Transformer bridge-based metrological unit for scanning thermal microscopy with resistive nanoprobes

Scanning probe microscopy (SPM) is a broad family of diagnostic methods. Common restraint of SPM is only surficial interaction with specimen, especially troublesome in case of complex volumetric systems, e.g. microbial or microelectronic. Scanning thermal microscopy (SThM) overcomes that constraint, since thermal information is collected from broader space. We present transformer bridge-based setup for resistive nanoprobe-based microscopy. With low-frequency (LF) (approx. 1 kHz) detection signal bridge resolution becomes independent on parasitic capacitances present in the measurement setup. We present characterisation of the setup and metrological description—with resolution of the system 0.6 mK with sensitivity as low as 5 mV K−1. Transformer bridge setup brings galvanic separation, enabling measurements in various environments, pursued for purposes of molecular biology. We present results SThM measurement results of high-thermal contrast sample of carbon fibres in an epoxy resin. Finally, we analyse influence of thermal imaging on topography imaging in terms of information channel capacity. We state that transformer bridge-based SThM system is a fully functional design along with low driving frequencies and resistive thermal nanoprobes by Kelvin Nanotechnology.


Introduction
Scanning probe microscopy (SPM) enables high-resolution surface investigations.The mechanism of SPM relies on the analysis of interactions between a tip-shaped nanoprobe and a surface of interest.When the nanoprobe is positioned over a specimen, it can operate with subnanometre precision and perform imaging at subatomic resolution [1].One type of SPM method is scanning thermal microscopy (SThM), in which the Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.heat flux between the probe and the investigated surface is recorded.In this technology it is possible to image temperature distribution on the sample, structure thermal resistance or thermal conductivity [2].In the SThM mode, the thermal nanoprobe is formed by a thermocouple or a resistive temperature detector (RTD).Both types of SThM nanoprobes are manufactured by thin film and micromachining technologies [3], which ensures the high repeatability of the mechanical and electrical properties of SThM cantilevers and high production yield.The thermocouple SThM cantilevers are the so called passive sensors because the heat flux between the nanoprobe and the investigated sample cannot be controlled electrically.In contrast, RTD SThM cantilevers can be used both as temperature detectors and local heat sources.In this case it is possible to analyse the thermal resistance between the tip and the specimen by monitoring the heat dissipated by the nanoprobe [4].In RTD SThM, very weak resistance changes reflect the heat flux from or to the nanoprobe.In this case development and application of a high resolution measurement setup is necessary to record reliable images of the surface thermal properties.Among possible solutions the AC architecture of the measurement electronics is preferable as it ensures immunity to thermoelectrical parasitic voltages, which occur in the circuitry.Moreover, in the AC architecture the bandwidth of the signal acquisition can be flexibly defined, improving the signal-to-noise ratio (SNR) and enabling simultaneous detection of signals at various frequencies [5].In all the above mentioned solutions, the RTD nanoprobe is electrically biased, which leads to self-heating of the sensor, an effect that can generally be described as the so called back action phenomenon.Moreover, because SThM cantilevers are usually the multilayer structures, Joule heating in nanoprobe wiring induces parasitic structure deflection [6].From that perspective, the entire measurement setup must be designed so as to ensure the highest SNR at the lowest possible sensor bias.
In addition, the measurement electronics should also be immune to other electrical parasitic effects linked, e.g. with stray capacitances, which occur when the beam platform and the nanoprobe are in contact with the investigated conductive sample.Only in such a setup will the entire system respond to the nanoprobe resistance changes induced by the heat transfer from and to the investigated surface.In our previous experiments we used the AC measurement electronics in configuration of the Wheatstone bridge, in which the power dissipated in each bridge arm is monitored [7,8].
Unfortunately, the response of this setup was influenced by the stray impedances, which existed in the bridge setup as formed by the nanoprobe and cantilever metallisation layers.In general, these effects can be eliminated, as is often the case in precise electrical metrology, by the use of the so-called Wagner earthing devices [9].However, in the miniaturised SThM systems an application of a quite complex and bulky Wagner setup is just not possible.Solutions to these problems are the transformer-based setups [10].In the transformer bridge small reactance of the transformer wiring shortens the stray capacitance between the nanoprobe metallisation layer and the ground.This effect is especially efficient, when the bridge is biased with LF signals.In our previous transformer bridge based electronics we operated with the bias frequency of 10 kHz and probe bias current of 1 mA [8].Moreover, the bridge was balanced manually by the modification of the reference resistor, which due to the complex balancing procedure was of limited efficiency.In this setup we obtained the resolution of the temperature change measurements of 10 mK [11,12].
In this study, we describe the improved transformer-based measurement setup for RTD SThM technology operating at frequency of 1 kHz with a maximal sensor bias current of 122 µA root mean squared (RMS).We demonstrate how the designed and fabricated system is integrated with the optical beam deflection (OBD) head of the applied SThM.We also present the calibration procedure of the entire system, demonstrating the RMS resolution of the temperature changes of 0.6 mK in the bandwidth of 30 Hz.The proposed system was applied in thermal investigations of carbon fibre epoxy test samples.The obtained results make it possible to identify the composition of the imaged specimen.The recorded topography and thermal images are analysed using the information capacity theorem [13][14][15], which indicates at which transformer bridge bias conditions the optimal measurements are performed.
The developed transformer bridge unit is balanced using microprocessor-controlled direct digital synthesis (DDS) generators defining the amplitude and phase of the voltages in each bridge arm instead of manual wiring switching [11,12] in real and imaginary domains.In this way, the transformer bridge operation's flexibility and precision, involving the highest possible resolution stemming from the immunity against thermoelectrical voltages, are ensured.
In addition, the proposed setup is designed so as to isolate the RTD nanoprobe ground from the ground of the entire microscope electronics.As the result, investigations of operating (biased) micro-and nanocircuits are possible without disturbing or influencing their operation, which is of the highest interest for the metrology of the modern integrated circuits (ICs).The need and solution for such measurements has been voiced by authors of [16].Since then little improvement in terms of SThM analysis of powered devices was made.Only possibility was to measure passivated devices to prevent crosstalk between a substrate and the probe [17] For measurements of living organisms such methods have be applied, that do not convey signal into aqueous substrate.Alternative methods, such as scanning near-field microscopy are inferior in resolution to SThM at the order of 10 −1 K [18].SThM finds its applications in biological measurements, however on dry substrates such as cell walls or carbonised plant cells [19,20].Transformer bridge setup would enable spatial measurements, currently performed in static microcalorimetric devices, which separate sensor from specimen with insulation layer [21][22][23].
The assessment of recorded image quality is considered as a challenge in SThM technology.The evaluation of SThM processes depends on the modulation transfer function and SNR resulting from the uncertainties involved in the measurement process.Therefore, an in-house-developed SThM hardware and software system, in addition to the possibility of evaluating recorded images qualitatively, allows for the quantitative assessment of their quality.This functionality is particularly attractive since information about potential improvements in image quality can often be acquired early in the measurement process.Therefore, we employ the maximum capacity of the information channel (information channel capacity (ICC)) measure proposed by Shannon [13] and subsequently adopted in various disciplines to measure the image quality [14,15,24].Specifically, in SPM-based technologies, the ICC-based metric was first proposed by Kopiec et al [14] as the successful successor of the method to normalise variance in the power spectrum [24].More recently, the use of the ICC measure for image quality assessment combined with the wavelet-based approach for power estimation has evolved further [15].
Although an ICC measure is a well-known tool recently adopted to assess the quality of SPM images (see, e.g.[14,15,24]), we briefly discuss its definition for the convenience of readers.The ICC metric is a function of bandwidth B and SNR (S/N) expressed as where S N and N denotes to the power spectrum of the noisy signal and the estimated level of the white noise.The filter function F (•) filters negative values in the integration operation of the biased power spectrum estimator.

Transformer bridge SThM unit architecture
The proposed transformer bridge SThM unit is formed by two input transformers, Tr 1 and Tr 2, biasing two arms, in which the reference and tip sensing resistors R ref and R meas , respectively, are implemented-as shown in figure 1.The current I meas in transformer Tr 3 yields a current, which secondary winding corresponds to the difference between the currents flowing through resistors R ref and R probe .The current I 3 in the Tr 3 secondary winding I meas is then fed to a current-to-voltage converter (I/V) of the gain R f .The Tr 3 secondary winding operates in the short-circuit regime through the virtual ground of the operational amplifier (OP), ensuring no signal losses.The low reactances of the transformers Tr 1 , Tr 2 and Tr 3 short the parasitic capacitors C p1 , C p2 , C p3 , and C p4 .Therefore, the parasitic capacitances do not influence the current flow through resistors R probe and R ref .
Compared to solutions without transformers, the RTD bias current needed to yield a resolvable signal can be reduced.As a result, the thermomechanical parasitic cantilever actuation and probe self-heating effect are reduced.Moreover, in contrast with classical transformer bridges, which are usually balanced using inductive voltage dividers, our system is compensated using external DDS generators.The amplitude and phase difference of the DDS generator output signals are set with a microcontroller, which makes the entire system flexible.Moreover, as DDS generators operate remotely, the printed circuit boards integrating transformers and basic preamplifier electronics can be miniaturised and integrated with the head of a SThM-as shown in figure 2.
To reduce iron losses and ensure high saturation induction, the T r1 , T r2 and T r3 transformers integrate VITROPERM 500 nanocrystalline ferromagnetic cores.They operate with low eddy currents and exhibit a narrow hysteresis loop with a magnetic flux density ranging between 0.4 T and 0.6 T.
The entire system was designed to operate with probe bias current smaller than 1 mA Considering the typical R probe resistance of hundreds of ohms, the required magnetic flux density in Tr 1 and Tr 2 primary windings are obtained by 20 turns in primary and 10 in secondary winding with 0.5 mm enamelled wire.The inductance of ten turn winding is 2.9 mH.The operating frequency of 1 kHz has been chosen as a sweet-spot between frequency too high causing significant magnetic core losses and too low in which the transformer winding reactance is comparable with its series resistance.It should be noted, that the ground of the microscope electronics GND amp and the inner ground of the transformer core and the SThM probe GND probe are galvanically separated.The I/V converter s built using AD8512 OPs powered with ±5 V. Two AD9833 IC DDS generators controlled by a Raspberry Pico controller are applied to bias and balance the transformer bridge.
The transformer bridge unit operates in the imbalanced configuration in the scanning experiments.The unit output U out , which is the output of the I/V converter, is measured differentially with an external SR530 lock-in amplifier by Stanford Research Systems.This configuration ensures the highest resistance against measurement disturbances in ground loops.Additionally, the measurement selectivity can be set in the range from 100 Hz down to 1 Hz, depending on the SNR and surface scanning speed.In our experiments, Kelvin Nanotechnology KNT-SThM-2an probes were applied with a nominal resistance of 325 Ω measured at 300 K.While surface scanning one of the KNT SThM-2an probes is used to contact the specimen and the second one is applied as the reference in R ref position.In this way, the influence of the temperature air currents in the head vicinity is reduced, which improves the reliability of the temperature measurements on the sample surface.In the calibration procedure, a precise adjustable resistor R probe and a fixed resistor R ref are applied.

SThM architecture
The applied SThM head is based on the design presented by Kopiec et al [25]-as shown in figure 2. This head is an optical beam deflection (OBD) element that integrates an RFmodulated low-noise semiconductor laser.The beam of the laser, whose output power is precisely controlled, is focused on the SThM nanoprobe.The position of the laser beam and the position of the nanoprobe over the sample were observed using an optical microscope with a CCD camera (figure 3).The SThM controller operates with signal acquisition software [26] and an MCL Nano-MET3 closed loop stage, enabling surface scanning in the field of up to 100 × 100 × 10 µm in the XYZ axis correspondingly.

Scanning process
In our investigations, we imaged a VITA-TS-SThM test sample fabricated by Bruker, Inc. [27].This test sample is formed by carbon fibres (approx.5 µm in diameter) immersed in epoxy resin.The material surface finish is nonuniform throughout the composite material.Therefore, the height difference between soft (resin) and hard (fibres) materials reaches 50 nm.The carbon fibre exhibited a thermal conductivity of approximately 20 W mK −1 , whereas the thermal conductivity of the epoxy resin reached a maximum of 1 W mK −1 [28,29].The topography and thermal properties of the selected sample should converge because it was vertically extruded.
In the experiments, the RTD nanoprobe resistance change corresponded to the thermal flow between the sensor and the imaged surface.When the RTD nanoprobe was in contact with the resin the tip temperature was higher than when the RTD nanoprobe touched the carbon fibres (thermal conductivity of  carbon fibres was ca.20 times higher than the thermal conductivity of polymer matrix).Therefore, the recorded thermal image presented a map of the averaged thermal resistance between the tip heat source and the specimen.Hence, the identification of the structure components was possible.
In the recorded topography and thermal images, depending on the measurement parameters, the surface structure details are identified with different contrasts.To assess the image quality, we calculated the ICC for every recorded image.For description solely of the thermal images, ubiquitous measures as noise density would be perfectly suitable.However, our goal was to qualitatively compare pictures containing two types of information-namely topography and temperature.We failed to find introduced description combining thermal and topography resolution.We therefore referred to more complex, but broader term of ICC.The unit for the ICC measure is the bit per micrometre (b µm −1 ), which is calculated as the relation of the wavelet-based spectral power density of the information signal to the total spectral power density [14,15].

Transformer bridge SThM unit calibration
The sensitivity of the developed transformer bridge was analysed when the temperature changes were simulated by the variable R probe resistance (figure 1).In the first step, the transformer bridge was balanced for R probe = 100 Ω and R ref = 100 Ω by setting the U 1 and U 2 voltages, which were defined by the DDS external generators exciting in each bridge arm current of 350 µA rms .In the second step, R probe was varied in a stepwise manner up to 119 Ω.In this case, assuming that R probe simulated a platinum Pt100 RTD, a resistance change   of 4.7 Ω corresponded to a temperature change of 11.9 Ktable 1.The RMS output of the I/V converter, which integrated an R f of 10 kΩ resistance, was recorded by the lock-in amplifier for each R probe resistance in the bandwidth of 30 Hz.These results are shown in figure 3. The transformer bridge unit sensitivity S was calculated as the ratio of the lock-in amplifier output to the temperature range change.The performed experiments show that at higher R probe temperatures, the transformer unit sensitivity deteriorates to 4.0 mV K −1 when the temperature is between 310 K and 320 K (table 2).The performed calibration routine enables quantitative description of the images recorded during sample scanning.
The results show that the best operational conditions for the bridge are for a small resistance difference, i.e. close to the balanced bridge.The most significant noise sources influencing the temperature resolution T res of the designed system are the thermal noises of R ref and R probe .The RMS thermal current noise of these resistors is described by the follow-

Surface investigations
The test sample was measured across an area of 8 × 7 µm.
In the scan field, two highly thermally conductive carbon fibres embedded in epoxy resin were identified (as shown in figure 4).The thermal data were measured for nanoprobe bias currents ranging from 81.6 to 122.4 µA with a step of 6.8 µA.The topography and thermal images were recorded at the same position and load force of 10 nN.The results are summarised in table 3. The sample was scanned at a scanning speed of 0.1 Hz (corresponding to a scanning speed of 1.4 µm s −1 ), thus the output of the transformer bridge unit was probed for a time period of 20 ms.The frequency of the bias signal and the lockin time constant were 1 kHz and 30 ms respectively.Hence, the Shannon frequency of the thermal signal is 17 Hz.In relation to the scan rate, the band is 170 times broader.Effective sampling cannot exceed 170 points per trace, so 85 points per line.Subsequently, the ICCs were calculated for all the recorded images.The assumed error in the ICC is no greater than 10%, caused by the noise in the derived periodogram.The ICC values are ordered as a function of the nanoprobe bias current.According to the models, the ICC for thermal maps should increase with increasing current (resulting in a higher SNR).However, the ICC for the topography should decrease with increasing vibration due to the growing vibrations resulting from the thermal power dissipated in the cantilever.The recorded results confirm these assumptions-as shown in figure 5 Imaging characteristics and the measurement mechanism cause the blurry halo around the carbon fibre edges in the thermal maps.The proximity of the core material influences the effective thermal conductivity near the carbon edge.Although this may be viewed as an obstacle in high-resolution  measurements of surface features, subsurface features are to be detected easily with a transformer-bridge SThM.

Discussion
RTD SThM technology makes it possible to observe and analyse thermal phenomena at the nanoscale, including high resolution temperature metrology, thermal conductivity and/or thermal resistance mapping.In all these experiments development and application of high resolution measurement electronics is required.The superior parameters of the measurement circuitry should be obtained for low probe bias current reducing back action and parasitic cantilever deflection.Moreover, the developed system should ensure the galvanic isolation between the RTD nanoprobe and the investigated sample.
In this article we present the transformer bridge setup for SThM technology.The miniature unit integrates three transformers forming two forcing arms and a differential branch, constituting an excellent solution for galvanic separation between measurement subsystem and the probe-sample system.Moreover, because the proposed circuitry is designed and fabricated as the differential system it ensures high common mode rejection ratio leading to high SNR.As the result resolution of 2 mK at the bias current of 122 µA is ensured.The quality of the recorded images was analysed using ICC measures.
The tendency of the increasing thermal contrast the epoxy resin and carbon fibres is confirmed by the ICC vs. bias current characteristics.Information capacity grows with the bias current.Simultaneously, the difference in the temperature between regions grows in relation to the noise floor.Regarding the bias current, the ICC of the topography images decreases.The growing cantilever oscillation amplitude causes this effect, imperfectly damped in the microscope system.As calculated, there exists an equilibrium at which both topography and temperature maps are equally distorted (that is the ICC is equal).However, judging by the slope disproportion, it is possible to improve thermal imaging ICC evaluating the slope distortion with little deterioration in the topography imaging.
The proposed technology, as it ensures the nanoprobe electrical isolation from the investigated surface, opens new application fields for RTD SThM including microbiology and biotechnology.

Figure 1 .
Figure 1.Schematic of the transformer bridge SThM unit.

Figure 2 .
Figure 2. Measurement head of the scanning thermal microscope head with inserted micrograph of an SThM probe (to be found in manufacturer promotional materials).

Figure 3 .
Figure 3. Lock-in output signal as the function of R probe and corresponding RTD temperature.
ing equations:I ref = √ 4kBBT R ref and I probe = √ 4kBBT R probe , where T is

Figure 4 .
Figure 4. Schematic material composition of the applied test sample.
. Moreover, linear regression values representing the b µm −1 per ampere tendency strongly disproportionate in slope.With these slope values, it is possible to calculate the ICC for any given bias value.Since the slopes associated with topography and temperature signals have opposite values, equilibrium should be achieved for the bias 250 µA, with an ICC of 9,63 b µm −1 for nominal values; error analysis however provides range of values from 163 to 428 µA.

Figure 5 .
Figure 5. Thermal ICC results in relation to the tip current for (a) topography measurement and (b) temperature measurement.Fitted linear regression is depicted with slope values denoted.

Table 1 .
Temperature for Pt100 RTD resistance values.

Table 2 .
Sensitivity of the transformer bridge SThM unit.