Breakdown of Far-Field Raman Selection Rules by LightâPlasmon

Letter Cite This: J. Phys. Chem. Lett. 2017, 8, 5462-5471

pubs.acs.org/JPCL

Breakdown of Far-Field Raman Selection Rules by Light−Plasmon Coupling Demonstrated by Tip-Enhanced Raman Scattering Emanuele Poliani,*,† Markus R. Wagner,† Asmus Vierck,† Felix Herziger,† Christian Nenstiel,† Florentina Gannott,‡ Manuel Schweiger,‡ Stephanie Fritze,§ Armin Dadgar,§ Jana Zaumseil,∥ Alois Krost,§ Axel Hoffmann,† and Janina Maultzsch†,⊥ †

Institut für Festkörperphysik, Technische Universität Berlin, 10623 Berlin, Germany Nanomaterials for Optoelectronics Group, Institute of Polymer Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91054 Erlangen, Germany § Institut für Experimentelle Physik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany ∥ Physikalisch-Chemisches Institut Lehrstuhl für Angewandte Physikalische Chemie, Ruprecht-Karls-Universität Heidelberg, 69117 Heidelberg, Germany ⊥ Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91054 Erlangen, Germany ‡

S Supporting Information *

ABSTRACT: We present an experimental study on the near-field light−matter interaction by tip-enhanced Raman scattering (TERS) with polarized light in three different materials: germanium-doped gallium nitride (GaN), graphene, and carbon nanotubes. We investigate the dependence of the TERS signal on the incoming light polarization and on the sample carrier concentration, as well as the Raman selection rules in the near-field. We explain the experimental data with a tentative quantum mechanical interpretation, which takes into account the role of plasmon polaritons, and the associated evanescent field. The driving force for the breakdown of the classical Raman selection rules in TERS is caused by photon tunneling through the perturbation of the evanescent field, with the consequent polariton annihilation. Predictions based on this quantum mechanical approach are in good agreement with the experimental data, which are shown to be independent of incoming light polarization, leading to new Raman selection rules for TERS.

T

interaction: so far, three different approaches for the description of the TERS mechanism are typically used in the literature, (i) the classical approach of downscaling the antenna theory to the optical range,21,22 (ii) the semiclassical approach in quasi-static approximation considering the electromagnetic field (EF) of a subwavelength dipole,23−25 and (iii) the quantum mechanical approach.5,26 On the basis of the first approach (i), Zhang et al.9 calculated a theoretical limit for the spatial resolution of TERS of 7.2 nm. Subsequently, the same authors modified the conventional model by including both the polarizability of the studied molecules and the polarizability of the tip and thereby obtained a spatial resolution limit of 2.2 nm.9 Using the same classical approach (i), Meng et al.12 explained the experimentally observed subnanometer resolution in terms of an electric field gradient at the tip apex. They calculated, for a 2 nm tip radius, a theoretical resolution limit of around 1 nm. Despite other works try to explain classically the subnanometer resolution with an ultrathin tip apex27 or with an atomic size protrusion,28 classical physics is unable to explain a

ip-enhanced Raman spectroscopy (TERS) has already demonstrated its success as a nondestructive method for the determination of physical and chemical properties of materials down to the subnanometer scale with a wide spectrum of applications, from biology to materials science.1,2 Despite its tremendous potential, TERS still remains a demanding research technique even after almost two decades since the first pioneering works. This is due to the relatively low interlaboratory reproducibility of the experimental data, which leads to a scarce spread of large-scale applications.3,4 The main challenges for the consistency and interpretation of the TERS data lie not only in the technical complexity of the experimental systems but also in the lack of a comprehensive understanding of the underlying near-field light−matter interaction. Since the development of surface-enhanced Raman spectroscopy (SERS) in the late 1970s, the physical mechanism behind the optical enhancement has been widely discussed.5−7 Recently, the report of forbidden Raman modes observed by TERS and the unexpected high spatial resolution down to the subnanometer scale refueled the long-lasting debate8−13 as expressed by several independent review articles.14−17 The subnanometer spatial resolution of TERS, which has been reported by two independent groups,10,18−20 cannot be explained by the classical approach to the physical mechanism of near-field light−matter © XXXX American Chemical Society

Received: September 22, 2017 Accepted: October 24, 2017 Published: October 24, 2017 5462

DOI: 10.1021/acs.jpclett.7b02505 J. Phys. Chem. Lett. 2017, 8, 5462−5471

Letter

The Journal of Physical Chemistry Letters

oriented with the c-axis perpendicular to the substrate. Ge doping of GaN allows higher carrier concentrations and gives higher homogeneity than doping with silicon. After discussing the polarization dependence on low-doped samples, we will analyze the dependence of TERS enhancement on carrier concentration on highly doped GaN samples. Figure 1 shows a sketch of the experimental setup and defines the used angles and axes. Here, z is the direction parallel

spatial resolution that is significantly smaller than a realistic tip apex, thus requiring a quantum mechanical approach. The main limitation of classical theories stems from the fact that they do not consider the many-body nature of the near-field scattering process, i.e., the coupling between photons and plasmons, and the peculiar properties of the quasiparticles involved described below. The near-field scattering process differs from classical Raman scattering for two main reasons: first, it involves plasmon polaritons instead of uncoupled photons and plasmons, and second, the scattering process takes place in a subnanometer region, a length scale well below the excitation wavelength, preventing a fully classical treatment. In other words, due to the subnanometer size of the interaction region, the electromagnetic excitation cannot be considered as a wave anymore, and the classical concept of polarization could not be valid. Instead, the gold nanotip becomes part of the scattering process by mediating the excitation. The presence of the tip allows the creation of surface plasmon polaritons (SPPs), i.e., photons coupled to surface plasmons, and localized surface plasmons (LSPs). Recently, it was reported that polaritons, and the associated evanescent field, reveal many interesting properties of light such as the quantum spin Hall effect in photon tunneling, transverse spin, and extraordinary momentum and spin.29−31 The photon tunneling mediated by LSPs and SPPs and the spatial localization of the tunneling photons have been experimentally and theoretically extensively studied.32−37 These peculiarities arise from the spin−orbit interaction of photons coupled with plasmons, which are not observable in freely propagating light. The physics of the evanescent field is therefore still unknown and under debate, making TERS a very promising technique to investigate fundamental phenomena on the subnanometer scale such as wave−particle duality38 or near-field light−matter interaction, where the definition of light polarization is questioned.39 The effect of the strong coupling between photons and plasmons and the interaction of the evanescent field with matter are purely quantum mechanical effects that, to the best of our knowledge, have been rarely experimentally studied or theoretically considered in TERS. In this Letter, we present an experimental TERS study on three different material systems. The purpose of this work is to explain our experiment results, which do not respect classical Raman selection rules, by suggesting a novel approach to the scattering mechanism and selection rules for TERS. The nearfield light−matter interaction mediated by polaritons is explained in terms of photon tunneling into the sample through the air gap by perturbation of the evanescent field at the tip apex.40 We present TERS data of bulk gallium nitride (GaN), graphene, and single-walled carbon nanotubes (CNTs), which show that the enhanced Raman signal is independent of the incoming light polarization. This implies a modification of the Raman selection rules in TERS compared to far-field Raman scattering.25,41 We describe the scattering process by including photon tunneling by perturbation of the evanescent field. We use a tentative quantum mechanical model to calculate the Raman selection rules for bulk GaN in quasi-static approximation and compare the calculations with the experimental data. Finally, we show that the purely plasmonic contribution to the scattering process is reflected in the dependence of the enhancement factor on the sample carrier concentration. The first experiment is carried out on a GaN epilayer doped with Ge (doping level 2.6 × 1019 cm−3) grown on sapphire and

Figure 1. (a) Sketch of the experimental setup. The confocal Raman instrument is coupled to the AFM with an electrochemically etched gold tip. The excitation and detection objective is tilted by 60° with respect to the z axis, θ = 60°. The incoming light vector is decomposed in the x, y, and z components in (b) and (c). The polarization angle φ is defined with respect to the z axis in the yz plane. φ is equal to 90° when the light polarization is parallel to the y axis laying in the xy plane (in-plane polarization) and equal to 0° when it is parallel to z laying in the xz plane (out-of-plane polarization). It is important to highlight that even when the polarization is out-of-plane the in-plane component of the incoming light is equal to 1/2, as shown in (b). The decomposition of the polarization vector for arbitrary polarization angles is given by the matrix of the Euler angles, as described in ref 66.

to the c-axis of GaN. The angles θ (tilt) and φ (polarization) are defined with respect to this axis in the xz plane and yz plane, respectively (Figure 1b,c). The Raman spectra of a Gedoped GaN epilayer are displayed in Figure 2a. The measurements are performed with controlled linearly polarized excitation in three different configurations: normal incidence (θ = 0°) micro-Raman in backscattering configuration z(−,−)z̅ (black curve), tilted (θ = 60°) far field (FF) configuration (red curve), and the extracted pure near-field (PNF) spectrum (blue curve). The PNF spectrum is obtained by subtraction of the tip-retracted signal (FF) from the tip-approached signal (see the Supporting Information). In the z(−,−)z̅ configuration, we detect the typical GaN lattice modes E2(high) and A1(LO) at 567 and 734 cm−1, respectively, whereas the E1(TO) mode at 559 cm−1 is only weakly observable.42 The weak signal at 658 cm−1 is a local vibrational mode related to structural defects.43,44 The additional Raman modes at 378, 417, and 747 cm−1 originate from the sapphire substrate.45 Compared to the normal-incidence backscattering geometry, we detect the same Raman modes of sapphire and GaN with different relative intensities in the tilted θ = 60° (FF) geometry. This intensity variation is caused by the decomposition of the light polarization vector in in-plane and out-of-plane components. Because the long-range electrostatic force dominates over the crystalline anisotropy in GaN, the E1 mode can mix with the A1 mode in this scattering geometry; it appears at an intermediate frequency depending on the excitation and detection angle.46 We detect the A1/E1(TO) mixed mode at 555 cm−1, in 5463


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Figure 2. (a) Raman spectra of Ge-doped GaN for backscattering geometry z(−,−)z̅ (black curve), tilted geometry (θ = 60°) (FF) (red curve), and the PNF signal (blue curve). The lack of enhancement of the sapphire modes in the PNF spectrum demonstrates the surface sensitivity of TERS. (b) Magnification of the E1(TO) spectral region. In the PNF spectrum, the E1(TO) loses its mixing character with the A1(TO) Raman mode and is detected at its original spectral position.

Figure 3. Independence of the PNF from the incoming light polarization. While the FF spectra strongly change in relative peak intensities because of the different in-plane and out-of-plane components of the incoming light polarization, the PNF spectra do not change in relative peak intensities or spectral position. The change of the absolute intensity is due to the lightning rod effect,75 which changes the LSP and SPP population.

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Figure 4. Polarization-dependent measurements (a−c) for a mechanically exfoliated single-layer graphene and (d−f) for CNTs arrays. The incoming light polarization is rotated from 0 (out-of-plane) to 90° (in-plane). The FF Raman spectra in (a) and (d) strongly change in overall intensity according to the Raman selection rules of the system. The PNF spectra of both samples do not present large variation in intensities, as shown in (b) and (e). The intensity variation in counts/s of the PNF (blue curve) and FF (red curve) as a function of the incoming light polarization angle are compared in (c) and (f) for the G and 2D Raman modes of graphene and for the G+ mode of nanotubes, respectively.

agreement with theory.47 In contrast to that, the PNF TERS spectrum reveals significant differences: the Raman modes of sapphire are no longer visible due to the intrinsic surface sensitivity of TERS. The A1(LO) mode strongly gains in intensity, while the frequency of the E1(TO) is detected at its nominal spectral position without mode mixing (Figure 2b). The lack of mixed modes demonstrates that the frequency of the PNF signal is not affected by the deviation from the far-field normal incidence geometry in excitation and detection. This observation raises the question if the FF and PNF Raman signal intensities also differ with respect to the light polarization. In order to address this question, we show in Figure 3a,b the FF and PNF Raman spectra of the same Ge-doped GaN sample for two different incoming light polarizations with φ = 60 and 10°, respectively. The FF spectra strongly change in relative

peak intensities, whereas the PNF spectra remain almost unchanged. In the FF, the intensity ratio between the Raman modes E2(high) and A1(LO) varies from I

( ) = 20 (for φ = E2 A1

( ) = 65 (for φ = 10°), whereas it remains roughly constant at I( ) = 12 in the PNF. The E (TO) mode appears

60°) to I

E2 A1

E2 A1

1

at its nominal spectral position (without mode mixing) and with constant intensity for both light polarizations. Consequently, the PNF spectra are not only independent of the farfield excitation and detection direction but also unaffected by the polarization of the incoming light. A comparison of allowed, forbidden, and observed Raman modes in the canonical z(−,−) 5465


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The Journal of Physical Chemistry Letters z̅ configuration, tilted θ = 60 °FF configuration, and PNF TERS signal is given in the Supporting Information. In order to understand the reason for the differences between the FF and PNF intensity ratios, we performed the same experiments with different polarization directions on two other material systems: a mechanically exfoliated monolayer graphene flake on SiO2 and an oriented single-walled CNT small bundle on SiO2 (for sample details, see the SI). The intensity of their Raman modes strongly depends on the polarization components in-plane and along the CNT axis, respectively.48,49 The 2D and G Raman modes of graphene can be excited only by the in-plane component of the incoming light. In the tilted θ = 60° FF scattering geometry, rotating the polarization from φ = 90 (in-plane) to 0° (out of plane) means reducing the in-plane component from 1 along the y axis to sin 30° = 0.5 along the x axis, as shown in Figure 1b. Due to these geometrical considerations, the intensities of both Raman modes decrease approximately by a factor of 2, as seen in Figure 4a. On the contrary, the PNF intensities of the 2D and G modes of graphene remain almost unaffected by the rotation of the incoming light polarization (Figure 4b). Thus, we can conclude that even in the case of a pure 2D material such as graphene, the PNF signal does not depend on the polarization of the incoming light (Figure 4c). In order to explore the general validity of this observation beyond a particular material or geometry, we carried out the same experiment with polarized light on single-walled CNTs (Figure 4d,f), which are aligned along a defined direction and transferred on SiO2, as described in refs 50 and 51. The signal intensity of the Raman G mode in the CNT is maximized for incoming light polarized parallel to the CNT and 0 for light polarized perpendicular to the tube.48 The sample was oriented in such a way that individual CNT arrays were aligned parallel to the y axis. This configuration allowed us to rotate the polarization angle φ from 0 (out-ofplane) to 90° (in-plane) thus to increase the polarization component parallel to the tube from 0 to 1. Indeed, we observe in tilted FF geometry that the G mode reaches its intensity maximum for a polarization angle of 90° (in-plane) and is almost 0 for a polarization angle of 0° (out of plane), as shown in Figure 4d. In contrast, the PNF intensity of the G mode exhibits a much weaker dependence on the polarization angle (Figure 4e,f). The FF and PNF intensities as a function of the polarization angle are summarized in Figure 4f. Once again, the experiment confirms that the outgoing photons are independent of the incoming far-field light polarization. The experimental data based on these three different material systems indicates that the information on the incoming light polarization is lost in the case of near-field light−matter interaction, which results in different Raman selection rules for TERS. In analogy to scanning tunneling microscopy, where the tunneling by perturbation of the exponentially decaying electron wave function allows a spatial resolution much smaller than the tip radius, we describe the intrinsic TERS mechanism as photon tunneling by perturbation of the exponentially decaying evanescent field. On the basis of theoretical and experimental reports in the literature, we suggest in the next paragraph a tentative quantum mechanical model that explains the experimental data beyond classical theories. The coupling between light and plasmons creates quasiparticles, SPPs, and LSPs, with their own particle properties like lifetime, spin, etc. The EF associated with SPPs is described in semiclassical approximation, i.e., neglecting retardation effects of LSP and SPP,52 by a particular solution of Maxwell’s equations, which

owns an evanescent EF component in the nonpropagating direction (i.e., evanescent field). The perturbation of the evanescent field leads to a photon tunneling event that is the physical process behind other near-field subwavelength microscopy techniques, for instance, photon tunneling microscopy and total internal reflection microscopy.53−57 The evanescent field considered in this work is generated by the creation of SPPs in a metallic surface.40,58 If an optical medium, e.g., a metallic surface or another material, is brought in proximity to the surface, the photon can tunnel through the air gap32,33 while consequently annihilating the SPP. The role of LSPs, due to their nonpropagating nature, is to act as a localized point for creation or annihilation of SPPs.59 On the basis of these considerations, we can now understand why the polarization information is lost: by means of these couplings, the photon changes its properties and the EF is now following the common charge oscillations of plasmons, as shown in Figure 5a, in a nanometer range, which is well below the range

Figure 5. (a) Qualitative sketch of electric field lines of the evanescent field in a quasi-static approximation. The EF of the polaritons is curved in order to match the common charge oscillations and the exponential intensity decrease from the gold surface. The decay by photon tunneling is a decay channel open by the proximity of the sample, which acts as a perturbation of the evanescent field. (b) Feynman diagrams of the scattering process, from left to right, are shown: the incoming photon, the photon−plasmon interaction (photon−tip interaction), and the energy dissipation due to LSP damping, the incoming polariton, the polariton−phonon interaction (photon tunneling), the outgoing polariton, the outgoing photon−plasmon interaction (antenna effect), and the outgoing photon. The red numbers are the steps described in the main text. In principle, all of the permutations obtained by different orders of the vertices can contribute to the scattering process.

where the classical polarization vector is defined but where the spin of polaritons is defined29,31 and photon tunneling can occur.32−37 A tentative quantum mechanical approach to the TERS mechanism, which considers the coexistence of LSPs and SPPs in a conical bulk gold tip, can be described as follows in four steps as sketched in Figure 5a: (1) SPP and LSP creation. The incoming photons excite LSPs and SPPs by means of “diffraction on a surface feature”,40 i.e., a subwavelength-sized metallic feature 5466


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The Journal of Physical Chemistry Letters allows the generation of SPPs overcoming the phase matching required for flat surfaces by the decay of LSPs.59 In general, every sharp surface feature that breaks the surface translation symmetry is able to supply a quasiwave vector to the incident light in order to excite SPPs because it can be described in spatial Fourier transform terms as a superposition of gratings.59 This is in analogy with random rough surfaces where SPPs and LSPs can be generated by just shining light.59 In the case of TERS, the surface feature that breaks the translational symmetry is the tip apex, as depicted in Figure 5a. (2) Decay channels of SPPs and LSPs. LSPs can decay into SPPs and vice versa. Without any perturbation, this is the only radiative decay channel for SPPs. When a perturbation is brought in the proximity of the tip, e.g., a sample, a new decay channel can be opened, as described in the next paragraph. The role of SPPs in TERS has been already demonstrated by other authors39,60 where the SPPs are created elsewhere and sent toward the tip apex by adiabatic nanofocusing. The decay into SPPs is the nonradiative channel of LSPs; however, LSPs can also decay radiatively. The radiative decay of LSPs does not contribute to enhanced Raman scattering but contributes to the typical TERS background, as sketched in Figure 5a. The broad spectrum of the radiative decay of LSPs is caused by photon energy loss on the tip surface. A perturbation could open a new decay channel also for LSPs in case of incoming resonance. LSPs could probably contribute to Raman scattering with photons that do not lose their energy by damping. (3) Photon tunneling. The possibility for the photon to tunnel into another medium through the air gap is the new decay channel opened by the perturbation. From a quantum mechanical point of view, the perturbation destroys the polariton. When perturbation of the evanescent field takes place, the photon uncouples from the plasmon by photon tunneling inside of the medium, which annihilates the SPP. In TERS, the sample is the perturbing medium, by analogy with the case of photon scanning tunneling microscopy (PSTM)56 or total internal reflection microscopy.55 The only difference with PSTM is that the evanescent field is created in TERS directly on the surface of the gold tip. Therefore, photons tunnel through the air gap into the sample, as shown in Figure 5a. The particular case of gold substrate, i.e., the “gap modes” configuration, can be described as the case of resonant tunneling.33 The same decay channel could be also opened for LSPs not affected by damping in case of resonance. (4) Raman scattering. After tunneling into the sample, the photon excites the electronic system, which creates or annihilates a phonon. The emitted photon becomes detectable in the far field as a TERS signal. The maximum signal intensity is achieved when the outgoing photon is in resonance with the LSP. The photon can couple again with plasmons and uncouple by LSP radiative decay without damping, i.e., the antenna effect.21 The antenna effect could be viewed as the pure contribution of the LSP where the coupling between light and the plasmon is weak within a range of interaction from 80 to 20 nm, much larger than the one for SPPs, which is a few nanometers.39,61 The

population of LSPs strongly depends on the shape of the, tip and it could be more or less important as a function of experimental conditions. We can summarize the scattering process in a Feynman diagram shown in Figure 5b, where the three vertexes represent the two Hamiltonians: / pol−ion describes the polariton− phonon interaction, and /γ−pl describes the photon−plasmon interaction, which can be split into a photon−surface plasmon interaction /γ−Spl and photon−localized plasmon interaction /γ−Lpl . Apart from the sequence of events described above, all of the permutations are possible for the scattering process. More details about this model are given in the Supporting Information. A change of the selection rules from the classical Raman scattering process is expected for the near-field light−matter interaction.25,41 In literature, the selection rules for TERS have usually been calculated with the point dipole model,62 from the antenna theory,22 and more recently from symmetry considerations.63 The point dipole model approximates the tip as a single gold particle, and its polarizability is added to the material polarizability.25,62 In the antenna theory, the shape of the tip and its orientation are taken into account.22 In the symmetry-derived approach, the tip is considered as an infinite conical antenna, where the symmetry constituted by the combined system of the sample and tip or plasmonic structure is taken into account in a higher-order Raman scattering process.63 All of these approaches consider uncoupled plasmonic modes (i.e., dipoles, weak coupling regime) but not the nanometric range of near-field light−matter interaction39 nor the quantum mechanical properties of light due to strong coupling with plasmons, i.e., the polaritons.39 Here, we take into account these properties, i.e., we assume that our experiments are in the regime of strong coupling between incoming light and surface plasmons of the tip. For the example of GaN, we calculate the TERS selection rules using the evanescent field expression, which represents a polariton in semiclassical quasi-static approximation.31 A rigorous semiclassical treatment of the elementary properties of surface polaritons, as well as the electric field vectors of the coupled light, was reported by Nkoma et al.64 in 1974 and recently interpreted by Bliokh et al.29−31 as interesting properties of the spin of polaritons that are not observable in the free propagating light. The evanescent field has a strong EF component perpendicular to the surface and an imaginary longitudinal component that allows the electric field vectors to follow the common charge oscillations of plasmons, as shown in Figure 5a. As a consequence, due to mediation of the tip apex, which allows creation of the SPPs, the EF that interacts with the sample becomes imaginary and confined a few nanometers close to the surface, therefore strongly different from the incoming light. In Figure 5a, a qualitative sketch of the EF lines in the case of a conical shape is drawn for the quasistatic approximation model in TERS.25,65 In the Supporting Information, we calculate the TERS selection rules for a bulk crystal with C6v symmetry (i.e., wurtzite GaN) for the particular case of evanescent field excitation. As a formula for the incoming light, we use the same as that used in ref 31 to derive the transverse spins of surface polaritons originating from the longitudinal component of the electric field. Here, information about the incoming light polarization is lost because of the light coupling with plasmons. The EF of the coupled light becomes 5467


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exhibit any pronounced changes in relative peak intensities. Our model explains the independence of the PNF signal on the incoming light polarization and predicts a constant value for the ratio of the Raman modes E2(high) to A1(LO) in GaN, as shown in Table 2. Finally, we discuss another aspect predicted by the presented model: the sensitivity of TERS to the free carrier concentration. In the case of high carrier concentration, such as in highly doped GaN, the plasma frequency of the sample can be inresonance or out-of-resonance with the laser excitation. In the case of resonance, the scattering process in TERS can be considered as a resonant tunneling event, in analogy with the case of flat surfaces in metal−insulator−metal structures or, as called in TERS literature, “gap modes” configuration.67−69 Outof-resonance, after the photon uncouples from the plasmon by tunneling into the medium, the purely plasmonic contribution of the common charge oscillations is mirrored in the sample by Coulomb interaction. The purely plasmonic contribution to the scattering can play a different role depending on the sample carrier concentration. In order to analyze the dependence of the TERS signal on the free carrier concentration, we studied four different Gedoped GaN samples with carrier concentrations of 1 × 1020, 5 × 1019, 2.6 × 1019, and 3 × 1018 cm−3. The carrier concentrations were determined by Hall effect measurements and confirmed by micro-Raman spectroscopy.43 In highly doped GaN, plasmons interact with lattice vibrations. Depending on the carrier concentration, the plasma frequency can be in resonance with the A1 phonon, giving rise to two different phonon−plasmon branches: LPP− coupled with the A1(TO) phonon and LPP+ coupled with the A1(LO) phonon.70−72 In highly doped GaN, we are able to detect only the lower LPP− branch, whereas the A1(LO) frequency remains unchanged. In the FF, the intensity of the plasmon-coupled Raman mode already increases when the plasma frequency gets close to the PNFmax in host mode. Hence, we consider the gain as the ratio

imaginary, leading to new Raman selection rules. This is different from tip-induced depolarization in elliptically polarized light, which still remains a microscopic effect, and the polarization is defined by only the real part. The polarization of the evanescent field associated with plasmon polaritons lies in the nanometer scale where the concept of polarization is different from the one applicable to the free propagating light.31 The Raman tensor used for calculation of the wurtzite GaN crystal can be found in ref 66. The calculated selection rules for our TERS configuration and their comparison with the experimental data of GaN are shown in Tables 1 and 2, Table 1. Raman Selection Rules for near-Field Scatteringa near field

symmetry

a

A1

⎞ k+ ⎛ 3 1 b −⎜ + 1⎟i a ⎠ kp ⎝ 2 N2 2

E1

⎛ c2 ⎜ 1 k+ 1− i 2⎜ 2 kp 2N ⎝

E2

2 7d 2 ⎛⎜ k+ ⎞⎟ ⎜ ⎟ 4N2 ⎝ k p ⎠

2

+

2

1 k+ 3 − i 4 kp 2

2⎞

⎟ ⎟ ⎠

Selection rules for TERS of a wurtzite C6v symmetry crystal. Here,

k+ = kp = k 0

k p2 − k 0 2 is the complex wave vector of the evanescent field, εm 2 − εmμm εm 2 − 1

is the wave vector along the surface, ω0 is the

frequency, k0 = ω0/c, εm and μm are the permittivity and permeability ⎛ k+ ⎞ 2 respectively and N = 2⎜ k ⎟ + 1 is a normalization factor. The values ⎝ p⎠ a, b, c, and d are the Raman tensor elements reported in ref 66. The derivation of the formula is reported in the Supporting Information.

Table 2. Comparison between Calculation and Experiment of the E2(high)/A1(LO) Intensity Ratioa intensity ratio

calculations

PNF (TERS)

E 2(high) A1(LO)

13.4 (φ = 60° and 10°)

12 (φ = 60° and 10°)

far field

E 2(high) A1(LO)

27.1 (φ = 60°)

20 (φ = 60°)

52.1 (φ = 10°)

65 (φ = 10°)

FFmax

counts/s for each peak and normalize the gain values to the gain of the mode A1(LO), which is almost constant among the samples. In Figure 6a, the normalized gains of the LPP− and the E2(high) Raman modes are shown as a function of carrier concentration. The E2(high) gain increases approximately linearly with a slope of 0.1. In contrast, the LPP− gain increases rapidly in the two samples with highest doping concentration. In the highest doped sample, the LPP− gain exceeds all of the other ones, as shown in Figure 6b. In general, the Raman cross section of this interaction is modulated by two mechanisms: the deformation potential mechanism and the electro-optic mechanism.42 The first one is the modulation of Raman polarizability by atom displacements. The second is instead modulation via the longitudinal electric field of the carriers, which takes place because of the electronic charge density fluctuations.42 It has been demonstrated that the latter mechanism plays a much smaller role than the deformation potential effect, and hence, it is usually neglected in conventional Raman spectroscopy.71,73 However, in TERS, the scattering mechanism and the Raman cross section change, including also the term due to the charge density fluctuation. Calculations of the generalized structure function including this term were already reported in the frame of electronic Raman scattering for strongly correlated electron systems.74 The purely plasmonic contribution by Coulomb interaction with the sample makes the electronic charge density fluctuations play a

experiment

a

Comparison between calculations and experimental data of the E 2(high) intensity ratio. The value of the intensity ratio E2(hight) in TERS A1(LO)

A1(LO)

is calculated using the formula in Table 1. The intensity ratios based on the new Raman selection rules are in excellent agreement with the experimental data. Calculations and experiments show the independence of the TERS signal on the incoming light polarization φ in contrast to the FF case. More details are given in the Supporting Information.

respectively. We find good agreement for the calculated intensity ratio based on the presented quantum mechanical model of near-field light scattering with the experimentally observed PNF spectra. In all three material systems, the experimental FF data show dependence on the polarization and propagation direction of the incoming light, as expected from the classical Raman selection rules. The PNF spectra, on the contrary, do not 5468


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Figure 6. (a) Dependence of the relative intensity gain as a function of the sample carrier concentration. The Coulomb interaction between common charge oscillations and ions strongly increases the intensity of the plasmon coupled Raman mode. (b) PNF spectra related to the two highly doped samples with carrier concentrations of 5 × 1019 and 1 × 1020 cm−3. The LPP− mode shifts in frequency and strongly gains in intensity with respect to all other modes.

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ACKNOWLEDGMENTS We acknowledge support from the Deutsche Forschungsgemeinschaft (DFG, German research foundation) within the Collaborative Research Center “Semiconductor Nanophotonics” (CRC 787). F.G., M.S., and J.Z. thank the DFG for funding via the Collaborative Research Center “Synthetic Carbon Allotropes” (CRC 953).

larger role than that in standard Raman scattering, leading to stronger enhancement of the LPP−, as shown in Figure 6. In summary, we investigated the near-field light−matter interaction in TERS experiments in three different material systems: GaN epilayers, graphene, and CNTs. The experimental data shows that the relative intensities in the TERS signal are largely independent of the incoming light polarization in all of the studied materials. This results in an apparent breakdown of the selection rules for TERS as compared to classical Raman scattering. We therefore suggested a quantum mechanical interpretation of the physical mechanism of TERS. In analogy with electron tunneling, which allows a spatial resolution well below the tip apex in STM, the main TERS mechanism responsible for the breakdown is photon tunneling by perturbation of the evanescent field. On the basis of this model, we calculated the selection rules considering the evanescent field associated with the polaritons, which mediate the Raman scattering. The calculations are in good agreement with our experimental data. Finally, we have shown that the TERS signal intensity depends strongly on the free carrier concentration in the sample.

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(1) Pozzi, E. A.; Sonntag, M. D.; Jiang, N.; Klingsporn, J. M.; Hersam, M. C.; Van Duyne, R. P. Tip-Enhanced Raman Imaging: An Emergent Tool for Probing Biology at the Nanoscale. ACS Nano 2013, 7, 885− 888. (2) Poliani, E.; Wagner, M. R.; Reparaz, J. S.; Mandl, M.; Strassburg, M.; Kong, X.; Trampert, A.; Sotomayor Torres, C. M.; Hoffmann, A.; Maultzsch, J. Nanoscale Imaging of InN Segregation and Polymorphism in Single Vertically Aligned InGaN/GaN Multi Quantum Well Nanorods by Tip-Enhanced Raman Scattering. Nano Lett. 2013, 13, 3205−3212. (3) Blum, C.; Opilik, L.; Atkin, J. M.; Braun, K.; Kämmer, S. B.; Kravtsov, V.; Kumar, N.; Lemeshko, S.; Li, J.-F. F.; Luszcz, K.; et al. Tip-Enhanced Raman Spectroscopy - an Interlaboratory Reproducibility and Comparison Study. J. Raman Spectrosc. 2014, 45, 22−31. (4) Langelüddecke, L.; Singh, P.; Deckert, V. Exploring the Nanoscale: Fifteen Years of Tip-Enhanced Raman Spectroscopy. Appl. Spectrosc. 2015, 69, 1357−1371. (5) Pettinger, B. Light Scattering by Adsorbates at Ag Particles: Quantum-mechanical Approach for Energy Transfer Induced Interfacial Optical Processes Involving Surface Plasmons, Multipoles, and Electron-hole Pairs. J. Chem. Phys. 1986, 85, 7442−7451. (6) Jeanmaire, D. L.; Van Duyne, R. P. Surface Raman Spectroelectrochemistry. J. Electroanal. Chem. Interfacial Electrochem. 1977, 84, 1−20. (7) Fleischmann, M.; Hendra, P. J.; McQuillan, A. J. Raman Spectra of Pyridine Adsorbed at a Silver Electrode. Chem. Phys. Lett. 1974, 26, 163−166. (8) Moskovits, M.; DiLella, D. P. Surface-Enhanced Raman Spectroscopy of Benzene and Benzene-D 6 Adsorbed on Silver. J. Chem. Phys. 1980, 73, 6068−6075. (9) Zhang, C.; Chen, B.-Q.; Li, Z.-Y. Optical Origin of Subnanometer Resolution in Tip-Enhanced Raman Mapping. J. Phys. Chem. C 2015, 119, 11858−11871. (10) Zhang, R.; Zhang, Y.; Dong, Z. C.; Jiang, S.; Zhang, C.; Chen, L. G.; Zhang, L.; Liao, Y.; Aizpurua, J.; Luo, Y.; et al. Chemical Mapping

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b02505.

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REFERENCES

Methods, quantum mechanical model, and contamination check (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Emanuele Poliani: 0000-0003-1802-4775 Markus R. Wagner: 0000-0002-7367-5629 Jana Zaumseil: 0000-0002-2048-217X Notes

The authors declare no competing financial interest. 5469


Letter

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