Resistance mapping in mesoscopic films of low dimensional materials

Abstract

We present a low-cost, scalable technique for mapping local electrical properties across large areas with micrometer-scale lateral resolution. The method utilizes a flexible polymer cantilever coated by microfabricated graphite electrodes to probe local surface resistance. Samples can be scanned on a motorized translation stage, enabling automated, spatially resolved electrical measurements over centimeter-scale regions. The use of graphite electrodes ensures low friction and wear for both the sample and the electrodes, allowing repeated measurements on thin films without sample damage, unlike conventional metal probes. We demonstrate robust, pixel-by-pixel resistance maps on various samples, including patterned graphite thin films and ITO on glass structures. Its simplicity, adaptability, and user-friendly operation make this platform well-suited for rapid electrical testing and high-throughput quality control in advanced electronics research.

We present a flexible polymer cantilever featuring microfabricated graphite flake film electrodes. This design enables continuous, large-scale electrical raster mapping while ensuring low wear on the sample measured.

Introduction

The ability to map and quantify local electronic properties across large areas is a foundational challenge in the study and application of functional thin films and networks of interconnected flakes, nanotubes or nanowires. Among the main tools used, scanning probe microscopy (SPM) has established itself as an indispensable technique for nanoscale and microscale electrical characterization. Methods such as conductive atomic force microscopy (C-AFM) and Kelvin probe force microscopy (KPFM) routinely achieve nanometer-scale spatial resolution, providing detailed maps of local conductivity, work function, and surface potential.^1–3 These measurements have been transformative for the study of semiconductors, organic electronics, ferroelectrics, and more recently, the rapidly growing class of 2D materials.⁴

However, the capabilities of SPM are inherently limited by its scanning range, speed and throughput. C-AFM and related techniques provide high spatial resolution but are less suitable for assessing uniformity, defects, or mapping properties over large areas. This limits their use in wafer-scale quality control or industrial screening of thin-film devices. In such cases, high-throughput and robust mapping become crucial, motivating the development of new platforms that combine high resolution and large area coverage.

One strategy to extend electrical mapping to larger areas involves the automation of the classic four-point probe (4PP) measurement. In modern scanning four-point probe systems, a multi-probe array is scanned across the sample to record local sheet resistance at each position.⁵ This approach has proven valuable in the characterization of conductive thin films,^6,7 photovoltaic materials,⁸ and large-area printed electronics.^9,10 However, the millimeter-scale separation between the four probes imposes an intrinsic limit on spatial resolution, making it unfeasible to resolve microscopic features or local inhomogeneities that can critically affect device behavior.

Microscale four-point probe (μ-4PP) techniques have attempted to overcome this by fabricating cantilevers or probe arrays with micrometer-scale spacing between contacts.^11,12 These devices offer improved spatial discrimination but at the cost of significantly increased technical complexity. The microfabrication of robust, low-resistance contacts is challenging and often leads to variability between devices.^12–14 The scanning range of μ-4PP is typically limited to the field of view of an atomic force microscope, restricting measurements to sub-millimeter areas. Additionally, this technique does not allow for true raster scanning, as the probes cannot glide across the surface without risking damage to the films under study or to the micro-probes themselves, leading to tip wear and the need for frequent recalibration. Although low-friction graphene coatings have successfully mitigated tip degradation and enhanced reproducibility in nanoscale scanning probe microscopy,^35,36 scaling these compliant carbon-based interfaces to larger macroscale contact mapping remains unaddressed.

Non-contact methods such as terahertz time-domain spectroscopy (THz-TDS) provide a different avenue for large-area conductivity mapping.¹⁵ By probing the interaction of terahertz pulses with the sample, THz-TDS yields information about sheet conductivity and carrier dynamics in a contact-free manner. This approach has been particularly fruitful for the study of graphene and other 2D systems.^16–18 However, the lateral resolution of THz-TDS is fundamentally limited by diffraction, typically on the order of 150 μm, and can only be overcome through the use of highly complex near-field configurations.¹⁹ Interpretation of THz data is also non-trivial requiring detailed electromagnetic modeling,¹² and the method is sensitive to environmental factors such as humidity and temperature.²⁰

In summary, the landscape of electrical mapping techniques is characterized by a trade-off between area, resolution, throughput, and complexity. A technological gap exists for platforms that provide high-resolution, large-area, and scalable electrical mapping with simple operation and non-restrictive sample preparation.^4,21

In this work, we present a flexible polymer cantilever platform with microfabricated graphite electrodes, whose position and tilt are adjusted by an XYZ and goniometric stage to ensure reliable contact with the measured film. The film is mounted on a precision motorized stage enabling programmable raster scanning. The low friction coefficient of graphite allows the probe to glide in contact over the sample without damaging it. Consequently, the gentle and stable contact enables repeated measurements^22–25 and provides mechanical robustness with minimal wear. The system is accessible and adaptable, as resolution is decoupled from complex microfabrication and relies on easily patterned graphite films. The programmable stage supports large-area scanning with customizable resolution and mapping parameters. We benchmark the method on two different films, namely one composed of a network of stacked graphite flakes and another one consisting of patterned ITO electrodes on glass, demonstrating in both cases pixel-by-pixel mapping of local resistance and observation of mesoscale electronic heterogeneity. This technique enables rapid, high-sensitivity characterization of the homogeneity of thin films, 2D materials, and other emerging electronic systems.

Results and discussion

Fabrication and optimization of flexible graphite cantilevers

The fabrication of the flexible graphite cantilever is illustrated in Fig. 1a. First, a polycarbonate sheet was cut using a Cricut cutting plotter system in the designed shape for the device as shown in Fig. 1a.1. Then a multilayer graphite flakes film is fabricated starting from a Graphoil sheet by means of a roll-to-roll mechanical exfoliation and thermal-release transfer technique,^26,27 which is selected for its scalability, reproducibility, and ability to produce continuous, uniform coatings across large substrates. In this method, two cylinders are wrapped with adhesive tapes used widely for manual mechanical exfoliation of 2D materials, one loaded with the bulk graphite precursor, so that the rotation of the cylinders against each other leads to repeated mechanical exfoliation graphite flakes. By sequentially transferring seven coated tapes onto a polycarbonate substrate, a high density network of interconnected flakes is created to achieve optimal electrical conductivity and film percolation comparable with bulk material conduction properties. We do not observe significant resistance changes or spikes during the scan (unrelated to the resistance changes expected for the sample under study), which would be indicative of the loss of long-distance percolation in the probe due to wear.^26,27 This multilayer network serves as the starting material for subsequent device patterning.

Fig. 1. Fabrication and basic electrical characterization of graphite-based flexible cantilever test probes. (a) Sequential optical images illustrating the fabrication process: (a.1) Polycarbonate sheet cut to obtain the cantilever device shape. (a.2) Film composed of a network of interconnected graphite flakes (prepared by roll-to-roll high throughput mechanical exfoliation) was transferred onto the polycarbonate substrate by seven consecutive thermal-release transfer steps to improve electrical percolation. (a.3) Patterned graphite film obtained via laser ablation. (a.4) Electrical connections made using silver paste in contact with graphite leads. (b) Optical detail of the device channel (inset), alongside a transmission-mode micrograph of the graphite film, highlighting its homogeneity in the vicinity of the channel region. (c) Sheet resistance measurements performed on 39 locations within the region outlined by the dashed yellow line in panel (a.2). (d) 100 consecutive current–voltage characteristics measured sequentially on an ITO sample while maintaining continuous contact (schematic in the inset).

Patterning of the shape and channel of the graphite probe is then performed using an infrared laser ablation process, obtaining a channel width of approximately w = 50 ± 3 μm over a length of 0.8 mm (highlighted by black arrows in Fig. 1b).²⁷

The overall yield and quality of the patterning process are assessed via optical microscopy in transmission mode (see Fig. 1b). As confirmed by the optical image of the device, the laser ablation enables a clean and controlled removal of the graphite film, with the unexposed regions remaining unaffected with a coverage exceeding 95%. Such uniformity is essential for ensuring reproducible electronic properties across the device, since local inhomogeneities can strongly impact carrier transport in 2D materials films.³

Electrical characterization: sheet resistance and contact effects

Following fabrication, the electrical properties of the devices are systematically characterized. Four-probe resistance measurements are performed at multiple locations on the graphite film to assess its sheet resistance. Fig. 1c presents a histogram summarizing 39 individual measurements, revealing that the sheet resistance is consistently around 13.6 ± 1.6 kΩ sq⁻¹. This value aligns well with those reported for uncompressed graphoil film in previous literature.²⁸

To further probe the device performance in a realistic configuration, two-probe current–voltage (I–V) measurements are carried out using a 100 nm thick conductive indium tin oxide (ITO) substrate, whose sheet resistance is lower than that of the multilayer graphite film.^29,30 As shown in Fig. 1d, a set of 100 sequential I–V curves acquired in the 0–10 V range yields an average two-probe resistance of approximately 30 kΩ (Fig. S1).

Resistance scanning raster device mapping setup

Fig. 2a–c provide an overview of the experimental configuration employed for electrical measurements. The sample under investigation is mounted on a cylinder post, fixed at the center of a motorized XY stage. The graphite-based cantilever probe device is mechanically fixed in a manual XYZ + goniometer stage, ensuring stable contact geometry. The width of the patterned graphite (w ≈ 50 μm) defines the lateral resolution. The low friction exhibited by graphite at the micro-scale,^31–33 originating from its atomically smooth, layered structure allows the probe to glide across the sample surface with minimal mechanical wear or risk of damage (see Fig. S2 and S3 in SI).

Fig. 2. Scanning probe setup and contact reliability. (a) Overview of the experimental setup, featuring a motorized XY stage on which the sample holder is mounted. On the right, a manual XYZ stage coupled with a goniometric stage supports the cantilever, maintained at a fixed height and angle relative to the sample surface. (b) Close-up of the sample holder. (c) Representative contact configuration between the device and a graphite film transferred onto a 290 nm Si/SiO₂ substrate, previously treated by oxygen plasma. (d) Current–time trace measured under a 1 V bias while repeatedly bringing the cantilever in and out of contact with the sample (seven cycles), demonstrating stable and reproducible current readout between contact and open-circuit states. (e) Histogram of the measured current values measured in (d), exhibiting two distinct peaks corresponding to contact and no-contact states. The contact peak is well described by a normal distribution (blue Gaussian curve). The dashed blue line indicates the mean of the current distribution in the contact state, also indicated by the inset text.

Reliability and repeatability of probe–sample contact

To verify the reliability and reproducibility of the contact (Fig. 2d) we applied 1 V bias and measured the change in current response bringing the probe in and out of contact with the ITO substrate used previously in Fig. 1d.^29,30

The resulting data, summarized in the histogram shown in Fig. 2e, reveal two peaks corresponding to the non-contact and contact states, with the contact peak centered at 1.57 ± 0.02 μA. The small standard deviation relative to the mean highlights a narrow Gaussian distribution, reflecting the high precision of the measurements. The clear separation between these two peaks demonstrates the reliability of the device in distinguishing contact from non-contact conditions. Furthermore, this separation is indicative of the absence of electrode sticking and confirms that no filaments or other atomic structures form when the electrodes and sample are in close proximity, ensuring reproducibility for repeated, stable operation.

Spatial mapping benchmarking with patterned graphite films

To demonstrate the scanning resolution and reliability over large areas, we perform spatially resolved electrical measurements on a film composed of a network of exfoliated natural graphite flakes. The film contains regions with different number of transfers, between one and six transfers, which lead to increased thickness and better coverage and percolation. A single transfer typically yields a coverage of graphite flakes of nearly 65%, with limited flake overlap and only sparse percolation pathways. Increasing the number of transfers to six raises the coverage to about 95% and significantly enhances both the number and characteristic length of the percolation paths.²⁶

The spatially resolved electrical measurements were carried out by applying a bias voltage of 100 mV between the two electrodes of the cantilever probe while raster scanning across a region of 15 × 2.5 mm², with pixel dimensions of approximately 125 × 125 μm².

Fig. 3a presents an optical image of the sample, showing the distinct regions corresponding to increasing numbers of graphite transfers. The boundaries between adjacent zones are clearly visible and highlighted by white dashed lines, indicating transitions in film thickness and morphology.

Fig. 3. Gradient resistance in multi-transfer graphite film step structures. (a) Optical micrograph of the step-graded sample, showing regions with increasing numbers of graphite film transfers from one transfer (1T) to six transfers (6T). (b) Scanning resistance map of the sample. White dashed lines indicate the boundaries between steps. The mixed areas observed at the step edges arise from the fabrication process, with the resistance gradient reflecting the gradual increase in the number of graphite film layers transferred.

Analysis of the resistance map (Fig. 3b) reveals a strong correlation between the number of transfers and both the absolute value and spatial homogeneity of the measured current. In particular, the region with only a single transfer exhibits insulator behavior with local resistances larger than 1 MΩ, consistent with insufficient coverage of graphite flakes to form a continuous percolative network connecting the two electrodes.^3,34 Upon increasing the number of transfers to two, the resistance response becomes finite, indicating the emergence of percolative conduction pathways, although the spatial distribution remains highly inhomogeneous (i.e. there are regions where percolative paths are not long enough to bridge the two electrodes of the probe). With three or more transfers, a substantial improvement in homogeneity and decrease in resistance is observed. Upon reaching five or more transfers the measured resistance saturates.

Reliable large area mapping presently requires careful adjustment of the sample tilt to maintain approximately constant probe contact during raster scanning. Since the probe is flexible, varying the probe's pitch does not intrinsically alter the electrical readings, as long as physical contact is sustained (see Fig. S13). Instead, these geometric variations alter the local contact pressure, meaning that any uncompensated tilt will introduce a gradual drift in the measured resistance during the scan (see Fig. S4). The platform operates similarly to the constant-height mode in AFM without active automated feedback. To regulate the contact force and eliminate macroscopic tilt prior to a scan, the setup is monitored under an optical microscope with coaxial illumination. The operator evaluates light reflection from the substrate to visually verify that the sample is flat. This alignment approach is effective for planar substrates. Also, a careful selection of the initial probe-sample pressure is needed. Increasing the probe pressure generally improves electrical contact and mapping reliability; however, excessive force can occasionally displace graphite flakes from the electrode film. These flakes may either remain on the substrate surface (Fig. S3c), appearing as regions of decreased resistance in the map, or accumulate within the probe channel (Fig. S3a), which can temporarily bridge the electrodes and produce spurious current signals. Such effects are readily identifiable in the maps and can be avoided by operating within moderate contact-force conditions.

Benchmarking spatial resolution

To explore the limits of lateral spatial resolution achievable in this setup, we performed detailed resistance mapping on a test structure consisting of interdigitated ITO electrodes patterned on a glass substrate (Fig. 4a). The map shows good stability in the resistance reading over the entire 8 hours of measurements (see Fig. S12). Each individual electrode in this structure has a width of 110 μm, with a separation of 40 μm between adjacent electrodes. From the resistance map in Fig. 4b (top), the mean measured widths are ≈ 20 μm for the interelectrode gap and ≈ 110 μm for the electrodes. We acquired higher resolution, 1000 steps line scan, orthogonal to the electrode edges, yielding apparent widths of ≈ 12 μm (gap) and ≈ 132 μm (electrodes), see Fig. 4b, bottom. The apparent reduction of the interelectrode gap and the corresponding apparent widening of the electrodes arise from the finite size of the electrical probing region defined by the graphite electrodes in the cantilever. In the present probes, the two graphite contacts are separated by approximately 50 μm, which defines the effective lateral footprint over which the current is collected. When the probe approaches a boundary between conductive and insulating regions, the two electrodes can simultaneously contact both regions, resulting in a mixed signal that effectively averages the conductivity over the footprint of the probe. As a consequence, insulating gaps appear narrower in the resistance map, while conductive regions appear correspondingly wider.

Fig. 4. High-resolution mapping of ITO interdigitated electrodes on glass. (a) Optical micrograph of the sample; the black rectangle indicates the scanned area. (b) Top: Resistance map of the interdigitated electrodes, recorded with a scanning step of tens of micrometers over a millimeter-scale scanning area. Bottom: High-resolution current line scan along the X direction, clearly distinguishing the glass substrate from the ITO electrodes.

The results therefore indicate that the spatial resolution of the present implementation is primarily determined by the electrode spacing in the probe. Reducing this spacing through improved probe fabrication would directly translate into improved lateral resolution.

Multi-material mapping

To prove the technique's ability to distinguish materials based on their electrical properties, we have conducted a set of spatially resolved resistance measurements on a heterogeneous sample comprising three distinct materials. Via four successive roll-to-roll processes we transferred a graphite film on the Glass-ITO sample studied in Fig. 5, obtaining an area of approximately 1 × 0.5 mm² with the three materials (Fig. 5a).

Fig. 5. Material-specific resistance response on a substrate with various materials. (a) Optical micrograph of the sample, showing three distinct materials: graphite film, ITO, and glass substrate. (b) Resistance map of the area depicted in (a), highlighting the direct discrimination between materials based on their electrical response. (c) Histogram of current values, with three distinct peaks corresponding to the different conductivity levels of graphite, ITO, and glass.

The resulting resistance map, shown in Fig. 5b with pixels of 30 × 25 μm², clearly reveals the three materials as distinct zones: the glass substrate appears as a light blue, non-conductive region; both the ITO area covered by the graphite film and the uncovered ITO region are highlighted in dark pink, corresponding to the lowest resistance; while the graphite film on glass is shown in yellow-green, reflecting its intermediate, percolative resistance.

An analysis of the measured current distributions, presented in Fig. 5c, provides further insight into the resistance of the constituent materials. The current histogram exhibits three distinct peaks: those corresponding to glass (completely insulating) and ITO are well separated and sharply defined, reflecting their uniform electronic response. In contrast, the peak associated with the graphite film is broader and less sharply defined. This behavior is attributed to the inherently percolative nature of charge transport within the graphite film, where local inhomogeneities, flake boundaries, and variations in thickness lead to a distribution of local conductivities.^3,34 As the graphite film is in parallel with the less resistive ITO, the current bypasses the inhomogeneous graphite flake network to flow preferentially through the ITO, resulting in the lower resistance measured.

The current probes employ graphite electrodes, which provide low-friction contact and mechanical compliance but also introduce a relatively high series resistance. As a consequence, the present configuration is best suited for mapping moderately conductive films. To explore possible strategies for extending the measurable resistance range, we performed preliminary experiments incorporating metallic leads and a four-point probing geometry, as illustrated in Fig. 6a. In this design, gold leads are patterned on the polycarbonate substrate and coated at their free-end with graphite to ensure smooth mechanical contact with the sample. The graphite coating minimizes friction and reduces the risk of sample damage, while the metallic leads combined with the 4-graphite probe configuration eliminate the effect of contact resistance and greatly reduce the intrinsic resistance of the electrodes.

Fig. 6. Extension of the concept to a 4-probe configuration. (a) Schematic of the 4-probe cantilever device showing the dimensions and materials used. (b) Resistance measurements over time of four different materials obtained with the 4-probe cantilever device. The data are ordered by resistance value and plotted on a logarithmic scale to illustrate very different resistance magnitudes. The “off” levels correspond to the non-contact conditions between the device and the sample.

As shown in Fig. 6b, this method clearly differentiates materials according to their intrinsic resistance. Au, ITO, graphite, and MoS₂ display resistances of approximately 10⁻², 10, 10², and 10⁷ Ω, respectively, confirming the wide operational range of the approach. To clarify the consistency of these readings, the underlying dataset has been reformatted into individual distribution histograms for each material, provided in section 8 of the SI.

Despite these advantages, the present implementation remains primarily suited to static measurements. In its current geometry, achieving reliable simultaneous contact of all four probes during scanning is challenging, which limits the robustness of large-area mapping in this configuration. Future iterations could address this limitation by reducing the probe footprint and inter-probe spacing through miniaturization of the cantilever, potentially reaching sub-millimeter probe spacing. In addition, integrating closed-loop force control (for example using a piezoresistive strain gauge at the cantilever base) could compensate for sample tilt and variations of the surface topography during scanning. Lithography-based microfabrication could also improve probe alignment and reproducibility, enabling more reliable four-point contacts. These developments are promising but require substantial redesign and fabrication effort and are therefore beyond the scope of the present proof-of-concept study.

Conclusions

In this work, we present a flexible polymer cantilever platform with microfabricated graphite electrodes, mounted on a precision motorized stage for programmable raster scanning. Exploiting the van der Waals structure and chemical stability of graphite, the probe achieves excellent lubricity, mechanical robustness, and minimal wear, enabling gentle and stable contact with a wide range of surfaces. This allows for long-duration, high-resolution measurements in raster mode without damaging the sample. The system is accessible and adaptable, as resolution is decoupled from complex microfabrication and relies on easily patterned graphite films. Rapid probe production and replacement are possible and the programmable stage supports large-area scanning with customizable step size and mapping parameters. We benchmark this approach studying disordered graphite films and patterned ITO electrodes, demonstrating microscale mapping of local resistance and mesoscale electronic heterogeneity. Furthermore, the 4-probe configuration broadens the operational range of the platform, accessing the intrinsic film resistance and allowing customization according to specific measurement geometries or material properties. This technique enables rapid, high-fidelity characterization of thin films, 2D materials, and other low-dimensional electronic systems. The applicability of the current platform may be extended by introducing a force-monitoring feedback loop to precisely control the contact conditions during scanning. The cantilever geometry may also be modified, for example introducing rounded, micro-molded shapes in order to eliminate sharp boundaries and prevent sample damage.

Materials and methods

Crystals and substrates

For the realization of the probes with roll-to-roll mechanical exfoliation method we have used Graphite Foil sheet purchased from ProGraphite as starting material. Natural graphite flakes were purchased from ProGraphite GmbH and prepared in thin films via roll-to-roll mechanical exfoliation.

Polycarbonate sheet with 250 µm thickness (Modulor) were used as flexible substrates and, using a cutting plotter (Cricut Maker 4), are shaped into a cantilever shaped substrate in which seven layers of graphite flakes thin films are deposited.

The same procedure was used to prepare substrates for the samples adjusting the number of deposited layers to reach a coverage of approximately 95% in each one.

ITO Glass Substrate was purchased form Ossila (product code S161-20) with a nominal ITO thickness of 100 nm.

Laser ablation of 2D films

We use a laser engraving system from Atomstack (Fiber laser model M4, 1064 nm) to pattern 2D films fabricated with high-throughput roll-to-roll exfoliation. The pattern designs were prepared using SeaCAD software, which also offers precise control over engraving parameters such as laser power, speed, and frequency. The patterning process of films was carried out using 15% of the laser's total power (total power is 20 W) with a constant speed of 50 mm s⁻¹, ensuring controlled ablation without damaging the substrate.

Electronic measurements

Conductivity mapping and IV measurements were conducted at room temperature using a Keithley 2450 source-meter unit.

Characterization of sheet resistance was performed with an Ossila Four-Point Probe System (Ossila T2001A-0510) configured for high resistive samples.

Stages

The samples were mounted on a vertical cylindrical stand fixed to a Standa XY motorized stage (Standa 8MTF-75LS05, 107291, 107293, controller no: 8SMC4-USB-B9-2), which was controlled using MATLAB.

A set of 60 × 60 mm² XYZ manual linear stages and goniometer were assembled to control relative positions of sample and cantilever.

Author contributions

N. G. and R. L. M. led data curation; formal analysis; investigation; methodology; the original draft writing; contributed equally to review and editing. Y. S. and J. R. provided support to methodology. R. F. performed the LFM characterization of the films. A. C-G. led conceptualization, funding acquisition, project administration, resources, supervision, supported the methodology, and original draft writing, and contributed equally to review and editing.

Conflicts of interest

There are no conflicts to declare

Data availability

Data for this article are available at Zenodo at https://doi.org/10.5281/zenodo.19710771.

Supplementary information (SI): further details about film characterization, samples used, the devices and calibration of the measuring system. See DOI: https://doi.org/10.1039/d6nr01610c.