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Apparatus schematic and the lumped element scheme for the tip impedance in the case of a thin dielectric film on an arbitrary substrate. Tip-sample distance ; tip size .
(a) 2D finite element model simulations of the normalized frequency shift for a -thick film on a metallic substrate at three tip-sample distances , 225, and . The tip geometry is shown in Fig. 1. It is evident that is linear (within simulation precision ) at . For these simulations . Solid lines are guides to the eye. (b) Typical experimental dependence for vs obtained on a set of six films, the parallel plate capacitor model , and the results of 2D simulation. The solid lines are guides to the eye. Note that in this graph is not absolute but is measured relative to , which was determined by extrapolating the experimental data to .
(a) Correlation between NSMP and Hg probe measurements on log-log scale for a number of low- and high- films. The solid line is the linear fit with correlation coefficient . (b) Histogram based on 100 measurements performed at the same site on an -thick low- film. Mean -value is 3.237, with a standard deviation of 0.29%.
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