Cantilever tilt compensation for variable-load atomic force microscopy

Abstract

In atomic force microscopy ͑AFM͒, typically the cantilever's long axis forms an angle with respect to the plane of the sample's surface. This has consequences for contact mode experiments because the tip end of the cantilever, which is constrained to move along the surface, displaces longitudinally when the applied load varies. As a result, the AFM tip makes contact with a different point on the surface at each load. These different positions lie along the projection of the lever's long axis onto the surface. When not constrained by static friction, the amount of tip-displacement is, to first order, proportional to the load and is shown to be substantial for typical AFM and cantilever geometries. The predictions are confirmed experimentally to within 15% or better. Thus, care should be taken when performing load-dependent contact mode experiments, such as friction versus load, elasticity versus load, or force versus displacement measurements, particularly for heterogeneous or topographically-varying samples. We present a simple method to reliably and precisely compensate for in-plane tip displacement that depends only on the range of vertical motion used to vary the load. This compensation method should be employed in any load-varying AFM experiment that requires the tip to scan the same line or to remain at the same point at each load.

Reduced hardness at the onset of plasticity in nanoindented titanium dioxide

“…There are some effects reported concerning tilt between tip and sample in nanoindentation experiments. 11,12 However, from the regular shape of the traces on the AFM images shown in Fig. 1, any tilting effects can be safely ruled out.…”

“…Also, some precautions were implemented in our data analysis routine: ͑i͒ only F vs z curves corresponding to regular traces were used; ͑ii͒ large homogeneous regions of the sample were selected for performing the nanoindentations, and finally; ͑iii͒ original deflection V vs piezodisplacement ⌬ data were carefully inspected to eliminate the curves showing artifacts such as equidistant pop-ins, oscillations, or nonmonotonic behavior. 11,12 To illustrate the later, a typical original V vs ⌬ curve is displayed as Fig. 2.…”

Subnanometric stabilization of plasmon-enhanced optical microscopy

“…In general, the force-induced drift is characterized simply by the cantilever's physical properties such as the length of the cantilever's long axis, the tilt angle and the spring constant. Cannara et al established a simple calculation method to predict the amount of the drift under a certain tip-applied force with an accuracy of within 15% [23]. Here we applied the above-described experimental technique to in situ compensation of the force-dependent drift with subnanometric precision.…”

Three-dimensional vector electrochemical strain microscopy

“…The first leads to rotated surface normal vectors which are different on different sides of the grain which can lead to additional offsets in the measured OP and IP ESM values. [30][31][32][33] For the latter, step edges or other topographical features can lead to an enhanced Li-ion extraction and thus an enhanced ESM signal which is not considered in the analytical calculations. This will be subject to future studies as well as the influence of an asymmetric tip shape on the ESM signal.…”