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Study of Surface Plasmon Induced Hot Electron Relaxation Process and Third-Order Optical Nonlinearity in Gold Nanostructures Hong-Wei Dai,† Ying Yu,† Xia Wang,‡ Zong-Wei Ma,† Cheng Chen,† Zhang-Kai Zhou,§ Jun-Bo Han,*,† Yi-Bo Han,*,† Shao-Ding Liu,¶ and Liang Li† †

Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China ‡ Wenhua College, Wuhan, 430074, People’s Republic of China § State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-Sen (Zhongshan) University, Guangzhou 510275, People’s Republic of China ¶ Taiyuan Univ Technol, Minist Educ, Key Lab Adv Transducers and Intelligent Control Sys, Taiyuan 030024, People’s Republic of China S Supporting Information *

ABSTRACT: The relaxation dynamics of hot electrons and the third-order optical nonlinearity in gold nanorods (GNRs) with different aspect ratios were investigated with the help of femtosecond optical Kerr (OKE) technique. Relaxation process on the time scale of picosecond (ps) was obtained at the longitudinal surface plasmon resonant (SPR) wavelength. As the aspect ratio (AR) of the GNRs varied from 4.2 ± 0.3 to 3.3 ± 0.3, the SPR wavelength changed accordingly from 808 to 750 nm, but the corresponding relaxation time and the third-order optical susceptibility did not change much. However, as the pump power increased from 150 mW to 400 mW, the relaxation time of the nanorod with AR = 4.2 ± 0.3 increased by 50% from 1.20 ± 0.01 ps to 1.84 ± 0.04 ps, indicating that the pump power is an important factor that affects the response time of the nanostructures. Comparative studies between Au nanorods, Au nanobipyramids, and Au triangular prisms measured under the same setup demonstrated that excitation conditions (excitation wavelength or pump power) and structure shapes were key factors to modulate the relaxation time of hot electrons. These results are important for the control and modulation of the response time in metallic nanostructures, which is essential for their applications in photovoltaic, photocatalytic, and ultrafast optic devices.

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enhanced by the local electric field enhancement induced by the surface plasmon resonances in metallic nanostructures. Then, the generated surface plasmon resonances transfer their energy to the electrons through Landau damping. These energized electrons redistribute their energy through a threestep relaxation process. First, a Fermi−Dirac-like distribution is formed in less than 1 ps through electron−electron (e-e) scattering. Second, the electron−phonon (e-ph) interaction grows stronger with the reduction of electron velocity, and the metal lattice is heated in this process lasting for several picoseconds. In the final step, energy in the form of heat is propagated to the surroundings of the metallic structure through a phonon−phonon (ph-ph) interaction process which takes a time span of hundreds of picoseconds to tens of nanoseconds, depending on the material, the particle size, and the thermal properties of the environment.24 Although some

INTRODUCTION Noble metallic nanostructures have been widely applied in plasmonics,1−8 ultrafast optics,9−12 and photovoltaic devices13,14 because of their outstanding properties in surface plasmon resonance (SPR) absorption, third-order optical susceptibility, and ultrafast response time. Many works have been done in design, fabrication, characterization, and photonic and biochemical applications of the plasmonic structures, and great achievement has been obtained.15−23 Recently, the fast development of plasmon-induced hot carrier science and technology demonstrate that the time scale of the hot carriers’ responses plays a fundamental role in determining the energy distribution, energy transferring, and reaction activities of the hot carriers-based devices. Therefore, experimental determination and modulation of the hot carrier relaxation time scales are of particular importance for their applications in photovoltaic, photocatalytic, and ultrafast optics.24,25 The generation and the decay behavior of hot carriers have been extensively studied theoretically.24−29 Generally, hotelectron generation is started from the absorption of light and is © 2015 American Chemical Society

Received: September 6, 2015 Revised: November 6, 2015 Published: November 6, 2015 27156

DOI: 10.1021/acs.jpcc.5b08695 J. Phys. Chem. C 2015, 119, 27156−27161

Article

The Journal of Physical Chemistry C

Figure 1. (a) TEM image of GNR with AR of 4.2 ± 0.3. (b) Absorption spectra of GNR with different ARs. The longitudinal surface plasmon resonant (LSPR) peak positions of the three samples with AR = 3.3 ± 0.3, 3.8 ± 0.3, and 4.2 ± 0.3 are 750, 780, and 808 nm, respectively. The different positions of the LSPR peaks for the three samples indicate that the average lengths of the GNRs are different. (c) Electric-field distribution of GNR with AR of 4.2 ± 0.3. (d) Charge distribution of GNR with AR of 4.2 ± 0.3.

well as the third-order optical nonlinearities was performed by using femtosecond (fs) OKE technique.35,37 In the OKE setup, a Ti:sapphire laser (Coherent, Mira 900) with output pulse duration of 130 fs and repetition rate of 76 MHz was used as light source. The laser beam was divided into two branches for pumping and probing. The polarization angle between the two beams was set as 45°. The pump beam passed through a delay line and then was focused with the probe beam at the same point within the sample solution which was 1 mm thick in a quartz cuvette. The optical Kerr signal recorded after the polarization analyzer was detected by a photodiode. A lock-in amplifier equipped with a dual slots chopper was used to improve the signal-to-noise ratio of the system (see Figure S2).

works have been carried out to investigate the relaxation processes of metallic nanostructures,29−32 few works have been done to control and modulate the relaxation processes. Gold nanorod (GNR) is a good candidate for various kinds of plasmon-related investigations for the reason that it has strong SPR absorption, tunable SPR peak position, and controllable rod size and morphology, which are essential for comparative studies. In this work, GNRs with different aspect ratios (ARs) and different diameters were selected for the investigations of the relaxation dynamics of hot electrons and the corresponding third-order optical susceptibility using optical Kerr effect (OKE) technique.33 Comparative studies in different kinds of nanostructures, including nanorods, nanobipyramids, and nanotrianglar prisms, were also taken to figure out the key factors for modulating and controlling the response time of nanostructures. Then, the results were discussed and summarized.

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RESULTS AND DISCUSSION

GNR samples with diameters of 20 ± 2 nm and ARs of 3.3 ± 0.3, 3.8 ± 0.3, and 4.2 ± 0.3 (GNR-1) as well as the nanorod with diameter of 10 ± 1 nm and AR of 4.3 (GNR-2) have been used in our experiment. TEM images for all the samples have been obtained, but only one typical TEM image for the sample with AR = 4.2 ± 0.3 was demonstrated for simplicity. As shown in Figure 1a, the sample is rod shape with semispheres at both ends, and the diameter is about 20 ± 2 nm. For nanorods with different ARs, the diameters are almost the same, while the average length varies from 66 to 84 nm. The absorption spectra of these three samples are shown in Figure 1b. Two absorption bands arising from the transverse and longitudinal surface plasmon resonant (TSPR and LSPR) absorptions of the nanorods can be clearly observed around 515 and 800 nm, respectively. By tuning the AR of the nanorods, a shift of the LSPR peak position can be clearly observed, and the LSPR peak

EXPERIMENT

The GNR aqueous samples used in the experiment were prepared by seed-mediated growth method with the use of aromatic additions in addition to cetyltrimethylammonium bromide (CTAB).34 The photothermal stability of the samples were tested by comparing the absorption spectra taken before and after a long time of laser irradiation with laser power of 400 mW, and the results demonstrate that no clear change can be observed (see Figure S1). Transmission electron microscopy (TEM) images were acquired by using an FEI Tecnai Spirit microscope. Optical absorption spectra were recorded through a UV−vis−NIR spectrophotometer (Hitachi U-3501). The relaxation response time of plasmon-induced hot electrons as 27157


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the biexponential decay function can fit them well. To get the real origin of the two different response processes, comparative OKE measurements were taken in the identical quartz cell that had been used in the GNR solution measurements with and without pure deionized water. The results demonstrated that both the quartz cells with and without deionized water have the same fast quasi-periodic oscillation signals which are very similar to those obtained from the GNRs samples with quartz cells, see Figure 2a and b. This means that the fast process from the samples comes from the quartz cell and not from the GNRs themselves. After removing the influence of the quartz cell’s signal, a perfect single exponential decay curve was obtained, as shown in Figure 2c. Then, the decay curves could be fitted according to the equation I(t) = Ae(−t/τ), where A is the amplitude which relates to the OKE intensity, and τ is the corresponding decay time which is related to the relaxation of hot electrons in the nanostructures. The results show that this decay signal lasts for several picoseconds and can be attributed to the destruction of the transient grating induced by the electron−phonon (e-ph) scattering.37 The fast signal from the quartz cells originates from the coherent phonon vibrations excited by the femtosecond laser.38 The third-order optical nonlinear susceptibility χ(3) of the sample can also be extracted from the same data in Figure 2. To get the absolute values of χ(3) in the samples, the reference OKE signals in CS2 were aslo obtained under the same experimental conditions (see Figure S3). The calculation function for χ(3) in Au nanorod solution samples is expressed as follows:

positions for the three GNRs are located around 750, 780, and 808 nm, respectively. The electric field distribution of the LSPR mode and the charge density of the sample with AR = 4.2 ± 0.3 were calculated by using finite difference-time domain (FDTD) simulation and are represented in Figure 1c and d, respectively. A maximum electric field enhancement can be obtained at the LSPR peak position wavelength and higher charge density located at the ends of the nanorod. The response curves of the three samples measured at their corresponding LSPR peak wavelengths are shown in Figure 2a. The pump power was set to 300 mW. The dots are experimental data, and the solid lines are guides to the eyes. From the figure, two different response processes can be clearly observed. However, neither the exponential decay function nor

I n l χs(3) = χr(3) ( s )1/2 ( s )2 r f (α) Ir nr ls

(1)

where the subscripts s and r represent the signals from the Au nanorod solution samples and the references, respectively. Is, ls, ns and Ir, lr, nr refer to the intensities of OKE signals, the interaction lengths, and the refractive indexes of the GNR solution samples and CS2 reference, respectively. Also, f(α) is the absorption correction factor of Au nanorod solution: f (α ) =

(1 − e

αl t −αl t

)e−αl t /2

(2) 1

( ) is the

where lt is the thickness of the sample and α = − l ln t

I I0

linear absorption coefficient, which is calculated to be 0.31, 0.30, and 0.28 mm−1 for the three samples with AR = 3.3 ± 0.3, 3.8 ± 0.3, and 4.2 ± 0.3 measured in our experiment, respectively. The parameter values for the reference (CS2) are −13 nr = 1.6 and χ(3) esu at 800 nm. In addition, lr/ls = r = 1.0 × 10 1, and Is/Ir of the three samples is obtained as 2.2, 2.0, and 2.2 from the experimental data, where the influences of the quartz cells have been excluded. Therefore, the third-order nonlinear optical susceptibilities at their corresponding LSPR peaks are calculated and listed in Table 1. From the table, one can see that both the third-order optical susceptibilities and the figures of merit for the three GNRs are very close, indicating that the change of AR from 3.3 ± 0.3 to 4.2 ± 0.3 does not affect much about the third-order optical susceptibilities of GNRs. The relaxation times (τ) for nanorods with different ARs are also given in Table 1. As shown in the table, the relaxation time remains about 1.7 ps as the AR changes from 3.3 ± 0.3 to 4.2 ± 0.3. This demonstrates that the increase of the nanorod length (diameter = 20 ± 2 nm) does not affect the e-ph coupling of

Figure 2. (a) Femtosecond time-resolved OKE signals of the GNRs with different ARs. The dots are experimental data, and the solid lines are guides to the eye. The incident wavelengths are centered at their LSPR peaks which are 750, 780, and 808 nm for AR = 3.3 ± 0.3, 3.8 ± 0.3, and 4.2 ± 0.3, respectively. The pump power was set to 300 mW. (b) Typical OKE data of the empty quartz cell. (c) Calibrated OKE signal of the GNR aqueous solution with different ARs by removing the influence of quartz cell. 27158


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Table 1. Third-Order Optical Susceptibility χ(3), the Figure of Merit, and Response Time τ for Au Nanorods with Different ARsa samples GNR-1 (AR = 3.3 ± 0.3) GNR-1 (AR = 3.8 ± 0.3) GNR-1 (AR = 4.2 ± 0.3) a

χ(3) (esu)

wavelength (nm)

−13

1.6 × 10 1.5 × 10−13 1.5 × 10−13

750 (on resonance) 780 (on resonance) 808 (on resonance)

χ(3)/α (esu·cm)

τ (ps)

5.1 × 10−14 4.9 × 10−14 5.3 × 10−14

1.70 ± 0.02 1.70 ± 0.02 1.69 ± 0.02

The pump power is fixed at 300 mW.

Table 2. Comparative Results of Wavelength-Dependent Response Times for Different Au Nanostructuresa λ1 and τ1

samples GNR-2 (d = 10 ± 1 nm) GNR-1 (AR = 3.3 ± 0.3) GNR-1 (AR = 3.8 ± 0.3) GNR-1 (AR = 4.2 ± 0.3) Au-nanobipyramid37 a

750 750 750 750 790

λ2 and τ2

nm, 3.76 ± 0.06 ps nm*, 1.70 ± 0.02 ps nm, 1.87 ± 0.02 ps nm, 2.12 ± 0.02 ps nm, 3.2 ± 0.2 ps

780 780 780 780 805

nm, 3.72 ± 0.05 ps nm, 1.95 ± 0.02 ps nm*, 1.71 ± 0.02 ps nm, 1.93 ± 0.02 ps nm, 2.8 ± 0.2 ps

λ3 and τ3 808 808 808 808 825

nm*, 3.60 ± 0.05 ps nm, 1.81 ± 0.02 ps nm, 1.91 ± 0.02 ps nm*, 1.69 ± 0.02 ps nm*, 2.3 ± 0.2 ps

The wavelengths marked with * are SPR wavelengths of the corresponding nanostructures.

together for comparison. Two significant features can be summarized as follows: first, the shortest response time usually occurs at the SPR wavelength for each kind of nanostructure. Second, nanostructures of different kinds of shapes usually have roughly different response times: the smaller the size in longitudinal dimension of the structure, the slower the response time that can be obtained. Also, the sizes of the nanostructures in the longitudinal dimensions are much larger than 10 nm, and so the size-dependent results for nanostructures smaller than 10 nm26 are not suitable for our case. For the transverse dimension size dependent response time of the nanostructures with fixed length but different diameters, more experiments need to be done in the future. To better recognize the data given in Figure 3, comparative results for wavelength-dependent response times and shape- or geometry-dependent response times are summarized in Table 2 and Table 3, respectively. From both data demonstrated in the figure and the tables, it is clear that wavelength and geometry (shape and size) are two important parameters that can affect the response time greatly. For the wavelength-dependent response time in the same nanostructure with fixed excitation power, electron-surface-scattering probability is the main factor to affect the response time. The increase of probability for electron-surface scattering at SPR wavelength would shorten the response time.37 For the shapeand geometry-dependent response times in different nanostructures, surface electron distributions would be a big issue which can affect both the electron-surface-scattering process and the initial electron temperature. From the data in both Table 2 and Table 3, one can see that the slowest time is 3.76 ± 0.06 ps, which is nearly 8 times longer than the shortest one of 0.48 ± 0.04 ps. Figure 4 is the pump power dependent response time data of Au nanorods with AR of 4.2 ± 0.3, and the inset is the extracted OKE signal curves of the sample under 200, 300, and 400 mW. As the pump power goes up from 150 mW to 400 mW, the relaxation process becomes slower and the response time increases from nearly 1.2 to 1.8 ps, which increases almost 50% compared to the initial response time under the pump power of 150 mW. This result is very significant and important because it provides people a simple way to control and modulate the response time of hot electrons, so as to open a way to investigate the response time dependent properties of hot electron-based photovoltaic and photocatalytic devices. This result can be explained by using the two-temperature model (TTM) theory.26,29,31,40,41 From this theory, the time evolution

the hot electron relaxation process observably. These results agree well with the theoretical prediction of size-dependent hot electron responses.29,31,39 The relaxation time of the GNR-2 (diameter = 10 ± 1 nm, AR = 4.3 ± 0.3) sample is given in Table 2 (see the experimental data, calibrated curve, and absorption spectra in Figure S4). The response time is about 3.60 ± 0.05 ps at the resonant excitation wavelength, which is much longer than that of GNR-1 (diameter = 20 ± 2 nm, AR = 3.3 ± 0.3 to 4.2 ± 0.3) samples, which demonstrates that the rod size could be used as a factor to modulate the response time of GNRs. To find the key parameters that could be used to modulate the relaxation time of hot electrons, two series of experimental data have been obtained under the same setup. One is the response time of different kinds of gold nanostructures under different wavelengths, and the other one is the response times of Au nanorods with AR of 4.2 ± 0.3 at different pump powers. The former is demonstrated in Figure 3; as shown in the figure, the wavelength-dependent response time curves for Au nanorods with different diameters and aspect ratios, Au nanobypyramids,37 and Au triangular prisms35,36 are drawn

Figure 3. Summarization of the relaxation times at different pump wavelengths for kinds of nanostructures, including GNRs with different diameters and ARs, nanotriangular prisms, and nanobipyramids. The pumping power was 300 mW for all the GNRs and nanobipyramids and 400 mW for nanotriangular prisms. 27159


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The Journal of Physical Chemistry C Table 3. Response Time of Au Nanostrucutures with Different Shapesa samples

SPR wavelength

geometry sizes

τ

GNR-1 GNR-2 Au-nanobipyramid37 Au-triangular35,36

750−808 nm 808 nm 825 nm 1240 nm

d ∼ 20 nm, L ∼ 66−84 nm d ∼ 10 nm, L ∼ 43 nm w ∼ 32 nm, L ∼ 92 nm t ∼ 7 nm, L ∼ 170 nm

1.70 ± 0.02 ps 3.60 ± 0.05 ps 2.3 ± 0.2 ps 0.48 ± 0.04 psa

a

All the data were obtained at their SPR wavelengths except the one marked with a which is obtained at 800 nm. d and L are the diameter and side length of NRs, respectively, w is the width of the nanobipyramid, and t is the thickness of the triangular prism.

For example, when the pump power was changed from 150 mW to 400 mW, the response time of the nanorods with AR = 4.2 ± 0.3 was tuned significantly from nearly 1.2 to 1.8 ps, while the change in Au nanostructure shapes and the corresponding excitation conditions drove the response time changes from 0.48 ± 0.04 ps (Au triangular nanoprisms) to 3.8 ± 0.3 ps (GNRs with diameter of 10 ± 1 nm and AR = 4.3 ± 0.3). These tailoring methods and the obtained results are of great importance because the control of hot electron relaxation time is very essential for noble nanostructures to be applied in hotelectron-based photovoltaic and photocatalytic devices and ultrafast all-optical processors.

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Figure 4. Relaxation time of a GNR sample (AR = 4.2 ± 0.3) under different pump powers. The inset shows the corresponding OKE signals under 200, 300, and 400 mW laser pump.

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b08695. The photothermal stability test of the samples, OKE setup, and data of CS2 reference and experimental data of GNR-2 (PDF)

of the electron temperature (Te) and the lattice temperatures (Tl) after the excitation of a laser pulse can be quantitatively described by a set of coupled differential equations: Ce(Te)

dTe = −g (Te − Tl) dt

and

C l(Tl)

ASSOCIATED CONTENT

S Supporting Information *

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dTl = g (Te − Tl) dt

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected].

(3)

where Ce(Te) and Cl(Tl) are specific heats of electron and lattice, and g is the e-ph coupling constant. The Ce(Te) is given by Ce(Te) = γTe, where γ = π2k2Bg(ϵF/3). kB is Boltzman’s constant, and g(ϵF) is the electronic density of states at the Fermi level. On the basis of these two equations, the effective decay rate of the e-ph interaction process, marked as Re‑ph, can be given by Re‑ph = g/γTe, where Re‑ph is inverse to the response time of the e-ph interaction process. It is clear that the increase of Te will result in a decrease of Re‑ph, so as to lead to an increase of the response time of τe‑ph. For a given nanorod with fixed AR, the parameter g/γ is nearly a constant. Therefore, the increase of pump power will increase the initial temperature Te of the electron, so as to result in the slowing down of the response time.26,31,41

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported partially by National Basic Research Program of China (2014TS143), Natural Science Foundation of Hubei province (2015CFB631), National Scientific Foundation of China (11404124 and 11104097), and the Project of Scientific and Technological Innovation Team of Hubei Province (T201531).

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CONCLUSION The electron−phonon interaction relaxation time of surface plasmon induced hot electrons and the third-order optical nonlinear susceptibility in GNRs with different aspect ratios have been investigated. A comparative study of Au nanorods and some other Au nanostructures under the same setup indicated that the variation of GNRs’ aspect ratios (the diameter is about 20 nm) from 3.3 ± 0.3 to 4.2 ± 0.3 could hardly affect the relaxation time and the third-order optical susceptibility, while the change in the excitation conditions (excitation wavelength or pump power) and in the shape of nanostructures can modulate the response time significantly. 27160


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