Coaxial tips for a scanning microwave microscope and its calibration with dielectric references

Scanning microwave microscopy (SMM) is a combination of an atomic force microscope with a vector network analyzer (VNA) to measure locally resolved impedances. The technique finds application in the realms of semiconductor industries, material sciences, or biology. To determine quantitative material properties from the measured impedances, the system must be calibrated. Transferring the calibration from the calibration substrate onto the material under test is strongly limited when using unshielded probes, as the electromagnetic coupling to the surroundings can reach several centimeters. This work reports the fabrication of coaxially shielded probes for a scanning microwave microscope and their integration into such an instrument. We discuss a calibration method with dielectric references, using a simulation-assisted 1-port VNA calibration algorithm. Uncertainty considerations of the measurement process are included and propagation throughout the algorithm is performed. The calibration is verified with an additional dielectric reference. As an application example, the results for a static-random-access memory sample are presented. We identified system-related drift and trace noise as the dominant contributors to the uncertainties of the calibrated results. The here presented shielded tips can broaden the application scope of SMM, as they are door-openers for measurements in liquids.


Introduction
The demand for characterization at the micro-and nanoscale is steadily increasing in both industry and research, particularly in the realms of integration, miniaturization, material properties, and quality control.This need spans various fields, ranging from the semiconductor industry, bionanotechnology to electrochemistry, where scanning probe microscopes, equipped with a diverse array of measurement modes, play a crucial role [1][2][3].In addition to pursuing higher sensitivities of these instruments, the importance of achieving reliable, quantitative, and therefore comparable results is becoming more important.Moreover, the broadening of application scopes, such as extending to in situ measurements of battery materials or biological tissues, introduces new requirements on the measurement systems [4,5].
In scanning microwave microscopy (SMM) a microwave signal in the range of typically 1 GHz to 50 GHz is coupled into a metallic or metalized tip of a scanning probe microscope.The forward traveling wave gets reflected at the tip-sample interface and the reflection coefficient S 11 is measured by a vector network analyzer (VNA) or dedicated measurement electronic, see figure 1.The impedance formed by the tip and the material under test (MUT) alters the magnitude and phase of the reflected signal.Consequently, S 11 carries locally resolved information about the MUT which can be transformed into material properties such as complex permittivity, capacitance and resistance, or dopant density using an appropriate measurement model [6].However, to obtain quantitative information, calibration is required.This can be done using e.g.capacitive, resistive, or inductive standards [7,8] or different dopant densities [9].
Most SMMs use either straight metallic tips (e.g. from Unisoko Co. Ltd) or cantilever-based tips (e.g. from Rocky Mountain Nanotechnology LLC).Due to the exposed metal on the cantilever or tip shaft, the measured reflection coefficient is a combination of an undesired stray impedance Z stray and the impedance Z MUT , formed by the tip apex and the sample below.This effect can be strongly reduced by shielding most of the tip, only leaving the last part of the signal carrier exposed, see figure 2. The confinement of the electrical interaction between the tip and the MUT allows for better lateral resolution, higher signal-to-noise ratio (SNR), and more accurate calibration, as we will discuss in section 2.2.Moreover, unshielded tips have significant limitations when employed for measurements in liquids [10], as the tip shaft and cantilever contribute to electrochemical reactions and the measured S-Parameter depends on the immersion depth.Probes with a shielded cantilever [11] to reduce the stray capacitance are commercially available (PrimeNano Inc.).These probes are batch-fabricated in SiN technology and expose a few micrometers of the metallic tip.
Preliminary results of coaxially shielded tips for SMM based on pipette pulling were published in [12] by some of the authors.In this study, we first discuss a calibration method for SMM and present simulation results that compare the performance of unshielded and shielded tips in SMM measurements.Subsequently, we describe the fabrication process of these tips in more detail and their integration into the scanning microscope.Lastly, we showcase an application example where we calibrate the system using three reference standards and discuss the results of the MUT including uncertainties.

The mSOL calibration
We will briefly discuss the calibration scheme employed, stemming from 1-port VNA calibration [13].There, the SOL calibration uses three standards (short, open, and load) to relate the measured reflection coefficients with known impedances.Our slightly modified method mSOL uses a similar approach.For more detail on the algorithm, we refer to [14].The 1-port error model for VNA calibration S 11m = e 00 + S 11 e 01 1 − e 11 S 11 (2) relates the measured raw reflection coefficient S 11m with the tip-sample impedance Z tip via three error terms e 00 (directivity), e 01 (tracking), and e 11 (port-match).In principle, the reference impedance Z ref can be chosen arbitrarily.However, as we will see later, we will directly extract S 11 from the simulation for a given standard.By measuring at least three different substrates with known permittivities, the obtained values S (i) 11m for i = 1, 2, 3, . . .together with the theoretical values S (i) 11 and equation (2) form a system of equation that is solved for the three complex error coefficients e 00 , e 01 and e 11 .
The measurement of an unknown substrate can then be calibrated using S 11 = S 11m − e 00 e 01 + e 11 (S 11m − e 00 ) . (3)

Simulation
We will first discuss the general differences between an unshielded and shielded SMM tip through simulation results.Then, the specific simulations supporting our calibration method are presented.A conceptual view on the benefits of coaxially shielded probes is given through finite element analysis using COMSOL Multiphysics ® with the radio frequency module.The simulated regions comprise the metallic center conductor with a length of 500 µm and a diameter of 5 µm tapering down to 2 µm, a substrate below the tip, and the surrounding air.In the case of a shielded tip, a dielectric sheath (ϵ r = 4.2) with an outer diameter of 50 µm is added.The untapered section of the dielectric is covered by an ideal conductor.Figure 2 shows the simulated electric fields of an unshielded and shielded tip at f = 10 GHz placed over a dielectric substrate (ϵ r = 8) and a schematic of the different regions.The simulations indicate, that a large part of the energy is radiated into the air, rather than transported to the sample.This is further stressed by comparing the relative energy of the electric field within the sample and the surrounding air, as plotted in figure 3.For an unshielded tip, energy is mostly radiated and only a small fraction of the energy is delivered to the sample.Consequently, changes in the material properties of the sample result in only small changes in the measured reflection signal.In contrast to this, a shielded tip confines the electric field, and the energy is delivered at a much higher rate to the sample.The reflected signal is consequently more dependent on the material properties and the SNR is increased.
Besides an expected improvement in SNR, the undesired stray capacitance formed by the tip and any structures nearby is reduced for a shielded tip as demonstrated in figure 4. A conductive structure is placed at distance d in the vicinity of the tip and the relative change in the reflection signal is plotted.The shielded tip is less sensitive to its direct surroundings.This is an important property for transferable calibrations, i.e. the instrument is calibrated using standards that are not directly incorporated in the MUT or placed next to it.
Our calibration routine is supported by the results of finite element analysis using the same regions as mentioned before.We employed a 3D analysis instead of a 2D axisymmetrical simulation to mitigate numerical problems related to the conversion of the magnetic vector potential to the electric field.We simulate the reflection coefficients S i,j 11 of a coaxial tip on a dielectric substrate for a variety of relative permittivities ϵ i r and loss tangents tan δ j , i, j = 1, 2, 3, . . ., n defining the material's complex permittivity as where ϵ 0 is the permittivity of the vacuum.The simulations include the sets (ϵ i r , tan δ i ) that correspond to the definition of  the reference substrates i = 1, 2, 3.These results are then used to determine the error coefficients in equation (2).

A fabrication method for coaxial tips
The fabrication method presented here is based on well-known procedures for nanopipette pulling used in several fields such as electrochemistry [15,16].On one hand, the process is laborintensive and highly dependent on factors such as the laboratory environment, material selection, and equipment.This complicates achieving consistent production and transferring Fabrication procedure for coaxial probes for SMM using a laser puller.1.A thin Pt wire is inserted into a glass capillary (Quartz or Borosilicate). 2. Heat is applied while the capillary is evacuated and restricted from being pulled.3. The compound is further heated and pulled until separation.4. A stainless steel pin is placed inside the capillary and soldered using a hot air gun. 5.The outer conductor is evaporated or sputtered.To avoid a short circuit between the center and the ground, the capillary is inclined.6.The coaxial tip can be polished if needed.Our setup allows for simultaneous rotation of the tip and the polishing disc.
recipes to different laboratories.On the other hand, individual production of pipettes allows for remarkable flexibility and variability compared to batch production.Thus, once the basic concept of tip pulling is mastered, changes in tip shape and size are relatively easy to achieve.As depicted in figure 5, in the first step, a 1 cm short piece of thin platinum wire (25 µm-300 µm) is inserted into a glass capillary made from quartz or borosilicate.In our case, the tip must guide the microwave signal and the dimensions of the glass capillary are therefore chosen to obtain a characteristic impedance close to 50 Ω.For a stable production process, the working environment should be as clean as possible and all working materials should be cleaned beforehand.The puller should be placed in a room with minimal temperature variations.
Next, the capillary is placed in a laser puller (Sutter Instrument P-2000), and a good bond between the glass and metal is formed by applying heat while simultaneously evacuating the capillary via attached silicon tubes.A clamp is placed to restrict the machine from pulling the capillary at this step.This causes the glass to collapse onto the Pt wire and leads to a tight seal.
In the third step, the glass-wire compound is heated further and a strong pull separates the capillary into two sharp tips.Different tip shapes and sizes are achieved by varying pulling strength, velocity (criteria to activate the hard pull), or filament (the region in which the laser heats the capillary).
Next, a stainless steel pin together with a tiny piece of solder are inserted into the capillary.Using a heat gun, the pin and the thin Pt wire are soldered, making the center conductor accessible.
To form an outer conductor, gold or platinum is shadow evaporated onto the capillary.The probe is inclined to avoid a short circuit between the center and outer conductors.To cover both sides of the probe, the process is done twice and the probe is rotated by 180 • in between.This process can be simplified if an additional polishing step is performed later on.In this case, sputtering the outer conductor is preferable.
An additional polishing step can be performed to give the tip its final shape.Our setup allows for simultaneous rotation of the sanding disc, as well as the tip itself.By changing the angle between the tip and the sanding disc, flat tips or pencillike tips are produced.Two examples of tips produced using this method are shown in figure 6.

SMM setup
In contrast to a typical SMM setup as shown in figure 1, where cantilevered tips are used for scanning, our coaxial tips are straight and another type of feedback signal is required for distance control.We employed shear force detection [17][18][19] by attaching an excitation piezo (shaker) and readout piezo (microphone) to the tip, see figure 7. The shaker is excited (∼0.1 V, 100 kHz-500 kHz) and brings the tip in motion.Upon approach, the signal generated by the readout piezo changes in phase and amplitude.The signal of the readout piezo is tracked by a lock-in amplifier and fed into a PID controller that steers the expansion of the Z-piezo.Either the change in phase or amplitude from the readout signal can be used as input for the PID.To minimize cross-talk due to e.g.capacitive coupling, all cables should be either shielded or led as twisted pairs.To ensure shear-force sensing at the tip of the center conductor, the capillary must be mounted vertically and any tilt of the sample should be minimized.A poorly mounted tip would typically result in reduced SNR in the measured S-Parameter or inconsistent topography between trace and retrace.

Application example SRAM
This section describes the SMM measurements with a coaxial tip and the application of the earlier described calibration method onto the scanning capacitance microscopy (SCM) test sample commercially produced by Bruker [20].It is a partially processed static random-access memory (SRAM) showing different topographical features and implant regions.The entire surface is covered with SiO 2 of a few nanometers in thickness.This sample is widely used in the community of SCM to test and demonstrate system performance.
We use the three reference standards air, YAG, and LaAlO 3 (the latter two from CrysTec) and fused quartz (CrysTec) as a verification standard.Details are listed in table 1.To reflect uncertainties on the standards, several sources were considered and the standard deviations of the normal distributions are declared as uncertainties (k = 1).The uncertainties stemming from the measurement process and the definition of the references were considered and propagated through the entire data analysis chain using the METAS UncLib library [21,22].All samples were placed next to each other below the tip and the frequency of the VNA was fixed to f = 10 GHz.The measurement of air was performed a few mm above the xystage.For each standard, 50 × 50 px were measured on a scan size of 5 ×5 µm 2 and the medians were used for calibration.
After retrieving the error coefficients e 00 , e 01 , and e 11 , the raw S m 11 data from the SCM test sample and the verification standard were corrected using equation (3).Interpolation was employed on the simulated grid to determine the corresponding permittivities and loss tangents.Again, full uncertainty propagation was included in this step.The values retrieved by the calibration algorithm for the verification sample (fused quartz) are ϵ quartz r = 3.49(0.43)and tan δ quartz = −0.014(142).The relative permittivity deviates by about 8% from the considered literature values.The negative loss tangent is found by extrapolation, which is unphysical for passive materials, but the uncertainty associated with it covers the literature value.Table 3 lists the uncertainty budget for the verification standard.The main contributions stem from the system-related drift and trace noise.Additionally, the uncertainties of the calibration substrates contribute about 8.8%.As we did not assign uncertainties to the definition of air, there are no contributions from this standard.In a parallel plate capacitor model, variations in the real part of the permittivity impact the imaginary component of the reflection coefficient.Likewise, the loss tangent influences the real part of the reflection coefficient.However, in the case of low-loss materials, these alterations are small and overshadowed by the drift and trace noise of the measurement system.
Figures 8-13 show the calibrated relative permittivities, loss tangents, and associated standard uncertainties.Three zones A, B, and C are chosen for a more detailed analysis.Zone A is a section of the epitaxial p-type silicon layer with a dopant concentration of 2×10 −16 cm −3 .Zone B lies within the heavily n-doped source/drain of an NMOS with a dopant concentration of 2 ×10 −20 cm −3 .Zone C is a section of the p-channel in a PMOS, which is n-doped with a dopant concentration of 1 ×10 −17 cm −3 .
The calibration algorithm retrieves a median value of ϵ r = 10.9 for zone A. This seems plausible, as the epitaxial layer is dielectrically similar to undoped silicon (ϵ r = 11.7).However, the uncertainties in this zone are very high at around ∆ϵ r ≈ 150.The major contributions here are drift (∼50% ) and trace noise (∼45%).In the same zone, find the median loss tangent tan δ = 1061 with an uncertainty of ∆ tan δ ≈ 4000.Again, the uncertainty is very high, mainly due to drift (∼65%) and the definition of standards (∼30%).
For zone B we find ϵ r = 286 with uncertainties ∆ϵ r ≈ 500.The main contributions are drift (∼5%) and the definition of  standards (∼35%).Finding the highest effective permittivity in this zone seems reasonable, as the conductivity in the zone is highest and a capacitor between the tip and doped region is formed with SiO 2 as a dielectric.The median loss tangent for that zone is tan δ = 0.12 with an uncertainty of ∆ tan δ ≈ 1.5.Drift contributes with ∼55% and trace noise with ∼40%.
For zone C, the median effective permittivity ϵ r = with uncertainties ∆ϵ r ≈ 80 are retrieved.The uncertainties are dominated by drift (∼50%) and standard definition (∼35%).Finding the intermediate value for the effective permittivity can be explained by the moderate doping level in the zone.A median loss tangent of tan δ = −0.05 with an uncertainty of ∆ tan δ ≈ 0.94 is found.Drift with ∼60% and trace noise with ∼40% dominate the uncertainty contribution here.

Discussion
The presented method for coaxial tip production is very versatile and can be used to produce a large variety of tips, depending on the measurement task.For flat samples, a short protrusion of the center conductor is often desired.For samples with deeper trenches, the risk of contacting the sample with the dielectric sheath or outer conductor while scanning can be avoided by a longer protrusion of the center conductor.To adapt the process to another laboratory, it is essential to consider a learning curve.However, once the fabrication steps are mastered, implementing modifications becomes relatively straightforward.
The integration and use of shielded tips were demonstrated by employing SMM measurements where calibration, verification, and measurements on a MUT were performed.The permittivity of the verification standard was well reproduced within a deviation of 8% from the literature value, confirming the methodology of the simulation-assisted calibration scheme and the transferability of calibration using a shielded tip.Loss tangents were reproduced within the associated uncertainties.However, these are notably high.
The transfer of the calibration onto the SCM test sample revealed effective permittivities and loss tangents with relatively high uncertainties.From the uncertainty analysis, we have identified drift and trace noise as the dominant contributors and much effort should be made to minimize their influences.The influence of the drift is not necessarily directly visible in one frame (e.g.figure 8), as capturing a single frame took around 20 min, whereas scanning all calibration and verification standards and the MUT took around 3 h.Additionally, the samples were moved by a motorized stage, producing heat upon every sample change.Efforts to reduce drift influence can involve adjustments to the measurement system itself (e.g.temperature/humidity stabilization) or modifications to the measurement protocol (e.g.duty cycle, control measurements, or repetitive calibrations).Trace noise can be decreased by e.g.additional low noise amplifiers with better noise figures compared to the VNA internal amplifiers.As trace noise scales with the level of the reflected signal, a better matching technique resulting in lower signal levels is also beneficial.This could be achieved by e.g.utilizing an interferometric measurement scheme or a tuner [37].
A common problem in uncertainty considerations is incomplete information on the reference standards.The purity of dielectrics strongly influences their loss tangent, which is not directly covered by the uncertainty considered in this work.To take this effect into account, several literature sources for the definition of the standards were considered.We want to stress the importance of well-known standards (including uncertainties) that ideally cover the full range of expected dielectric and electric properties of the MUT.
Despite the incorporation of uncertainty considerations in this study, it is worthwhile to investigate additional potential sources.This might include other parameters of the sample properties such as roughness, tip geometry, and mechanical noise from the feedback system, to name a few.

Conclusion
Within the first part of this work, we have discussed that using a shielded tip is a prerequisite for achieving transferable calibration.Numerical simulations were utilized to illustrate how the measurement outcome is influenced by the surrounding environment of the MUT when using unshielded tips.Additionally, the enhancement in SNR for shielded tips was discussed.
In the second part, a production method for coaxially shielded tips based on nanopipette fabrication schemes was presented.The method includes laser-pulling a glass pipette with a platinum wire as a center conductor and the deposition of an outer conductor.The production method is relatively laborintensive but provides remarkable flexibility to tip properties.A quick overview of the integration of shielded tips into our home-built SMM was given.As a feedback mechanism for distance control, shear force detection was used.
Finally, we have demonstrated the use of a coaxial tip in an SMM by simulation-assisted calibration using three dielectric reference substrates.The method was verified using a fourth standard and yielded agreement within the uncertainties.The methodology has been proven to be generally suitable for this kind of measurement but also revealed the importance of well-known calibration standards (including uncertainties) and minimizing system-related uncertainties such as drift or trace noise.
The successful fabrication of coaxial tips and their demonstration for SMM measurements broadens the field of applications and paves the way towards SMM in liquids, where stray effects of an exposed cantilever and tip shaft prohibit calibration.The addressed scopes include for instance in situ measurements of battery electrodes or impedance characterization at the cell level of living tissue.

Figure 1 .
Figure 1.Schematic of a typical SMM setup.A vector network analyzer feeds a microwave signal via a coaxial cable into the tip of an atomic force microscope.The incident wave gets reflected at the end of the tip as a function of the material properties of the measurand under test.The reflection coefficient S 11 is recorded.

Figure 2 .
Figure 2. Simulation results for the electric field distribution at f = 10 GHz for an unshielded tip (left) and a shielded tip (right).The insets show schematically the different domains of the simulation.Quartz is used as a dielectric and platinum as an inner and outer conductor.The substrate has a relative permittivity of ϵr = 8.The fields of the shielded tip are more localized to the region at the apex and the measured S 11 is therefore less sensitive to the further surroundings of the tip.

Figure 3 .
Figure 3. Simulated relative energy contributions for an unshielded (black) and shielded tip (red).The solid lines show the relative energy contribution of the surrounding air, whereas the dashed lines show the energy contribution inside the substrate.For an unshielded tip, only a small fraction of the energy is delivered to the sample, and the SNR of S 11 is expected to be much lower compared to a shielded tip.

Figure 4 .
Figure 4.Relative change in the reflection signal of a shielded tip (solid line) and an unshielded tip (dashed line) when a conductive structure is in the vicinity of the tip.The inset shows the simulated geometry.The results are normalized to the maximal change in signal.Note that for a shielded tip, the total signal change is ∼18 times larger compared to an unshielded tip.

Figure 5 .
Figure5.Fabrication procedure for coaxial probes for SMM using a laser puller.1.A thin Pt wire is inserted into a glass capillary (Quartz or Borosilicate). 2. Heat is applied while the capillary is evacuated and restricted from being pulled.3. The compound is further heated and pulled until separation.4. A stainless steel pin is placed inside the capillary and soldered using a hot air gun. 5.The outer conductor is evaporated or sputtered.To avoid a short circuit between the center and the ground, the capillary is inclined.6.The coaxial tip can be polished if needed.Our setup allows for simultaneous rotation of the tip and the polishing disc.

Figure 6 .
Figure 6.SEM images of two types of coaxial tips.The tip in (a) is made from quartz and platinum wire and the outer conductor is sputtered gold.The tip is pencil-like polished to achieve a smaller diameter and disconnect shorted shield and center conductor.In (b) a tip made from borosilicate glass and platinum wire is shown.The center conductor protrudes after pulling and the shadow-evaporated Pt shield does not short circuits with the center conductor.

Figure 7 .
Figure 7. (a) CAD rendering of a coaxial tip in brass mount with 2.4 mm coaxial connector.For shear force distance control, two piezos are attached to the tip.The upper piezo excites the tip's motion and the lower serves for readout.(b) Schematic of the feedback loop for distance control.The upper piezo is dithered by an AC signal.The amplitude or phase from the lower piezo is tracked by a lock-in amplifier and a PID controller steers the expansion of the Z-piezo.

Table 1 .
Definition of the reference and verification standards with standard uncertainties (k = 1).

Table 3 .Figure 8 .
Figure 8. Real part of the effective relative permittivities for the SCM test sample.The upper structures are PMOS islands, the horizontal band is p-epitaxial silicon, and the lower structures are NMOS islands.Three zones (A), (B), (C) are chosen for further analysis.

Figure 9 .
Figure 9.Standard uncertainties of ϵr for the SCM test sample.

Figure 11 .
Figure 11.Effective loss tangent for the SCM test sample.Three zones (A), (B), (C) are chosen for further analysis.

Figure 12 .
Figure 12.Standard uncertainties of tan δ for the SCM test sample.

Table 2 .
Uncertainties from the measurement system.