Giant Electron–Phonon Coupling Detected Under Surface Plasmon Resonance in Au Film

4590 Vol. 44, No. 18 / 15 September 2019 / Optics Letters Letter

Giant electron–phonon coupling detected under surface plasmon resonance in Au film

1,2 3 3 1,2, FENG HE, NATHANIAL SHEEHAN, SETH R. BANK, AND YAGUO WANG * 1Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA 2Texas Materials Institute, The University of Texas at Austin, Austin, Texas 78712, USA 3Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78758, USA *Corresponding author: [email protected]

Received 4 July 2019; revised 22 August 2019; accepted 23 August 2019; posted 23 August 2019 (Doc. ID 371563); published 13 September 2019

Surface plasmon resonance (SPR) is a powerful tool to am- small change in reflectance/transmittance and can hardly be plify coherent phonon signals in metal films. In a 40 nm Au captured by regular coherent phonon spectroscopy. film excited with a 400 nm pump, we observed an abnor- Surface plasmon resonance (SPR) has been proven a power- mally large electron–phonon coupling constant of about ful tool to enhance the detection of CPs in metal films 17 3 8 × 10 W∕ m K, almost 40× larger than those reported [2,17–19] and dielectrics [14]. SPR is the coherent excitation in noble metals, and even comparable to transition metals. of a delocalized charge wave that propagates along an interface. We attribute this phenomenon to quantum confinement SPPs, which are the evanescent waves from the coupling be- and interband excitation. With SPR, we also observed tween light and SP in metals, can create a strongly enhanced two coherent phonon modes in a GaAs/AlAs quantum well electric field at the metal/air interface [20]. The most conven- thin film. Our finding provides a new approach to generate ient way to couple the light with the SP wave (collective elec- high-frequency acoustic phonons in noble metals and to tronic modes) is using a prism or a grating. The two most study their nonlinear nature of propagation. © 2019 popular prism coupling geometries are the Kretschmann con- Optical Society of America figuration Fig. 1(a)] and the Otto configuration [20]. To excite SPR, the wave vector k of incident light must satisfy the fol- https://doi.org/10.1364/OL.44.004590 x lowing criteria [20]:

pffiffiffiffiffi ω ω ε ε 1∕2 ε sin θ m α kx P ksp ε ε , (1) c c m α Au nanostructures, e.g., films and nanoparticles, are the most ε ε ε studied plasmonic materials for terahertz emission [1], gas de- where P, m, α are the dielectric constant of the prism, metal, ω tection and biosensing [2–8], electromechanical devices [9], and material under detection, respectively. is the photon fre- 2π∕λ λ photothermal therapy [10], photoacoustic imaging [11], etc. quency of incident light, which is equal to , where is the θ The localized surface plasmons (SPs) and propagating surface wavelength of the incident light. is the incident angle and c is plasmon polaritons (SPPs) in Au nanostructures are highly tun- the speed of light in vacuum. To satisfy Eq. (1), the real part of able by manipulating the structure geometry and shape. Au the dielectric constant of the metal must be negative, and its nanostructures can also be easily hybridized with a wide range magnitude must be greater than that of the material under of semiconductors, dielectrics, and organic materials [10–14]to detection. This criterion can be satisfied at interfaces of noble enhance their performance. Under light excitation, electrons metals (Au, Ag, Al) with many common semiconductors. As first absorb photon energy and then pass it to phonons (quan- shown in Fig. 1(b) in an Au film, when the incident angle tized lattice vibration). The electron–phonon (e–ph) coupling of probe beam is close to the SPR angle, dR∕dθ becomes very determines how fast the energy is deposited into phonons from large and a small disturb of the SPR angle will induce large the electrons and hence is critical for many applications. Noble reflectivity changes [21]. When CPs travel into the region of metals like Au and Ag usually possess a small e–ph coupling the surface plasmon, the collective oscillation of atoms will constant (∼1016 W∕m3K), much less than some transition modulate the local dielectric constant and slightly alter the metals, such as Ni and Co (∼1017 W∕m3K). For most of the SPR angle. Owing to the large dR∕dθ, the reflectivity change studies, to extract the e–ph coupling constant of Au nanostruc- from coherent phonons can be amplified substantially. It has tures, the electronic decay signals from femtosecond pump- been reported that the coherent phonon signals in metal films probe experiments were used [15]. The obtained e–ph coupling could be enhanced by 10–100 times [14,17,18]. Recently, constant is a value averaged over all phonon modes. Rarely a surface plasmon has been utilized to detect coherent thermal measured is the e–ph coupling between electrons and specific phonons in gold film up to 1 THz [19]. phonon modes [16] that requires excitation/detection of coher- In this work, we incorporate the Kretschmann configuration ent phonons (CPs). CPs in Au nanofilms produce an extremely into a coherent phonon spectrometer to excite SPR and detect

was obtained, which was then transferred onto a 25 nm Au film deposited directly on a prism. A home-built coherent phonon spectrometer used laser pulses out of a mode-locked Ti:Sapphire femtosecond laser (Spitfire ACE, Spectra Physics, 800 nm wavelength, 100 fs pulse duration, 5 kHz repetition rate). For the pump, a second-harmonic-generation crystal (beta-barium borate, BBO) was used to double the photon energy to 3.1 eV. All experiments were carried out in a “front pump back probe” configuration, where the pump irradiates from the air/sample interface and the probe detects from the prism side. A 15 cm lens was used to focus both the pump and probe beams, with spot sizes (diameter at the 1∕e2 intensity level) of 245 μm and 60 μm, respectively. The pump fluence was fixed at 1.27 mJ∕cm2. The rotational stage on which the samples sat was used to control the incident angle of the probe beam. All devices were synchronized through a home-built LabView program for real-time data acquisition [22,23]. Fig. 1. (a) SPR generated in Kretschmann configuration. The red- First, we measured the angle-resolved static reflectance of shaded region represents the SPP excited resonantly (ksp kx). a 40 nm Au thin film in the Kretschmann configuration A p-polarized probe beam incident from prism side along the SPR [Figs. 1(a) and 1(b)]. The reflectance displays a minimum value angle θ0; (b) angle-resolved static reflectance change at different angles. around 41.3°, marked by angle a, at which the criteria of Four angles marked as a, b, c, d were chosen to perform coherent Eq. (1) is satisfied and SPR excitation occurs. For comparison, phonon measurements; (c) time-resolved ΔR∕R signals measured in four incident angles (a, b, c, d) were selected to perform co- a 40 nm Au film with a coherent phonon spectrometer, at four differ- herent phonon measurements, where a is the SPR angle, b and ent incident angles marked in (b); (d) coherent echoes after removing c are angles located in the linear dR∕dθ regions on two sides of electronic background. Orange-dashed lines mark the duration of sin- the dip, and d lies in a region far away from the SPR angle. gle acoustic echo. Blue-dashed lines mark the separation time between As shown in the inset of Fig. 1(c), we generated coherent two echoes. acoustic phonons by heating the air/Au interface with a weakly focused pump beam and detecting from the prism side with a p-polarized probe beam. The pump beam size is about ∼4 CPs in a bare Au film. We observed an abnormally large e–ph times larger than the probe beam. Figure 1(c) shows the tran- coupling constant of about 8 × 1017 W∕m3K, almost 40× sient reflectivity changes at four different incident angles, larger than those previously reported in Au films, and even marked in Fig. 1(b). At all angles, ΔR∕R shows a sharp positive comparable to transition metals. SPR-enhanced detection of peak around time zero, which is due to the excitation of the hot CPs in semiconductors has not been reported. In semiconduc- electrons, and the decaying processes reveal hot electron relax- tor, CPs are usually detected through the stimulated Raman ation via electron–electron and e–ph coupling. The angle a light scattering mechanism; hence, only the phonons with wave gives the highest peak signal, which is reasonable because of Δ ∕ vectors kphonon 0 ∼ 2kprobe can be detected. With SPR, the the resonant condition. R R peaks at angles b and c have detected reflectivity change of the probe beam comes from the almost the same height because of their similar dR∕dθ values. interference between the surface plasmon and coherent pho- Angle d shows the smallest ΔR∕R peak due to its off-resonant nons; therefore, a broader band of CPs might be detected. condition. Compared to angle d, the ΔR∕R peak at angle a is In this study, substantial CP enhancement is also demonstrated enhanced by more than 75 times. in a GaAs/AlAs superlattice (SL), when the incident light fol- After removing the electronic background, we can see echo- lows an angle close to the SPR angle. Our results reveal that like oscillations in Fig. 1(d) at angles a and b, while at angles under optimum conditions, e–ph coupling in Au films could c and d, no obvious echoes show. These oscillations are pump- be enhanced substantially due to quantum confinement and induced acoustic strain waves bouncing back and forth between interband transition, which is important for many applications. the Au/air and Au/prism interfaces [17]. Their velocity can be υ 2 ∕ 40 nm This study also provides a new route to enhance the detection estimated by s d Au tr, where d Au is the Au film 25 3ps of CPs in semiconductors. thickness, and tr . is the time interval between two A 40 nm gold film was deposited onto a BK7 glass slide with echo peaks, as marked by the blue-dashed line in Fig. 1(d). e-beam evaporation, which is then attached to the hypotenuse The calculated velocity is 3.16 km/s, agreeing well with the side of a right-angle prism (PS908, Thorlabs) with an index- longitudinal sound velocity of 3.24 km/s reported in bulk gold matching optical glue (NOA 65, Thorlabs). The whole device [21]. The amplitudes of the acoustic echoes decrease with time, was exposed under UV light for 1 min to cure the glue with due to scatterings at boundaries and with background phonons strong bonding. The second sample under study was a 3 nm/ and electrons. It is interesting to observe that the acoustic waves 3 nm GaAs/AlAs SL (period D 6nm) of 30 periods grown at angle a and b have a π phase shift, which suggests an opposite with molecular beam epitaxy (MBE). High-quality SL struc- sign of dR∕dθ at these two angles. tures were grown on a 500 nm AlA etch release layer and fol- The time duration of the first acoustic echo, τ, can be lowed by a 150 nm GaAs buffer layer on a GaAs (001) wafer extracted by taking the time difference between the rising substrate. After etching away the AlA layer, a suspended SL film and completely relaxed points [marked by orange lines in 4592 Vol. 44, No. 18 / 15 September 2019 / Optics Letters Letter

Fig. 1(d)]. At angle a, τ is estimated to be around 12.5 ps. The echoes are shown in Fig. 1(d). These oscillations come from the spatial expansion of this acoustic echo can be calculated by superposition of acoustic waves reflected at two interfaces. To τ∕2 12 5ps 3 160 m∕s 19 8nm L vs . × , . . This value is generate such a feature, the spatial expansion of the acoustic comparable to the optical absorption depth of Au at 400 nm, wave needs to be much longer than the film thickness. ∼16.3nm. The spatial expansion of a strain wave is mainly Since the pump photon energy (1.55 eV) is smaller than the determined by two factors: hot electron (photoexcited) diffu- interband transition energy in Au (2.4 eV), weak e–ph coupling sion and e–ph coupling strength. Hot electron diffusion can allows the hot electrons to propagate to a region much deeper redistribute electrons and transfer energy deep into the sample than the optical absorption depth and generate a long-range ∼106 m∕s very fast, with a velocity close to Fermi velocity vF . acoustic wave. From these oscillations, it is impossible to de- The e–ph coupling strength determines the interaction time termine the spatial expansion of the generated acoustic wave. between hot electrons and phonons, and hence limits the dis- Kolomenskii et al. used a 400 nm pump and SPR of an 800 nm tance hot electrons could travel before reaching equilibrium probe to study a 47 nm Au film [27]. They observed acoustic with phonons. In noble metals, such as Cu, Ag, and Au, waves with a different shape from those reported by Wang et al. e–ph coupling is usually weak, and strain waves generated in However, the poor signal-to-noise ratio of their results prevents these materials are generally broad. For example, Wright et al. the identification of the shape of their acoustic wave. [16] directly measured the coherent longitudinal acoustic pho- We need to point out that there are two ways to extract the nons in a 470 nm polycrystalline gold film and observed an e–ph coupling constant. One is using a two-temperature model acoustic echo time duration about 100 ps, which is about 8× to simulate the decaying curve of the electronic background, broader than what observed here. We can estimate the e–ph and a second approach is estimating the coupling constant from coupling strengthpffiffiffiffiffiffiffiffiffi from the time duration of acoustic echo by the duration of the acoustic wave generated. The latter looks at τ∕2 κ ∕ κ 314 W∕mK L vs e g. Where e is the electron the rate of energy going into a range of acoustic phonon modes, thermal conductivity of Au, and g is the e–ph coupling con- such as the one used in this work and in Wright et al.’s work stant [16]. The value obtained is about 8 × 1017 W∕m3K, [16]. The standing point of the first approach is the rate of almost 40× larger than those reported values in noble energy transferring out of the hot electron system, which gives metals, 2.2×1016 W∕m3K−4×1016 W∕m3K for Au [24], a general e–ph coupling constant between the hot electrons and 16 3 17 3 et al. 3.5 × 10 W∕m K for Ag [25], and 10 W∕m K for Cu all phonon modes. The work of Wright suggested that [24]. This value is even comparable to transition metals, such as without quantum confinement and interband transition, the Ni (3.6 × 1017 W∕m3K − 10.5 × 1017 W∕m3K [24]), Pt coupling constant between hot electrons to the longitudinal (2.5 × 1017 W∕m3K − 10.9 × 1017 W∕m3K [24,15]), and acoustic phonons is essentially the same as the general one. Co (9.3 × 1017 W∕m3K [15]), which are well known mate- Our work suggests that under certain conditions the coupling rials with strong e–ph coupling. between hot electrons to the longitudinal acoustic phonons can Observing such a large g in Au film is a surprise. Under our be enhanced substantially. experimental condition (40 nm Au film, 400 nm pump, and This finding is useful to generate high-frequency acoustic SPR of 800 nm probe), two possible reasons could contribute phonons in noble metals and study their nonlinear nature of to e–ph coupling enhancement: quantum confinement and propagation [23]. Even though the coupling between hot elec- interband transition. Quantum confinement describes the trons and longitudinal acoustic phonons has been enhanced by 40 change of electronic, phononic, and optical properties when about ×, the acoustic echo can be observed only when probing the sample size is sufficiently small. In Au film, quantum con- under SPR. However, SPR does not contribute the observed en- – finement will have three consequences. One consequence is the hancement of e ph coupling since the acoustic wave is generated stronger scattering of hot electrons at air/Au and Au/glass in- by the pump, and SPR is excited by probe only. terfaces that accelerates energy transfer to the lattice. A second To study the contribution of SPR in the detection of CPs in consequence is higher hot electron temperature because of lim- semiconductors, we performed measurements in a 3 nm/3 nm ited space for hot electron diffusion. The hot electron diffusion GaAs/AlAs SL. The sample configuration is shown in Fig. 2(a). length in Au is about 100 nm [16]. The larger temperature The SL film (30 periods) was grown with MBE and then trans- difference between hot electrons and the lattice will drive faster ferred onto a 25 nm Au film that was deposited onto a thin glass energy exchange [24]. The third consequence is the phonon slide and attached to the prism, and Raman spectroscopy was dispersions folded into a smaller momentum region along used to identify the SL quality. 25 nm was chosen because sim- the film growth direction, which increases the phonon density ulations show the best sensitivity (large dR∕dθ) at this thickness. of states and provides more available channels for e–ph scatter- The reflection of SL/Au at angles near SPR displays a much ing [26]. Interband transition means when photon energy is broader feature compared to the case of pure Au film [Fig. 1(b)], larger enough (>2.4eV for Au), valence electrons on the which indicates a smaller dR∕dθ. We measured the SL/Au 5d band will be excited to above the Fermi level and become sample at two angles, where a is close to the resonance angle free electrons, leaving holes behind. This process will reduce the and b lies on the far-left side. The time-resolved reflectivity data screening effect between free electrons and ionic cores and for both angles are presented in Fig. 2(c). The peak value at angle hence enhance e–ph coupling. a is larger than that of angle b, but the difference is not as drastic Even though both quantum confinement and interband compared to the pure Au case [Fig. 1(c)]. However, we can transition can induce stronger e–ph coupling, individually they observe some weak low-frequency oscillations at angle a but could not generate such a large effect observed here. Wang et al. not at angle b. The FFT spectra of ΔR∕R at angles a and b are [21] used an 800 nm pump to excite acoustic waves in a 50 nm plotted in Fig. 2(b).Atanglea, two peaks show up, one around Au film and detected them with SPR of an 800 nm probe. The 19 GHz and another around 38 GHz. To exclude the possibility observed coherent acoustic oscillations, instead of the acoustic that these acoustic oscillations come from Au film itself, we also Letter Vol. 44, No. 18 / 15 September 2019 / Optics Letters 4593

SPR. This work not only demonstrates the SPR enhancement of coherent phonon detection but also provides an approach to generate high-frequency acoustic phonons in noble metals.

Funding. National Science Foundation (CBET-1351881, CBET-1707080, DMR-1720595, EEC-1160494; CAREER).

Acknowledgment. We acknowledge the help from Joon- Seok Kim and Xianghai Meng with low cutoff Raman measure- ment in Jung-Fu Lin’s lab.

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