--- title: "Operation of scanning plasmon near-field microscope with gold and silver tips in tapping mode: demonstration of subtip resolution." authors: ["V.N. Konopsky"] affiliation: "Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow region 142190, Russian Federation" journal: "Optics Communications" year: 2000 volume: "185" pages: "83-93" doi: "10.1016/S0030-4018(00)00994-9" type: journal-article site_group: "Scanning plasmon near-field microscopy" url_abstract: "" url_pdf: "https://valery.konopsky.com/additional_pdf/Operation of scanning plasmon near-field microscope with gold and silver tips in tapping mode_demonstration of subtip resolution.pdf" language: en source_tex: "" source_pdf: "" --- ## Abstract We present a scanning plasmon near-field microscope (SPNM) which operate in tapping mode of atomic force microscope (AFM). We interpret the observed maximum in light scattering intensity during a tip approach to (and withdrawal from) a surface as an electromagnetic (em) resonance in a tip-surface (sphere-plane) structure. This em resonance is of greater intensity when the tip and the surface are noble metals. At the em resonance in such a structure, the dimension of the light field localization is of the order of $L\simeq(2dR)^{1/2}$, where $d$ is the tip-surface distance and $R$ is the tip radius. Therefore at $d< **Abstract.** We present a scanning plasmon near-field microscope > (SPNM) which operate in tapping mode of atomic force microscope (AFM). > We interpret the observed maximum in light scattering intensity during > a tip approach to (and withdrawal from) a surface as an > electromagnetic (em) resonance in a tip-surface (sphere-plane) > structure. This em resonance is of greater intensity when the tip and > the surface are noble metals. At the em resonance in such a structure, > the dimension of the light field localization is of the order of > $L\simeq(2dR)^{1/2}$, where $d$ is the tip-surface distance and > $R$ is the tip radius. Therefore at $d< near-field images is less than tip radius ($L record the light signal at the second harmonic of tapping frequency to > pick out the signal associated with the sphere-plane em resonance. > Different registration modes of the light signal are considered and > the nature of negative contrast of surface hillocks in certain of the > registration modes is analyzed. Near-field images of rough silver > surfaces are presented and it is shown that distribution of the > near-field intensity on the surface is the result of the interference > between scattering plasmons and the initial plasmon beam. PACS: 07.79.Fc; 61.16.Ch; 73.20.Mf # Introduction Near-field microscopy makes it possible to overcome Abbe’s diffraction limit of conventional far-field optical microscopy . At present, "standard" scanning near-field optical microscopes (SNOMs) employ aluminum-coated optical fibers tapered at their end as sub-wavelength light source. The smallest aperture that can be made at the very end of the aluminum-coated fiber cannot be much smaller than twice the optical skin depth in aluminum (skin depth $\simeq$12 nm at 633 nm wavelength). Thus, typical lateral spatial resolutions achieved in SNOM are in 30–50 nm range. Moreover, aperture-based SNOM often suffers from reduced optical power which can be delivered through the subwavelength aperture. In apertureless scanning near-field optical microscope (aSNOM) a sharp tip of a scanning tunneling microscope (STM) or AFM is illuminated from the outside by an external light source and scatters the evanescent field which is then far-field detected . The lateral resolution of aSNOM is determined by the tip size and reaches the value of 17–20 nm . Without doubt there is a strong interest to push this limit further to the 1 nm scale in order to obtain information about optical properties at molecular resolution. Even in the early proposals about aSNOM  it was pointed out at importance of excitation of the em resonance in a metalized tip, which is considered as a small particle (as a sphere or as an elongated ellipsoid). For better excitation of the electromagnetic resonance in the visible region, the noble metal tip must be used. In these proposals the lateral resolution of such aSNOM is also anticipated to be about the dimension of the tip. In this paper we develop the approach, which enables to reach the resolution less than the tip radius of aSNOM. The central idea is to use the em resonance in a tip-surface (sphere-plane) structure where tip and surface are the noble metals. Dimension of em field localization in such a structure at the em resonance is less than radius of the curvature of the tip. Partially such experimental situation is realized, for example, in scanning plasmon near-field microscopes (SPNMs)  where traveling surface plasmon field on the *silver* surface (which is important) is used as an external excitation source of aSNOM tip. Specht et al. in the work  reported that ultrahigh lateral resolution (3 nm) was reached. We will return to this work when we will discuss the distance dependence of the light scattering intensity in our setup. The plan of this paper is as follows: section 2 gives an account of the main features of the em resonance in sphere-plane structure, section 3 describes our experimental setup and different registration modes of the light signal, section 4 presents our experimental results and discussion and section 5 is the conclusions. # The em resonance in a sphere-plane structure The em resonance in a sphere-plane structure was thoroughly studied in the early 80s in the context of light emission from small particle tunnel junctions , and in context of surface-enhanced Raman scattering . For a detailed consideration of this subject one can see these excellent works, but we shall confine our account to a purely qualitative discussion of the problem. An isolated small metal sphere with radius $R<<\lambda$ and permittivity $\epsilon_2=\epsilon_2'+i\epsilon_2''$ has an em resonance at the Frölich frequency $\omega_{\mathrm F}$, that is at the frequency where $\epsilon_2'(\omega_{\mathrm F})=-2\epsilon_0$ and $\epsilon_2''(\omega_{\mathrm F})\approx 0$ ($\epsilon_0$ is the real permittivity of the environment). For metal particle with the permittivity given by the Drude’s model $\omega_{\mathrm F}=\omega_{\mathrm p}/(1+2\epsilon_0)^{1/2}$, where $\omega_{\mathrm p}$ is the plasma frequency of electrons (see, for example, ). When the sphere approaches to a metal surface an interaction between the Frölich mode of the sphere (i.e. localized plasmon) and an eigen mode of an em excitation of a metal-dielectric interface (i.e. surface plasmon) takes place. This interaction shifts the Frölich mode frequency in the lower frequency region. When distance between the metal sphere and the metal plane becomes small ($d< d_{\mathrm res}$. Notice also that the presence of intermediate layers with $\epsilon_0>1$ has a pronounced effect on $d_{\mathrm res}$ ($d_{\mathrm res}\sim \epsilon_0^2$). The important characteristic feature of the sphere-plane em resonance is the lateral dimension $L$ of the em field localization between the sphere and the plane. It is approximately equal : ``` math \begin{equation} L\approx\sqrt{2dR}\; . \end{equation} ``` Therefore at $d<4.2)) is used to obtained this dependence. One can see that light intensity decreases during the tip withdrawal from the surface, but some maximum ("bump") takes place at the curve at $x=35$ nm. Similar "bumps" was also detected by other authors in different registration modes of SPNM. See, for example,  and  ( "internal reflection registration mode") and also  ( "internal scattering registration mode"), but we have found that in the "external scattering registration mode" this maximum is more pronounced. A strong narrow peak of the light scattering intensity was also observed in the work , when a gold-coated polystyrene particle is approached to a sample surface, but experimental situation in this work differs from the one in the SPNM. To the best of our knowledge, only the work  gives some discussion about origin of the maximum on distance-dependent intensity of the SPNM light signal. Specht et al. considered the tip as an oscillating dipole immersed in the "driving" em field and claimed that strong decrease of light intensity on the short distance from the metal surface is the result of the radiationless energy transfer from the tip ("dipole") to the metal surface. Specht et al. also believed that it is the mechanism of radiationless energy transfer which is responsible for ultrahigh resolution (3 nm) in their setup. We believe that our model of the sphere-plane em resonance is more adequate in this case (in other words we think that one must consider the dipole moment of the tip-surface system taken as a whole, but not the isolated dipole moment of the tip). Though we must note that in our model radiationless energy losses are also very important, especially for ultrasharp tips (Specht et al. used tungsten tips with radii of curvature about 10 nm). For ultrasharp tips, and as a consequence at ultrasmall dimension $L$ of the localization of the em field under tip (see equations ([L=]) and ([d=])), the process of generation of electron-hole pairs by the short-wavelength Fourier component of the em field ($k_{\mathrm em}\sim 1/L$) becomes the main damping mechanism of the sphere-plane em resonance. The decay time of the em resonance in this case is  ``` math \begin{equation} {1\over\tau}\approx {1\over 2}{v_{\mathrm F}\over L}\; , \end{equation} ``` where $v_{\mathrm F}$ is the Fermi’s velocity of electrons in the metal ($v_{\mathrm F}\simeq 1.4\cdot 10^8$ cm/sec for Au and Ag). Increasing of the absorption of the em radiation by the tip-surface structure (when ultrasharp tips are used) becomes important at comparison of signal/noise ratios of different registration modes. Returning to the Figure 3 one can see on insets in dashed-line frames the elucidation of the mechanism of the $2\Omega$ frequency generation at the tip-surface distance modulation by $\Omega$ frequency. It is clear that the light signal at $2\Omega$ frequency associated with the sphere-plane em resonance will have the lateral resolution about $L$. ## Determination of the radii of the tips For quantitative comparison of the equation ([d=]) with experiment we must know the radii of the tips used in our setup. For this purpose we used a commercial test grating TGT 01 of the "NT-MDT" firm . This test grating is the set of ultrasharp silicon needles with radii of curvature $r\approx 10$ nm. Radii of curvature of images of these needles $R^\ast$ is $R^\ast=r+R$, where $R$ is the radius of the cantilever tip that was used to obtain the image. Our experiments with ultrasharp "Park Scientific Instruments" cantilevers have shown that needles of the test grating TGT 01 are actually ultrasharp. We obtain the value $R^\ast\approx 30$ nm from these experiments and we get conclusion that $r$ of the test needles lies in the range $r\simeq (10-15)$ nm. Typical image of the test grating TGT 01 is given on Figure 4a (gold-coated silicon cantilever was used). From cross-section of a needle (see Figure 4b) one can see that $R^\ast\simeq 200$ nm, and therefore our gold-coated cantilever tips have the radii of curvature $R_{\mathrm Au}\simeq 185-190$ nm. From analogous images we get the conclusion that our silver-coated cantilever tips have the radii of curvature $R_{\mathrm Ag}\simeq 150$ nm, and that our uncoated silicon tips have the radii of curvature $R\simeq (85-100)$ nm. Now, using the equation ([d=]) with $R_{\mathrm Au}\simeq 190$ nm, $\epsilon_{\mathrm Ag}\simeq -18$, $\epsilon_{\mathrm Au}\simeq -12$ at $\lambda=632.8$ nm  and $\epsilon_0=1$ we obtain $d_{\mathrm res}\simeq 8$ nm. But from the Figure 3 one can see that experimental value $d_{\mathrm res}\simeq 35$ nm. We assume that this discrepancy is due to differences between the real experimental situation (schematically shown on the Figure 1b) and idealized situation (schematically shown on the Figure 1a) that was used to obtain the equations ([Mal]), ([d=]). We believe that the presence of intermediate layers on the silver surface in the air (chiefly silver sulfide tarnish layer : $\varepsilon'_{\mathrm Ag_2S}=8.7$ and adsorbed water: $\varepsilon'_{\mathrm H_20}=1.8$) may account for this discrepancy. From equation ([d=]) one can see that $d_{\mathrm res}$ is strongly depend on $\epsilon_0$ ($d_{\mathrm res}\sim \epsilon_0^2$). For good agreement with observed value of $d_{\mathrm res}$ it is necessary that "effective" permittivity of the media between the tip and the silver surface was about $\epsilon_0\approx 2$. Presence of the silicon core in the tip and the fact that in our case $R<\lambda$, but not $R<<\lambda$ may be of importance for this discrepancy as well. ## Demonstration of the lateral resolution in our setup In Figure 5 one can see the topography (a) and optical signal (b) of some surface hillock on silver surface. Scan size is 700 nm$\times$700 nm. Optical signal was recorded at $2\Omega$ frequency in the "internal scattering registration mode" (i.e. $2c$ mode in our notation, see section (3)). Reasons for the common *negative contrast* of near-field images of surface hillocks in this registration mode will be discussed in the subsection (4.5). On the Figures 5c and 5d one can see cross-sections of the 5a and 5b images correspondingly, taken at $x\simeq 150$ nm (designated by arrows on 5a and 5b images). From these cross-sections we get conclusion that the lateral resolution of near-field images in our setup lies in the range $\simeq (50-70)$ nm. One can see that this resolution is less than radius of curvature of our tip ($R\simeq 190$ nm). From equation ([L=]), using experimental value of $d_{\mathrm res}\simeq 35$ nm one can obtain the dimension of the light field localization $L=115$ nm. Resolution is determined by the light intensity (that is by the square of the light field) and it is better than $L$. ## Distribution of the near-field intensity of the surface plasmons on rough silver surface: interference between scattering plasmons and initial plasmon beam Figure 6b illustrates the distribution of the near-field intensity of the surface plasmon field on a silver surface (direction of the initial surface plasmon beam designated by the arrow). Scan size is 8810 nm$\times$8810 nm. Optical signal was recorded at $2\Omega$ frequency in the "internal scattering registration mode" (i.e. $2c$ mode). From mathematical data processing of the topography of this part of surface (Figure 6a) we obtain the root-mean-square height of the surface roughness $\delta=<(\Delta z)^2>^{1/2}\simeq 5.1$ nm. The comparison of the surface topography (Figure 6a) and near-field (Figure 6b) images reveals two main features:\ 1) There is a correlation between the two images, i.e. the hillocks on the surface topography correspond to the white spots on the near-field image.\ 2) Apart from that, some additional structure (ripples and fringes) is appearing on the near-field images. The similar near-field pictures have been observed by other authors using SPNM (see, for instance ) and SNOM . But to our knowledge, the reasons of appearance of such "cluster structure" of the em field which not associated with any particular features in the surface topography have not been clearly illuminated. To attain such an understanding one must perform the fast Fourier transformation (FFT) of the near-field image. On the Figure 6d one can see a distinct circle in the FFT of the near-field image (the second circle arises because of inherent feature of Fourier transformation: a FFT image is symmetric respective to the origin of the coordinates). The explanation of the appearance of such a circle in the FFT image is given on the Figure 6c. The initial surface plasmon beam is scattered by surface roughness and interference between initial surface plasmon beam and scattering plasmons takes place. At elastic scattering the wavevector of the initial plasmon ${\mathbf k}_{\mathrm pl}$ changes its direction, but its magnitude remains the same ($|{\mathbf k}_{\mathrm pl}|=|{\mathbf k}_{\mathrm sc}|$). The distribution of the SP near-field intensity on the surface is $I_{\mathrm pl}+ I_{\mathrm sc}+ 2\sqrt{I_{\mathrm pl}I_{\mathrm sc}} \cos\left(({\mathbf k}_{\mathrm pl}- {\mathbf k}_{\mathrm sc}) {\mathbf r}\right)$ So the "vectors of the interference gratings" ${\mathbf K}_{\mathrm int}={\mathbf k}_{\mathrm pl}-{\mathbf k}_{\mathrm sc}$ are distributed so that their ends lie on the circle with radius equals $|{\mathbf k}_{\mathrm pl}|$. One can see from the FFT image that forward scattering (small ${\mathbf K}_{\mathrm int}$) is of the greatest intensity. The angular dependence of surface plasmon scattering by surface roughness is of great concern, for example, in studies of a laser damage of metal mirrors. The surface plasmons play a crucial role in such a damage  and elimination of the surface plasmons caused by the surface roughness is of considerable importance for increasing the laser damage threshold of metal mirrors . But for quantitative analyzes of plasmon scattering by FFT of near-field images it is better to use "internal reflection registration mode" or "internal scattering registration mode" in which the overall conical light radiation is collected by a cylindrical mirror (like it was done in ), because a nonuniformity in the registration of the scattered light leads to some artifacts in near-field images. These questions will be considered in details elsewhere . It must be also noted that for very large surface hillocks (when a cross-section of surface plasmon scattering of a large hillock and the one of the tip becomes comparable in magnitude) the effects of multiple scattering are important. In this case typical V-shaped figures near the large point-like hillock occur in the SPNM image. The explanation of this effect can be found in . Other effects of the multiple scattering such as backscattering enhancement of surface plasmons have been also observed on specific surfaces . ## Nature of the negative contrast of the surface hillocks in the "internal scattering/reflection registration modes" The nature of the *negative contrast* in the SPNM images of the surface hillocks, as far as we know, has not been yet clearly illuminated. Indeed, one can expect an increasing of the em field at a hillock while we (and other authors) observed the negative contrast of the surface hillocks in "internal scattering registration mode" and in "internal reflection registration mode", whereas we have found that in *"external scattering registration mode"* the surface hillocks display the *positive contrast*. To explain such a property of SPNM images one must recall how near-field images are produced in these registration modes. In "internal scattering registration mode" the AFM tip causes the *elastic* scattering of the *traveling* surface plasmons. And only plasmons with $|{\mathbf k}_{\mathrm sc}|=|{\mathbf k}_{\mathrm pl}|$ transfer to the conical em radiation which is then detected. But above a hillock there are no *traveling* surface plasmons, which can be elastically scattered by the tip. Whereas the strong em field above a hillock it is the field of the *localized* surface plasmons (with $|{\mathbf k}_{\mathrm local}| \not= |{\mathbf k}_{\mathrm pl}|$). An analogous situation takes place in "internal reflection registration mode", where elimination of *traveling* surface plasmons, which would transfer to the photons and destructively interfere with the light reflected from the silver-quartz interface is the cause of the SPNM signal. In other words in these two modes SPNM displays the intensity distribution of only *traveling* plasmons on the surface. # Conclusions In this paper a scanning plasmon near-field microscope operating in tapping mode of atomic force microscope was presented. The gold and silver-coated cantilevers were used to enhance an electromagnetic resonance in a tip-surface (sphere-plane) structure. At the em resonance in such a structure, the dimension of the light field localization is of the order of $L\simeq(2dR)^{1/2}$, where $d$ is the tip-surface distance and $R$ is the tip radius. Therefore at $d<