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Sandbox Physics
How physics instruments measure

Inside the instrument

Why an AFM makes a bump look wider

A bump in an AFM image carries information about both the surface and the probe. The tip’s side may touch the bump before its apex arrives. The feedback loop also takes time to raise the head. The recorded height is the movement the instrument makes to maintain a force signal.

Sandbox Physics ·

A fine tip bends a small spring

Mount a fine tip at the end of a flexible cantilever and move it across a surface. A raised feature pushes upward on the tip and bends the lever. Knowing the lever’s stiffness lets us convert deflection into force. An atomic force microscope, or AFM, uses these small interactions to explore a surface.

The lever is tiny, so the instrument usually reads its bending with light. A laser reflects from the lever onto a split photodetector. A small change in the reflecting surface’s slope shifts the reflected beam and changes the light received by each half. This optical lever converts a small angle into a detectable spot displacement. A feedback process then connects that response to a height image.

Sources: [1][2]

Height records how the scanner follows a force signal

Contact imaging often holds cantilever deflection at a chosen value. Excess force makes the scanner raise the head; insufficient force makes it lower the head. As the tip passes over successive lines, the instrument assembles the vertical scanner movements into an image. The loop has a finite response time, making both scanner height and deflection error useful observations.

A narrow bump shows that response clearly. At low speed, the scanner can rise and return. At high speed, the tip may cross the summit before the rise is complete. The measured bump can become lower and its edges can shift. Comparing scans of the same place at different speeds helps identify a contribution from tracking lag.

Sources: [2][1]

The side of a rounded tip can touch first

Even a sufficiently fast loop leaves the effect of finite tip size. Imagine tracing a narrow raised dot with a rounded needle. The needle’s side touches the dot before the apex reaches it, making the path of the needle centre wider than the object. A blunter tip generally broadens the feature further.

This is contact geometry. Given the specimen and tip shapes, we can find the lowest apex position that avoids penetrating the surface at each lateral position. The resulting envelope is called geometric dilation. It explains why tip information helps interpret a scan and why a narrow trench may never have been reached by the apex.

Consider a step with broad upper and lower terraces. If the tip can settle on both with the same interaction, their height difference can be retained even as the edge broadens. Changing the tip can move the apparent edges while leaving the terrace levels close. A known step is useful for height calibration; a suitable sharp structure can help estimate tip shape. These independent comparisons address different parts of the measurement and give a firmer interpretation of its boundaries.

Sources: [3][2]

Force curves describe how the surface deforms

A soft surface can also indent under the tip. Approach one location slowly, retract, and retain displacement and deflection to obtain the two force-curve branches. Converting detector output into deflection and then force requires separate optical and spring-stiffness calibration. The scanner’s displacement scale matters too.

A spherical-contact model relates force to indentation for shallow elastic deformation of a flat, nonadhesive surface. Uncertainty in radius and stiffness propagates into material parameters. Adhesion, plasticity or viscoelasticity can separate the approach and retract branches and require additional physical processes.

Other AFM modes bring the tip into repeated contact. Resonant tapping commonly uses amplitude as its feedback signal; an off-resonance cyclic-force mode can control the peak load during each contact. These modes read different signals. Interpreting either image means following the measurement through force, cantilever, detector and feedback.

Sources: [4][1]

Sources and further reading

  1. Bruker — The Definitive AFM Modes Handbook, EB103 Rev. A3, 2026

    The current download is 2026 Rev. A3 despite its older filename. Pages 7, 13–15 explain optical beam deflection, contact feedback, resonant amplitude modulation and off-resonance peak-force control.

  2. Nanosurf — How does AFM work?

    The working-principle, sensitivity-calibration and feedback sections connect cantilever bending to detector readout and scan-rate error.

  3. J. S. Villarrubia — Algorithms for Scanned Probe Microscope Image Simulation, Surface Reconstruction, and Tip Estimation, J. Res. NIST 102, 425–454 (1997)

    The introduction and section 3, pages 428–429, describe finite-tip geometric dilation and the need for tip information when interpreting a measured surface.

  4. JPK/Bruker — A practical guide to AFM force spectroscopy and data analysis

    Pages 3–5 distinguish approach/retract interactions, hard-surface detector calibration, scanner response and independent spring-constant calibration.

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