910

14

( 10

2

Figure 7 shows the biexcitonic Auger lifetime and CM quantum yield of the Si nanocrystals and nanorods as a function of aspect ratio and Figure 8 compares the biexciton lifetimes of the nanorod samples to the biexciton lifetimes of other nanomaterials reported in the literature.8,26-28,30,47,75 The Auger lifetime for the Si nanorods increases with nanoparticle volume and aspect ratio, very similar to what has been reported for PbSe nanocrystals and nanorods.54,56 The QY of the nanorods increases with length when the aspect ratio is less than 20 and then decreases when the aspect ratio is larger than this. A similar peaking in QY with aspect ratio was observed for PbSe nanorods.47 This behavior has been attributed to competing effects of enhanced Coulomb interactions in the nanorods that favors CM and a restoration of translational momentum conservation in long nanorods that reduces CM efficiency.5,47


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Figure 7. (A) Biexcitonic Auger lifetime and (B) CM quantum yield (QY) determined at h  3.86 eV for Si nanocrystals and nanorods with varying aspect ratio.


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Figure 8. Biexcitonic Auger lifetimes plotted as a function of (A) nanocrystal volume and (B) energy gap for the Si nanocrystals and nanorods in this study compared to various other literature reports. Black squares represent CuInSe2 nanocrystals,28 purple circles represent Si nanocrystals,30 blue top-facing triangles represent PbSe nanocrystals,73 green bottom-facing triangles represent Ag2S nanocrystals,27 pink left-facing triangles represent PbS nanocrystals,8 gold right-facing triangles represent InAs nanocrystals,26 grey pentagons represent PbSe nanorods,47 red and gold stars represent the Si nanorods and nanocrystals, respectively, from this study.


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The photon energy threshold h th , for CM and the efficiency of electron-hole pair multiplication MEG , are usually determined by measuring QY at a range of photon energies approaching h th .3 For Si nanocrystals, these measurements are especially demanding because the induced absorption signal is very weak near h th . Therefore, we estimated h th and  MEG from QY and E g using the relations derived by Beard, et al.2

 h   1MEG QY   E   g  h th  E g 

Eg

MEG

(2)

(3)

The quantity E g  MEG is the energy required to create an additional electron-hole pair (i.e., a multiexciton) in the nanocrystal after the energy threshold for CM (i.e., h th ) is passed.2,6 In the energy conservation limit, the energy required to create an additional electron-hole pair is E g , and h th  2 E g and MEG  1 .2 Based on Eqns (2) and (3), the Si nanocrystals studied here have values of  MEG  0.63 and h th  3.29 eV ( h th E g  2.59 ), and the Si nanorods with aspect ratio of 20 have  MEG  0.85 and h th  2.89 eV ( h th E g  2.18 ). Having a nanorod shape makes CM more efficient. . The values of h th ( MEG ) are slightly higher (lower) than most published reports of CM in Si nanocrystals; however, the CM efficiency may have been overestimated in those studies due to photocharging.19,30 In our study, TAS measurements were performed on solvent-dispersed Si nanocrystals that were stirred to help ensure that photocharging—and the resulting appearance of artificially high CM—did not occur.


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The Si nanocrystals and nanorods studied here all displayed efficient CM. The CM QYs were ~1.3 and ~1.6 for nanocrystals and nanorods (with aspect ratio of ~20) with similar Eg with photon energies of 2.9-3.0 E g . The multiexciton yield in nanorods was about twice as high as in spherical nanocrystals.

The nanorods also exhibited longer Auger lifetimes than the

nanocrystals, which increased with increasing aspect ratio. The long Auger lifetimes may further the opportunity for multiexciton extraction in PVs. Further tuning of nanorod size could allow for even higher CM efficiencies, as needed for multiexciton solar cells.

Supporting Information

Experimental details for Si nanocrystal and nanorod synthesis, XPS data, additional TA spectra and tabulated values of absorption cross-sections. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgements

Financial support of this work was provided by the Robert A. Welch Foundation (Grant No. F1464) and the National Science Foundation (Grants No. CHE-1308813 and IIP-1134849). Financial support was also provided to C.J.S. by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-11100007.

Use of the Center for

Nanoscale Materials was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Science, under Contract No. DE-AC02-06CH11357.

References


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