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Photoluminescence of gold nanorods: Purcell effect enhanced emission from hot carriers Yiyu Cai, Jun G. Liu, Lawrence J. Tauzin, Da Huang, Eric Sung, Hui Zhang, Anneli Joplin, Wei-Shun Chang, Peter Nordlander, and Stephan Link ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b07402 • Publication Date (Web): 28 Dec 2017 Downloaded from http://pubs.acs.org on December 28, 2017
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ACS Nano
Photoluminescence of Gold Nanorods: Purcell Effect Enhanced Emission from Hot Carriers Yi-Yu Cai,†∥ Jun G. Liu,‡∥ Lawrence J. Tauzin,†∥ Da Huang,†∥ Eric Sung,†∥ Hui Zhang,‡∥ Anneli Joplin,†∥ Wei-Shun Chang,†∥ Peter Nordlander,‡§⊥∥ and Stephan Link,*†§∥ †
Department of Chemistry, ‡Department of Physics and Astronomy, §Department of Electrical
and Computer Engineering,
⊥Department
of Materials Science and NanoEngineering
and ∥Laboratory for Nanophotonics, Rice University, 6100 Main Street, Houston, Texas 77005, United States
KEYWORDS: one-photon photoluminescence, surface plasmon resonance, interband transition, intraband transition, quantum yield, single-particle spectroscopy, gold nanoparticle TOC Figure
ABSTRACT. We demonstrate, experimentally and theoretically, that the photon emission from gold nanorods can be viewed as a Purcell effect enhanced radiative recombination of hot carriers. 1 ACS Paragon Plus Environment
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By correlating the single-particle photoluminescence spectra and quantum yields of gold nanorods measured for five different excitation wavelengths and varied excitation powers, we illustrate the effects of hot carrier distributions evolving through interband and intraband transitions and the photonic density of states on the nanorod photoluminescence. Our model, using only one fixed input parameter, describes quantitatively both emission from interband recombination and the main photoluminescence peak coinciding with the longitudinal surface plasmon resonance.
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The collective oscillation of conduction band electrons in metal nanoparticles, known as the surface plasmon resonance, can be engineered to absorb photons at desired wavelengths.1 Following absorption, photon excitation results in hot carriers that are generated through plasmon decay.2,3 Here, we refer to hot carriers as any electron or hole with an energy larger than can be acquired by thermal excitations at ambient temperatures.4 By tuning factors like the size, shape, and composition to determine the resonance energy, photocurrent generation with controlled hot carrier flow5 and selective photocatalytic reactions have been achieved using plasmonic nanomaterials.6 The applicability of these plasmon-driven processes is often limited though by the ultrafast relaxation of the hot carriers.7 In order to maximize photocurrent generation8,9 and create efficient as well as selective photocatalysts, the decay pathways of hot electrons and holes must be understood.4 Ultrafast pump-probe experiments probe these dynamics in metal nanoparticles either directly through time-resolved photoemission10,11 or often indirectly by monitoring changes of the plasmon resonance.12,13 In molecules, fluorescence has long been a very powerful tool for following electronic and vibrational relaxation including coupling to solvent modes.14,15 In metals, emission is much weaker than in molecular systems because of strong electronelectron interactions and coupling to phonons with energies similar to electronic excitations of the partially filled conduction band. The emission in metal films has been assigned to the radiative recombination between conduction band electrons and valence band holes.16 This photoluminescence (PL) is enhanced in nanomaterials due to surface plasmons.17 In particular for gold nanoparticles, the single-particle PL spectrum has been found to closely resemble the main plasmonic mode seen in dark-field scattering.18,19 Hot carriers created either directly through interband excitation or generated by plasmon excitation and decay are viewed as
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intermediate states in energy relaxation pathways,18-24 and plasmonic modes are considered to be the main PL channels for enhancing the emission through an antenna effect.17,25,26 However, this picture is still incomplete and moreover heavily debated. In fact, it has been argued that emission from metal nanoparticles actually arises from electronic Raman scattering and does not involve the radiative recombination of hot carriers.27-30 A comprehensive experimental and theoretical understanding of emission from plasmonic nanostructures is therefore necessary to resolve this controversy. Furthermore, if the emission can be linked to hot electrons and holes it should become possible to use PL spectroscopy to study electronic energy relaxation in plasmonic nanomaterials and to optimize the efficiency of photodectors and photocatalysts. We show here that the one-photon PL in gold nanorods (AuNRs) can be viewed as a Purcell effect enhanced spontaneous emission from the radiative recombination of hot carriers. Typically, the Purcell effect describes the enhanced emission rate from a dipole emitter inside a photonic cavity when their resonance energies match.31,32 To apply this concept to plasmonic nanoparticles, we consider hot carriers generated by the absorbed photons as the emitters and the plasmonic modes of the nanoparticle as cavities.33 More specifically, the surface plasmon resonance determines the photonic density of states (PDOS), which represents the number of electromagnetic states averaged over the entire nanoparticle available for the emission of a photon.34 The two factors that determine the PL in the theory introduced here are then hot carriers and the PDOS. This view is in agreement with previous mechanisms suggesting that the surface plasmon acts as an enhanced emission channel.17-22,24 Importantly, our model quantitatively describes all spectral features in the emission spectra of single AuNRs with only one adjustable parameter that remains the same for five different excitation wavelengths covering both interband and pure intraband transitions. In addition, emission quantum yields
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(QYs) correlated for all single AuNRs and excitation power dependent studies indirectly reveal the intricate dynamics of the evolving hot electron and hole distributions even in these steadystate measurements.
RESULTS AND DISCUSSION The plasmonic structures used in our study were chemically synthesized single crystalline gold AuNRs35 (Figure S1-2) because of their narrow and highly tunable plasmon resonance in the visible spectral range. The effects of sample heterogeneity were eliminated by performing singleparticle experiments, and the resonance energy of the longitudinal surface plasmon for each AuNR was obtained using single-particle dark field scattering (DFS) spectroscopy36 (Figure S3). Two AuNR samples with average aspect ratios of 3.5 (sample 1) and 5.3 (sample 2) were prepared so that single particle scattering resonance energies varied between 693 and 933 nm. PL spectra and QYs for five different excitation wavelengths (405, 488, 532, 633, and 785 nm) were collected for 80 individual AuNRs and correlated with each other, as illustrated in Figure 1A. Scanning electron microscopy (SEM) imaging of the same AuNRs ensured that only single AuNRs were considered, and furthermore provided the size of each AuNR. These AuNR dimensions were used as input parameters in finite difference time domain (FDTD) simulations to calculate accurate absorption cross sections for the QY calculation (Figure S4). Of the five excitation wavelengths, 785 nm was special because it was the only one below the threshold for exciting interband transitions in gold (1.7-1.8 eV).37,38 Additional information regarding experimental details is presented in the supporting information.
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. Figure 1. (A) Schematic illustration of the single-particle PL experiments using five different excitation wavelengths covering both interband and intraband transitions. Representative singleparticle PL spectra of one low aspect ratio (sample 1, dashed) and one high aspect ratio (sample 2, solid) AuNR with 405 (B), 488 (C), 532 (D), 633 (E) and 785 nm (F) excitation. The
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resonance wavelengths of the two AuNRs, as determined from their DFS spectra (G), were 704 (--dashed lines, AuNR dimension of 72.7 x 21.0 nm) and 871 nm (-solid lines, AuNR dimension of 94.2 x 18.5 nm). The incident power densities for each wavelength are listed in the supporting information. Simulated PL spectra of the two AuNRs for 405 (H), 488 (I), 532 (J), 633 (K) and 785 nm (L) excitation. Simulated DFS spectra are compared to the calculated PDOS in panel (M) for the two AuNRs with resonance maxima at 707 (dashed) and 863 nm (solid).
Similar to previous reports, the PL spectra of all AuNRs showed a main peak with a resonance energy and lineshape similar to the longitudinal surface plasmon resonance (LSPR) observed in the correlated DFS spectra.19 This basic behavior, except for some small differences discussed below, was independent of the excitation wavelength, and hence independent of whether exciting interband or intraband transitions. The experimental and simulated PL spectra of two AuNRs chosen as examples from sample 1 (small aspect ratio) and sample 2 (large aspect ratio) for each excitation wavelength are displayed in Figures 1B-F and 1H-L, respectively. The corresponding DFS spectra are given in Figure 1G,M where we also overlaid the calculated PDOS for these two AuNRs. The PDOS spectrally track the plasmon resonances observed in the DFS spectra perfectly. The simulated PL spectra were calculated assuming that the excitation of hot carriers is followed by radiative recombination of the same or different hot carriers. The rate of PL emission on resonance with the AuNR LSPR was greatly enhanced because of the high PDOS induced by the plasmonic mode. The PDOS enhancement, as will be shown below, is a property of the nanoparticle and independent of the excitation wavelength. The direct connection between near-field maps of two-photon PL and the surface plasmon PDOS was reported before,39,40 suggesting similar enhancement mechanisms for one- and two-photon PL. Another comparison 7 ACS Paragon Plus Environment
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can be made to molecules following Kasha's rule which explains why fluorescence spectra are independent of the excitation wavelength. The PL peak in the AuNR spectrum originates from hot carriers that can have different energies rather than being emitted from a certain electronic excited state, but its spectral shape is ultimately determined by the PDOS. In the simple model we have developed for the simulation of PL spectra we assumed an electronic density of states (EDOS) which included both the Au sp-band and a narrow d-band with its upper edge well below the Fermi level (Figure S5A). The transition matrix elements were assumed to only depend on energy with transition energies equal to the incident photon energy. The most likely transitions occur near the surface of the nanoparticles where the local electric field is largest and the emitted photons are less likely to be reabsorbed. We modeled the nanoparticle as a spherical well of radius a and depth .
In the independent electron
approximation, the radial wavefunction for the electrons is e > ~ e < with =
( || ) ℏ
and ! =
|| ℏ
(1)
. Thus the energy dependence of the transition matrix
element can be parameterized as
|"#||$%| = &' ∗ ( )) ( )* + , - . / 0 & ~* 1(2, 2- )
(2)
where α is the only adjustable parameter in our model. Its value is fixed to unity in all of our PL simulations. The excitation of the hot carriers was determined by the EDOS 4 (5) as well as the transition matrix elements according to 6 = 7(5 ) − ∑< :→< 4 (5< )7(5 ) =1 − 7+5< .? @A + ∑< :
