Massively parallel cantilever-free atomic force microscopy

Since its invention in 1986, AFM has become a leading method to measure surface topography and functional properties at micro- and nanoscales. Conventional AFM uses a cantilever and optical lever to detect tip-sample forces, but serial scanning imposes a tradeoff: finer spatial resolution reduces field-of-view. Prior attempts to address throughput include higher-bandwidth probes and probe arrays (e.g., IBM Millipede), yet modern imaging arrays still have only ~30 probes, underscoring challenges in parallelizing cantilever-based sensing. Arrays are common in scanning probe lithography, where a cantilever-free architecture—rigid probes on a compliant film—offers scalability to millions of probes, but loses the cantilever’s force sensing. If cantilever-free probe arrays could detect probe-sample contact in parallel, AFM could be massively parallelized, increasing throughput for studying complex, hierarchical samples. The authors propose a cantilever-free architecture with an optical mechanism termed the distributed optical lever to enable massively parallel AFM.

The paper reviews limitations of serial, cantilever-based AFM and prior efforts to increase throughput: high-speed/high-bandwidth cantilevers; small arrays including heated microcantilevers (~30 probes); and the IBM Millipede for data storage with >1000 tips. It highlights broad use of probe arrays in scanning probe lithography (mechanical deformation, anodic oxidation, direct deposition), and the cantilever-free architecture used there (probes on a compliant film), which provides scalability but lacks force sensing. Rigid probe fabrication via prior methods is contrasted with two-photon polymerization direct laser writing (2PP-DLW), which enables arbitrary geometries with optically pristine interfaces. This sets the context for adapting cantilever-free architectures to enable parallel contact detection for massively parallel AFM.

Concept and modeling: A rigid probe on a compliant backing (e.g., PDMS on sapphire) creates a distributed optical lever: vertical probe motion deforms and tilts the reflective backing, modulating reflected intensity. Contact mechanics yields an effective spring constant k_eff = 2 R E, where R is probe base radius and E is the backing’s effective elastic modulus. A ray-optics model relates normalized reflected intensity to probe motion: I = I_max (1 − (2 δ0)/(π R sin(β/2))) at the probe perimeter, where β is the optical angular aperture and δ0 is probe displacement. The response is predicted to be linear in force and deformation with nanometer-scale precision. Finite element simulations indicate probe-sample compliance softening <10% for substrates with stiffness >1 GPa.

Probe fabrication: Sapphire wafers are spin-coated with PDMS (Sylgard 184, 25:1 base:crosslinker) at 1000 RPM for 60 s, cured at 100 °C for 1 h to yield a compliant film. Rigid conical (and cylindrical for tests) polymer probes are written directly on PDMS using 2PP-DLW (Nanoscribe Photonic Professional GT, IP-Dip resin, 63×, 100 nm slicing/hatching). Arrays are rendered reflective by depositing 30 nm Al via e-beam evaporation (0.2 Å/s). SEM confirms planar probe arrays. Mechanical characterization shows linear spring behavior with ~10 N/m spring constants.

Imaging setup: A 1088-probe array is mounted downward in a scanning probe instrument (Tera-print TERA-Fab E series) with piezo-controlled z-motion and tilt; the sample stage scans in x–y. Bright-field imaging through the sapphire uses a 10× Mitutoyo objective (NA 0.28) and a Point Gray Grasshopper GS3-US-3254C-C camera. Samples: AFM calibration artifacts (MikroMasch TGXYZ02). The array is leveled using force feedback. Imaging proceeds by raster scanning the sample relative to the stationary array in 15 × 15 µm² tiles (set by 15 µm array pitch) with 1 µm steps; high-resolution line scans use 100 nm steps. Probes do not move laterally while in contact; for each frame, the array approaches, contacts, holds, withdraws to out-of-contact, then moves laterally.

Calibration and signal extraction: For each probe, normalized intensity I is computed by averaging pixel brightness within a 15 µm-diameter ROI centered on the probe, normalized to an out-of-contact image. I is constant versus Z (array extension) out of contact and decreases linearly with Z upon contact. Linear fits use I = α (h − Z) to extract slope α and the intercept h, the contact height. Once calibrated, a single I measurement at contact yields h.

Image reconstruction: A video of the raster scan is imported into MATLAB. Probe centers are detected once using a Hough transform (circular feature detection) and reused across frames. For each frame: (1) compute I at each probe ROI; (2) convert I to h via calibration to obtain a per-probe 15 × 15 µm² field-of-view; (3) stitch overlapping square fields (each probe overlaps four neighbors due to 15 µm hexagonal pitch) into a continuous image. Artifact corrections: (a) Probe height variation is corrected via least-squares using overlaps: for overlapping regions between probes i and j, Δh_ij = h_i(x,y) − h_j(x,y) = H_i − H_j; solve H from Δh = K H with H = (K^T K)^{-1} K^T Δh. The observed standard deviation of H is 1.4 µm. (b) Frame-to-frame Z offsets (mean h per frame) with 32 nm standard deviation are removed by zero-meaning each frame. (c) Mechanical crosstalk between neighboring probes (neighbors move 35% of a deformed probe) is removed by deconvolution using an empirically estimated point spread function; finite element modeling predicted ~29%, consistent with measurements. The deconvolved image is the final reconstruction.

Data and code: Data available upon request; custom MATLAB code available at kablab.org/data.

• Demonstration of massively parallel AFM using a cantilever-free architecture with 1088 probes operating simultaneously.
• Distributed optical lever effect provides a linear, scalable optical readout of probe deformation that is linear in force and displacement; sub-10 nm vertical precision is achieved (estimated 9 nm RMS on flat regions over >0.4 mm; ~6 nm from AFM-based single-probe estimate).
• Imaging performance: mapped sample height with ~100 nm lateral sampling (line scans at 100 nm steps) and 9 nm vertical precision over ~0.4–0.5 mm spans; reconstructed complex calibration features.
• Calibration: intensity I is constant out of contact and decreases linearly with Z upon contact; fit I = α (h − Z) yields per-probe sensitivity α and contact height h. Histogram of α obtained for all 1088 probes.
• Mechanics: individual probes behave as linear springs (~10 N/m). Effective probe-sample softening expected to be <10% for substrates >1 GPa.
• Crosstalk: neighboring probes move 35% of a deformed probe, consistent with finite element prediction of 29%; linear deconvolution removes the artifact.
• Variability and repeatability: probe height standard deviation 1.4 µm corrected via overlap; frame-to-frame Z repeatability offset 32 nm corrected by zero-meaning; step height on a 110 nm-deep fiducial measured as 126 nm (within ~15% of AFM); intra-probe step height variation ~6%; inter-probe average variation ~3% when measuring comparable regions.
• Operational advantages: no lateral sliding during contact, reducing abrasion; overlapping fields allow robustness to potential broken probes.

The work addresses the fundamental resolution–throughput tradeoff in AFM by replacing cantilevers with a cantilever-free, optically read architecture that scales to thousands of probes. The distributed optical lever translates vertical probe motion into a robust, linear optical intensity change, enabling per-frame, per-probe height extraction without mechanical lateral scanning, and thereby parallelizing acquisition across >1000 points. Modeling and experiments confirm linear mechanics and optics with nanometer sensitivity. Image reconstruction leverages overlap-based height leveling, frame offset correction, and PSF deconvolution to remove probe variability, stage-induced offsets, and mechanical crosstalk. The approach reproduces calibration features with nanometer vertical precision over millimeter-scale distances, indicating suitability for multiscale metrology where both large field-of-view and nanoscale resolution are required. The authors note opportunities to extract more than topography (e.g., gradients or lateral forces via asymmetric deformation from torques) and discuss durability and robustness, including reduced wear due to no lateral motion and tolerance to probe failures through overlapping coverage. Potential application domains include integrated circuit and metasurface inspection and multiscale biological tissue studies.

The paper introduces a scalable, cantilever-free AFM platform that uses a distributed optical lever to enable massively parallel topographic imaging with arrays of over 1000 probes. By integrating 2PP-DLW-fabricated reflective probes on compliant films, optical readout with nanometer sensitivity, and robust reconstruction algorithms, the system achieves ~9 nm vertical precision and ~100 nm lateral sampling over sub-millimeter spans. Modeling and experiments validate linear mechanical and optical responses, and crosstalk is mitigated via deconvolution. The approach holds promise for high-throughput, large-area nanoscale metrology across diverse fields. Future work could include scaling to larger arrays and areas, enhancing optical sensitivity and speed, integrating measurements of lateral forces/gradients, expanding to different substrates and sample stiffness regimes, and developing automated calibration and artifact correction pipelines for industrial metrology.

• Mechanical crosstalk between neighboring probes necessitates deconvolution; while linear and correctable, it adds processing complexity and assumes consistent coupling.
• Probe height variability (standard deviation ~1.4 µm) requires overlap-based leveling; accuracy depends on sufficient overlap and uniform contact.
• Frame-to-frame Z repeatability (32 nm SD) requires per-frame offset correction.
• Substrate stiffness dependence: to limit effective softening to <10%, sample substrates should be >1 GPa; softer samples could increase compliance-induced errors.
• Reflectivity requirement: the backing layer must be reflective; added coatings (Al) and optical access constrain materials and geometries.
• Tip wear and probe damage were not observed here but remain considerations; longevity under varied samples and conditions requires further study.
• Reported step height error (~15% vs AFM) indicates calibration and reconstruction can be further refined for quantitative accuracy.
• Current lateral sampling and field-of-view are constrained by array pitch (15 µm) and objective; scaling to larger areas and finer sampling may require optical and mechanical upgrades.