Interpreting motion and force for narrow-band intermodulation atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 45–56, doi:10.3762/bjnano.4.5

• , amplitude A(t), phase (t) and force envelope function can be considered to be constant during each interaction cycle, and the motion and the partial force during the i-th tip oscillation cycle are given by where A(i), Φ(i) and are constant and are determined at the time t(i) of the ith lower turning point

• the frequencies ω1 = 2π · 299.75 kHz and ω2 = 2π · 300.25 kHz are chosen such that in the absence of a tip–surface force, the tip oscillation amplitude is sinusoidally modulated between 0 and 30 nm. For the tip–surface force Fts we assume a van-der-Waals–Derjaguin–Muller–Toporov (vdW-DMT) force with

Calculation of the effect of tip geometry on noncontact atomic force microscopy using a qPlus sensor

• Julian Stirling and
• Gordon A. Shaw

Beilstein J. Nanotechnol. 2013, 4, 10–19, doi:10.3762/bjnano.4.2

• (marked on Figure 4a) for both images. The results presented in Figure 5 show that for points 1 and 3, where the lateral force is near zero throughout the tip oscillation, the spectra align with a relative error of less than 3% at the point of highest interaction. However, for point 2 where the lateral

• , the overall amplitude of motion at the tip apex is larger. If the lateral force is near zero throughout the tip oscillation then this has minimal effect on either imaging or spectroscopy measurements, thus explaining the ability of qPlus AFM to gain both subangstrom spatial resolution, and agreement