Quantitative atom-resolved force gradient imaging using noncontact atomic force microscopy

~Received 4 April 2001; accepted for publication 11 June 2001! Quantitative force gradient images are obtained using a sub-angstrom amplitude, off-resonance lever oscillation method during scanning tunneling microscopy imaging. We report the direct observation of short-range bonds, and the measured short-range force interaction agrees well in magnitude and length scale with theoretical predictions for single bonds. Atomic resolution is shown to be associated with the presence of a prominent short-range contribution to the total force interaction. It is shown that the background longer-range interaction, whose relative magnitude depends on the tip structure, has a significant effect on the contrast observed at the atomic scale. © 2001 American Institute of Physics. @DOI: 10.1063/1.1389785# The atomic force microscope ~AFM! 1 was originally de- vised as an analog of the scanning tunneling microscope ~STM!, using forces rather than the tunnel current between tip and surface atoms to generate atomic resolution images. Forces associated with short-range bonding have, like the tunnel current, an exponential dependence on distance, 2,3 making atomic resolution possible. However, most of the actual applications of AFM have been at lower than atomic resolution because of the extreme sensitivity required to re- solve single bonds, and the instability of soft levers against the high force gradients of short-range interactions. Atomic resolution AFM has been achieved only recently using reso- nant cantilevers with large, ;100 A oscillation amplitudes in ultrahigh vacuum ~UHV!. 4-6 This technique has also been used to measure the force interactions between the tip and sample, 7 but the oscillation amplitudes employed are much greater than the interaction range. Hence the interaction has to be inferred by mathematical deconvolution, which as- sumes both single valuedness of the interaction and the ab- sence of dissipation processes during the measurement. There have been more direct measurements of the interac- tion. Durig et al. 8 observed short-range interactions using an Ir sample, but their work did not involve imaging. Other direct measurements have shown unexpectedly large length scales for the interaction potentials 9,10 implying the domi- nance of forces other than atomic local bonding. In this let- ter, we report the direct observation of short-range bonds, and we show that they are indeed associated with atomic resolution in AFM as predicted by theory. 11 Experiments are performed with a specially constructed high force resolution AFM/STM operating in UHV. 12 The force gradient between the tip and sample is measured by vibrating the cantilever base at a frequency well below the resonance, with a very small oscillation amplitude of typi- cally 0.25-0.5 A peak to peak. Excellent displacement sen- sitivity is thus very important. An all-fiber interferometer is used to detect the cantilever deflections, 13 and the reflectivi- ties of the fiber end and the lever are tailored to enhance the cavity's finesse. The system has a 3310 24 A/ AHz noise floor, which enables ,1 N/m stiffness changes to be ob- served with sub-A oscillation amplitudes using reasonable integration times. The amplitude at the tip, which is altered by the tip-surface interaction, is detected from the interfer- ometer output using a lock-in amplifier. The interaction stiff- ness ~negative of the force gradient! between the tip and sample k int can be obtained from the simple relation 14