Size-Dependent Optical Nonlinearities and Scattering Properties of PbS Nanoparticles

M. S. Neo,† N. Venkatram,‡ G. S. Li,† W. S. Chin,*,† and Ji Wei*,‡

Department of Chemistry, National UniVersity of Singapore, 3 Science DriVe 3, Singapore 117543, andDepartment of Physics, National UniVersity of Singapore, 2 Science DriVe 3, Singapore 117542

ReceiVed: July 14, 2009; ReVised Manuscript ReceiVed: September 10, 2009

We report the size-dependent optical nonlinearities of PbS nanoparticles both in solution and as a compositefilm. Different sizes of PbS nanoparticles were synthesized by chemical methods, with the sizes controlledby varying reaction temperature and time. Transparent PbS/polystyrene thin films deposited on glass slideswere successfully prepared by a simple imprinting-thermal cross-linking method. We found that smallernanoparticles show higher nonlinear absorption and refraction of photoexcited free carriers, as well as largeroptical Kerr nonlinearity. Our studies also revealed that nonlinear scattering is strongly dependent on sizeand plays a dominant role in the case of bigger nanoparticles in solution at higher excitation energy.

1. Introduction

Semiconductor nanoparticles or quantum dots (QDs) haveattracted considerable interest in the past 2 decades due to theirexceptional luminescenceandnonlinear-optical(NLO)responses.1,2

The Bohr exciton radius of lead sulfide (PbS) is ∼18 nm,3 andhence PbS nanoparticle with a size smaller than 18 nm isexpected to show strong confinement effects. In particular, PbSQDs possess strong photoluminescence (PL) that can be tunedfrom the visible (vis) to the near-infrared (near-IR) spectralregime and thus have been actively explored in variousapplications such as photovoltaic cells, light-emitting diodes(LEDs), and biological applications.4-6 Here, we present ourinvestigation on the NLO responses of colloidal PbS QDs inhexane and PbS/polymer composite films to a femtosecond laserpulse of 780 nm wavelength.

PbS QDs can be incorporated into polymers to form thin filmsof nanocrystal/polymer composites by several different methods.The in situ synthesis of the nanocrystals at either roomtemperature or at elevated temperature in the presence ofpolymers have been carried out by several research groups.7,8

A slight variation of the method is the simultaneous polymer-ization of the polymer such as acrylamide and the thermaldecomposition of a lead-dithiooxamide complex to form thePbS/polyacrylamide nanocomposite.9 Highly luminescence PbSnanocrystals synthesized from an organometallic method canbe dispersed in different polymers forming PbS/polymer filmswith high PL quantum yield at near-IR region by properly tuningthe polymer and concentration.10 PbS/polystyrene composite canalso be formed by the dispersion of the preformed nanocrystalsin a suitable monomer mixture followed by polymerization toform thin films, which is the method used in this study. Theadvantage of this latter method over the in situ method is bettercontrol of the size of PbS nanocrystals in the films andconsequently their bright PL and large NLO properties, as shownin this paper.

In the past decade, significant research has been performedin the determination and maximizing of the NLO properties such

as nonlinear absorption and/or nonlinear refraction of differentQDs, so as to develop better optical limiting and faster opticalswitching devices.11-16 Optical limiting in inorganic and hybridnanomaterials typically arises from a collective response of someof the following nonlinear mechanisms: nonlinear refraction,nonlinear scattering (NLS), free-carrier absorption (FCA),multiphoton absorption (MPA), and reverse saturable absorption(RSA).17 For example, large optical limiting can be observedin CdS nanoparticles dispersed in dimethylformamide (DMF)due to strong two-photon absorption and NLS,18 while efficientoptical limiting can also be observed in PbS QDs stabilized ina poly(vinyl alcohol) glue due to FCA.7,11 Moreover, severalstudies have also been carried out on the NLO properties ofpolymers, glasses, and zeolites doped with PbS QDs.8,19 Largeexcited-state absorption and self-defocusing have been reportedin PbS nanocrystals in zeolites at 532 nm excitation.19

However, most of these studies were conducted on PbS QDsin different types of thin films while little was known aboutPbS nanocrystals synthesized and dispersed in organic solvents.Furthermore, most of the above-mentioned reports aimed atunderstanding the two-photon absorption process, but there wasno report on the effects of excess free carriers induced by one-photon absorption. FCA was found to be enhanced by ordersof magnitude in smaller nanocrystals compared to its bulkcounterparts.20 The FCA process is more dominant for long pulseexcitations and for samples having intraband carrier lifetimesfaster than the laser pulse duration. In PbS nanoparticles, theintraband carrier lifetimes are fast enough to generate free-carriereffects.21,22

Only a few reports are available on the theoretical explanationof size-dependent FCA of quantum wells,23 but neither atheoretical nor an experimental report is found on the size-dependent FCA of semiconductor QDs. Moreover, the sizes ofthe PbS QDs studied vary greatly from different investigators,with few attempts to study the size effect on their NLOresponses. In the present Z-scan study, we attempt to give asystematic investigation into the size-dependent FCA, free-carrier refraction (FCR), optical Kerr nonlinearity, and NLS inPbS QDs with sizes between 4.5 and 11 nm dispersed in eitherhexane or in polystyrene (PS) polymer films. By using Z-scantheories, the nonlinear parameters such as the FCA cross-section(σc), FCR cross-section (σr),24,25 optical-Kerr refractive index,

* To whom correspondence should be addressed. Fax: +65-6779-1691(W.S.C.); +65-6777-6126 (J.W.). E-mail: chmcws@nus.edu.sg (W.S.C.);phyjiwei@nus.edu.sg (J.W.).

† Department of Chemistry.‡ Department of Physics.

J. Phys. Chem. C 2009, 113, 19055–19060 19055

10.1021/jp9066263 CCC: $40.75 2009 American Chemical SocietyPublished on Web 10/12/2009

and NLS coefficient (Rs) are unambiguously determined andtheir dependence on size is quantified.

2. Experimental Section

We adapted the literature method with slight modificationfor the synthesis of our PbS QDs.26 First, 9.6 mmol of PbCl2

was mixed with 16 mL of oleylamine in a 50 mL three-neckflask. The solution was vigorously stirred and heated to 100 °Cand degassed for 5 min before it was heated and kept at thereaction temperature (110 or 120 °C) for 30 min. In anothertwo-neck flask, a red solution was formed by dissolving 0.0451g of sulfur in 12 mL of oleylamine and heating to 80 °C. An 8mL aliquot of the resulting red solution was withdrawn andswiftly injected into the three-neck flask. The solution wasallowed to age at different temperatures (100, 120, and 210 °C)at varying reaction times from 1 min up to 1 h to produce thesize of QD desired. At the desired time, 4 mL of the solution

was withdrawn and quenched by injecting into 4 mL of coldhexanes and further cooled by immersing in an ice bath. Ethanolwas added, and the solution was centrifuged to precipitate thePbS along with some PbCl2. The precipitate was re-dispersedin hexane and then added with twice the amount of oleic acidand centrifuged to obtain a black precipitate. The PbCl2 wasremoved by re-dispersing the precipitate in hexane and centri-fuging to obtain a dark red supernatant since PbCl2 is insolublein hexane. The dark red supernatant solution was then precipi-tated with ethanol to obtain the PbS precipitate. This precipitatewas dried to give PbS QDs, which were re-dissolved in hexaneof concentration 5 × 10-3 M for all our optical measurements.

Next, we describe a simple imprinting-thermal cross-linkingmethod to prepare transparent PbS/polystyrene (PbS/PS) thinfilms on glass slides. Polished glass plates A and B were soakedin a concentrated sulfuric acid solution for 5 min and rinsedextensively with deionized water. To enhance the adhesionbetween cross-linked polymers and glass plate A, surfacemodification was conducted. A coupling agent, [3-(methacryl-oyloxy)propyl]trimethoxysilane (γ-MPS, 98%, Aldrich) washydrolyzed in methanol/water (80:20 by volume) under a valueof pH 4. Glass plate A was then immersed in this solution for10 min. After treatment, glass plate A was rinsed sequentiallyin water, 2-propanol, and acetone before use. A thermally cross-linkable recipe, containing styrene (99%, Fluka) as monomer,divinylbenzene (80%, mixture of isomers, Aldrich) as cross-linker, and benzyl peroxide (Aldrich) as thermal initiator in themolar ratio of 60:13:1, was mixed and stirred over 6 h. Filtrationthrough a 0.2 µm filter was performed, and then PbS QDs weredispersed into this mixture by sonication to form the precursor.A small amount of this precursor was added to the surface ofglass plate A, on top of which glass plate B was brought intocontact. The precursor was allowed to spread between the twoplates, and then imprinting was carried out on a 4 in. imprinter

Figure 1. Typical XRD pattern for a sample of PbS QDs indexed toJCPDS 05-0592.

Figure 2. TEM micrographs of PbS QDs with average sizes of (a) 4.6 ( 0.5, (b) 5.3 ( 0.5, (c) 6.0 ( 0.6, and (d) 11.0 ( 2.0 nm. Inserts givehistograms of the respective size distributions.

19056 J. Phys. Chem. C, Vol. 113, No. 44, 2009 Neo et al.

(Obducat Inc.) at 110 °C for 10 min under a pressure of 4 MPa.Glass plate B was carefully separated from A, yielding a uniformcomposite film on glass plate A. Postcure treatment undervacuum was then carried out at 110 °C for a period of 1 h.Transparent and uniform composite films were obtained thisway, except for the 11 nm PbS QDs because the solubility waspoor in the monomer mixture.

The XRD patterns were obtained using Siemens D5005 X-raydiffractometer with Cu KR radiation. The purified PbS QSs werecrushed into fine powder for the analysis. Transmission electronmicroscopy (TEM) was performed on a JEOL JEM 2010F fieldemission electron microscope with an acceleration voltage of200 kV. The nanoparticles were dispersed in hexane or toluene,dripped onto a 200 mesh carbon-coated copper grid, and driedin vacuum before analysis. UV-vis absorption spectra wererecorded on a Shimadzu UV-3600 UV-vis-near-IR spectro-photometer using either pure hexane or tetrachloroethylene(TCE) as reference. Solid measurements were recorded by usingan integrating sphere attachment (ISR-3100) with PM and PbSdetector. The PL spectra for IR emission were recorded by usinga Horiba Jobin Yyon FluoroLog-3 with an iHR320 attachmentequipped with lock-in amplifier and liquid nitrogen cooledInGaAs photodiode detector with detection limit to 1600 nm.

The NLO properties of the PbS QDs dispersed in hexane wereinvestigated by femtosecond (fs) Z-scan27 at wavelength of 780nm, ∼300 fs laser pulses at a 1 kHz repetition rate. The laser

pulses were generated by a mode-locked Ti:Sapphire laser(Quantronix, IMRA), which seeded a Ti:Sapphire regenerativeamplifier (Quantronix, Titan). The laser pulses were focusedonto a 1 mm thick quartz cuvette (or ∼10 µm thick film) whichcontained the PbS QDs, with a minimum beam waist of 30 µm.The linear transmittance of all the solutions (or films) wasadjusted to 70% (or 80%) at 780 nm. The incident andtransmitted laser powers were monitored as the cuvette (or film-coated glass slide) was moved along the propagation directionof the laser pulses. An aperture was introduced before thedetector for the collection of closed-aperture Z-scan curves. Onemore detector was introduced for the collection of NLS at anangle of 10° to the propagation direction.18

3. Results and Discussion

A typical XRD pattern of the PbS QDs synthesized is shownin Figure 1. All of the diffraction peaks can be indexed to thePbS face-centered cubic (fcc) phase (JCPDS 5-0592). TEMimages in Figure 2(a-d) show relatively monodispersed nano-particles having an average size of 4.6 ( 0.5, 5.3 ( 0.5, 6.0 (0.6, and 11.0 ( 2.0 nm, respectively.

In Figure 3, the UV-vis-near-IR absorption spectra ofthese four samples are measured in solution. The first andsecond excitonic peaks for the 4.6, 5.3, and 6 nm PbS QDsare well-resolved, showing that good size distributions havebeen achieved. The first excitonic absorption peak blue-shiftsas the particle size decreases due to quantum confinementeffect, as summarized in Table 1. The lack of a distinct peakfor the 11 nm QDs may be attributed to its broader sizedistribution and weak quantum confinement. This lattersample is also more difficult to disperse homogeneously forluminescence measurement. The near-IR bandgap emissonsof the other three samples measured in hexane are displayedin Figure 4a, with the peaks red-shifting with size as expected.The small Stoke shift tabulated in Table 1 suggests that theluminescence is due to bandgap excitonic recombination andcan be attributed to efficient passivation of the nanocrystalssurface by oleylamine ligands, similar to that observedpreviously.28

By mixing the PbS QDs in a thermally cross-linkable recipe,followed by imprinting cum polymerization, uniform andtransparent PbS/PS composite films of a few micrometerthicknesses are prepared on glass substrates. The normalizednear-IR spectra of these homgeneous PbS/PS films are shownin Figure 4b. Slight broadening of the luminescence is observedas expected, and the strong near-IR signals confirm that the fastpolymerization method has successfully retained the originalluminescence properties of the PbS QDs. The abrupt drop atwavelengths higher than 1520 nm is due to the spectral limit ofthe detector.

Figure 3. Typical UV-vis-near-IR absorption spectra of the PbSQDs in solution. The spectra are labeled with the corresponding samplesizes determined from Figure 2.

TABLE 1: Summary of the Average Sizes of PbS QDsEstimated from TEM, the Respective First ExcitonicPosition, and Bandgap Luminescence Measured in Hexane

sampleav sizes from

TEM (nm)first excitonicposition (nm)

bandgap luminescence(nm)

A 4.6 ( 0.5 1220 1269B 5.3 ( 0.5 1290 1323C 6.0 ( 0.6 1473 1511D 11.0 ( 2.0 NA NA

Figure 4. Typical near-IR luminescent spectra of the PbS QDs in (a) hexane and (b) polystyrene composite film. Excitation wavelength ) 532 nm.

Optical Nonlinearities of PbS Nanoparticles J. Phys. Chem. C, Vol. 113, No. 44, 2009 19057

Next, the NLO properties of the PbS QDs were character-ized with the Z-scan method. Open-aperture Z-scan curvesof the QDs in hexane and PS films respectively are shownin Figure 5a,b. It is noted that the absorptive nonlinearitiesof these QDs show different behavior in different matrices.All the sizes of PbS QDs display reverse saturable absorption(RSA) at all the intensities in solutions. In the PS films, onthe other hand, all the samples except the smallest size QDs(4.6 nm, showing saturable absorption at lower intensitiesand RSA at high intensities) show RSA behavior. As statedbefore, the RSA behavior could result from FCA and/or NLSmechanisms. Thus, these size-dependent Z-scan curves showinteresting behaviors-i.e., at lower intensities, there is alarger nonlinear absorption signal (or the change in thetransmittance at the focus) for the smaller sized QDs thanthe bigger sized QDs, while, at higher intensities, the reversedbehavior is observed. This implies that more than onenonlinear phenomenon is manifesting itself in these samples.

To investigate this additional nonlinear effect, we per-formed intensity-dependent NLS experiments on these QDs.Figure 6 confirms that, at higher intensities, the bigger sizeQDs show more NLS than the smaller ones, and NLS is thedominant phenomena for bigger QDs at higher intensities.

Combined losses of NLS and FCA lead to lower nonlineartransmission at the focus for bigger size QDs at higherintensities. Since our pumping photon energy is much greaterthan the band gap, FCA is speculated to be the dominant process.However, at higher intensities, NLS becomes significant forbigger QDs. NLS contribution is negligible in the case of film

samples, nevertheless, below the damage thresholds (∼125 GW/cm2). As such, in the Z-scan theory, both FCA24 and NLS18

should be taken into consideration as follows:

where

Here R0 is the linear absorption coefficient, N1 is the intensity-dependent carrier density, σc is the FCA cross-section, Rs isthe effective scattering coefficient, I is the peak intensity, gs isa parameter which is independent of intensities but depends onlyon the size, shape, concentration of particles, and wavelengthof light, ∆nl is the difference in the linear refractive index ofPbS particle and hexane, and ∆nnl is the difference in thenonlinear refractive indices of PbS particles and hexane. Since∆nnl is a function of the intensity inside the medium, it can bederived further in the following manner. The relaxation of light-induced changes in the refractive indices of the componentscan be taken into account by introducing a Debye-type equationfor femtosecond pulses as ∆nnl ) ∆nthI/(1 + (τth/tp)). Here, ∆nth

is the difference between the nonlinear thermal refractive indexof PbS particles and hexane, τth (∼ms) is the relaxation time ofthe thermal nonlinearity, and tp (∼1 ms) is the time periodbetween two laser pulses. We can integrate both eqs 1 and 2numerically over time and length and along the radial directionby using Runge-Kutta fourth-order method. The best fits (solidlines in Figure 5) between the numerical solutions and the Z-scandata generate the nonlinear parameters as tabulated in Table 2.

For the smallest QDs in the case of the composite films, wenoted that saturable absorption (SA) occurs at lower intensity,

TABLE 2: Fitted FCA Cross-Section (σc), NonlinearRefractive Index (n2), FCR Cross-Section (σr), andScattering Coefficient (rs) of the PbS QDs in Solution (AllValues Listed Are within 10% Error)

Ra ) 4.5nm

R ) 5.3nm

R ) 6.0nm

R ) 11nm

σc × 1019 (cm2) 61.3 30.2 23.4 8.2n2 × 106 (cm2/GW) -4.2 -3.0 -2.0 -0.5σr × 1022 (cm3) -1.5 -1.4 -0.4 -0.3Rs (cm-1) 2.1 2.4 3.9 7.1

a R ) size.

TABLE 3: Fitted FCA Cross-Section (σc), NonlinearRefractive Index (n2), FCR Cross-Section (σr) of the PbSQDs in PS Films (All Values Listed Are within 10% Error)

Ra ) 4.5 nm R ) 5.3 nm R ) 6.0 nm

σc × 1019 (cm2) 204 159 110n2 × 106 (cm2/GW) -5.4 -2.5 -1.8σr × 1022 (cm3) -1.4 -0.7 -0.2

a R ) size.

Figure 5. Open-aperture Z-scans at varying laser intensities fordifferent sized PbS QDs in (a) hexane and (b) PS film. Solid linesrepresent the theoretical fits.

Figure 6. Nonlinear scattering measurements of different sized QDin solution collected at 10°.

dIdz

) -R0I - σcN1I - RsI (1)

∂N1

∂t)

R0I

pω(2)

Rs ) gs[∆n]2

∆n ) ∆nl + ∆nnl ) ∆nl +∆nthI

1 + (τth/tp)

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while RSA dominates at higher intensity. To include this SAphenomenon in the theoretical calculation, we consider thesaturation equation. This saturation is mostly due to one-photonbleaching, and we may modify the one-photon absorptioncoefficient to R0s:29,30

where Is is the one-photon saturation intensity. Saturationintensities of bigger QDs are not measurable due to highersaturation intensities of bigger QDs. All the coefficients usedin the fittings are tabulated in Table 3.

Figure 7 displays typical closed aperture Z-scan curves ofthe PbS QDs. All the samples, in film and solution, shownegative nonlinear refraction, indicating self-defocusing effect.It is well-known that thermal nonlinearities also contribute tonegative nonlinear refraction, and high single-photon absorptioncross-sections may be responsible for these thermal nonlineari-ties. Thus, to minimize thermal effects, all our closed-apertureZ-scan curves were collected at lower intensities.

Free carriers induced by one-photon absorption also contributesignificantly to the phase changes of the wave in the sample.Including the free-carrier refraction (FCR) contribution, thenonlinear phase equation is given by24

Here, n2 is the nonlinear refractive index (or optical Kerrnonlinearity), σr is the FCR cross-section, ∆�0 is the phasechange, z is the sample position, z0 is the Rayleigh range, TCA

is the closed aperture transmittance, and Leff is the effectivesample length.13 It is known that FCR is a self-defocusingphenomenon added to the overall nonlinear refraction.24 Boththe n2 and σr values of the PbS QDs are obtained from the bestsimulations to the experimental data and listed in Tables 2 and3. PbS QDs with the smaller sizes show higher FCR and opticalKerr nonlinearity.

It is observed that the FCA cross-sections of the films aregreater than the ones in the solution. The FCA cross-sections

of smaller QDs in PS films show at least three-times enhance-ment compared with the particles in hexane, as shown in Figure8. The FCA cross-sections of PbS QDs in both hexane and PSfilms are linearly dependent on 1/R2, where R is the QD size.Our results are consistent with size-dependent theoreticalsimulations on quantum wells and wires.23

Surface structure and ligand have been previously suggestedto give strong influence on the nonlinear-optical properties ofPbS nanoparticles. Oleic acid capped PbS nanocrystals synthe-sized by the popular Hines and Scholes method showedpreviously to possess only saturable absorption at high intensity.This was suggested to be due to quenching at the interfacebetween the adsorbed oleic acid ligands and the nanocrystalsurfaces, which were shown to have an excess of sulfur at thePbS nanocrystal surfaces.8,31 The synthesis method we followfor PbS QDs has been previously shown to produce Pb-richparticles passivated with Cl- and oleylamine.28 More theoreticaland experimental work needs to be done to establish if thedifference in surface structure or ligand can explain oursuccessful attempt in obtaining RSA from the PbS QDs in thesolution phase. A previous study of a series of sizes of PbSnanocrystals grown in polymer solutions did not correlate theirnonlinear absorption to FCA but instead to two-photon absorp-tion.8 These authors suggested that the absence of size depen-dence was due to their similar surface chemistry. Unlike theirobservation with nanosecond laser pulses, we believe that, byusing a femtosecond laser, the size-dependent nonlinear absorp-tion of PbS QDs cannot be smeared by thermal effects.

4. Conclusions

In conclusion, PbS QDs have been synthesized by chemicalmethods and their sizes have been well-controlled by varyingreaction temperature and time. PbS/PS thin films deposited onglass slides have also been successfully prepared by a simpleimprinting-thermal cross-linking method with the PbS near-IRluminescence preserved in the final films. Their nonlinear-opticalresponses have been studied with femtosecond Z-scans. The

Figure 7. Closed-aperture Z-scan curves of different sized PbS QDs in (a) hexane and (b) PS film with theoretical fits.

R0s )R0

√1 + I/Is

(3)

d∆�0

dz)

2π(n2I + σrN1)

λ(4)

∆�0 )2πLeff(n2I + σrN1)

λ(5)

TCA ) 1 -4∆�0(z/z0)

[1 + (z/z0)2][9 + (z/z0)

2](6)

Figure 8. Size-dependent FCA cross-section of PbS QDs in hexaneand in PS film and its linear fits with 15% error bars.

Optical Nonlinearities of PbS Nanoparticles J. Phys. Chem. C, Vol. 113, No. 44, 2009 19059

size-dependent free-carrier absorption, free-carrier refraction, andoptical Kerr nonlinearity are determined and discussed at laserexcitation wavelength of 780 nm. In addition, nonlinear scat-tering is also found to play an important role in solution at highexcitations.

Acknowledgment. This work is supported by the Ministryof Education Academic Research Funding through NationalUniversity of Singapore Grant Nos. R-143-000-255-112 andR-144-000-213-112. N.V. gratefully acknowledges the receiptof a research fellowship from the National University ofSingapore.

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