Atomic force microscopy

Atomic force microscopy maps surfaces and measures small interactions using a sharp tip attached to a compliant cantilever. In a common modern readout, a laser reflects from the cantilever onto a split photodetector, turning bending into an electrical signal. A scanner moves the tip relative to the sample; feedback can adjust height to maintain a chosen interaction signal. With calibrated stiffness $k$, a small static deflection $\delta$ gives force $F\approx k\delta$. The measured image combines surface geometry, tip geometry and interaction physics, so narrow features can appear broadened. Gerd Binnig, Calvin Quate and Christoph Gerber introduced the instrument in 1986.^[ref] Modern force measurements additionally require calibrated cantilever stiffness.^[ref]

Dynamic atomic force microscopy using the resonance-frequency change of an oscillating cantilever as the interaction-sensitive signal. Small-amplitude oscillations and weak force gradients give the small-amplitude AFM frequency shift; larger amplitudes require an averaged interaction analysis.

At equilibrium separation $z_0$, expanding the tip force gives $m_{\mathrm{eff}}\ddot{x}=-[c-F^{\prime }(z_0)]x$. Thus $\omega /{\omega }_0=\sqrt{1-F^{\prime }(z_0)/c}$, and Taylor expansion gives the displayed result for $|F^{\prime }|\ll c$. The displacement convention takes positive $z$ away from the surface. A positive gradient of an attractive force softens the resonance; a large-amplitude oscillation samples more than the local gradient.

A positioner using the converse effect of piezoelectricity to move a probe or specimen. Its calibrated motion can form an atomic force microscopy height image under closed-loop control. piezoelectric hysteresis, piezoelectric scanner creep, travel and control bandwidth limit faithful motion.

An electrostatic null method that adjusts probe–sample bias to cancel an alternating force or force-gradient component. The compensation voltage estimates a spatially weighted contact potential difference, with the sign set by the electrode-bias convention. Calibration and surface-state effects matter for work-function interpretation.

A two-pass scan method recording topography first, then retracing it at an offset height to measure a longer-range interaction with reduced contact contributions. It is a Bruker mode name.^[ref]

Mapping electrical current through a conducting probe contact while recording topography. Local current depends on bias, contact geometry, surface layers and contact resistance as well as the specimen's electrical response.

An electrical scanning-probe technique measuring resistance associated with current spreading from a small probe contact into a specimen. Inferring carrier concentration or conductivity requires appropriate contact conditions and calibration.

A force-microscopy mode keeping the probe in contact while monitoring cantilever deflection. Constant-deflection feedback records the vertical actuator motion needed to maintain an approximate normal-force setpoint; finite probe geometry and specimen deformation still affect the image.

An apparent image change caused by alteration of the effective probe apex during acquisition. A shifted height baseline may be corrected using a suitable reference, but changed geometric access, duplicated features and lost data are not generally repaired by AFM image flattening.

Scanning-probe mapping of local capacitance response. Conventional semiconductor dopant profiling measures a bias-modulated $dC/dV$ signal involving an insulating layer and a changing semiconductor depletion region; an electrically isolated conducting flake on glass is not automatically that device geometry.

Mapping of local mechanical response from calibrated AFM force curves. Deformation, adhesion and a model-dependent contact elastic modulus can be separated more directly than by interpreting oscillation phase alone. Tip radius, indentation depth, loading rate and substrate response constrain quantitative interpretation.

Current-sensitive atomic force microscopy using a conducting tip and a low-current amplifier. A steady conductivity map requires a complete electrical path through the contacted specimen region, even when force-based topography can be recorded without it.

A scan distortion caused by the finite bandwidth or instability of the height-control loop. Streaks, lag and ringing can be diagnosed by changing speed, controller gains and scan direction and comparing trace with retrace.

Geometrical broadening of a surface feature by the finite shape of an AFM probe. The same geometry can narrow the accessible part of a surface depression. The measured height envelope is more precisely a morphological dilation than an ordinary linear convolution. Repeated identical particle outlines can be tip images; inaccessible sidewalls prevent a unique inverse reconstruction.

A measured tip–sample force versus displacement or separation during approach and withdrawal. Contact deformation, adhesion and instrumental compliance must be separated before extracting a material property.

A sharp tip carried by a calibrated AFM cantilever and brought near a surface to sense forces. Tip geometry and contamination influence both lateral resolution and mechanical or electrical measurements.

A compliant beam whose deflection senses tip–sample force in atomic force microscopy. In its calibrated linear range, normal force is $F=k_c{\delta }_c$.

The normal restoring-force coefficient of an AFM cantilever, $k_c=F/{\delta }_c$, with units $\mathrm{N}{\mathrm{m}}^{-1}$. A quantitative force measurement requires both this stiffness and the optical deflection sensitivity.

Subtraction of fitted background planes or polynomials from an AFM height image. This removes tilt or scanner curvature only to the extent that the chosen fit represents the instrument rather than real specimen topography.

A curved height background caused by coupling of lateral scanner displacement to vertical motion, particularly the arc followed by a bending piezoelectric tube. A real curved specimen and instrumental bow cannot be separated from one height image without additional information.

A force-curve mapping mode that controls the peak repulsive normal force during repeated low-frequency tip-surface contacts. Calibrated force curves provide topography and spatial maps of adhesion, deformation, modulus and dissipated energy. Mechanical-property accuracy depends on tip geometry, cantilever calibration and the contact model.

An instability in a compliant force probe when the attractive force gradient exceeds the restoring stiffness of the cantilever. The tip then jumps from a noncontact branch into contact; the missing branch cannot be followed quasistatically with that stiffness.

Signals acquired in the two opposite scan directions, registered to common laboratory coordinates.

Measurement of lateral tip–surface forces from torsion of an atomic-force-microscope cantilever.

A contact measurement of electrically driven local surface displacement, detected by cantilever bending or torsion and often demodulated by a lock-in amplifier. Electrostatic and contact-mechanical cross-talk must be separated from converse piezoelectric effect response.

A distortion caused by the finite shape or multiple contact points of a scanning tip. For a single-valued sample height $h$ and a tip profile $t$ measured upward from its apex, nonpenetration requires the indicated apex height to satisfy $z(x)\ge h(u)-t(u-x)$ for every $u$. The ideal accessible envelope is consequently $z(x)={\max }_u[h(u)-t(u-x)]$. This geometric operation is distinct from an ordinary linear convolution and from feedback lag.

Duplicated or distorted surface features arising when more than one effective apex contributes to the measured envelope. Attachment or loss of a particle can change the image abruptly without changing the sample.

An AFM approach using calibrated side-sensitive tip geometry and position control to measure steep or reentrant features. A flared tip can reach surfaces that an ordinary tapered probe cannot; calibration must account for its effective width.^[ref]

An oscillatory probe mode in which a controller uses changes in the cantilever amplitude to adjust probe-surface separation. The recorded topography depends on both tip geometry and tracking dynamics.

Attach a sphere to an atomic force microscope cantilever and approach a planar surface in a controlled fluid. Calibrated cantilever bending measures force as a function of corrected surface separation. The sphere's known curvature allows comparison with planar interaction models through the Derjaguin approximation. Approach speed, charge, roughness, hydration and jump-to-contact can limit interpretation.

A 1991 demonstration used a $3.5\mu \mathrm{m}$ radius silica sphere against a plane in sodium chloride solutions. The reported double-layer agreement and short-range deviations illustrate both the method and the need to distinguish electrostatic forces from a presumed purely dispersive interaction.^[ref]

An atomic force microscope measures interactions through the deflection or dynamics of a calibrated compliant cantilever. In a static force curve, calibrated deflection $d$ and spring constant $k_c$ give $F=k_{c}d$; converting stage position to a surface gap also requires the bending correction and a contact reference. The colloidal probe technique replaces a sharp probe with a sphere of controlled radius.