**5. Spatial resolution**

The resolution of *s*-SNOM by its operating principle depends on the size and the shape of the tip apex. In Fig. 5 above, the near-field amplitude image of the 4th harmonic order of the tip dithering frequency shows a one-to-one correspondence with the topography image. This match reflects that the spatial resolution of the recorded near-field image is comparable to that of the topography image. That is, the lateral resolution is at least 5 nm that is greatly dependent on the tip apex. On the other hand, the fit of the *s*-SNOM signal of the 4th harmonic order as a function of the tip-sample separation, Fig. 5(a), shows that it follows an exponential decay with a decay length of 9.8 nm. This result is an evidence for the vertical resolution of *s*-SNOM. Similar to other scanning probe microscopic techniques, many other factors can have great influences on the spatial resolution. Besides the tip shape specifically the radius of the tip apex, the dielectric property of the sample under study and the geometric structure of the sample in vicinity of the tip apex are anticipated to play two additional key roles in *s*-SNOM on the basis of the tip-sample near-field interaction. Such considerations are worthy of further exploration.

Fig. 6. Scanning topography (a) and *s*-SNOM optical amplitude (b) images of silver nanoparticle array embedded in anodic aluminum oxide. The gap between two counterpointing arrows indicates the region where strong intensity resides. Scale bars represent 40 nm.

process is necessity to increase its production yield. The resonance wavelength of a silver coated tip is about 450 nm while that of a gold one is about 600 nm. For such reason, the silver-coated tip is often used with the excitation wavelengths shorter than 600 nm, while the gold-coated tip is with the wavelengths longer than 600 nm. Furthermore, silver has a smaller optical loss than gold, but it can oxidize or sulfurize in ambient condition, altering its optical property in time. On the other hand, gold is rather stable in air, while it is softer than silver and thus does not endure during scanning probe operation. One has to place such factors into account while choosing tip coating for *s*-SNOM. For the applications of retrieving local field, the disturbance by the tip has to be minimized as much as possible. For such reason, the electromagnetic resonance of the tip needs to be avoided and therefore silicon or silicon nitride tips are commonly used directly. This is so because their electromagnetic resonance wavelengths are distant from the visible wavelength range. One concern has to be placed in the use of silicon tips. As silicon oxidizes in air, a thin silicon oxide coating (1-2 nm) can modify the optical response with respect to the excitation laser

The resolution of *s*-SNOM by its operating principle depends on the size and the shape of the tip apex. In Fig. 5 above, the near-field amplitude image of the 4th harmonic order of the tip dithering frequency shows a one-to-one correspondence with the topography image. This match reflects that the spatial resolution of the recorded near-field image is comparable to that of the topography image. That is, the lateral resolution is at least 5 nm that is greatly dependent on the tip apex. On the other hand, the fit of the *s*-SNOM signal of the 4th harmonic order as a function of the tip-sample separation, Fig. 5(a), shows that it follows an exponential decay with a decay length of 9.8 nm. This result is an evidence for the vertical resolution of *s*-SNOM. Similar to other scanning probe microscopic techniques, many other factors can have great influences on the spatial resolution. Besides the tip shape specifically the radius of the tip apex, the dielectric property of the sample under study and the geometric structure of the sample in vicinity of the tip apex are anticipated to play two additional key roles in *s*-SNOM on the basis of the tip-sample near-field interaction. Such

Fig. 6. Scanning topography (a) and *s*-SNOM optical amplitude (b) images of silver nanoparticle array embedded in anodic aluminum oxide. The gap between two counter-

pointing arrows indicates the region where strong intensity resides. Scale bars

beam considerably, accordingly diminishing the scattering signal [38].

considerations are worthy of further exploration.

**5. Spatial resolution** 

represent 40 nm.

The following two examples illustrate how the field interaction and the geometric factors around the tip influence the spatial resolution of *s*-SNOM. The first sample is an array of silver nanoparticles embedded in aluminum oxide matrix. The silver nanoparticles were electrodeposited into a two-dimensional hexagonal ordered nanochannel array that was formed during anodization of smooth aluminum foil [40]. The gap between adjacent nanoparticles is about 5 nm and confirmed by electron microscopy. Figure 6 shows its topography and near-field intensity amplitude images recorded with a silicon tip with a radius of curvature of less than 10 nm. Notice that the close examination of the two images shows that a large intensity extends for ~6 nm between adjacent nanoparticles. In this observation, the nanoparticle array with a specific interparticle spacing serves as a ruler and confirms the lateral resolution of this *s*-SNOM measurement. An *s*-SNOM image of aggregated gold nanoparticles were reported previously [32] to portray the coherently oscillating nature of plasmon resonant of individual nanoparticles, expect that no confirmation of the gap by other means was provided. As an example, using a carbon nanotube attached on a silicon tip, Hillenbrand and his workers successfully recorded both amplitude and phase images of gold nanoparticles with a good spatial resolution, though no direct proof by electron microscopy was given [41]. The second example is a square array of annular trenches on a gold film of 200 nm thickness. These carved rings were made by focused ion beam. The diameters of the inner and outer circles are 250 and 330 nm, respectively; the depth is 200 nm; the spacing between adjacent rings is 600 nm. Figure 7 shows the topology and near-field amplitude scanned with sharp and blunt PtIr5-coated

Fig. 7. Topology images of annular trench array on gold film made by focused ion beam recorded with (a) sharp and (c) blunt tips and their corresponding intensity amplitude images, (b) and (d), respectively. The diameters of the inner and outer circles are 250 and 330 nm, respectively. Scale bars represent 200 nm.

High-Resolution Near-Field Optical Microscopy: A Sub-10

acquire interference results owing to electrical contact.

*I*

*I*

Nanometer Probe for Surface Electromagnetic Field and Local Dielectric Trait 335

silicon transistor [44] with a resolution of 40 nm at 2.54 THz by the use of the Drude contribution: the carrier concentration influences the plasma contribution of the dielectric constant of silicon, yielding visible contrast to resolve the regions of different doping concentrations. This approach of recording local electrical property is non-contact and is better than the contact counterparts, such as surface capacitance microscopy, that often

Fig. 8. Images of (a) topography and (b) near-field amplitude of the third-harmonic order,

*sca*(3), of a Fischer's pattern [10] excited at 632.8 nm; (c) comparison between calculated

imaginary-part values of -0.1 (solid line) and -10 (dashed line) and measured values extracted from the corresponding regions of Si (blue dot), PMMA (green dot) and Au

(red dot) in (b). Scale bars represent 100 nm.

*sca*(3) as a function of the real part of the dielectric constant of the sample, Re(), with the

The capability of resolving local dielectric property with *s*-SNOM has been utilized by us to examine nanometer-scale optical contrast of the phase-change layer of blue-ray recordable and erasable disks [45]. The quality of recording or reading data is greatly dependent on the detailed variation of optical characteristics within the recorded mark that is within 150 nm in size. Fast temperature quenching induces amorphous phase, while slow temperature

silicon tips. The recorded near-field amplitude image Fig. 7(a) with the sharp tip shows a good correspondence with the corresponding topology image Fig. 7(b) that reflects the examination with scanning electron microscopy. In contrast, the use of the blunt tip blurs the resultant topology image Fig. 7(c) and creates a peculiar near-field amplitude image Fig. 7(d) that is quite distinct from the one obtained with the sharp tip.

#### **6. Applications in nanomaterials**

In the sphere of nanomaterials, manifold materials are architecturally configured with nanometer-scale precision, aiming for specific and contingent, multiplex while coherently collaborative functions. It is requisite to comprehend their structural arrangement through innovative material processing methods and, even furthermore, their inter-correlated properties directly. The demonstration of *s*-SNOM being capable of resolving dielectric characteristic of surface in nanometer scale exemplifies one prototypical case. At first, such effort entails a sample that is made of distinct materials with known dielectric constants. Fischer's pattern [42] is chosen here to serve as the first example. Such pattern is made with the following nanosphere lithography procedure. First, polymethylmethacrylate (PMMA) spheres of 300 nm in diameter are self assembled into a hexagonal closely packed pattern on a silicon surface. Second, gold is thermally deposited to overlay such pattern with a gold film of 50 nm in thickness. Finally, the sample is immersed in an acetone solution to remove the PMMA spheres, yielding a hexagonal array of triangular gold disks. Some PMMA residues remain in the vicinity of the gold disks owing to incomplete dissolution of PMMA spheres. The resultant pattern sample thus bears three differing materials (silicon, gold and PMMA) that represent archetypal semiconductor, metal and polymer. The AFM topography image, shown in Fig. 8(a), only shows such hexagonally packed pattern devoid of material composition. In contrast, the scanned image of the scattering intensity of the third-harmonic order, *Isca* 3 , is shown in Fig. 8(b) and clearly portrays three regions with distinct scattering intensities: triangular areas with the highest signal, round areas with a medium signal and peripheral areas surrounding the triangular areas with the smallest signal. The correspondence with the simultaneously recorded topography image suggests that the brightest areas stand for gold, the less bright areas signify silicon and the dimmest areas are indicative of PMMA. Such assignment can be confirmed with the quantitative comparison of their relative intensities with respect to the calculation according to the quasi-static dipole model, Eqs. (1)-(5). Figure 8(c) displays the calculated *Isca* 3 as a function of the real part of the dielectric constant of the sample, Re(). The measured scattering intensities of the three areas are also plotted in the figure according to the dielectric constants of the assigned materials. The experimental data points agree with the calculated values, if the imaginary part of the dielectric constant, Im(), is assumed to be -0.1 that is valid for these three lossless materials at 632.8 nm. This correspondence demonstrates the exploitation of *s*-SNOM to extract local dielectric property within sub-10 nanometers. The dielectric constant of material contains Lorentz and Drude contributions. The former one represents local oscillators coming from electronic and vibrational transitions, while the latter one reflects the influence of free carriers. Huber *et al.*, via taking advantage of the variation of the Lorentz contribution, used *s*-SNOM, operating at 10.7 μm, to resolve different materials of tungsten, aluminum, silicon and silicon oxide on the polished cross section of a pnp transistor [43]. More recently, they mapped the doping concentration distribution of a

silicon tips. The recorded near-field amplitude image Fig. 7(a) with the sharp tip shows a good correspondence with the corresponding topology image Fig. 7(b) that reflects the examination with scanning electron microscopy. In contrast, the use of the blunt tip blurs the resultant topology image Fig. 7(c) and creates a peculiar near-field amplitude image

In the sphere of nanomaterials, manifold materials are architecturally configured with nanometer-scale precision, aiming for specific and contingent, multiplex while coherently collaborative functions. It is requisite to comprehend their structural arrangement through innovative material processing methods and, even furthermore, their inter-correlated properties directly. The demonstration of *s*-SNOM being capable of resolving dielectric characteristic of surface in nanometer scale exemplifies one prototypical case. At first, such effort entails a sample that is made of distinct materials with known dielectric constants. Fischer's pattern [42] is chosen here to serve as the first example. Such pattern is made with the following nanosphere lithography procedure. First, polymethylmethacrylate (PMMA) spheres of 300 nm in diameter are self assembled into a hexagonal closely packed pattern on a silicon surface. Second, gold is thermally deposited to overlay such pattern with a gold film of 50 nm in thickness. Finally, the sample is immersed in an acetone solution to remove the PMMA spheres, yielding a hexagonal array of triangular gold disks. Some PMMA residues remain in the vicinity of the gold disks owing to incomplete dissolution of PMMA spheres. The resultant pattern sample thus bears three differing materials (silicon, gold and PMMA) that represent archetypal semiconductor, metal and polymer. The AFM topography image, shown in Fig. 8(a), only shows such hexagonally packed pattern devoid of material composition. In contrast, the scanned image of the scattering intensity of the third-harmonic order, *Isca* 3 , is shown in Fig. 8(b) and clearly portrays three regions with distinct scattering intensities: triangular areas with the highest signal, round areas with a medium signal and peripheral areas surrounding the triangular areas with the smallest signal. The correspondence with the simultaneously recorded topography image suggests that the brightest areas stand for gold, the less bright areas signify silicon and the dimmest areas are indicative of PMMA. Such assignment can be confirmed with the quantitative comparison of their relative intensities with respect to the calculation according to the quasi-static dipole model, Eqs. (1)-(5). Figure 8(c) displays the calculated *Isca* 3 as a function of the real part of the dielectric constant of the sample, Re(). The measured scattering intensities of the three areas are also plotted in the figure according to the dielectric constants of the assigned materials. The experimental data points agree with the calculated values, if the imaginary part of the dielectric constant, Im(), is assumed to be -0.1 that is valid for these three lossless materials at 632.8 nm. This correspondence demonstrates the exploitation of *s*-SNOM to extract local dielectric property within sub-10 nanometers. The dielectric constant of material contains Lorentz and Drude contributions. The former one represents local oscillators coming from electronic and vibrational transitions, while the latter one reflects the influence of free carriers. Huber *et al.*, via taking advantage of the variation of the Lorentz contribution, used *s*-SNOM, operating at 10.7 μm, to resolve different materials of tungsten, aluminum, silicon and silicon oxide on the polished cross section of a pnp transistor [43]. More recently, they mapped the doping concentration distribution of a

Fig. 7(d) that is quite distinct from the one obtained with the sharp tip.

**6. Applications in nanomaterials** 

silicon transistor [44] with a resolution of 40 nm at 2.54 THz by the use of the Drude contribution: the carrier concentration influences the plasma contribution of the dielectric constant of silicon, yielding visible contrast to resolve the regions of different doping concentrations. This approach of recording local electrical property is non-contact and is better than the contact counterparts, such as surface capacitance microscopy, that often acquire interference results owing to electrical contact.

Fig. 8. Images of (a) topography and (b) near-field amplitude of the third-harmonic order, *I sca*(3), of a Fischer's pattern [10] excited at 632.8 nm; (c) comparison between calculated *I sca*(3) as a function of the real part of the dielectric constant of the sample, Re(), with the imaginary-part values of -0.1 (solid line) and -10 (dashed line) and measured values extracted from the corresponding regions of Si (blue dot), PMMA (green dot) and Au (red dot) in (b). Scale bars represent 100 nm.

The capability of resolving local dielectric property with *s*-SNOM has been utilized by us to examine nanometer-scale optical contrast of the phase-change layer of blue-ray recordable and erasable disks [45]. The quality of recording or reading data is greatly dependent on the detailed variation of optical characteristics within the recorded mark that is within 150 nm in size. Fast temperature quenching induces amorphous phase, while slow temperature

High-Resolution Near-Field Optical Microscopy: A Sub-10

**7. Applications in nanophotonics** 

including the nanometer-scaled features within the recorded marks.

size made by focused ion beam on metal film are present.

Nanometer Probe for Surface Electromagnetic Field and Local Dielectric Trait 337

observed by TEM measurement. This nanometer-scaled optical signature could potentially deteriorate the carrier-to-noise ratio in reading this optical storage medium. On the other hand, the studies of BD-RE with conductive AFM [47-48] only presented either conducting or non-conducting state of the phase-change layer, thus prohibiting from using this technique to investigate the intricate phase-change characteristics within the recorded marks. Compared with the result obtained with aperture-typed SNOM by Yoo and coworkers [50], its spatial resolution is not enough to extract the detailed variation,

In the sphere of nanophotonics, the energy of electromagnetic field is concentrated or controlled with some specially prepared nanostructures beyond the limit set by traditional optical theory where the optical mode density on which the principles of optics rely in the region of interest is assumed as in free space or only slightly perturbed from it. In contrast, the optical mode density in the content of nanophotonics has drastically distinct distribution that is governed by the nanostructured materials in proximity. Because of such distinct optical mode density, its understanding and therefore control are limited by itself that is beyond the traditional optical theory. Moreover, transferring its information content to our macroscopically sensible realm is also influenced greatly by such limitation, entailing unconventional experimental means to truthfully convey the optical information. The *s*-SNOM is representative of one of such many innovative techniques. According to Eq. (5), the scattering intensity induced by the tip-sample near-field interaction is also dependent on the field in the vicinity of such tip-sample complex. Specifically, the scattering radiation can be induced upon the presence of certain surface electromagnetic field. Surface plasmon wave (SPW) exemplifies such surface electromagnetic field, by which the evanescent wave propagates on the metal-dielectric or metal-vacuum interface [29, 43, 50]. In this section, the near-field characteristics of the SPW emanating from single hole or hole arrays of nanometer

The first example is single hole of 150 nm in diameter on a silver film of 200 nm in thickness. Figure 10 schematically shows the application of *s*-SNOM to such sample. In the case like that, three scattering field contributions are present in the thus obtained *s*-SNOM images. The first contribution is the outcome of the interaction between the incident wave and the tip apex that is in vicinity of the sample surface, producing the first scattering field, *E*1. The second contribution is made by the SPW induced by the interaction of the incident wave and the hole. The thus induced SPW propagates to the tip apex, producing the second scattering field, *E*2. The third contribution is made the SPW induced by the tip apex that is approached to the sample surface, which propagates to the hole, reflects back to the tip apex, and gives the third scattering field, *E*3. The wave vector, *kSPW* , this surface plasmon wave follows the following dispersion relation, *k k SPW* 0 12 1 2 [51], where 0 *k* is the wave vector of the incident wave, and 1 and 2 is the dielectric constants of vacuum and silver, respectively. The detailed derivation of the resultant scattering wave as well as the corresponding one in inverse space is given in Ref. 50 and is not repeated here. According to the derived results, the interference between *E*1 and *E*2 produces two *kSPW* -radius circles centered at 0 sin *<sup>i</sup> k* . Furthermore, the interference between *E*1 and *E*3

cooling yields polycrystalline. The optical signature within such mark is not discernible with conventional aperture-typed SNOM owing to its >50 nm resolution, but would be possible with high-resolution *s*-SNOM. The near-field image of the AgInSbTe phase-change layer of a blue-ray disc obtained by the *s*-SNOM is shown in Fig. 9(a). The recorded marks are revealed by the prominent near-field optical contrast. According to the dielectric constants of crystalline and amorphous AgInSbTe at 632.8 nm (3.63+*i*21.2 and 8.14+*i*9.35, respectively) [46], the ratio between the calculated tip-induced scattering intensities of the crystalline and amorphous phases is 1.28 that that is very close to the experimentally determined value of 1.30. This observation indicates that the dark regions along the protruding track in Fig. 9(a) are amorphous AgInSbTe created during the recording process. This inference agrees with TEM observation. The scattering intensity profile of the recorded disc shows that the marks have the minimum width of ~160 nm by measured the cross section (dash lines), while no such feature is present in the non-recorded disc, shown in Fig. 9(b). Such prominent marks are not recognizable in the corresponding topographic image. In addition, 30-nm isolated crystalline domains within the amorphous recorded mark emerge in Fig. 9(a) and also were

Fig. 9. (a) Image of the scattering intensity of third-harmonic order of BD-RE disc; (b) intensity profile along the track, marked by the dashed line in (a). Scale bar represents 200 nm.

observed by TEM measurement. This nanometer-scaled optical signature could potentially deteriorate the carrier-to-noise ratio in reading this optical storage medium. On the other hand, the studies of BD-RE with conductive AFM [47-48] only presented either conducting or non-conducting state of the phase-change layer, thus prohibiting from using this technique to investigate the intricate phase-change characteristics within the recorded marks. Compared with the result obtained with aperture-typed SNOM by Yoo and coworkers [50], its spatial resolution is not enough to extract the detailed variation, including the nanometer-scaled features within the recorded marks.
