VOLUME 104, NUMBER 1, JANUARY 13, 2000
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LETTERS Size Dependence of Second Harmonic Generation in CdSe Nanocrystal Quantum Dots Michal Jacobsohn and Uri Banin* Department of Physical Chemistry and the Farkas Center for Light-Induced Processes, The Hebrew UniVersity, Jerusalem 91904, Israel ReceiVed: July 21, 1999; In Final Form: October 15, 1999
Second harmonic generation in CdSe nanocrystal quantum dots is observed by Hyper-Rayleigh scattering. The size dependence of the first hyperpolarizibility β was investigated for the nanocrystals in solution. The value of β per nanocrystal decreases with size down to approximately 13 Å in radius. An increase is observed with further size reduction. The unit cell normalized second harmonic coefficient, β, shows a substantial systematic enhancement in small diameters. The observed size dependence of the second harmonic generation is explained assuming two contributions. The first is a bulklike contribution, from the noncentrosymmetric nanocrystal core, and the second, a contribution from the nanocrystal surface. The latter contribution is most significant in small nanocrystals with a substantial proportion of surface atoms. This result suggests that the second harmonic generation technique may be used as a probe of nanocrystal surfaces, in analogy to its common use as a probe of bulk surfaces.
Introduction Semiconductor nanocrystals manifest the transition from the molecular regime to the solid state.1 In recent years, optical techniques have been used to investigate the size dependence of linear and third-order optical nonlinearities in nanocrystals in relation with the effects of quantum confinement.2-4 Secondorder optical nonlinearities of the nanocrystals have received much less attention.5 In this letter we investigate the size effect on second harmonic generation (SHG) of CdSe nanocrystals. The nonlinear polarization response of a molecule, can be expanded as a power series of the inducing optical field strength E6
P ) R ‚ E + β: EE + γlEEE+...
(1)
where R is the linear polarizibility, and β is the first hyperpolarizibility, which determines the second-order optical nonlinearity. In chromophores such as paranitroaniline, the asymmetry * Corresponding author. E-mail:
[email protected].
of the molecular structure is the primary source of the secondorder optical nonlinearity.7 On the other hand, in solid-state nonlinear inorganic materials such as potassium titanyl phosphate (KTP), the second-order nonlinear response is typically related to individual bond polarizabilities. The nanocrystals investigated here represent the intermediate regime between these two cases in the sense that they can be viewed as a class of large molecules, composed of a limited number of bulklike unit cells. An additional feature of the nanocrystal size regime, with possible significance for their second-order nonlinear optical response, is the enhancement of the ratio of surface atoms to volume atoms. SHG is forbidden in centrosymmetric media within the dipole approximation.6 But at an interface, the centrosymmetry intrinsically brakes. As a result, second-order nonlinear optical spectroscopies such as second harmonic generation, have found widespread utility as probes of bulk surfaces and interfaces.8,9 Eisenthal and co-workers have recently demonstrated the expansion of this capability to probe surfaces of micron and submicron-sized particles.10,11 In the even smaller
10.1021/jp9925076 CCC: $19.00 © 2000 American Chemical Society Published on Web 12/04/1999
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Figure 1. Left frame: Absorption spectra for the seven CdSe nanocrystal samples with the following average radii: (I) 45 Å, (II) 28 Å, (III) 23 Å, (IV) 17 Å, (V) 13.5 Å, (VI) 12 Å, (VII) 11.5 Å. The left arrow depicts the energy of the inducing laser light, and the right arrow depicts the second harmonic energy. Right frame: Representative HRS spectra at various excitation intensities ranging between 0.05 and 0.6 W, for the largest nanocrystal sample with radius of 45 Å showing a well-defined peak at the second harmonic frequency 2ω.
nanocrystal size regime that we investigate here, the surface contribution to the second-order nonlinear optical response may also be important. This is particularly interesting since the smallness of size of the nanocrystals compared to the wavelength of light suggests that there may be a cancellation of the surface contribution due to the symmetry of the particles. Cancellation can be expected for high-symmetry shapes, such as a sphere, which have inversion symmetry. In this letter, we report on a systematic study of SHG from CdSe nanocrystals versus the size, and investigate both bulklike and possible surface contributions to their second-order nonlinear optical response. Experimental Section CdSe nanocrystals were synthesized by a solution-phase pyrolytic reaction of organometallic precursors.12 The wurtzite crystals have mean radii ranging from 10 to 50 Å with standard deviation of ∼5 to 10% and are slightly prolate (aspect ratio is size dependent13). Organic ligands (trioctylphosphine oxide, TOPO) on the nanocrystal surface prevent their aggregation and confer their solubility in common organic solvents. Figure 1, left frame, displays the absorption spectra for the samples investigated in this work measured by a standard absorption spectrometer (Shimadzu, UV1601). The samples span a size range between 45 and 11 Å in radius, and the typical linear quantum confinement related blue shift and the appearance of discrete states is clearly observed. To measure β, we used the Hyper-Rayleigh scattering technique (HRS).14 A 1 cm four-sided cuvette containing the solution with the nanocrystals at varying concentrations (solvent is toluene) was irradiated by a continuous wave mode-locked femtosecond Ti-Sapphire laser at 820 nm (Coherent Mira). The pulse width was measured by auto-correlation, and was determined to be 120 fs. The laser was vertically polarized, and the excitation intensity was controlled using a circular neutral density filter with varying optical density. The typical range of irradiated intensities was 0.05-0.6 W, as measured by a power
Letters meter, focused to a spot size of 0.5 mm. The scattered second harmonic signal was collected at right angle, filtered with a short pass filter to suppress the fundamental light, dispersed using a monochromator (Acton, 300i), and detected with a liquid nitrogen cooled CCD detector (Princeton Instruments). The nanocrystal concentrations were calculated from the optical densities of the solutions. The molar extinction coefficient, , for each size, was determined by a set of measurements of optical density, for quantitatively diluted solutions of nanocrystals of measured weight. The nanocrystals were reprecipitated by methanol to remove excess TOPO from their powders. Three to four repetitions of this kind of measurement were carried out for each size to reduce the error. The molar weight for each size was calculated using the radius of the nanocrystals, summing the mass of the CdSe units and of the TOPO ligands on the nanocrystal surface. The primary source of error in our measurements is the uncertainty in the mass of the TOPO ligands on the nanocrystal surface, which becomes a substantial portion of the total mass in the smallest particles. We assumed that half of the surface atoms are bound to TOPO,15,16 and based on the variations of our repeated measurements we estimate the uncertainty in the determination of to be (20%. Results and Discussion In all the CdSe nanocrystal samples that we studied, as depicted in Figure 1, the fundamental inducing laser wavelength (820 nm), is below the band gap, while the second harmonic (410 nm) is in deep resonance with highly excited transitions. Upon 820 nm excitation, we observed intense two-photon excited luminescence similar to the typical (mostly band gap) luminescence of the nanocrystal samples.3,17 The luminescence intensity was found to depend quadratically on the intensity of the inducing field I(ω), as expected for a two-photon excited process. In the right side of Figure 1, we show the collected signal at the higher energy range for the largest CdSe sample with radius of 45 Å, for several representative excitation intensities. We observed a peak at the second harmonic frequency, at 410 nm, well separated from the luminescence signal and over 2 orders of magnitude weaker. Unlike the luminescence peak, this peak shifted in frequency upon changing the frequency of the inducing laser. The intensity dependence of this second harmonic signal, I(2ω), on the intensity of the induced field I(ω) is presented in Figure 2 (inverted triangles). Good agreement to a quadratic fit is observed (solid line, e). In the incoherent HRS method that we are using, the contribution of solvent and solute to the SHG signal can be written14,18
I(2ω) ) G (NS〈β2HRS〉S + Nn〈β2HRS〉n) I(ω)2
(2)
The SHG response, I(2ω), depends quadratically on the intensity of the inducing optical field I(ω), with G a geometrical factor that also includes the contribution of local field factors. NS, Nn represent the number concentrations of solvent and solute molecules, respectively. 〈β2HRS〉S, and 〈β2HRS〉n are the squares of the first-order hyperpolarizibilities of the solvent and solute respectively, and the parentheses represent the geometrical averaging of their tensorial elements over the isotropic distribution of angular orientations of the molecules in solution. An advantage of the HRS technique, over alternative methods for determining β.19,20 is that the solvent itself can be used as an internal reference to determine the absolute value of βn.18
Letters
Figure 2. Intensity dependence of I(2ω) on I(ω) for five solutions with varying concentration of the nanocrystals for the sample with radius of 45 Å. Nanocrystal concentrations are (a) neat toluene, (b) 0.33 × 1014 cm-3, (c) 0.51 × 1014 cm-3, (d) 0.68 × 1014 cm-3, (e) 1.1 × 1014 cm-3. The solid lines are quadratic fits for the dependence of I(2ω) on I(ω). Inset: Quadratic coefficients extracted from the intensity dependence for the 5 solutions, versus the number concentration of the nanocrystals, corrected for the internal absorption of the second harmonic signal as described in the text. The solid line is a fit according to eq 2.
To extract the value of βn for the 45 Å sample, we carried out intensity dependence measurements of I(2ω) versus I(ω) using identical experimental conditions, for four nanocrystal solutions with varying concentrations and for the neat toluene. The results are presented in Figure 2. For each concentration the data is well represented by a quadratic fit of the dependence of I(2ω) on I(ω) depicted by the solid lines. The slopes of the parabolas were extracted and are plotted in the inset of Figure 2 versus the number density of nanocrystals. Using the measured optical density at 410 nm and the distance of the laser beam from the cuvette edge, we corrected the second harmonic response for the internal absorption effect of the 410 nm signal, using the Beer-Lambert law. A linear dependence is clearly observed following the expected behavior from eq 2. Similar measurements were carried out for the other six nanocrystal sizes. For all samples, we measured the dependence of I(2ω) on I(ω) for 4-5 nanocrystal concentrations and for neat toluene. The quadratic dependence of I(2ω) on I(ω) was always observed. Figure 3 shows the extracted quadratic coefficients for all the sizes after correction for the internal absorption effect, versus the number concentration of the nanocrystals. For each size, this dependence was fit by a straight line, as predicted by eq 2. The data sets for each size, were normalized by the measured quadratic coefficients of neat toluene assuming a value of unity for βs. The slopes of the straight lines vary considerably with the nanocrystal size reflecting the size dependence of βn. The relative βn values for the CdSe nanocrystals were extracted as the square root of the slopes of the graphs (eq 2), and their size dependence is plotted in Figure 4. In part A, we show the value of βn per nanocrystal. The dependence is nonmonotonic. Upon decreasing the radius from 45 to 13.5 Å, βn decreases, while below 13.5 Å, βn increases. This behavior can be rationalized considering two possible contributions to
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Figure 3. Dependence of the quadratic coefficients, corrected for the internal absorption effect, on the nanocrystal concentrations for the seven sizes studied, with the following radii: (I) 45 Å, (II) 28 Å, (III) 23 Å, (IV) 17 Å, (V) 13.5 Å, (VI) 12 Å, (VII) 11.5 Å. The solid lines are linear fits according to eq 2. The dashed line represents the dependence for the sample with radius of 45 Å, shown in Figure 2. The intercepts represent the contribution of the neat solvent, toluene, which is a common point used to normalize the SHG response for all sizes. We assumed unity value for βs of toluene.
the second harmonic response of the nanocrystals. First, a bulklike contribution resulting from the noncentrosymmetric wurtzite structure, and second, a contribution from the nanocrystal surface. The source of the bulklike contribution is the polarizibility of the individual cadmium selenide bonds. At first approximation, this contribution is expected to scale linearly with the number of unit cells, i.e., with the volume of the nanocrystal. To account for this volume dependence of βn, we divided its values by the number of unit cells in each nanocrystal size and obtained β, the per unit cell normalized value of the hyperpolarizibility. Figure 4b displays the size dependence of the normalized β. This graph, excludes the “trivial” size dependence of the bulk contribution. A substantial enhancement of β for the small nanocrystals is seen. An empirical fit shows that the scaling of the dependence in the small sizes is very strong, approximately as 1/r6. Before discussing the possible sources of the observed size dependence, we comment on the absolute value of βn. For this we use the reported value for βs for the solvent toluene at 1.06 µm, 0.18 × 10-30 esu.20 After correction to the wavelength of our measurements, we deduce the value of βs as 0.25 × 10-30 esu at 820 nm. For a nanocrystal of an intermediate size, e.g., radius of 23 Å, the value of βn is thus 1000 × 10-30 esu. In comparison, the value of β for paranitroaniline in methanol is 36 × 10-30 esu.21 The large value of βn, compared with values of nonlinear organic chromophores, results primarily from the large number of unit cells in nanocrystals of this size, but the above comparison is useful for appreciating its absolute magnitude. The significant increase of β in the small nanocrystals is consistent with a contribution of the surface to the second harmonic response, in line with the enhanced surface-to-volume ratio. But before reinstating this conclusion, we first consider other factors that may contribute to the size dependence in the second harmonic generation process from the nanocrystals.
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Letters β, we mention that the band gap optical transition in CdSe can be viewed in first approximation as a charge-transfer excitation from the Se (4p) atomic orbital to the Cd (5s).3 We used the two-level model, which assumes that the nonlinear optical properties of the chromophore are governed by a ground state and a low-lying charge-transfer excited state.22 In this model, β depends on
ωeg/[(ω2eg - ω2)(ω2eg - 4ω2)]
Figure 4. Size dependence of the SHG response from CdSe nanocrystals. Frame A shows on a log scale, the size dependence of βn, the value of the hyperpolarizibility per nanocrystal which decreases as size is decreased to radii of 13.5 Å. For the smallest radii, this trend is reversed and βn increases. Frame B depicts the size dependence of the normalized value of the hyperpolarizibility per unit cell, β, which shows significant systematic enhancement for small sizes. The primary contributions to the error bars is the uncertainty in the determination of nanocrystal concentrations from the measured extinction coefficients as discussed in the Experimental Section. A (20% error in propagates to (10% error in the values of βn.
First, SHG can be enhanced by resonance of the inducing frequency ω, or of the second harmonic frequency 2ω, with an electronic transition.6 In the present case, the band gap energy, Eg, of all studied samples is substantially higher than ω, i.e., nonresonant. The observed enhancement is actually opposite to the expected trend for the resonance enhancement since the separation between ω and Eg increases as size is reduced. The second harmonic frequency, 2ω, also lies far from Eg, and is in deep resonance with high excited transitions in all our samples. Thus, we do not expect substantial size dependence related to this factor. To further investigate the possible contribution of the resonance enhancement to the observed size dependence of
with ω the inducing field frequency, and ωeg the frequency of the optical transition which we take as Eg, the size-dependent particle band gap. We found that the relative resonance enhancement factor is reduced by approximately 30% in the smallest nanocrystals relative to the largest ones, opposite to the observed dependence of β on nanocrystal size. We conclude that resonance effects can be ruled out in the explanation of the observed enhancement of β in small sizes. This conclusion is further supported by our observation that in the smallest sizes, a substantial enhancement of β is observed, while the shift of Eg is small. Second, SHG can also be enhanced by the presence of a dipole moment. This effect has been investigated for molecular nonlinear chromophores.22 In CdSe nanocrystals, there has been a report on existence of a dipole moment.23 The dependence on size was reported for two radii, and in the larger nanocrystals, a bigger dipole moment was observed. This trend is again opposite to our observation of an enhanced β in the small nanocrystals. The above discussion leaves us with the surface contribution as the only plausible mechanism for the observed enhancement of β in small nanocrystals. In the smaller radius particles, a substantial proportion of the atoms are on the surface. As an illustration of this point, we note that a nanocrystal with radius of 45 Å, has a total of 13500 atoms with 2200 surface atoms, while a nanocrystal with radius of 11 Å, has a total of 240 atoms, with 130 surface atoms. Several mechanisms may contribute to the observed enhancement. First, the electron distribution around surface atoms is inherently highly noncentrosymmetric. The CdSe nanocrystals are slightly prolate, and have faceted surfaces.24 The wurtzite lattice implies that the nanocrystal surfaces will not have inversion symmetry. As a result, the surface contributions to the SHG do not necessarily cancel in this case. Another source for the enhanced surface contribution may be the surface polarization instability of the electron and hole in the quantum dot.25,26 For a small quantum dot with a finite barrier within a dielectric medium, the heavier hole was predicted theoretically to have an enhanced probability of presence at the surface. This leads to stronger electron-hole charge separation in small nanocrystals, also possibly contributing to an enhanced nonlinear optical response. Finally, imperfect surface passivation15,16 is an additional possible source for the enhancement of the SHG response in small nanocrystals. In particular, dangling orbitals of unpassivated sites on the nanocrystal surface are highly polarizable and this may contribute substantially to the second-order nonlinear signal. Conclusions We investigated the size dependence of second harmonic generation in CdSe nanocrystals using the Hyper-Rayleigh scattering method. β, the normalized per-unit cell value of the first hyperpolarizibility, exhibited substantial enhancement in small nanocrystals. The observed behavior reveals two contributions to the SHG signal. The first, a bulklike portion which scales
Letters as the nanocrystal volume, and the second, a surface contribution. The surface contribution dominates the signal for the smallest nanocrystals. In future work, we will directly test the effects of nanocrystal surface modification via ligand exchange, on the SHG response. Our observations suggest that the SHG technique can be used to probe surface processes in nanocrystals in a manner analogous to its application as a surface probe in bulk materials. Acknowledgment. This research was supported in part by the Israel Science Foundation founded by the Israel Academy of Sciences & Humanities, and by a grant from the JamesFranck program. The Farkas Center for Light-Induced Processes is supported by the Minerva Gesellschaft fu¨r Forschung of the German Ministry for Research and Technology (BMFT). U.B. thanks the Israeli Board of Higher Education for an Alon fellowship. References and Notes (1) Alivisatos, A. P. Science 1996, 271, 933. (2) Brus, L. E. Appl. Phys. A 1991, 53, 465. (3) Norris, D. J.; Bawendi, M. G., Brus, L. E. In Molecular Electronics; Jortner, J., Ratner, M., Eds.; Blackwell Science: Oxford, 1997; Chapter 9. (4) Banin, U.; Lee, J. C.; Guzelian, A. A.; Kadavanich, A. V.; Alivisatos, A. P.; Jaskolski, W.; Bryant, G. W.; Efros, A. L.; Rosen, M. J. Chem. Phys. 1998, 109, 2306. (5) Aktsipetrov, O. A.; Elyutin, P. V.; Fedyanin, A. A.; Nikulin, A. A.; Rubtsov, A. N. Surf. Sci. 1995, 325, 343. (6) Shen, Y. R. The Principles of Nonlinear Optics; Wiley: New York, 1984.
J. Phys. Chem. B, Vol. 104, No. 1, 2000 5 (7) Prasad, P. N.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules and Polymers; Wiley: New York, 1991. (8) Richmond, G. L.; Robinson, J. M.; Shannon, V. L. Prog. Surf. Sci. 1988, 28, 1. (9) Eisenthal, K. B. Chem. ReV. 1996, 96, 1343. (10) Wang, H.; Yan, E. C. Y.; Borguet, E.; Eisenthal, K. B. Chem. Phys. Lett. 1996, 259, 15. (11) Wang, H.; Yan, E. C. Y.; Liu, Y.; Eisenthal, K. B. J. Phys. Chem. B 1998, 102, 4446. (12) Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993, 115, 8706. (13) Efros, A. L.; Rosen, M.; Kuno, M.; Nirmal, M.; Norris, D. J.; Bawendi, M. G. Phys. ReV. B 1996, 54, 4843. (14) Clays, K.; Persoons, A. ReV. Sci. Instrum. 1994, 65, 2190; ibid. 1992, 63, 3285. (15) Katari, J. E. B.; Colvin, V. L.; Alivisatos, A. P. J. Phys. Chem. 1994, 98, 4109. (16) Becerra, L. R.; Murray, C. B.; Griffin, R. G.; Bawendi, M. G. J. Chem. Phys. 1994, 100, 3297. (17) Schmidt, M. E.; Blanton, S. A.; Hines, M. A.; Guyot-Sionnest, P. Phys. ReV. B 1996, 53, 12629. (18) Clays, K.; Persoons, A. Phys. ReV. Lett. 1991, 66, 2980. (19) Kurtz, S. K.; Perry, T. T. J. Appl. Phys. 1968, 39, 3798. (20) Levine, B. F.; Bethea, C. G. J. Chem. Phys. 1975, 63, 2666. (21) Chemla, D. S.; Zyss J. Nonlinear Optical Properties of Organic Molecules and Crystals; Vol. 2; Academic Press: Orlando, 1987. (22) Oudar, J. L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664. (23) Blanton, S. A.; Leheny, R. L.; Hines, M. A.; Guyot-Sionnest, P. Phys. ReV. Lett. 1997, 79, 865. (24) Shiang, J. J.; Kadavanich, A. V.; Grubbs, R. K.; Alivisatos, A. P. J. Phys. Chem. 1995, 99, 17418. (25) Brus, L. E. J. Chem. Phys. 1984, 80, 4403. (26) Banyai, L.; Gilliot, P.; Hu, Y. Z.; Koch, S. W. Phys. ReV. B 1992, 45, 14136.
