Detecting the Spring Deflection by Tunneling

The first SFM published by Binnig, Quate and Gerber[141] employed tunneling to detect the bending of the force sensing cantilever. Figure 4.408 shows a sketch of the arrangement. The authors sandwiched a cantilever between the tip of an STM and the sample. The sensitivity of the tunneling detector in the SFM is the best of all possible detectors. On clean surfaces the change in tunneling current might approach one order of magnitude for every 0.1 nm change in deflection. In air there are a few critical points which might degrade the performance of the SFM.

Abbildung 4.408: The principle of the SFM proposed by Binnig et. al.[141]. A lever with a spring constant of $\approx 1$ N/m is pressed into a sample mounted on a piezo tube. The deflection of the lever is measured by a tunnel junction. The tunnel gap is adjusted by a force sensor piezo. Alternatively the SFM tip on the lever can be operated in a non-contact mode via attractive forces.

An ideal deflection detector for an SFM should not have any sensitivity to the local surface structure of the force sensing cantilever. The tunneling current between the back of the cantilever and the sensing electrode, however, is confined to a narrow region whose width is mainly determined by the local curvatures of the sensing electrode and the cantilever. If the sensing electrode is a sharp tip, as used for STM experiments, the SFM can be very susceptible to the lateral bending of the cantilever.

A solution of the resolution problem is to use as smooth a cantilever back as possible and to increase the area of the tunneling current. However this aggravates a second problem which might occur in a tunneling SFM. Adsorbate layers are present on both the sensing electrode and on the back of the cantilever. Typical distances between the two electrodes in a tunneling junction are of the order of 1 nm. If two monolayers are present both on the sample and on the cantilever tip, the distance between the sensing electrode and the back of the cantilever might be too small to allow a tunneling current to pass. Therefore the sensing electrode has to be pressed against the back of the cantilever which will yield due to its low spring constant. It is possible that no tunneling current can be established. Furthermore the filled gap between the cantilever and the sensing electrode rigidizes the cantilever. The effective spring constant of the cantilever is then a function of the stiffness of the adsorbate layers. Whereas tunneling as a deflection detector has its deficiencies in air, it might become the method of choice in vacuum SFMs. We have seen that it is advantageous to use microfabricated cantilevers in an SFM. These cantilevers have a Q of about 100 in air and a Q of $>10^4$ in vacuum. Any sudden change in the surface topography starts a damped oscillation of the cantilever. The amplitude of the oscillation will decay to 1/e after Q oscillations. If the resonance frequency were 10 kHz the time constant would be 1 second. Such a time constant would impose such a small scanning speed that the whole microscope would become impractical. Here the additional, highly nonlinear force between the sensing electrode and the back of the cantilever could help in damping the oscillations of the cantilever.