1. Introduction

Near-field scanning microwave microscopy (NFSMM) is a well-established technique to characterize material properties such as conductivity, dielectric permittivity or magnetic permeability at centimeter and millimeter wavelengths [1]. Owing to very small probe sizes as compared to wavelength, high spatial resolutions at the micron scale have been achieved [2, 3]. Fee et al. [4] first demonstrated the advantage of near-field probes built from tips bonded on open-ended waveguides and later Grober et al. [5] showed a great increase in resolution by using a bow-tie antenna, especially if this probe is resonant with the incident wavelength. Practical implementations of such antennas in the optical domain require very high manufacturing skills [6,7] that become far easier at very high frequencies in the microwave domain [8]. One of us previously used this kind of tip probes at 100 GHz [9], eventually associated to wire modes that guide the mm-wave up to the tip end of a near-field scanner [10].

Very few NFSMM experiments have been proposed at mm-waves [11–14]. First two use a slit or 1D tapered waveguide that do not allow for direct 2D imaging. Last two are close to GHz NFSMM experiments and use resonant tips. In view of material and circuit inspection [15], we chose to develop a new NFSMM operating at 60 GHz. To the difference with previously published NFSMM, we chose to investigate the pyramidal tip or bow-tie antenna that was demonstrated only ones at mm-waves [8].

In this paper we illustrate the strongly sub-wavelength imaging capability of bow-ties at mm-waves and mostly focus on the near-field image formation with such antennas. Besides classical resonant and non-resonant tips which exhibit a natural sensitivity to the Z-component of the electric field that is normal to the sample surface, bow-tie probes are polarized in the XY principal plane of the sample. As a result non-isotropic features are expected and should be demonstrated both for topology variations and for dielectric constant spatial variations (namely, semiconductor vs metal). This is proposed in this paper with two kinds of samples exhibiting quite high contrast but having the two different purposes to illustrate the topological sensitivity with a semiconductor edge and the conductivity sensitivity with thin metallic films deposited on Si for which thicknesses are negligible as compared to the probe-sample distance.

2. Experimental setup and probe fabrication

The experimental setup involves a Gunn diode of 20 mW output power feeding a 20 dB directional coupler. Detection is obtained by collecting the reflectometry signal via a Schottky detector in the coupled return path of the coupler while in the direct path the probe is connected in series with a E/H tuner that matches the unloaded probe and thus makes it resonant. Probe location is controlled owing to two video cameras equipped with 12X zoom lenses offering a comfortable working distance and a micrometer resolution. A right angle arrangement between cameras allows precise positioning above the sample. By means of three reference points a constant probe-sample distance is then ensured with the computer controlled micrometer motorized XYZ stages. Finally a vertical oscillation of the sample at the μm-scale is imposed in the Z-direction by means of a piezo actuator in order to extract only the near-field component with a lock-in amplifier.

Since we are interested in samples for which the imaging result may depends of the electromagnetic field (E or H) and polarization, we manufacture our own probes on the basis of nanoantennas attached to the waveguide. This process involves the assembly of small pieces obtained from laser cutting of 25 μm thick tungsten sheets. Some realizations of the 60 GHz E-probe are shown in Fig. 1. They were obtained by bonding two tungsten equilateral triangles at the end of a WR15 waveguide. Triangles tips are very sharp owing to the laser cutting process that produces radius of curvature ≲ 2 μm. It was obviously not possible to solder correctly these triangles in the desired position without a mechanical support. An extra plastic piece fabricated with a 3D-printer was plugged in the waveguide to fix the problem. During assembly the two triangles are manually glued on this extra piece after correct positioning and thereafter electrically connected. Final adjustment of the air gap g is done manually at the end of the process.

 

Fig. 1 Photographs of near-field probes. (a) General view of the WR15 waveguide with the bow-tie attached. (b) & (c) Close view of the facing tips. (b) Probe#1, g = 25 μm. (c) Probe#2, g = 18 μm.

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Separate 3D electomagnetic calculations of the field emitted by the probe have been done using CST Microwave Studio. Although our probe does not include any dielectric material within the pyramidal arrangement, we obtained very similar behaviors and maps than [8] showing a high intensity concentration at probe end. From a polarization point of view, the resulting E-field exhibits two components. The first is transverse and applies in the direction joining the two facing triangle tips with a maximum intensity just in-between the two tips. The second is longitudinal along the waveguide and exhibits a significant value only in the very close vicinity of the tips, not in-between. These are in fact the closure of the evanescent E-field lines at both tip ends [16].

3. Spatial resolution

First near-field images involve a cleaved corner of GaSb substrate of 350 μm thickness. We know that this substrate is quite easy to cleave along its natural crystallographic axes and therefore produces a nearly perfect right angle which is the ideal sample for topographical resolution testing. Images at constant height h were acquired with the probe of Fig. 1(b). This probe exhibits a spacing g = 25 μm with a slight misalignment between the facing triangles. As a result its natural polarization joining the two tips is not aligned with the mechanical X-axis of the experiment that we set along the short side of the waveguide.

Near-field plots were obtained at constant heights h = 5 μm, 45 μm and 85 μm with a mesh size of 25×25 μm² in the XY -plane. The Fig. 2(a) gives the map obtained at the shortest probe-sample distance. The contrast between intensities when the probe flies over the sample and over the sample holder is very high making the sample edge well defined. X (respectively, Y) spatial resolution are deduced from this image by averaging the signal over a set of adjacent lines (respectively, columns). This is drawn in Fig. 2(b) for the X-direction. Owing to the template, a spatial resolution of 38 μm for an intensity change of 10% to 90% is obtained. Such a resolution correspond to ≈ λ/130 and is thus strongly subwavelength.

 

Fig. 2 (a) Near-field image of a cleaved GaSb corner obtained at height h = 5 μm. Image mesh is 25 × 25 μm². (b) Resolution determination using the averaged data between the white dashed lines in (a), dots: experimental values, lines: best piecewise fit and 10% to 90% resolution template.

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Using the procedure described in Fig. 2 resolutions were extracted for each height and direction. Results given in Table 1 show a resolution that deteriorates rapidly when h increases. Best resolution is obtained along X with a discrepancy particularly marked at small h. Our probe is therefore not isotropic in the XY -plane, a result consistent with the expected behavior of an in-plane electric dipole oriented along the line connecting the two tips. Recalling that this probe is not a perfect bow-tie and that we use here a step size of 25 μm only, these resolutions are thus higher bounds that one can expect to beat with more smaller and perfect probe.

Table 1. Spatial Resolution vs Height h and Direction.

View Table

4. Topographical profiles

Another probe exhibiting a gap g = 18 μm, see Fig. 1(c), was built and previous tests with the GaSb corner were reproduced with a reduced step size of 5 μm. The two tips of this probe are aligned along X producing a main component of the electric field along the same direction. We then define the electric field polarization interacting with the sample using common s- and p-denominations by assuming that the plane of incidence is described by the probe during its movement. Referring to axes defined in Fig. 1(a), the p-polarization is for profiles acquired along X while s-polarization is obtained along Y.

Near-field measurements acquired for various conditions are given in Fig. 3. All these profiles were obtained using the same vertical modulation of the sample position so as to be compared quantitatively. In the upper row we take benefit from the microwave technology and compare profiles obtained with the same probe for two different conditions. With the E/H tuner inserted the probe is resonant and without it is non-resonant. Usually in optics non-resonant probes are considered while this is the converse in microwave. Whatever the polarization, the measured signal above the GaSb sample is ×3 greater with a resonant probe, an effect that is apparently slightly more pronounced for p- than for s-polarization. The discrepancy between both polarizations is linked to the in-plane polarized nature of our probe: such feature differs from classical tip probes obtained from needles in microwave that are isotropic in the sample plane [1,13,17]. To enforce this contrast with classical tip probes, one also observes strongly localized oscillations at edge crossing that exhibit intensities and positions which depend on the polarization and resonant nature of the probe. For instance they are of similar intensities for p-polarization and exhibit a local maximum at edge crossing with a zero ≈ 50 μm away above the sample. To the contrary for s-polarization and resonant probe a zero is found at edge crossing while for non-resonant probe one only see a bend without minimum. Considering non-resonant probes, it looks like early SNOM observations that were interpreted by the near-field intensity produced by a point dipole in the electrostatic approximation [18]. As a result and like in SNOM, it is no more possible to simply estimate the resolution because of these complicated substructures [19]. Such behavior is emphasized in the lower row of Fig. 3 where profiles acquired in non-resonant probe mode are given for three different heights above the sample. The response at edge crossing depicts increasing oscillations when h decreases for p-polarization whereas gentle bends are only observed for s-polarization. Again this is in agreement with theoretical near-field calculations and related to the in-plane dipolar nature of the sample illumination [18].

 

Fig. 3 Near-field profiles measured at constant distance above a doped GaSb edge figured out by the grey shaded area. Left column is for p-polarization and right column for s-polarization. Upper row: Influence of resonant (red) vs non-resonant probe (blue). Probe-sample distance is h = 15 μm. Lower row: Influence of probe-sample distance h with a non-resonant probe; orange h = 10 μm; blue h = 15 μm; red h = 70 μm.

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The benefit of these first experiments is to illustrate the nontrivial nature of topological near-field imaging with a bow-tie antenna in the mm-wave range. To our knowledge comparison between resonant and non-resonant probes in the same experiment was not shown before and if the latter case is close to SNOM and has been described and theoretically evaluated, this is not the case for resonant probe. Extreme care must be taken in image interpretation as it strongly depends on h and on the field polarization.

5. Near-field metal sensing

In another experiment we investigate our NFSMM for material characterization [1, 2]. A new bow-tie probe with a geometry similar to that of Fig. 1(c) but with an enlarged gap of g = 50 μm between tips was used to measure the reflectivity of three 400 μm wide metallic lines deposited on Si substrate. These lines were fabricated using different metals, namely Al, Au and Cu, and their DC conductivities were measured at 16.9 × 10⁶ S/m, 26.0 × 10⁶ S/m and 24.4 × 10⁶ S/m respectively. Difference with previous experiment is here the negligible height of metal deposited to fabricate the lines (< 300nm) as compare to our minimal probe sample-distance. As a consequence the measured near-field profiles given in Fig. 4 for p- and s-polarizations and heights h = 5 μm and 15 μm are no more topological profiles but instead expected to reflect the local change of the dielectric constant. Notice that these profiles are compared by removing the baseline of each measurement so as to plot only the relative variations of the detected voltage when crossing the lines.

 

Fig. 4 Near-field profiles measured while crossing 400 μm wide metallic lines deposited on Si-substrate. Metal position is figured out by the grey shaded area. Profiles are given in variation of the detected voltage versus distance; orange, Al line; blue, Au line; red, Cu line. Left column is for p-polarization and right column for s-polarization. Upper row: probe-sample distance h = 15 μm. Lower row: probe-sample distance h = 5 μm.

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First consider Fig. 4(a) obtained at h = 15 μm for p-polarization. As expected the detected signal suddenly increases above the line because of a change of imaginary part of the dielectric constant in the close vicinity of the probe tip. The near-field response registered for the Al line is measured at ≈ 63% of that measured for Au and Cu lines, both having very close conductivities. This ratio is in very good agreement with the 65% and 69% ratios calculated for the conductivities of Al-line vs Au- and Cu-lines respectively. For p-polarization, this validates the ability to obtain quantitative comparisons between local conductivity or permittivity with our NFSMM operating at 60 GHz.

This picture changes drastically when considering s-polarization of Fig. 4(b). First, the total amplitude variation is reduced by a factor ≥ 2, and, above all large oscillations now superimpose to a homogeneous profile in accordance with the line geometry. As a consequence the near-field intensity in that case is no more proportional to the local conductivity. If the probe-sample distance is further reduced to h = 5 μm the situation becomes visibly worse, even for the p-polarization although the maximum of the profile intensities are still approximately proportional to line conductivities. A very interesting feature is obtained with s-polarization at h = 5 μm because one can not infer anymore the line geometrical profile, especially on gold line since measurements exhibit a complete contrast inversion. Within the image dipole approximation [20], this near-field phenomenon is eventually explained by the destructive interference that occurs between an in-plane exciting dipole and its image inside a metal with very high modulus of the dielectric constant such as our gold layer of thickness 300 nm. Although it seems that such contrast inversion is seen here for the first time in near-field, this simple picture does not explain the difference here observed between the two polarizations. Finally it is surprising to note that, at a given height, the most perturbed profiles are switched between the two polarizations, i.e. p in Fig. 3 and s in Fig. 4. This is probably due to the difference of the nature of the samples that enforces the topological effect in Fig. 3 and the local change of conductivity in Fig. 4. A clear interpretation is still to be provided.

6. Conclusion

We have described a NFSMM operating at 60 GHz that uses a bow-tie antenna probe. Resonant and non-resonant probe were both studied, and a better contrast in topological profiles was shown with resonant probe in constant height scan. Near-field intensity profiles clearly depict a true near-field detection with strongly marked in-plane dipolar nature that induce difficulties in image interpretation and apparatus resolution estimate. Provided that the probe-sample distance is not too small p-polarized measurements have been quantitatively related to the conductivity in the near-field. These first results obtained with high-contrast samples have to be complemented in the future with other samples involving either small dielectric constant changes and/or biological samples.