Hexagonal Boron Nitride Self-Launches Hyperbolic Phonon

Apr 28, 2017 - Our findings suggest that structural continuity between the fold and hBN crystal is crucial for creating self-launched waves with a con...
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Hexagonal Boron Nitride Self-Launches Hyperbolic Phonon Polaritons Leonid Gilburd,† Kris S. Kim,† Kevin Ho,† Daniel Trajanoski,† Aniket Maiti,†,‡ Duncan Halverson,† Sissi de Beer,†,§ and Gilbert C. Walker*,† †

Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada Department of Physics, Indian Institute of Technology, Kanpur, 208016, India § Materials Science and Technology of Polymers, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands ‡

S Supporting Information *

ABSTRACT: Hexagonal boron nitride (hBN) is a 2D material that supports traveling waves composed of material vibrations and light, and is attractive for nanoscale optical devices that function in the infrared. However, the only current method of launching these traveling waves requires the use of a metal nanostructure. Here, we show that the polaritonic waves can be launched into the 2D structure by folds within hBN, alone, taking advantage of the intrinsic material properties. Our findings suggest that structural continuity between the fold and hBN crystal is crucial for creating self-launched waves with a constant phase front. This approach offers a single material system to excite the polaritonic modes, and the approach is applicable to a broad range of 2D crystals and thus could be useful in future characterization.

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In numerous reports, launching and detection of HPhPs in thin hBN films was studied using metallic atomic force microscopy (AFM) probes6,11,22,23 or films of gold on top,14 as both serve as metal nanoantennas to couple energy into the material. It would be advantageous to have a metal-free method to excite phonon polaritons in 2D materials such as hBN and others, to better understand the photophysics of the polaritons, without damping from the metal. Furthermore, multilayer structures made of multiple (e.g., two) 2D materials are being considered for devices. If the mechanism of polariton excitation involves a metal nanostructure near both materials, then both materials will experience the field of the metal nanostructure polarized by an external light field. Depending on the properties of the 2D materials, they may both experience the excitation of polaritons. On the other hand, folds in materials could allow excitation of polaritons within itself, while the polaritons in the other material are not excited by the far-field. Herein, we report a simple method to launch long-range HPhPs by employing subwavelength folds of hBN crystals to generate self-launched HPhPs. We demonstrate how to identify self-induced phonon polaritons with well-defined phase fronts. The use of subwavelength folds offers broad utility because they can be prepared in a number of ways. Subwavelength folds can be generated during the synthesis stage of hBN, such as during

hen photons couple with optical phonons in polar dielectric materials, phonon polaritons (PhPs) can arise. This occurs in the Reststrahlen region of the material spectrum where the permittivity is negative.1 PhPs have recently gained significant attention because they can be employed to control energy transfer,2 allow for super-resolution imaging3,4 and construct superlenses.5 Hexagonal boron nitride (hBN) is a polar dielectric two-dimensional (2D) layered van der Waals crystal that has gained much attention as it exhibits natural hyperbolicity, which localizes the energy and enables hyperbolic phonon polaritons (HPhPs).6 HPhPs have recently been widely applied in combination with graphene7 to form graphene−hBN heterostructures.8−10 These heterostructures have been shown to exhibit plasmon−phonon hybridization,11−13 which offers the combined advantage of high wavelength compression, low loss, long propagation, and tunability, allowing for potential waveguide-based applications. Scanning near-field optical microscopy (SNOM) techniques have been previously used to study the dispersion relation in hBN by launching and observing volume confined HPhPs within the Reststrahlen band.6,14−17 Either the in-plane dielectric constants (ε∥ = εx, εy) or the out-of-plane dielectric constant (ε⊥ = εz) can be negative in hBN, giving rise to two Reststrahlen bands: the upper Reststrahlen band (URB), which lies in 1367−1610 cm−1 region, and the lower Reststrahlen band (LRB), which lies in the 746−819 cm−1 region.18−21 This work describes experimental observations within the URB. © 2017 American Chemical Society

Received: March 28, 2017 Accepted: April 28, 2017 Published: April 28, 2017 2158

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(at the excitation frequency ω = 1510 cm−1) is shown in Figure 1b. Periodic features or stripes are observed to propagate across the crystal. The stripe patterns are a map of the amplitude of the local evanescent fields induced by HPhPs that propagate through the bulk. The observed response near the fold is different from that near the edge of the crystal. The patterns observed near the edge of the crystal (indicated by light blue arrows in Figure 1b) are shorter in wavelength relative to the ones observed near the fold (indicated by dark blue arrows in Figure 1b). The oscillations exhibiting the shorter wavelengths are the well-known standing waves6 (λobs(ω) = λp(ω)/2; where λp(ω) is the surface wavelength of HPhPs) that occur between the tip and an edge of the crystal (see schematic representation in Figure 1d) and are created by the superposition of waves injected into the material by the tip, which then reflect at the edge, interfere, and are scattered to the detector by the AFM probe. The simulation shown in Figure 1c takes into account the HPhPs launched by the hBN fold and includes the standing waves created by the superposition of tip-launched waves and their reflection by hBN edges (see Supporting Information (SI) for more details). A phenomenological model for the dispersion relation has been proposed6 and is derived from the Fresnel equations for a three-layer structure. Large momenta, when imposing the Fabry−Perot quantization condition, are described by6

the growth phase of chemical vapor deposition.24−26 The features can be induced postsynthesis by a template method using protruding bars27,28 or channels,27 where the created folds are maintained upon transfer to another substrate. Moreover, prestraining the substrate before crystal transfer and consecutive relaxation after crystal deposition results in similar folds,29 for which the surface adherence can be employed to control the fold location.30 Furthermore, thermal annealing has also been shown to generate folded deformations,31,32 where the distance between the folds can be adjusted by tuning the annealing time.33 A representative, small hBN crystal is shown in Figure 1a. The crystal is 73 nm tall and exhibits a flat surface, except for a

⎤ ⎛ ε ⎞ ⎛ ε ⎞ ψ⎡ q(ω) = − ⎢arctan⎜ a ⎟ + arctan⎜ s ⎟ + πl ⎥ d ⎢⎣ ⎝ ε⊥ψ ⎠ ⎝ ε⊥ψ ⎠ ⎦⎥

(1)

where q(ω) = 2π/λp(ω) are the in-plane complex momenta, εa, εs and ε⊥ are the dielectric constants of air, silicon substrate (Si), and the perpendicular component of hBN, respectively, ψ = ε /i ε⊥ , d is the thickness of the hBN crystal, and l denotes the mode of the propagating wave. At the fold, the bright stripes observed to the left- and righthand sides have a wider separation than the stripes observed at the edges of the crystal. As illustrated in Figure 1c, the fold launches propagating waves (λobs(ω) = λp(ω)), which are scattered to the detector by the tip. As expected from the inplane symmetry of the dielectric function of hBN, the spatial orientation of the fold relative to the excitation laser beam was experimentally shown to be insignificant. Yoxall et al.14 have also recently reported propagating waves, however, in contrast to our work, those waves were launched by a thin gold film deposited on top of an hBN crystal. In contrast with previous works,17,35 which were the first to show the presence of HPhPs in 3D nanocones in the absence of metals, here, we show experimental observation of a thin 2D hBN crystal that selflaunches HPhPs from a fold. The self-launched HPhPs exhibit periodicities on the surface that are 2 times the wavelength of the tip-launched (standing) HPhPs, as shown in Figure 2a. Both these observed waves obey the HPhP dispersion relation of hBN, given by eq 1. The false color plot in Figure 2b is given by the imaginary part of the Fresnel reflection coefficient of a three-layer structure, previously derived by S. Dai et al.,6 now adapted to represent a Si−hBN−air system (see SI for more details). This illustrates the agreement between the calculated dispersion relation and the HPhPs’ in-plane momenta, generated by both tip-induced and self-launching mechanisms. The main experimental evidence that the HPhPs are selfinduced by hBN is that their periods are twice that of the observed tip induced waves that reflect at the edge. These

Figure 1. Observation of volume-confined tip- and hBN self-launched HPhPs on top of an hBN crystal. (a) AFM 3-dimensional topography image of an hBN flake, the corresponding SEM images (left) and a sketch depicting the fold (bottom). (b) Typical IR response, collected at 1510 cm−1 at the out-of-phase channel showing fringes from hBN self-launched (SL) and tip-launched (TL) HPhPs. (c) Simulation of the hBN SL and TL HPhPs. Schematic illustrations of (d) hBN selflaunched and (e) tip-launched waves. All scale bars represent 500 nm.

protruding fold. Top- and side-views of the fold by scanning electron microscopy (SEM) are shown in Figure 1a. The height of the fold is 50 nm above the main hBN surface and is a continuation of the surrounding material. To investigate the infrared optical consequences of this fold, a phase-controlled homodyne SNOM34 is used. A representative normalized out-of-phase near-field infrared (IR) response 2159

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Figure 3 also shows an asymmetry of the IR signal around the fold. This is due to a strong scattering response near the fold, which exhibits local phase evolution that is different on the left- and right-hand sides of the fold. The microscope’s readout of the evanescent field near the fold depends on the slope of the fold probed by the microscope’s tip. Qualitatively, this can be understood from the angle between evanescent fields that are perpendicular to each sloped region, and whose amplitudes are detected by the tip that is mainly sensitive to p-polarized fields. The 0.4 rad phase difference that we observe in the vicinity of either slope is consistent with the 15 degree difference in angle of the slopes on the left- and right-hand sides, which would give rise to a 0.3 radians phase difference. This agreement, though convenient, may be in part coincidental. We note that in addition, the tip can inject HPhPs, which can partially reflect from the fold, but this is not observed in our measurements. A full analysis of the local effect, which also depends on the finite size of the tip, is not yet available, but these do not detract from the main conclusion of this work, that the fold can induce long-range HPhPs. The role of van der Waals forces and the lattice structure in subwavelength features appear important for the energy transduction process to the surrounding hBN crystal. As long as the bonding within each layer is maintained (as observed in the fold) and there is registry between layers, the feature is capable of self-launching, or transducing, the incident excitation to the bulk, but with a different phase. However, there can be hBN fragments on top of a surface of hBN, which are not integral or in registry with the lattice beneath. We find that HPhPs can scatter off nonintegral objects on top of the crystal, similar to a buoy in water scattering a wave traveling beneath. In contrast to a fold, Figure 4 shows a representative fragment

Figure 2. Dispersion relation of self- and tip-launched HPhPs. (a) The wavelength (λobs) of the oscillations observed on the surface of the crystal as a function of the excitation wavenumber (ω). Self-launched (dark blue triangles) and standing waves (light blue circles) HPhPs are shown together with calculated results derived from the dispersion relation (black dash line and light blue solid). (b) Dispersion relation of a 73 nm thick hBN crystal on Si. Experimental data are plotted on top of the calculated imaginary part of the reflection coefficient. The black dash line in (a) is described by the approximation of eq 1 for large momenta, and the same parameters are used to describe the l = 0 dispersion relation in (b). The light blue solid line in (a) has been adjusted for standing waves (λobs(ω) = λp(ω)/2).

standing waves are not observed to be reflecting from the fold. The phase of the long-range HPhP is the same on the left or right-hand side of the fold (within an error of 0.1 radians). These long-range periodic features are highlighted by the dark blue SL wave diagrammed in Figure 1. The line profile of these stripes in Figure 1 is shown in Figure 3 (ω = 1510 cm−1),

Figure 3. IR Line profiles at the fold and edge of hBN. Normalized in(red) and out-of-phase (blue) near-field profiles at different ω (noted) shown together with topography profiles (black). The pink stars above the out-of-phase (blue) profile indicate the bright regions of the same self-launched (SL) waves shown in Figure 1b.

Figure 4. IR response at a fragment and edge of hBN. In-phase IR responses of a 120 nm thick hBN crystal (a) at an edge and (b) around an hBN fragment, found on top of the same crystal, and their (c,d) corresponding IR (blue; ω = 1500 cm−1) and height (black) profiles. Scale bars are 500 nm.

where the pink stars indicate the bright regions of the same selflaunched (SL) waves shown in Figure 1b. The fold can inject HPhPs to the rest of the crystal apparently due to intrinsic structural continuity through the fold, since a chip of hBN on top of an hBN crystal does not produce the same effect (see below). The result of our simulation suggests that the HPhPs launched at the fold have a quarter of the amplitude of the tiplaunched waves (more details are available in the SI). Similar to other works,17,35 if the Fourier transform of the hBN hyperbolic permittivity in real space of a fold (sharp edge) is considered, it will be able to provide the momentum for the propagating polariton.

of hBN material (see SI for chemical and SEM analysis) found on top of a flat hBN crystal. This hBN fragment has a diameter comparable to the width of the previously discussed fold, but is apparently not structurally in registry with the material underneath, like the fold. Due to this discontinuity, the IR response around this separate fragment shows a standing wave rather than a propagating self-launched wave, which leads us to believe that the fragment primarily scatters HPhPs rather than induce them. For comparison, a standing wave occurring 2160

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between the tip and an edge of the same flake is shown (more examples are in the SI). Due to the hyperbolicity of hBN, the tip-launched wave scattered from the fragment travels in a 3D cone-like pattern inside the crystal and creates a standing wave, which is picked up by the tip (Figure 4b). The absence of selflaunched waves from these fragments highlights the necessity for material continuity, as exhibited by a fold. In this work, we have observed a material self-launching mechanism in which a fold of hBN directly couples incident light to HPhPs with subwavelength confinement. The structural continuity of the folds allows for energy to enter and propagate into the rest of the crystal, giving rise to self-launched HPhPs of a different phase. Furthermore, fragments of hBN on top of larger hBN crystals, which do not have structural continuity with the underlying material, do not show strong evidence of self-launched HPhPs and exhibit primarily reflective properties for HPhPs that were already induced via other mechanisms, such as those induced by an AFM probe. Nevertheless, to induce the laterally localized self-launched HPhPs, structurally continuous features, such as folds, can be used. Methods of preparing hBN crystals with localized folds have been previously reported and will enable the hBN fold- and other self-induced launching mechanism for use in low-dimensional devices such as waveguides and room-temperature IR sensors or possibly to activate phonon polariton-enhanced chemical reactions.36

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Letter

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00748. Calculation of dielectric constants and dispersion relation of hBN; description of Bruker Inspire AFM IR setup; details of simulations; FTIR reflectance profile; characterization of hBN fragments; SEM and IR responses of other observed folds (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Gilbert C. Walker: 0000-0002-5248-5498 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge Peter M. Brodersen at the Ontario Centre for the Characterization of Advanced Materials, funded by the Canadian Foundation for Innovation and the Ontario Research Fund, for providing us with the SEM images, AES, and XPS data. S.dB. acknowledges the support of the Foundation for Fundamental research on Matter (FOM), which is financially supported by The Netherlands Organization for Scientific Research (NWO). S.dB. acknowledges the University of Twente Stimuleringsfonds, for financially supporting her research stay at the University of Toronto.

MATERIALS AND METHODS

The hexagonal boron nitride powder (grade B) was purchased from Manchester Nanomaterials, Limited (UK). The synthetic method naturally produces the observed folds. We employed a variety of preparation techniques, such as the well-established mechanical exfoliation technique using blue semiconductor tape (Semiconductor Equipment Corp., Moorpark USA) and others37 to deposit the freshly cleaved crystals on top of a diced Si/SiO2 substrate with a subnanometer thick oxide layer. The thickness of the oxide layer was determined to be about 0.6 nm (for more detailed calculation, see the SI). The AFM height and IR absorption images were obtained on a commercial s-SNOM instrument (Bruker Inspire). The operating principles are largely similar to a home-built system previously reported.15,34,38 A quantum cascade IR laser (MirCat Daylight Solutions) in the CW mode is focused onto the apex of the tip of the AFM cantilever (ARROW-NCPt, resonance frequency 270−290 kHz and spring constant of approximately 42 N/m). We employed the tapping IR module in which we harmonically tap the Pt/Ir coated AFM cantilever over the surface with an amplitude of approximately 90 nm. To reduce the effect of artificial background reflections, the IR signal is demodulated at either second or third harmonics of the tapping frequency. The SEM images and Auger electron spectroscopy (AES) results were acquired by an ULVAC-PHI 710 Scanning Auger Nanoprobe (Chigasaki, Japan). The images were obtained with an electron beam of 25 eV, 1 nA. Elemental analysis was obtained using an electron beam of 10 keV, 10 nA. During all measurements, the vacuum pressure in the main analytical chamber was 8.0 × 10−10 mbar. Side profile images were obtained by mounting the prepared silicon wafers on a pretilted stage.

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ABBREVIATIONS hBN, hexagonal boron nitride; PhP, phonon polariton; HPhP, hyperbolic phonon polariton; SNOM, scanning near-field optical microscopy; URB, upper Reststrahlen band; LRB, lower Reststrahlen band; AFM, atomic force microscopy; SEM, scanning electron microscopy; IR, infrared; FTIR, Fourier transform IR

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