DETECTING AND CONTROLLING FORCES IN ATOMIC-FORCE MICROSCOPY WITH MULTI-DEGREES-OF-FREEDOM

An atomic force microscope (AFM) with the function of measuring both bend theta(x) and twist theta(y) of a rectangular-shaped cantilever, with its longitudinal axis pointing in the y direction, was used with a controller, where square-root a X theta(x)2 + b X theta(y)2 roughly corresponding to the vectorial magnitude of the force acting on the tip in the x-z plane was kept constant by integral control of the z scanner. The control was effective during scanning in the repulsive mode, and by changing the parameters a and b, fluctuation of theta(y) corresponding to the lateral force could be maintained below a set threshold. Since the force acting on the end point of the tip changes its magnitude and orientation during scanning, the cantilever is expected to undergo various modes of deformation, resulting in, relative displacement of the base of the cantilever and the end point of the tip. For better understanding of the imaging process of AFM, the trajectory of the end point of the tip was plotted during image acquisition. When scanning mica, it was found that the end point meanders by up to 0.3 nm from the axis of the scan. This implies that the conventional imaging technique of plotting acquired data along the straight movement of the xyz scanners may result in artifacts when the relative movement of the end point of the tip and the base of-the cantilever is not negligible to the size of the features observed.