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Journal of Colloid and Interface Science 266 (2003) 377–381www.elsevier.com/locate/jcis

Size dependence of second-order optical nonlinearity of CdSnanoparticles studied by hyper-Rayleigh scattering

Yu Zhang,a,b Xin Wang,a Ming Ma,a,∗ Degang Fu,a Ning Gu,a Zuhong Lu,a Jun Xu,b

Ling Xu,b and Kunji Chenb

a National Laboratory of Molecular and Biomolecular Electronics, Southeast University, Nanjing 210096, People’s Republic of Chinab National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China

Received 8 November 2001; accepted 1 July 2003

Abstract

The second-order optical nonlinearity of CdS nanoparticles with different mean diameters of 28.0, 30.0, 31.5, 50.0, and 91.0 Å wby the incoherent hyper-Rayleigh scattering technique. Results show that the first-order hyperpolarizabilityβ value per CdS particle decreaswith decreasing size from 91.0 to 31.5 Å; however, as CdS particle size further decreases, this trend is reversed and theβ value increasesSubstantially, the normalized value of the first-order hyperpolarizability per CdS formula unit,β0, exhibits systematic enhancement wdecreasing size. This is interpreted in terms of a so-called surface contribution mechanism. The two aspects of quantum sizesize dependence of optical band-gap and oscillator strength, cannot be adopted to explain the size dependence of the second-nonlinearity of CdS nanoparticles. 2003 Elsevier Inc. All rights reserved.

Keywords: CdS nanoparticles; Hyper-Rayleigh scattering; Second-order optical nonlinearity; Size dependence; Surface contribution

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1. Introduction

In the field of semiconductor physics, considerable acity is dedicated to the study of quantum-confinement effein low-dimensional systems. Especially interesting arenonlinear optical properties of these structures, which mthem promising for various optical and electronic devicIn the past 20 years the third-order optical nonlineariof semiconductor nanoparticles have been widely stu[1,2]. And it has been demonstrated that the nonlineties are affected not only by particle size but also by sface structure, since nanoparticles are characterized bysurface-to-volume atom ratios. In contrast, only a few sties on the second-order optical nonlinearities of semicontor nanoparticles have been performed during recent yeZhang et al. [3–5] investigated the influence of nanopticle surface structure changes, involving the exchangsurface-capping ligands and the particle surface variatioaging of aqueous colloids, on the second-order nonlineties of CdS nanoparticles. It was indicated that the first-o

* Corresponding author.E-mail address: maming@seu.edu.cn (M. Ma).

0021-9797/$ – see front matter 2003 Elsevier Inc. All rights reserved.doi:10.1016/S0021-9797(03)00697-0

e

.

hyperpolarizability of nanoparticles is sensitive to surfaconditions. Santos et al. [6] studied the size dependencthe first-order hyperpolarizability of CdS nanoparticlesthree sizes. However, they explained the dependencethe viewpoint of the size dependence of nanoparticlecillator strength but ignored the contribution of the partisurface. In this work, we further study the size dependencthe second-order optical nonlinearity for CdS nanopartiof five sizes. The analysis shows that the surface contrtion to the size dependence has to be considered due tenhancement of the ratio of surface atoms to volume atand the inherent high noncentrosymmetry and high polaability of surface atoms for nanoparticles.

It should be indicated that the second-order optical nlinearity of nanoparticles can be studied owing to a powetool, the incoherent hyper-Rayleigh scattering (HRS) tenique, which is not constrained by orientational, size, ancharge restrictions compared with the conventional coent second harmonic generation (SHG) and electric-fiinduced SHG techniques. So far some experimental stu[3–5,7] have suggested that the surfaces of nanopartplay a crucial role in determining their second-order nlinear optical properties and therefore the HRS techniqu

378 Y. Zhang et al. / Journal of Colloid and Interface Science 266 (2003) 377–381

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expected to develop into a effective tool for the charactertion of nanoparticle surface.

2. Experimental

Using the reverse micelle method [8,9], CdS nanoticles modified by AOT–SO−3 (anion of surfactant of bi(2-ethylhexyl) sulfosuccinate, disodium salt) with meanameter 28.0, 30.0, and 31.5 Å were prepared, with contration of 1.67× 10−3 M calculated in terms of the CdS fomula unit. These nanoparticles are named CdS/AOT–S−

3CdS nanoparticles of mean diameter 50.0 Å were prepby a co-precipitation reaction between aqueous solutionCd(NO3)2 and Na2S in the presence of hexametaphosph(HMP) as stabilizer (named CdS/HMP, 5× 10−4 M) [10].For 91.0 Å CdS/HMP nanoparticles (cubic zinc blende strture), the first-order hyperpolarizability value is quoted frRef. [6], whose synthetic method and HRS experimeconditions are similar to those in our experiments.

The HRS experiments were performed using a setupilar to that in the literature [11]. The Q-switched Nd-YAlaser pulse (10 Hz, pulse width 8–10 ns) at 1064 nmfocused into a 5-cm-long glass cell with the pulse enelower than 3 mJ. The HRS signal was detected by a phmultiplier tube (PMT) at harmonic frequency using a 532interference filter with bandwidth 3 nm. The signal from tPMT was analyzed with a microprocessor-based boxcategrator (EG & G 4400, 4402) which is triggered by tQ-switch of the laser. To calibrate the experimental sewe utilized para-nitroaniline (p-NA) dissolved in chloro-form as a standard sample. The obtainedβ value ofp-NAwas 36.6× 10−30 esu, in satisfactory agreement with theerature value (34.5× 10−30 esu) [11].

3. Results and discussion

Figure 1 shows the absorption spectra of CdS/AOSO−

3 nanoparticles of three sizes and the 50.0 Å CdS/Hnanoparticles. As shown, a typical blue shift of the abso

Fig. 1. Absorption spectra of CdS colloids: a, b, c are the CdS/AOT–S−3

nanoparticles of mean diameter, 28.0, 30.0, and 31.5 Å, respectively, intane; d is the CdS/HMP nanoparticles of 50.0 Å mean diameter in wat

tion edges is clearly observed. From the absorption eof 380, 405, 420, and 477 nm, the mean diameters offour CdS nanoparticles were estimated to be 28.0, 331.5, and 50.0 Å, respectively, according to a finite depotential well model [12]. These results were in agreemwith TEM observations. Electronic diffraction experimeshowed that the four CdS nanoparticles have a cubicblende structure. In addition, the absorption spectrashow that the four CdS nanoparticles have negligible abstion for frequency-doubled light of 532 nm.

We use the internal reference method (IRM) to determtheβ value of nanoparticles. The intensity of the HRS sigfrom the sample cell is given by the equation [11]

(1)I2ω = G(N1

⟨β2

1

⟩ + N2⟨β2

2

⟩)(Iω)2,

whereIω is the incident intensity,I2ω the HRS intensityβ the first-order hyperpolarizability,N the number densitof each component, andG a constant parameter relatingcollection efficiencies and local field corrections. Subscr1 and 2 refer to solvent and solute, respectively.N1 is con-stant for low solute concentration andβ1 has been previouslestablished. The CdS particle number densityN2 was es-timated in terms of the CdS formula unit concentrationsolution divided by the mean agglomeration number of Cnanoparticles depending on their mean size. The meanglomeration number of CdS nanoparticles, i.e., the CdSmula unit number per particle, was calculated by the eqtion [13,14]

(2)n =(

4πr3

3

)(ρA

M

),

wherer is the mean radius of CdS nanoparticles,M the CdSformula unit molar weight (g/mol), ρ the density (g/cm3),andA the Avogadro number.

We previously studied the second-order optical nonlinities of the CdS/AOT–SO−3 [3] and CdS/HMP nanoparticle[10], including the HRS spectra, the quadratic powerpendence of HRS intensityI2ω on incident intensityIω, thelinear concentration relationship, and the influence offace modification and particle aggregation on HRS sigHere we mainly focus on the size dependence of the firsperpolarizability of CdS nanoparticles.

As predicted by Eq. (1), the linear dependencesthe HRS intensityI2ω on the CdS particle number desity N2 were obtained in Fig. 2 for the 28.0, 30.0, a31.5 Å CdS/AOT–SO−3 nanoparticles in heptane and 50.0CdS/HMP nanoparticles in water. Using heptane (β =0.61× 10−30 esu) and water (β = 0.56× 10−30 esu) as in-ternal standards, the “per particle”β values were evaluateto be 4.1× 10−27 esu, 4.0× 10−27 esu, and 3.5× 10−27 esufor the 28.0, 30.0, and 31.5 Å CdS/AOT–SO−

3 nanoparticlesand 13.3 × 10−27 esu for 50.0 Å CdS/HMP nanoparticleFigure 3a shows the size dependence of the first hypelarizability β value per CdS nanoparticle. It can be sethat theβ value reduces initially with decreasing particsize. However, as size is decreased to 31.5 Å, this tren

Y. Zhang et al. / Journal of Colloid and Interface Science 266 (2003) 377–381 379

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Fig. 2. The concentration dependence of the HRS intensity of CdS nanticles: a, b, c are the CdS/AOT–SO−

3 nanoparticles of mean diameter 28

30.0, 31.5 Å, respectively, in heptane; d is the CdS/HMP nanoparticlemean diameter 50.0 Å in water.

Fig. 3. The size dependence of the first-order hyperpolarizability pernanoparticle (a) and per CdS formula unit (b). The five CdS nanopartare CdS/AOT–SO−3 nanoparticles with mean diameter 28.0, 30.0, 31.5

and CdS/HMP nanoparticles with mean diameter 50.0, 91.0 Å.

reversed and theβ value increases. In Fig. 3, theβ value(72.4 × 10−27 esu) of 91.0 Å CdS/HMP nanoparticlesfrom Ref. [6].

Note that, due to similar structure between SO−3 and

PO−3 , we may ignore the influence of surface modific

tion on theβ value for the CdS/AOT–SO−3 and CdS/HMPnanoparticles. For the five CdS nanoparticles studied,cubic zinc blende crystal structure, as indicated above

noncentrosymmetric. From this, a bulk-like contributionsulting from the polarization of the individual cadmium sfide bonds should be considered. Hence, theβ value re-duces with decreasing particle size for CdS nanoparticlelarger sizes in Fig. 3a. However, for diameter� 31.5 Å CdSnanoparticles, the reverse change inβ values implies thathis bulk-like contribution becomes unimportant for smaCdS nanoparticles. This may be due to enhanced sucontribution for smaller nanoparticles with enhanced raof surface atoms to volume atoms.

To directly reflect the size dependence of the secoorder optical nonlinearity of CdS nanoparticles, the relatiship between size and normalized first hyperpolarizabvalue per CdS formula unit,β0 (β/n; n is CdS formula unitnumber per CdS particle), was obtained in Fig. 3b. A sstantial systematic enhancement inβ0 value with decreasing size is clearly observed. This is easily understood wconsidering a surface contribution mechanism and realithat nanoparticle surface atoms are inherently highly ncentrosymmetric and highly polarizable.

Before discussing the surface contribution, we first csider other possible contributions, quantum size effectsthe size dependence of the second-order optical nonlineof nanoparticles. Quantum size effects of nanoparticlesvolve two aspects: the size dependence of optical bandand of oscillator strength. We consider a two-level mobased on the optical band-gap of CdS nanoparticles [6],

(3)β0 ∝ 3µ212�µ12E

2op

2(E2op − E2

inc)(E2op − 4E2

inc),

whereβ0 is the first-order hyperpolarizability,Eop the elec-tronic transition energy, i.e., the optical band-gap,Einc theenergy of incident radiation,�µ12 the change in dipole moment between ground and excited states, andµ12 the transi-tion dipole moment.

Due to quantum size effects,Eop increases with decreaing CdS nanoparticle size. From Eq. (3),β0 decreases withincreasingEop. Henceβ0 reduces as CdS nanoparticle sdecreases, opposite to the observed size dependenceβ0.On the other hand,µ12 and�µ12 are proportional to the normalized oscillator strength per unit volume (f/V , f is thetotal oscillator strength per particle,V the volume of the particle), which increases with decreasing particle size duthe enhanced spatial overlap between the electron andwave functions [15]. This seems to lead toβ0 increasing withdecreasing particle size, in agreement with the experimeobservation. However, the size dependence of the norized oscillator strength for CdS is valid only when the Cparticle size is smaller than the Bohr diameter (60 Å) of bCdS. When the CdS particle size is much larger thanBohr diameter, the normalized oscillator strength is apprimately constant, becausef increases linearly withV [15].From the detailed work reported by Weller and co-workethe synthetic method of whose samples is similar tofor the samples of the 91.0 Å and 50.0 Å CdS nanopacles here studied, we conclude that the normalized oscil

380 Y. Zhang et al. / Journal of Colloid and Interface Science 266 (2003) 377–381

nt

Table 1The first-order hyperpolarizability of the CdS nanoparticles, their mean diameter, and their standard deviation estimated according to their synthetic methods

Sample D (Å) n C (M) N (cm−3) β (×10−27 esu) β0 (×10−30 esu)

1 28.0± 2.2 216±52 1.67× 10−3 (4.6±1.1)×1015 4.1± 0.5 19.0± 2.32 30.0± 2.4 265±64 1.67× 10−3 (3.8±0.9)×1015 4.0± 0.5 15.1± 1.83 31.5± 2.5 308±74 1.67× 10−3 (3.3±0.8)×1015 3.5± 0.4 11.4± 1.44 50.0± 6.5 1231±480 5× 10−4 (2.4±0.9)×1014 13.3± 2.5 10.8± 2.05 [6] 91.0 – – 1.8× 1013 72.4± 13.8 9.2± 1.7

Note. The CdS unit number(n) per particle is calculated by Eq. (2). The CdS formula unit concentration(C) is determined from the amount of reactaof Cd2+ or S2− (Cd2+:S2− = 1:1) and the error is negligible. The CdS particle number density(N) is calculated by the formulaN = CA/1000n (A theAvogadro number). The main error forβ is from the uncertainty in the determination ofN . The error ofN ± 24% for the sample 1–3 and ofN ± 39% for thesample 4 propagates to±12% and±19.5% error in the value ofβ, respectively.

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strength of the 91.0 Å CdS nanoparticles is not smaller tthat of the 50.0 Å CdS nanoparticles [16]. This will resin a nonmonotonic size dependence forβ0, which is not inagreement with Fig. 3b. Therefore, we conclude thatdependence of both the optical band-gap and the oscilstrength can be ruled out in the explanation of the obseincrease ofβ0 with decreasing CdS particle size.

Besides quantum size effects, another important feaof nanoparticles is the enhancement of the ratio of suratoms to volume atoms. For example, a 50.0 Å CdS nanoticle has∼15% of the atoms on the surface [15]. The extence of this vast surface can have a profound effect onphysical and chemical properties of nanoparticles. Mosthe nanoparticles synthesized so far have imperfect surfwhich may act as the source of the incoherent secondmonic generation (HRS). It has been shown that the secorder optical nonlinearity of CdS nanoparticles is stronaffected by surface structure changes [3–5]. In fact, surtermination of the crystalline lattice creates discontinusurface structure due to surface dangling bonds, surfactice constriction, and surface defects (dislocations, vacies, and so on). These lead to surface or defect-loca“molecule-like” scatterers (Cd–S polar bonds) being hignoncentrosymmetric and highly polarizable [5,17]. Escially, the surface defects can localize electrons or hin CdS nanoparticles, resulting in inhomogeneities of etronic distribution of the whole CdS nanoparticle. In adtion, the high-resolution transmission electron microsc(HRTEM) studies have demonstrated that the CdS nanoticles with the cubic blende structure are asymmetric polydra with nearly flat surfaces [18,19]. The blende lattice aimplies that the nanoparticle surfaces will not have inverssymmetry. As a result, the HRS signals on opposite sitenanoparticle surfaces cannot be canceled out complete

From the above analysis, it can be seen that theface atoms make an important contribution to the HRSnal. With decreasing CdS nanoparticle size, the ratiosurface atoms to volume atoms increases, resulting inhanced contribution toβ0. In addition, it has been showthat the electronic distribution on the nanoparticle surfacmore easily localized by surface defects for smaller nanoticles [17,20], leading to enhanced asymmetry of surfelectronic distribution, which is helpful for increasingβ0.

r

-

,--

-

-

-

Hence,β0 increases with decreasing CdS nanoparticle sand the enhancement inβ0 value becomes more obvioufor nanoparticles of smaller size. Previously, theβ0 valueper CdS formula unit for bulk CdS was estimated to1.3 × 10−30 esu according to the known value of the bunonlinear coefficient [6]. Thisβ0 value is 7.1 times smallethan that of the 91.0 Å CdS nanoparticles and 12.8 tismaller than that of the 28.0 Å CdS nanoparticles. Oously, these comparisons also provide evidence for theface contribution mechanism above.

Findings are summarized in Table 1.

Acknowledgments

This work was supported by the National Science Fodation of China (No. 50202009, 10074023) and the NatioPostdoctoral Foundation (No. 2002031222).

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