Spectroscopic nano-imaging of all-semiconductor plasmonic gratings

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Spectroscopic nano-imaging of all-semiconductor plasmonic gratings using photoinduced force and scattering type nanoscopy Yi Huang, David Legrand, Rémi Vincent, Ekoue Athos Dogbe Foli, Derek Nowak, Gilles Lerondel, Renaud Bachelot, Thierry Taliercio, Franziska Barho, laurent cerutti, Fernando Gonzalez-Posada, Beng Kang Tay, and aurelien bruyant ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00700 • Publication Date (Web): 22 Oct 2018 Downloaded from http://pubs.acs.org on October 22, 2018

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Spectroscopic nano-imaging of all-semiconductor plasmonic gratings using photoinduced force and scattering type nanoscopy Yi Huang,† David Legrand,†,‡,¶ Rémi Vincent,† Ekoué Athos Dogbe Foli,† Derek Nowak,§ Gilles Lerondel,† Renaud Bachelot,† Thierry Taliercio,k Franziska Barho,k Laurent Cerutti,k Fernando Gonzalez-Posada,k Beng Kang Tay,‡,¶ and Aurelien Bruyant∗,† †ICD-L2N, CNRS UMR 6281, Université de Technologie de Troyes, France ‡Electrical and Electronic Engineering Department, Nanyang Technological University, Singapore ¶CINTRA,CNRS-NTU-Thales, UMI 3288, 50 Nanyang Drive, Singapore 637553, Singapore §Molecular Vista, San Jose, USA kIES, Université de Montpellier, CNRS, Montpellier, France E-mail: [email protected],[email protected]

Abstract All-semiconductor plasmonic gratings are investigated by spectroscopic nano-imaging in the vicinity of the plasma frequency, where the material behaves as an epsilon nearzero (ENZ) material. Both phase-sensitive scattering type nanoscopy (s-SNOM) and Photoinduced force microscopy (PiFM) are carried out on this structure. The obtained

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data and models reveal that PiFM, as for s-SNOM, can have a mostly dispersive lineshape, in contrast with recent near-field spectra obtained with photothermal AFM nanoscopic imaging on ENZ material where absorption maxima are observed. On the obtained result, PiFM signal exhibited better sensitivity to the dielectric function variation while interferometric s-SNOM can provide additional phase information. Localized surface plasmon resonances (LSPR), highly confined on the structure edges were also observed with both techniques. A higher sensitivity was observed with PiFM for both dielectric contrast imaging and LSPR observation. In addition, for both microscopies, the near-field response is phenomenologically described using a similar formalism based on dipole-image dipole approach. In this model, the sensitivity difference between both techniques is mostly accounted for by probes having different polarizabilities.

Keywords Nanospectroscopy, Highly doped semiconductors, Infrared plasmonics, Epsilon-Near-Zero, Effective polarizability

Recently, the fields of infrared plasmonics and near-field nanoscopy are witnessing a converging momentum of interest with the rapid development of novel infrared materials and nano-spectroscopic imaging methods. In the past, scattering-type Near-field Microscopy 1–3 (s-SNOM) has notably been used to reveal and analyse surface modes of plasmonic resonators or to provide precious information on the dielectric function of nano-structures. The current blooming of systems combining scanning probe microscopy and spectroscopy 4–6 offers new opportunities to investigate local polaritonic effects, including local phononic or plasmonic resonances. Besides s-SNOM, optomechanical microscopies based on Photo-induced Force (PiFM) 7–9 , Photothermal induced Resonance (PTIR) 10–12 or even more recently Infrared Peak Force 13 (PFIR) have emerged as potentially equally relevant characterization techniques for chemical imaging and local investigation of light-matter interaction.

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Among the optomechanical detection methods, PTIR and PFIR rely on the detection of the photothermal expansion induced by light absorption and are used to perform local absorption spectroscopy. On the other hand, PiFM can measure, in non-contact mode, the photo-induced dipole force between the probe and the sample. Therefore, a certain similarity with s-SNOM signal can be expected, since in the usual dipole-image dipole mode 14 , the near-field scattered signal scales with the magnitude of an induced dipole representing the probe-sample system. However, the nature of the PiFM signal is actively discussed until now 15–18 . It was pointed out 15 that the peaks associated with material resonances in PiFM spectra should in principle exhibit so-called dispersive lineshapes distinct from the dissipative (absorptionrelated) lineshapes seen in the other optomechanical methods. For example, calculations on small particles show that photoinduced forces should in general produce assymetric lineshapes related to the real (i.e. dispersive) part of dielectric function. However, according to recent reports 15,17 , in the infrared range where absorption cross section can be high, the lineshape of the peaks present in the PiFM spectra were found to be mostly lorentzian-like and positioned on absorption line as for PTIR and PFIR. In this context, the influence of thermal photoexpansion in PiFM spectra must be further analyzed depending on the material nature 17 . The question of the dissipative or dispersive nature of the PiFM signal on the surface mode resonance of polaritonic material is therefore left open, as well as the potential ressemblance with s-SNOM signal. To answer these questions, cross-comparisons of these infrared methods on known plasmonic or phononic material exhibiting surface modes are needed. Such analysis should help to refine the validity domain of the dipole-based models and to determine the complementarity of these techniques for the characterization of polaritonic materials and devices. Of particular interest is the spectroscopic response in the epsilon near-zero (ENZ) range, occuring near the plasma frequency ωp for low-loss plasmonic materials or near the longitudinal optical phonon frequency ωLO for phononic materials. Such

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analysis was recently carried out on thin phononic material layers with PTIR 19 . Despite the relatively weak losses of the material, dissipative lineshapes were obtained near ωLO , due to the well-known presence of a leaky mode in ENZ material layer 20 , typically reffered to as Berreman mode. In plasmonics also, ENZ materials are attracting a lot of interest in recent years in the context of metamaterials due to the peculiar wave features in such media. The characteristics of emitters or antenna on ENZ substrates have been already investigated in several recent papers 21–23 . In fact, this is the situation encountered in near-field nanoscopy experiments since conventional scattering nanoprobes are regarded as vertically polarizable dipole or antenna. In this work, we have investigated a highly doped semiconductor (HDS) material in the form of subwavelength gratings, using the two s-SNOM and PiFM near-field techniques. The spectroscopic imaging is performed across the plasma frequency ωp , where the material acquires a metal-like behavior, and below ωp where plasmonic surface modes and localized resonances can be excited. We show how both signals can be phenomenologically accounted for using a dipole-image dipole based model, whose expression is slightly modified for the PiFM case. In order to predict the near-field signal and compare it with simulations, the dielectric function of the material is predetermined. Before presenting the near-field results, we introduce the HDS material and the s-SNOM signal expected from the radiation pattern of a vertical dipole antenna in interaction with the ENZ material. Plasmonic sample description In the list of infrared plasmonics materials 24 , HDS are relevant candidates for sensing applications, since their plasma frequency can be widely tuned across the fingerprint region (600-1600 cm−1 ) by adjusting the dopants density. With such adjustable ωp , localized surface plasmon resonances can be achieved at a designed frequency below ωp . In this context, Si-doped InAsSb, holds great promise 25,26 notably because of its compatibility with Si technology and its possible integration with infrared source and detectors. Because of its low

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loss, the complex dielectric function of this HDS approaches zero at ωp , where it can be categorized as an ENZ material 27 .

Figure 1: (a) Geometry and Scanning Electron Micrograph (SEM) of the sample consisting of highly doped semiconductor (HDS) strips on a dielectric substrate (GaSb). (b) Complex dielectric function (λ) of InAsSb obtained from IR reflectivity spectrum fitting, and absorption of a thin ENZ layer (t=100nm) determined from (λ) at p-polarized oblique incidence (60◦ ). (c) Plasmon-polariton dispersion of the semi-infinite HDS and finite HDS slab, assuming no loss (γ = 0). The Brewter mode (Br.) above the light cone is indicated by a black spot. The InAsSb grating on undoped, lattice-matched, GaSb substrate, is depicted on figure 1(a). As detailed elsewhere 27,28 , the dispersion (ω) of the considered HDS is well described by the Drude model in the investigated infared range: (ω) = ∞

ω 2p 1− ω (ω + iγ)

,

(1)

with ∞ = 10.4 the dynamic permittivity of the material which is fixed, and where the two other doping-dependent parameters ωp and γ are experimentally determined from the fitting of the IR reflectivity spectra of the HDS thin films. The real and imaginary part of the dielectric function given by Drude model are shown in figure 1(b), where the plasma 5


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wavelength corresponding to ωp =2.06 × 1014 rad.s−1 (at about 9.16µm) is indicated, while the relaxation rate γ was found to be (6 ± 2) × 1012 rad.s−1 . As can be seen, the imaginary part of the permittivity is small near the plasma frequency (about 0.24 at ωp ). On the other hand, the undoped GaSb substrate is satisfactorily accounted by nGaSb =3.77 on the investigated range. The relatively good precision on ωp and γ stems from the existence of a dip in the reflectivity spectrum for a p-polarized wave at oblique incidence, corresponding to the Brewster mode occurring when r = Re() is crossing zero. This leaky mode, which is clearly visible in thin films, coincides with an absorption maximum that can be calculated from the retrieved , as also shown in figure 1(b). As mentioned in the introduction, it can be noted 27 that this ENZ-related resonant absorption is also named “Berreman mode” rather than “Brewster mode” when the ENZ behaviour originates from LO phononic resonance (phonon polariton). In both cases, it corresponds to the high energy branch of the phonon- or plasmon-polariton dispersion curve, as shown here on figure 1(c). Because of the small thickness of the slab, we also see the that the surface plasmon polariton (SPP) tends tho shift from = −1 to = 0, as expected 20 . However, for high spatial frequencies of the light (large parallel wavector components k// ) as those generated by a near-field tip the surface mode still occurs near = −1 (i.e. the second interface is not seen). Before we focus our analysis on the peculiar near-field response of such polaritonic sample in the ENZ region, we note that the localized surface plasmonic resonances (LSPR) occuring at more negative value of r can also be observed on the HDS ribbon edges, as detailed elsewhere 28 (additional simulations are provided in supporting information). While clearly seen on near-field simulations, their far-field signature is very shallow for the considered thickness and doping and can hardly be detected. Near-field investigation of the ENZ material. Early experimental reports on polaritonic materials indicated that s-SNOM exhibits a characteristic response when the material acquires a metal-like behavior, i.e. when the real

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Figure 2: (a) Sketch of near-field zone from where the light scattered by the antenna probe is collected (s-SNOM). An exponential field decay from the surface induces an attractive photoinduced force (PiFM). Inserts: examples of s-SNOM and PiFM images. (b) Dipoleimage dipole model. The probe is considered as a small polarizable sphere (c) Black: total scattering cross section σ of a metal nano-sphere across the ENZ region (on top of a material described by = r + 0.2i) when excited by a vertical unit field. It is normalized by the free space scattering σo . Insert: 2 extinction maxima are clearly visible for small enough value of i (here 0.05). Pink: absorption of a thin ENZ material (p- polarization, grazing angle), the maximum scales linearly with i in the small absorption limit.

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part r of the dielectric function is crossing 0 (ENZ region) to become negative: the sSNOM signal lineshape is passing from a high to low value as we approach the ENZ region (referred to as the “High” and “Low” near-field signal region in figure 1(b)). In s-SNOM, the signal is provided by the amplitude A (and phase φ) of the field Escat = Aeiφ back-scattered from the nano-probe antenna, as sketched in the figure 2(a), where the probe operating in tapping mode is illuminated with a tunable laser source to achieve spectroscopic imaging across the ENZ region. In the simple but useful dipole-image dipole models 29 , this amplitude signal A (λ) is considered to be proportional to the amplitude |αef f | of a complex effective polarizability 00 0 αef f = αef f + iα ef f . The dominant vertical component of the effective polarizability is

given by:

αef f,z =

αz 1−

αz βKc 4h3

which is function of the fixed tip polarizability along its vertical axis αz , the probe sample distance h and the complex sample response of interest β =

−1 , +1

where is the complex,

frequency dependent, dielectric function of the sample underneath the tip. This phenomenological expression for αef f is re-derived in the supporting information, using Green’s dyadic formalism, considering a scattering dipole probe polarizable along the vertical direction only (z). The characteristic signal lineshape, which accounts for a sample induced resonance, is illustrated through the dipole model on figure 2(b-c). The plot shows R the total scattering cross-section σ = σ⊥ (θ)dΩ of a metal dipole scatterer as a function of r , in the case of a nearly ideal ENZ material (a small constant imaginary part i is added to account for some losses). The differential scattering cross-section σ⊥ (θ) = |αef f |2 ∗ f (θ) is proportional to the squared magnitude of the effective polarizability, while f (θ) accounts for the radiation pattern provided by the angle dependent Fresnel coefficients (cf. supporting information for a detailed expression). We observe a typical s-SNOM, sampleinduced, resonance characterized by a strong signal decay in the ENZ region, next to a 8


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pronounced maximum at a slightly smaller r value. For small i value, the nature of this lineshape described by σ, is mostly dispersive as the dissipative part is relatively weak in 00 0 this case (αef f >> αef f ) even if both contributions are present. We can note that, due to

the lack of bulk IR plasmonic material, such characteristic near-field response has been early observed in polar materials such as SiC 1 , where approaches zero and mimics the Drude response of a metal across a longitudinal phonon resonance ωLO . We note the possible presence of two distinguishable minima in the low signal region (cf. the insert of 2(c)). As described in more details in the supporting information, the origin of the minima at ≈ 0 in the very near-field region (distance smaller than the probe diameter) comes from the vanishing of the radiation pattern in all directions (i.e. f (θ) = 0), notably in reflection where direct scattering and the indirect contributions from the surface destructively interfere. A complete extinction can in principle be observed if i is small enough and for a sufficient thickness of the ENZ material. The second minimum at slightly smaller r value finds its origin in a strong attenuation of the effective polarizability. This minimum is present as long as the field confinement at the probe apex remains small compared to the material thickness. The s-SNOM signal is considered as insentive to the photothermal expansion effect. For comparison with the optomechanical methods exhibiting dissipative lineshapes, the absorption lineshape of a thin layer of ENZ material is shown on the same figure 2(c) for a ppolarized illumination at grazing angle and the same material response ( = r + 0.2i). While the intrinsic material absorption is relatively small and constant in the ENZ material, the vanishing of r entails indeed a strong Ez field inside the thin film that can lead to pronounced absorption. In the small absorption limit (weak i ) the maximum of the peak scales linearly with i . This Brewster resonance is excited by a direct far-field illumination and the corresponding absorption resonance, which is marked when the thickness is not too small (t ≥ about 40 nm), coincide with the strong scattering drop. In the previously mentioned PTIR measurement 19 made onto thin film and ultra-thin film of ENZ material (SiO2 near

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ωLO ), it was shown too that, in this case where the leaky mode is excited, the absorption induced in the sample by the tip itself is negligible compared to the direct illumination contribution.

Results and discussion To explore the near-field response of the sample, we have used a home-built phase sensitive s-SNOM which is detailed elsewhere 30 and sketched on figure 3. The probes we used were tungsten probes mounted on a tuning fork, following the method detailed elsewhere 31 . The controlled radius of curvature of the freshly prepared tungsten probe is about 15 nm.

Figure 3: Home-built phase sensitive s-SNOM setup 32 . F: Mid-IR fiber with collimator, W: Half waveplate, C: visible camera, L: Lens, S: beam splitter, D: HgCdTe detector, R: Reflective objective, H: Tuning-fork based AFM head comprising motors and piezo stages. N: Neutral density filter, M: Mirror mounted on piezo-actuators With the help of three tunable mid-IR quantum cascade lasers (QCL) from Daylight Solutions inc., we were able to image the HDS grating, obtaining topography, optical amplitude and optical phase simultaneously. The backscattered signal from the mirror objective is interferometrically detected with the method described in 30 in order to avoid the background contribution. In this method, based on a Michelson configuration, the reference beam is si-

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nusoidally phase-modulated at a frequency of 1kHz generating sidebands at tip modulation frequency and harmonics. These sidebands that are free from non modulated background contribution, are detected to determine the complex near-field signal. For the semi-infinite probes that we use and ultra-small amplitude (about 2nm), the tip harmonics contribution vanishes and approach curves reveal a signal nearly free from modulated background contribution. Selected images are shown in figure 4. The incident beam polarization was set along the tip axis to obtain the maximum backscattered signal. The obtained images are characterized by a wavelength dependent contrast between the two materials which is found to be rather well accounted for by the mentioned dipole-image dipole model. First, we note that on each of the two materials, the s-SNOM signal is spatially homogeneous except when the probe-sample interaction becomes more complex near the edges, where a marked drop in the signal is observed. At 9.3 µm, where we approach the ENZ region, the HDS surface is dark compared to the substrate (figure 4(d), top). On the contrary, for slightly smaller permittivity value, at 10 µm, the near field signal on the HDS is maximal and a clear positive material contrast between HDS and the GaSb substrate is observed. At 11,µm, finally bright edges are observed that can be associated with hyper confined localized surface plasmon resonance (LSPR). The phase signals on these two opposite bright edges are relatively out of phase (about 1.4 rad phase difference on figure 4(e), bottom). The dissymmetry observed on the amplitude image between the two edges are due to the side illumination condition, which is well reproduced by electromagnetic simulation (cf. FDTD calculation on figure 4(c)). We can note that the LSPR edge mode is actually expected at r = −3 according to theoretical prediction 33 for a 90◦ edge. It is here observed near r ≈ −4.2. Additional simulations show that the red shift can be attributed to an ultra-thin adlayer of native oxide (Cf. supporting information) while the tip-sample coupling and a residual coupling with the second edge formed by the HDS ribbon and the substrate can also play a role in this shift. Similar images were made with PiFM as shown on figure 5 at selected wavelengths with a

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Figure 4: Zoomed s-SNOM images of HDS gratings. (a) Topography; (b) Profile of topography; (c) FDTD simulation of HDS grating at 11 µm wavelength; (d) Optical amplitude images at 9.3 µm, 10 µm, 11 µm wavelength (the color bar scale is normalized by the optical amplitude on GaSb substrate); (e): Optical phase images at 9.3 µm, 10 µm, 11 µm wavelength.

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cantilever-based AFM from Molecular Vista inc. operating with gold coated silicon probes. In this experiment, the time-averaged photoinduced force induced by a pulsed laser source is measured at the 1st mechanical resonant frequency of the cantilever f1 , while the AFM feedback is operated in tapping mode on the amplitude of the second mechanical resonance f2 . In order to prevent less-local scattering forces to impact the PiFM signal, the side-band coupling mode described in 7 was used, were the light pulses are triggered at a frequency fm = f2 − f1 instead of a direct excitation at f1 . (More details on the experimental system are provided in the supporting information). Just as for the s-SNOM images, we observe a sample-induced resonance where the PiFM signal goes from small value in the ENZ region to much larger value for slightly negative value of . We note that the strongly confined LSPR signature can also be observed near 11 µm as shown in the high resolution image 5(c).

Figure 5: PiFM images of HDS gratings. (a)-(c): PiFM images at 9.02µm, 10.53µm, and 10.8µm wavelength (the colorbar scale is normalized by the optical amplitude on GaSb substrate). Finally, the signal spectra on the HDS material are shown, for both techniques on figure 6. For each point the signal on the HDS material is normalized by the (flat) GaSb substrate response which serves as reference to remove the chromatic contribution of several optical components such as the source itself and the detector response. This relative s-SNOM sigp nal on HDS AHDS /ASub is fitted using A = σ⊥ (θ) |1 + rp (θ)|, with σ⊥ (θ) the differential scattering cross section of a vertically polarizable nano-sphere. This signal is proportional to |αef f,z |, as described in the supporting information (eq.3) and the factor |1 + rp (θ)| is accounting for the illumination field which is considered as mostly reflected by the surface. For the PiFM signal, the force signal is correctly fitted without resorting to induced photoex13


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pansion. As for the s-SNOM intensity, a signal proportional to |αef f,z |2 is found to fit rather well the observed signal (Figure 6, bottom). As detailed in the supporting information (eq. 10), the expression of the time-averaged force < Fz >∝ |αef f,z |2 is derived starting from previous expressions 16,34 but considering the interaction between the local field described through αef f,z and a unique apex charge proportional to the induced dipole moment p also proportional to αef f,z . For both PiFM and s-SNOM modeling, the general signal lineshape accounted by |αef f |2 contains both a dispersive and dissipative contribution. Their respective weights strongly depend on the sample response β =

−1 +1

on HDS, which is included inside αef f . Here, this

sample response was fixed by the dielectric function values given by eq.1, independently and precisely determined by FTIR measurement (cf. supporting information). Beside the β value which is the main non adjustable parameter leading to the observed shape, the fitting parameters for both spectra were the probe-sample distance, and the complex polarizability of the model sphere α⊥ . The s-SNOM fit was obtained considering a distance of 2 nm between the s-SNOM probe apex and the sample, and the polarizability of a tungsten probe multiplied by a complex factor (1.2+0.68i). The PiFM data were fitted using a negligible distance between the probe apex and the polarizability of a Si sphere multiplied by a complex factor 1.89 + 0.45i. We note that the agreement between these simple analytical models and the experimental spectra tends to diverge in the ENZ region. Such divergence is expectable given the simplified, phenomenological, description provided by a vertically polarizable sphere. Notably, the contribution of non vertical fields and forces become relatively stronger near ωp since the signal for the p-polarized light tends to vanish. Regarding PiFM, it was notably pointed out that the side-band detection should induce a contribution proportional to the derivative of the force along z. Adding such contribution can allow a better description in the ENZ region where the field confinement can strongly vary, however additional damping mechanism must then be considered to avoid nonphysical results. As for s-SNOM, the lock-in amplifier

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Figure 6: Near-field spectra on HDS relative to the substrate signal obtained with s-SNOM (tungsten probe) and PiFM (gold-coated silicon probe). Blue and gray curves: experimental PiFM signal and simulation respectively (top figure). Circles and green line: experimental s-SNOM and simulation respectively (bottom figure). Red curve: phase difference between the HDS and the substrate.

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detection can be relatively straightforwardly taken into account, but didn’t lead to a better description, leading us to the conclusion that additional simulation effort, when required, should rely on finer description of the lightning rod effect as in 35 where flaws of analytical dipole model are detailed. Still, the difficulty to describe the electromagnetic interaction between a semi-infinite probe and a sample remains a difficult and probe dependent problem. To date, dipole-based models are the most commonly used approach for the analytical expression and the physical pictures it offers. As pointed out elsewhere, in the context of PiFM, the calculated forces compared well with reported experiments and can to predict the observed distant dependant signal. While ENZ materials described by a known dielectric function appear as excellent samples to determine the response of the near-field probes, a better modeling of the experimental near-field interaction will certainly be achieved by going one step further and combining information such as PiFM and s-SNOM signals within the same setup. Considering the phase spectrum, we notice a correspondence with the partial Local Density Of State (LDOS), see supporting information for the partial LDOS-expression (Eq. 1) and spectrum. This link has already been discussed in a recent paper on phase information resolved with sSNOM for a dielectric probe 36 . In conclusion, spectroscopic phase-sensitive s-SNOM and PiFM imaging in side-coupling mode were performed on HDS strips having a known dielectric function. In contrast with a previous PTIR study 19 on polaritonic material near Berreman modes, the PiFM exhibited essentially a non-dissipative lineshape like for s-SNOM. In both cases, a phenomenological point-dipole model based on the effective polarizability of the probe coupled to the substrate accounts relatively well for the observed lineshapes. In addition, signatures of LSPR on the structure edges were also observed with both techniques, although slightly shifted with respect to the simulations performed on ideal square shaped structures without probe. The latter results also indicate the possibility to reveal infrared plasmonic modes with PiFM. In our study, in contrast with PTIR measurement, photo-expansion effect needs not to be taken into account for describing the signal on ENZ samples. With the near-field probes used in

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these experiments (tungsten s-SNOM probes and gold coated Si for PiFM probes), PiFM exhibited a better sensitivity to the dielectric function in the ENZ region. Therefore, as for s-SNOM, PiFM technique should effectively probe the impact of influence quantities on LO frequency such as stress or temperature, or fluctuation in the doping quantity near the material plasma frequency. In a near-future, carrying out simultaneous PiFM and s-SNOM measurements with the same probe should make it possible to compare the spectroscopic signals more quantitatively and more particularly to evaluate whether the proposed or more advanced phenomenological models can account for PiFM and s-SNOM signals by using an identical probe polarizability. Finally, as for s-SNOM, the carried work shows the relevance of PiFM approach for the characterization of polaritonic materials, but also lossless photonic devices since the photoinduced force is found to be independant from the sample absorption. This analysis should trigger additional nanospectroscopic investigations using combination of optomechanical and scattering-type methods.

Methods Sample preparation. The HDS structures were made through photolithography and chemical etching. The sample surfaces were first cleaned with organic solutions, blew dried with dry-N2 and heated for 2 min at 120◦ C. The sample is then covered with positive photoresist (AZMIR-701). The gratings with a constant periodicity (pitch of 1.6 µm) and ribbon width (700 nm) were patterned by photolithography. Afterwards, wet etching was conducted with a citric acid (C6 H8 O7 ) and hydrogen peroxide (H2 O2 ) solution to define the grating. Finally, the photoresist is removed in acetone and the structure is then cleaned by isopropanol and dried. The structure homogenity is very good as detailed in supporting material (Section 1). Numerical simulation and analytical models. Numerical simulations of figure 4 were carried out by solving the Maxwell equations by finite-difference time-domain (FDTD) method (Lumerical FDTD Solutions 8.12.631 from Lumerical Solutions Inc.) as reported be-

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fore 28 using the predetermined dielectric function. Additional LDOS calculation and FDTD simulations of the LSPR resonance are provided in the supporting information (Section 3). The dipole-based models and additional related simulations are provided in sections (5-7). Near-field characterization methods. The experimental concept for PiFM is further detailed in supporting information (Section 4) with additional details on the home-made s-SNOM instrument.

Acknowledgement This work was partially funded by the French ANR (SUPREME-B, ANR-14- CE26- 0015), Nano’mat and the French Investment for the Future program (EquipEx EXTRA, ANR 11EQPX-0016) and by the Occitanie region. The authors from UTT gratefully acknowledge the PhD scholarship support of the China Scholarship Council (CSC).

Supporting Information Available Contents: Sample homogeneity; Determination of the Drude model parameters; FDTD modeling and LDOS; Near-field characterization methods; Desription of the s-SNOM signal in the dipole approximation; Additional simulation of s-SNOM signal; Signal expression for the PiFM. This material is available free of charge via the Internet at http://pubs.acs.org/. Author Contributions Yi Huang (PhD) carried out scattering type near-field measurements as well as some PiFM measurements, she made figures and wrote experimental details. She made preliminary simulations. David Legrand (PhD) fabricated the near-field probes and helped in some near-field measurements. Remi Vincent provided first LDOS calculation and wrote the related part. Dogbe Foli, Ekoue Athos (PhD) made electromagnetic simulations (FDTD) 18


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of the structures. Derek Nowak, performed additional large bandwidth PiFM measurement. Gilles Lerondel initiated the collaboration and co-supervised Yi Huang’s Work. R. Bachelot and Tay, Beng Kang supervised the works of David Legrand providing helpful discussions. Thierry Taliercio designed all the structures with Barho, Franziska (PhD). Gonzalez-Posada Fernando and Cerutti, Laurent defined the fabrication process. Aurelien co-supervised Yi Huang’s work, made the quasi-analytical simulations and wrote large parts of the paper.

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For Table of Contents Use Only Spectroscopic nano-imaging of all-semiconductor plasmonic gratings using photoinduced force and scattering type nanoscopy Yi Huang, David Legrand, Rémi Vincent, Ekoué Athos Dogbe Foli, Derek Nowak, Gilles Lerondel, Renaud Bachelot, Thierry Taliercio, Franziska Barho, Laurent Cerutti, Fernando Gonzalez-Posada, Beng Kang Tay, and Aurelien Bruyant

All-semiconductor plasmonic gratings are investigated by spectroscopic nano-imaging across the plasma frequency. Both phase-sensitive scattering type nanoscopy (s-SNOM) and Photoinduced force microscopy (PiFM) are carried out on this structure.

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Spectroscopic nano-imaging of all-semiconductor plasmonic gratings

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