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Plasmon Resonances of Mid-IR Antennas on Absorbing Substrate: Optimization of Localized PlasmonEnhanced Absorption upon Strong Coupling Effect Lukáš B#ínek, Michal Kvapil, Tomáš Šamo#il, Martin Hrto#, Radek Kalousek, Vlastimil K#ápek, Ji#í Spousta, Petr Dub, Peter Varga, and Tomas Sikola ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00806 • Publication Date (Web): 18 Oct 2018 Downloaded from http://pubs.acs.org on October 19, 2018

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Plasmon Resonances of Mid-IR Antennas on Absorbing Substrate: Optimization of Localized Plasmon-Enhanced Absorption upon Strong Coupling Effect Lukáš Břínek†, Michal Kvapil†,‡, Tomáš Šamořil†,‡, Martin Hrtoň‡, Radek Kalousek†,‡, Vlastimil Křápek†,‡, Jiří Spousta†,‡, Petr Dub†,‡, Peter Varga†,‡, and Tomáš. Šikola*,†,‡ †

Institute of Physical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic ‡ CEITEC BUT, Brno University of Technology, Purkyňova 123, 612 00 Brno, Czech Republic * [email protected], phone +420 5 4114 2707

ABSTRACT We report on the surface plasmon resonances of mid-infrared Au antennas deposited on an absorbing silicon-rich oxynitride (SRON) thin film, and on their utilization for enhancement of a spatially localized absorption of infrared (IR) radiation in SRON. The antenna resonances were experimentally determined from far-field IR reflection spectra measured over a broad mid-IR range. Due to a hybridization effect caused by the strong coupling of localized surface plasmon resonances with vibration modes - phonon resonances in SRON, these spectra show up the Rabi splitting of the reflection peaks and thus three hybrid branches where resonant wavelengths scale nonlinearly with the antenna length have become apparent. To maximize spatially localized plasmon-enhanced energy absorption in SRON, a compromise wavelength between that one related to optimum antenna resonances and the SRON resonant absorption wavelengths must be chosen. We stress that the principles of this method can be utilized in other dielectric or semiconductor materials resonantly absorbing in the mid-IR range, and, more generally, in other spectral regions, including the visible (e.g. due to excitons). Hence, in addition to the spatially localized heating, the principles can be exploited in an optimization of the efficiency of IR and light detectors, solar cells, biosensors and other applications. KEY WORDS: Mid-IR antennas, SRON, resonant absorption, strong coupling, Rabi splitting, localized absorption enhancement MAIN TEXT Much work has been done on metallic plasmonic resonant structures (antennas) with respect to their heating properties. The enhancement of heat generation via plasmon resonances (called localized surface plasmons – LSP) and a consequent temperature increase have not been only studied by simulations, 1 but also experimentally. 2 The heat power enhanced by this method was for instance utilized in infrared spectrometers and bolometers, 3-6 in the local growth of nanowires and phase transformation of materials in the antenna vicinity, 7, 8 and in other applications. 1, 9, 10 One of the most recent promising exploitation of plasmon induced heating is the so called Heat - Assisted Magnetic Recording (HAMR) to be introduced into the magnetic recording industry by Seagate Technology soon. 11 Taking into account the basic principles of absorption of electromagnetic radiation in a media, the heating can be provided by two different mechanisms. One is based on the dissipation of electromagnetic radiation within metallic plasmonic antennas surrounded by optically

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transparent, non-absorbing environments. 1, 10 Another heating mechanism exploits enhanced electric near-fields generated by antennas upon resonances in their close surroundings. If this small volumes contain absorbing materials, they dissipate the energy of these fields, as used in HAMR technologies. In all these cases, the plasmon resonance peaks in reflection and absorption optical spectra do not generally undergo dramatic shape changes, only their position is shifted and their width becomes larger (higher losses). However, it has been demonstrated that interesting phenomena occur if plasmonic antennas are coupled through their near fields with nearby dielectrics or semiconductors possessing absorption peaks or bands at specific resonant wavelengths (further also called “resonant absorption”). This is known from a series of works dealing with coupling between plasmon and other excitation resonances. For instance, it covers Surface Enhanced Infrared Absorption (SEIRA), 12 Surface Enhanced Infrared Spectroscopy (SEIRS), 13 Fano-type signals in the IR extinction spectrum, 14, 15 or intuitive models based on strongly coupled molecular and plasmonic resonators predicting effects such as the Rabi splitting and transition between electromagnetically induced transparency (EIT) and enhanced absorption. 16, 17 It is significant that in this case, depending on the strengths of coupling, the antenna plasmon resonances themselves might become noticeably influenced by their coupling to absorption resonance processes in these materials as shown in our previous paper 18 or in relevant literature on coupling. 17 Depending on the wavelength of electromagnetic radiation and thus the absorption mechanism (e.g. phonon resonances in IR, excitons in UV/VIS), absorption in such materials might preferentially lead to enhanced direct heat generation 19 or, for instance, also to enhanced photoluminescence (PL) and higher photovoltaic output of photodetectors or solar cells, etc. 20 As the maximum electric field enhancement generally occurs in the antenna gaps or nearby of them, the maximal absorption is spatially localized to small volumes of these resonantly absorbing materials forming the gaps or substrates underneath the gaps. Recently, the effects related to a large Rabi splitting caused by hybridization of resonant states due to strong coupling between plasmons and various types of excitations in non-metallic materials, have become a hot topic. It is especially true for the visible spectral region and for propagating surface plasmon polaritons (SPP). In this case splitting in ω (k) dispersion relation curves (the reciprocal space) caused by the strong coupling of surface plasmonpolariton modes to states mostly associated with quantum emitters such as excitons in Jaggregates, dye molecules or quantum dots has been reported in a number of papers. 21-23 As for the localized surface plasmons (LSP) their strong coupling with excitons in the visible has been for instance published in 16, 24, 25 and in a recent review paper on strong coupling 26 whereas 2D materials emitters (graphene, TMDCs) are reported as well. The Rabi splitting in the visible typically reaches the values of hundreds of meV. Despite the existence of flourishing field of phononic strong coupling in the mid-IR region using surface phonon polaritons 27, 28, fewer publications have been devoted to LSP coupling with optical phonons in the mid-IR. Experimental results on coupling of LSP in metamaterials (split-ring resonators) with the SiO2 phonon band in the mid-IR have been published e.g. in 29, theoretical modelling of the LSP coupling with surface phonons in a GaN semiconductor in 30. In accordance with our results, the Rabi splitting did not exceed 40 meV here. In our paper we report on coupling of LSP resonances to vibration modes – phonon resonances in an absorbing substrate made of silicon rich oxynitride (SRON) showing up the phenomenon of strong coupling and related effects (mode hybridization manifested as the Rabi splitting of resonant peaks) in the mid-IR. Note, that similarly to literature on coupling between plasmon and other excitation resonances, 21 we consider the system in the strong coupling regime, whenever the Rabi splitting is experimentally observable.


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The knowledge learned from the behavior of plasmon resonance peaks in the spectral vicinity of absorption resonant peaks/bands upon this strong coupling is then utilized in optimization of localized plasmon-enhanced absorption (LP-EA) of IR radiation in such a substrate. It is worth strengthening that the principles of this method can be also applied to other nonmetallic materials having significant absorption peaks/bands of various physical origin in other spectral regions, including the near-IR and visible, and so can find direct application not only in the local heating of materials, but also in IR and light detectors, energy harvesting (solar cells), (bio)sensing, etc. RESULTS AND DISCUSSION As the antenna substrate, a 110 nm-thick film of SRON deposited on a silicon substrate was used. This material is attractive for the development of a new generation of microelectronic and optoelectronic devices as it offers a large variability in adjustments of electrical and optical properties. 31, 32 For instance, upon its thermal annealing at about 1100 ºC, either integrally in an oven 33 or locally by a mid-IR (CO2) laser, 34 photoluminescence-active Si nanocrystals can be formed in the matrix of this material. SRON is typical for a significant resonance absorption in the mid-infrared in the wavelength range from 8.5 to 12.5 µm (similarly to SiO2), as proved by FT-IR spectroscopic reflectometry. 18 It is mostly caused by a stretching vibrational modes of Si – N bond at 11.6 µm and Si – O bond at 9.2 µm present in the material as specified in references 35, 36. The index of refraction 18 and its dispersion behavior shown in Figure 1a was determined by fitting these experimental spectroscopic data using a dielectric function modeled by 3 Lorentz oscillators. 37 The real part of index of refraction possesses a pronounced anomalous dispersion in the mentioned wavelength band (i.e. an increase of its value with the wavelength) leading through the Kramers-Kronig relations to a narrow band in the imaginary part of index of refraction, and thus to a significant resonant absorption. 37 Vice versa, such an anomalous dispersion appears always when a resonant (i.e. at a specific narrow frequency band) absorption occurs regardless of its physical principle To investigate plasmon resonances experimentally, gold plasmonic antennas (height: 60 nm of Au on a 3nm Ti buffer layer, width: 400 nm, length: 0.8 – 6 µm) were fabricated via electron beam lithography on the SRON thin film. The antennas consist of two rectangular arms (dimer antennas) separated by a gap (100 nm) to achieve the pronounced electromagnetic field there (see Figure 1b). The rectangular shape of the antenna arms was chosen to enhance energy absorption inside a larger volume beneath the gap in SRON compared to bow-tie antennas, although its radiation efficiency is smaller than that one of bow-tie or log-periodic antennas. 9 The antennas of the same dimensions and shape were arranged into an array of the area 50x50 µm2 in order to increase the reflection signal-to-noise ratio. To find a configuration with a minimized coupling between the individual resonant antennas, a series of arrays with different spacing between the antennas were designed for the same antenna geometry and tested.


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Figure 1: (a) Refractive index of silicon-rich oxynitride (SRON). 18 (b) Schematic of the investigated system. Unpolarized reflection spectra were obtained by a Fourier Transform IR microscope working in the spectral range 2.5-16.7 µm. The spectra were taken from the antenna arrays and divided by the reference ones corresponding to the bare SRON surface nearby the antenna structures. The resultant experimental spectra for antennas of various arm lengths are plotted in Figure 2a. For comparison, the simulated spectrum (FDTD) for the antenna with the arm length L = 2.8 µm is shown here in the inset as well. Almost each spectrum in this figure possesses three resonant peaks separated by valleys. This is known as a vacuum Rabi splitting, typical for strongly interacting multi-level systems, 16, 17, 21, 38 and caused here by a strong coupling of plasmon resonances with vibrational resonances in the SRON material (see Figure 1a). It is worth noting that the transmission spectra for the antennas with an arm length of 2.4 µm (see Figure S1 in Supporting info) showed a peak opposite to the valley in the reflected signal (the Rabi splitting) around the resonant absorption wavelengths of SRON (i.e. ≈ 9.2 and 11.6 µm). Thus, it proves the strong coupling effect and not just a simple enhanced absorption as discussed in 16. The presence of three peaks and two dips in the reflection spectra indicates the so called double Rabi splitting, the phenomenon already observed for the strong coupling between surface plasmon polaritons and excitons of dye molecules in the visible. 39 Because of the pronounced dispersion of the SRON index of refraction around the region of enhanced absorption a non-linear scaling between the position of the peaks, i.e. resonance wavelengths (λres), and the antenna arm length (L) should be expected. 18 Indeed, looking at Figure 2b, where the experimental peak positions from Figure 2a are plotted as a function of L, one can see that once the left resonance peak approaches the wavelength at which the absorption in SRON becomes substantial, it almost stops moving with the antenna arm length and does not exceed the value λres = 8.5 µm. In addition, the intensity of the peak goes down for the longest antenna lengths. This feature will be discussed later using Hopfield mixing coefficients.


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Figure 2: (a) Experimental IR reflection spectra of dimer Au antenna arrays of specific arm lengths with the 100 nm gap fabricated on a SRON/Si substrate. For comparison, the measured and simulated reflection spectrum (dashed line) for the antenna arm length L = 2.8 µm is shown in the inset as well. (b) Resonance wavelengths vs. antenna arm lengths (L). The experimental points in the branches were determined from the extremes of the peaks as indicated by the dashed-dotted line in (a). The red curve is obtained by the approximate formula λres = 2nSRONL. The data of the positions of the central peak from FDTD simulations are not shown, as this peak was less pronounced in simulations. Accordingly, the right resonance peak almost does not move with the small antenna arm lengths as the corresponding resonance wavelengths (λres ≈ 12 µm) are too close to the area of enhanced absorption in SRON. However, this peak starts to move when the arms become longer (L ≥ 2.5 µm) and thus the resonance wavelengths shift beyond this area. The peak is generally broader compared to the left resonance peak. The central resonance peak which is less profound in both, experimental and numerical, spectra exhibits only a relatively small shift with the antenna length, as the peak is surrounded by SRON absorption modes. The ref lection spectra of the antennas were also simulated by the FDTD method (Lumerical) 40 and the corresponding peak positions are plotted by the blue solid curves in Figure 2b. The good qualitative agreement between the experiment and the simulation up to L = 4.5 µm is obvious. For the antennas with L > 4.5 µm the experimental data for the upper branch are already missing as the quality of the peaks at the resonance wavelengths close to the upper limit of the spectrometer working range was very poor (see Figure 2a). The role of the SRON film thickness on the antenna resonant wavelength and field distribution around the antenna is demonstrated in Figure S2 of Supporting Information. Similarly to references 16, 17, 21, 38, the appearance of three resonant wavelength branches can be explained by a coupling-induced transformation of plasmon and substrate excitation (in our case vibrational) resonances into hybrid resonant modes. To stress the hybridization effects, the plasmon resonant wavelength of the antenna placed on a hypothetical non-absorbing 110 nm thick film with n = 1.5 (corresponding to SRON at λ = 4 µm, i.e. outside of the resonant absorption) on Si substrate (FDTD simulations) and absorption resonant wavelengths (equal to λ = 9.2 µm and λ = 11.6 µm, i.e. roughly to the central wavelength of the absorption bands) as a function of the antenna arm length are shown in Figure 2b The former dependence gives a growing straight line in accordance with an approximate formula λres = 2neffL 41, where neff represents the effective refractive index of the non-absorbing thin film on the Si substrate equal to neff ≈ 2.08 (obtained from the formula by fitting the data from FDTD numerical simulations of the antenna on such a composed substrate), and the latter ones are represented by horizontal straight lines. The concept of introducing an effective index of refraction into


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the formulas for the antenna resonant wavelengths, although of different effective forms, was for instance also used in references 30, 42, 43. As there is no interaction between the antenna and the non-absorbing substrate, these plasmon- and phonon-related lines cross each other. However, when the coupling is switched on (by utilizing the real absorbing SRON substrate), a characteristic anti-crossing of the resonant modes occurs and thus the three branches appear. Based on the generally accepted convention, 21 the appearance of the clearly split resonant branches allows us to talk about the strong coupling between plasmon and phonon resonances. For completeness, the curve (in red) obtained by putting the real part of SRON refractive index from Figure 1a into the above presented formula λres = 2nSRONL is added in Figure 2b. This curve possesses two major branches, interconnected with a “backward” line covering frequencies within the region of the SRON absorption band (i.e. 8.5 – 12.5 µm – see Figure 1a). Thus for the antenna arm length interval where both branches (lower and upper) exist, two resonant wavelengths roughly copying the experimental and numerical values can be found. The non-appearance of the upper branch of the curve at shorter wavelengths results most likely from an approximate character of the λres (L) formula being based on a simple λ/2 resonant condition.

Figure 3: (a) Comparison of the resonant wavelengths for the antennas of length L obtained experimentally and from the eigenvalues of the Hopfield-Bogoliubov matrix. (b)-(d) Hopfield mixing coefficients for resonant branches vs. the antenna length L. The character of the hybridized resonant peaks was further investigated in terms of the Hopfield mixing coefficients, similarly to ref. 27, 28, which express the fractions of individual uncoupled oscillations in the hybridized system. The Hopfield-Bogoliubov matrix corresponding to this three level system has the following form / 0

/ , / (1) 0 /

where Ep, ESi-N, and ESi-O are resonant energies of plasmonic, Si-N and Si-O phononic modes, respectively, and Vp/Si-N and Vp/Si-O are the coupling coefficients between the plasmonic and the respective phononic mode. Three eigenvalues of the matrix give the eigen energies of the hybridized system, where the resonant peaks should appear in the measured spectra. In Figure 3a, one can see the resonant wavelengths obtained by the Hopfield model are in reasonable agreement with those obtained from the experiment. The three eigenvectores of the matrix M are (XSi-N, C, XSi-O)iT, where i = 1, 2, 3. Since the eigenvectors are the unit vectors, the sum of their squares must equal unity. The squares of the eigenvectors give values of the Hopfield mixing coefficients (see Figure 3b,c,d) which


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express the fraction of individual oscillations in the system, here: |C|2 corresponds to the plasmon fraction, |XSi-N|2 to the Si-N phonon fraction, and |XSi-O|2 to the Si-O phonon fraction. The values of the Rabi splitting Ω obtained as Ωi = 2Vi from the coupling coefficients Vp/Si-N and Vp/Si-O of the matrix M are Ωp/Si-N = (14 ± 2) meV and Ωp/Si-O = (42 ± 11) meV. Using the mixing coefficients in Figure 3d, the drop in the intensity of the left resonant peak for antennas longer than 2 µm (see Figure 2a) mentioned earlier can be explained by the weakening of the plasmonic fraction in the lower hybridized branch with the increasing length of the antennas, reducing thus the coupling with the incident field.” The absorption of the electromagnetic energy in the material unit volume can be determined from the formula Im , 11 where Im[ε(r)] is the imaginary part of the dielectric function of SRON. To get the information about the spatially localized plasmonenhanced absorption of electromagnetic radiation in SRON beneath the antenna gap (1.2 µm x 1 µm x 110 nm) the near-field electric field in this volume was simulated first. The calculated spectra of electric field enhancement defined as the ratio of |E|2 values averaged over the domain to the incident field |Einc|2 (η= |Eaver|2 / |Einc|2) are plotted in Figure 4 for different arm lengths. In this plot the upper and lower resonance branches are clearly visible. In the lower branch the maximum is achieved for an antenna arm length of 2.4 µm and λ = 7.8 µm, and equals η = 45. In the upper branch the maximum reaches η = 38 and appears for L = 3.8 µm and λ = 17.4 µm. Note that the upper branch is noticeably shifted to longer wavelengths with respect to the corresponding curve plotted from the far field resonance values in Figure 2b. This is in agreement with the well known effect of mutual differences in near-field and far-field resonance wavelengths being more pronounced with the increasing damping of plasmon oscillations (as occurs for longer wavelengths – see Figure 1a) as discussed for instance in 13 and 44.

Figure 4: Simulated spectra of the electric field enhancement η averaged over a domain (with dimensions 1.2 µm x 1 µm x 110 nm) in SRON beneath the antenna gap for different antenna arm lengths specified in Figure 2. The absence of a significant field enhancement in the wavelength range corresponding to the central resonant branch can be explained by the values of mixing coefficients for this branch (Figure 3c). The fraction of the plasmonic mode in the central hybridized branch is much smaller than the fractions of other two phononic modes. Therefore, with the nearly missing plasmonic fraction, the central branch is predominatly phononic and the coupling of the mode with the incident field, as well as the values of the field enhancement are relatively insignificant with respect to the other two branches. It is obvious that the positions of maxima are achieved as a result of a trade-off between the size of the antenna and the absorption in SRON (decreasing intensity). In case of the upper


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branch the intensity of the electric field does not grow with the antenna arm length due to the increasing absorption in SRON from λ = 17 µm on (see Figure 1a) and, hence, the maximum occurs roughly at L = 4 µm and not at longer antenna arms. The slightly smaller maximum intensity in the upper branch compared to the lower one is caused by a higher absorption of IR radiation in SRON at λ = 17.4 µm with respect to that one at 7.8 µm. The above mentioned formula on absorption shows that in addition to the frequency, the energy absorption/dissipation depends on the product of the square of electric field intensity and the imaginary part of the dielectric function of SRON. Hence, the maximal enhancement of the absorption in the SRON domain caused by plasmon resonant effects is expected in the wavelength intervals 7.8 µm ≤ λ ≤ 8.5 µm and λ > 12 µm where an increased absorption of IR radiation in SRON together with still reasonably high resonant peaks of electric field intensity in the gap occur.

Figure 5: (a) Simulated spectra of the relative power absorbed in the SRON domain beneath the antenna gap with respect to that one absorbed in the identical domain of the sample without the antenna for different arm lengths of dimer antennas specified in Figure 2. (b) Absorption efficiency in the SRON domain beneath the antenna gap for different arm lengths of dimer antennas specified in Figure 2. To find the maximal influence of antennas on enhancement of absorption in SRON, the spectra of the relative power absorbed in the SRON domain beneath the antenna gap with respect to that one absorbed in the identical domain without the antenna were simulated for antennas of different arm lengths (see Figure 5a). For the lower branch of resonances, the maximum of this relative value reached almost 60 and was achieved for the antenna of the arm length L = 2.4 µm and corresponding wavelength λ = 7.8 µm. For the upper branch this value was 68 and was obtained for the antenna with the arm length L = 4 µm (λ = 17.7 µm). Simultaneously, the absorption efficiency defined as the ratio of the power absorbed in the SRON domain to the energy flux of IR radiation incident on the domain area was evaluated for the antennas of different lengths (see Figure 5b) and the bare SRON. In the lower branch of resonances, the maximal absorption efficiency reaches a value of 0.86 and occurs for the antenna arm length 3.2 µm (λ = 8.6 µm). The maximal absorption calculated in the same SRON domain of the sample without the antenna (bare substrate) was 0.068 and occurred for λ = 9.9 µm. Hence, the absorption efficiency was enhanced by the plasmonic antennas almost by the factor of 12.6. In the upper branch of resonances the absorption efficiency of the domain beneath the gap was even higher and, for instance, for the antenna arm length L = 4.4 µm (λ ≈ 20 µm) reached the value ≈ 1.3 which represents the enhancement by the factor 19 with respect to the bare SRON (please note the absorption efficiency higher than one is caused by a “funneling effect” of antennas). This value is not maximal as due to the presence


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of another peak at λ ≈ 23.4 µm (450 cm−1), related to the rocking vibration mode of the Si-O bond, 35 the maximum is shifted to λ ≈ 30.2 µm (L ≈ 5.2 µm) and reaches the value ≈ 1.8 (see Figure S3 in Supporting Information). However, the absorption enhancement caused by coupling the plasmons with SRON around this longer wavelength goes beyond the scope of this paper and will not be discussed here.

Figure 6. Maximum of the electric field enhancement η averaged over a domain in SRON beneath the antenna gap and the maximum absorption efficiency of this domain as a function of light wavelength. Using the data from Figures 4 and 5b, the maximum value of the electric field enhancement η averaged over a domain in SRON beneath the antenna gap and maximum absorption efficiency of this domain were extracted for each individual wavelengths and plotted in Figure 6. In this figure, the shifts between the maxima in curves for electric field and absorption efficiency, discussed previously, are obvious. Finally, to get an overall idea about energy absorption by plasmonic processes in the antenna setup, the FDTD numerical simulations of the electromagnetic energy dissipated inside the metallic antenna arms has been carried out as well. It was found that the energy absorbed in the antenna arm increases with its length until it reaches its maximum for L = 2.6 µm (λ = 7.65 µm) and L = 6.0 µm (λ = 18.1 µm) in case of the lower and upper branch, respectively (see Figure S4 in Supporting information). After that, it starts steeply to decrease. On the other hand, the absorption efficiency defined in this case as the ratio of the heat power generated in the antenna arm to the energy flux of IR radiation incident on the arm continuously decreases with the antenna arm length (see Figure S5 in Supporting information). The efficiency maximum in this figure achieves the value 1.4 and occurs for the antenna with the arm length L = 1 µm. In this case almost zero absorption in SRON takes place. Consequently, taking into account the results presented above, there is a chance that at longer wavelengths corresponding to the maximum absorption in SRON beneath the antenna gap the heat developed in this part could be significantly higher than in the antenna arms. Hence, the indirect heating of SRON by the arms would be less significant when the heat localized in SRON just beneath the antenna gap becomes maximal. The results in Figure 7 prove such a spatially localized heat development. In this figure the heat power density distribution in horizontal cross sections over the SRON (5 nm beneath the surface) and the middle of the arms with the length L = 1.0 µm and L = 4.4 µm upon the 480 Wcm−2 radiation with the wavelengths λ = 4 µm (absorption in the metal arms significantly higher than in the SRON


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domain) and λ = 20 µm (absorption in the SRON domain significantly higher than in the metal arms), respectively, is depicted. However, it is necessary to stress that the optimized absorption procedure discussed in this paper can be generally used for various spectral regions where the materials also exhibit strong absorption resonances, for instance in the visible. Naturally, in addition to the spatially localized heating the described principles can be exploited in optimization of the efficiency of IR and light detectors, solar cells, biosensors and other applications.

Figure 7: Computed heat power density distribution (nW/nm3) across the horizontal cross sections in the middle height of the arms (upper picture) and in the SRON thin film 5 nm below the surface (lower picture). The antennas of the length L = 1.0 µm (left) and L = 4.4 µm (right) were illuminated by the radiation with the intensity 480 Wcm−2 and wavelengths λ = 4 µm and 20 µm, respectively. In conclusion, resonance properties of the plasmonic infrared antennas deposited on the SRON thin film with a resonant absorption of radiation in the mid-infrared were studied. Far-field reflection spectrum obtained for antennas of a specific length generally possesses three resonant plasmon peaks being separated by valleys resulting from a strong coupling of plasmonic antenna resonances with absorption resonances in the SRON material (Rabi splitting). Due to the coupling-induced transformation of plasmon and vibrational resonances into hybrid resonant modes three resonant wavelength branches appeared. The absorbed energy primarily depends on the product of the square of electric field intensity and the imaginary part of the dielectric function of SRON. Hence, the highest plasmon enhancement of spatially localized absorption in this material will occur for the wavelengths closer to the absorption peaks of SRON and still associated with reasonable plasmon resonances in the antennas. Therefore, for lower and upper plasmon resonance branch the maximum relative values of the absorption enhancement and absorption efficiency enhancement (both related to bare SRON without antennas) in the domain below the gap occur at wavelengths in an interval between the wavelength corresponding to the maximum electric field intensity and that one where the plasmons start to be strongly coupled to the SRON vibration modes. For the lower branch, the maxima of relative absorption (60) and absorption efficiency (12.6) were found by numerical simulations at the wavelength λ = 7.8 µm and λ = 8.6 µm, respectively. For the upper branch the analogue relative values were 68 and 19 (not the maximal value) and the corresponding wavelengths λ = 17.7 µm and λ = 20 µm, respectively. In this paper, the discussions on behavior of plasmon resonances of antennas fabricated on the absorbing substrate and their utilization for spatially localized absorption enhancement of ACS Paragon Plus Environment

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electromagnetic radiation in this substrate have been carried out for the mid-IR. However, the conclusions are also applicable for other spectral regions where the materials exhibit strong absorption resonances, for instance in the visible.

METHODS

Fabrication. Silicon substrates (resistivity 6-9 Ω⸱cm) with a 110 nm-thick film of SRON (prepared by PE CVD) were obtained from company ON Semiconductors Czech Republic. The substrates were chemically cleaned (acetone, isopropanol and demineralized water, all in ultrasonic bath), pre-baked at 180 °C for 30 minutes and covered by a 170 nm-thick film of the PMMA resist deposited by spincoating (Laurel WS-400, 4000 rpm for 30s) from 4% solution of PMMA in anisole (MicroChem). Deposited PMMA was baked again at 180 °C for 90 s. Masks for antennas were fabricated in the resist by electron beam lithography (Tescan dual beam FIB/SEM Lyra3 XMH, electron dosage 250 µC/cm2) and developed in a 1:3 mixture of Methyl isobutyl ketone and isopropanol for 90 s. The masks were covered by a film of 3 nm of Ti and 60 nm of Au deposited by Ion Beam Sputtering deposition technique (in-house developed sputtering setup with a Kaufman-type Ar ion beam source). The lift-off process was carried out in acetone. Experiments. The complex dielectric function of SRON was determined experimentally by measuring the IR reflection curve of a SRON/Si structure with an IR spectrophotometer (Bruker IFS66v). The dielectric function was then expressed in the form of a series of three Lorentz oscillators fit to the spectrophotometer data. The optical response of fabricated structures was measured by Fourier-Transform InfraRed microspectroscopy (FTIR Bruker Vertex 80v with IR microscope Hyperion 3000, 36x Schwarzschild objective, SiC source, KBr beamsplitter, Hg-Cd-Te detector) mostly in reflection configuration (usually: range 6004000 cm-1, i.e. 2.5 – 16.7 µm, resolution 4 cm-1, 512 scans). Relative reflectance of the antenna arrays are then calculated as a ratio between the spectra taken from the antenna arrays and the reference ones corresponding to the bare SRON surface nearby the antenna structures. Simulations. Numerical simulations were carried out in a commercial grade simulator Lumerical FDTD Solutions which is based on the finite-difference time-domain method. 40 Dielectric functions of silicon substrate and gold film was taken from simulator’s internal material database. The dielectric function of SRON was imported into the simulator from the experimental results (see above). The presence of the titanium layer was neglected in simulations. Simulated antennas were illuminated from the top by IR white light in the spectral range between 4 and 20 µm, using simulator’s Total-Field Scattered-Field source of illumination. The structures were surrounded (outside the source volume) by a set of 2D monitors from which the spectra of antennas scattering cross-sections were calculated. The maxima of the spectra were taken as the resonant wavelengths. To determine the influence of antennas on enhancement of absorption in the SRON film, a 3D monitor was placed in the SRON domain beneath the antenna gap. This monitor recorded the spectra of power absorbed in the SRON. The same monitor was used in the calculation of absorption efficiency, where the absorbed power is normalized to the energy flux of IR radiation incident on the upper side (SRON/air interface) of the monitor. To determine the power absorbed in both, the SRON film and in the antennas, numerical calculations were carried out in COMSOL Multiphysics. 45 First, the RF module was used to calculate the field scattered by the antenna (the fields obtained from COMSOL and Lumerical


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were compared and found identical). Then, the electromagnetic energy absorbed in the structures was computed via the equation stated above in this text. Hopfield mixing coefficients. Scattering cross sections of the antennas on the SRON film were extracted from the FDTD simulations and fitted by a model of three oscillators. Parameters of the fit (energies of the plasmonic and phononics modes, damping and coupling coefficients) were then inserted into the Hopfield-Bogoliubov matrix (Eq. 1). Energies corresponding to the uncoupled plasmonic mode in the antennas of length L, inserted in the matrix, were estimated based on FDTD simulations for a hypothetical 110 nm thick nonabsorbing film of refractive index n = 1.5 resting on a silicon substrate (n = 3.42). Energies and mixing coefficients related to each of hybridized branches were found by determination of matrix eigenvalues and eigenvectors, respectively. ACKNOWLEDGEMENT We acknowledge the support by the Grant Agency of the Czech Republic (grant No. 1521581S and 17-33767L), Technology Agency of the Czech Republic (grant No. TE01020233), and MEYS CR (grant No. LQ1601 – CEITEC 2020). We also acknowledge the CEITEC Nano Research Infrastructure supported by MEYS CR within the project LM2015041 for providing us with access to their facilities. Dielectric function of SRON was determined experimentally by Josef Humlíček from Masaryk University, Brno, Czech Republic. SUPPORTING INFORMATION Supporting information available: Reflection and transmission spectrum of antennas on SRON (Figure S1), influence of SRON thickness on antenna resonance (Figure S2), maximum absorption efficiency (Figure S3), heat power generated in the antenna arm (Figure S4), absorption efficiency of the antenna arm (Figure S5). This material is available free of charge via internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Email: [email protected], phone: +420 5 4114 2707 ORCID Michal Kvapil: 0000-0002-2712-1991 Martin Hrtoň: 0000-0002-3264-4025 Vlastimil Křápek: 0000-0002-4047-8653 Author Contributions L.B. designed and performed the FTIR experiments together with M.K. and conducted numerical simulations with M.H. and R.K. T.Šam. carried out fabrication of antennas. V.K., J. S. and P. D. provided theoretical support; P. V. and T.Šik. supervised the project and co-wrote the manuscript. All authors discussed the results and reviewed the manuscript. The authors declare no competing financial interests.


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For Table of Contents Use Only Plasmon Resonances of Mid-IR Antennas on Absorbing Substrate: Optimization of Localized Plasmon-Enhanced Absorption upon Strong Coupling Effect Lukáš Břínek†, Michal Kvapil†,‡, Tomáš Šamořil†,‡, Martin Hrtoň‡, Radek Kalousek†,‡, Vlastimil Křápek†,‡, Jiří Spousta†,‡, Petr Dub†,‡, Peter Varga†,‡, and Tomáš. Šikola*,†,‡ †

Institute of Physical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic ‡ CEITEC BUT, Brno University of Technology, Purkyňova 123, 612 00 Brno, Czech Republic * [email protected], phone +420 5 4114 2707

Simulated spectra of the electric field enhancement |Eenh|2 averaged over a domain in SRON film beneath the antenna gap for different antenna arm lengths L (left). Resonance wavelengths vs. antenna arm lengths (right).


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Figure 1: (a) Refractive index of silicon-rich oxynitride (SRON). 18 (b) Schematic of the investigated system. 165x60mm (300 x 300 DPI)


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Figure 2: (a) Experimental IR reflection spectra of dimer Au antenna arrays of specific arm lengths with the 100 nm gap fabricated on a SRON/Si substrate. For comparison, the measured and simulated reflection spectrum (dashed line) for the antenna arm length L = 2.8 μm is shown in the inset as well. (b) Resonance wavelengths vs. antenna arm lengths (L). The experimental points in the branches were determined from the extremes of the peaks as indicated by the dashed-dotted line in (a). The red curve is obtained by the approximate formula λres = 2nSRONL. The data of the positions of the central peak from FDTD simulations are not shown, as this peak was less pronounced in simulations 170x60mm (300 x 300 DPI)


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Figure 3: (a) Comparison of the resonant wavelengths for the antennas of length L obtained experimentally and from the eigenvalues of the Hopfield-Bogoliubov matrix. (b)-(d) Hopfield mixing coefficients for resonant branches vs. the antenna length L. 160x55mm (300 x 300 DPI)


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Figure 4: Simulated spectra of the electric field enhancement η averaged over a domain (with dimensions 1.2 μm x 1 μm x 110 nm) in SRON beneath the antenna gap for different antenna arm lengths specified in Figure 2. 82x55mm (300 x 300 DPI)


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Figure 5: (a) Simulated spectra of the relative power absorbed in the SRON domain beneath the antenna gap with respect to that one absorbed in the identical domain of the sample without the antenna for different arm lengths of dimer antennas specified in Figure 2. (b) Absorption efficiency in the SRON domain beneath the antenna gap for different arm lengths of dimer antennas specified in Figure 2. 162x50mm (300 x 300 DPI)


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Figure 6. Maximum of the electric field enhancement η averaged over a domain in SRON beneath the antenna gap and the maximum absorption efficiency of this domain as a function of light wavelength. 82x54mm (300 x 300 DPI)


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Figure 7: Computed heat power density distribution (nW/nm3) across the horizontal cross sections in the middle height of the arms (upper picture) and in the SRON thin film 5 nm below the surface (lower picture). The antennas of the length L = 1.0 μm (left) and L = 4.4 μm (right) were illuminated by the radiation with the intensity 480 Wcm-2 and wavelengths λ = 4 μm and 20 μm, respectively. 140x54mm (300 x 300 DPI)


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