Sufficiency Condition for the Reliability of Surface Topography Measurements using Atomic Force Microscopy

A condition for determining the sufficient reliability of nanoscale surface topography measurements using atomic force microscopy (AFM) for relatively small cantilever inclination angles is proposed. Relationships between the basic geometrical parameters of surface roughness, geometric deviations of the probe, the angles of the cantilever and the inclination of the side faces of the probe, as well as the dimensions of the nonlocal point of the probable contact of its side faces with protrusions of roughness, were established. The requirement to determine the smallness of the ratio of the sizes of a nonlocal point to the distance between neighboring nonlocal points as a necessary condition for the sufficient reliability of surface topographical measurements using AFM, is asserted. Publications in which nanoscale surface topography measurement fails to indicate the roughness of the sample surface and the probe, the angles at the tip of the probe and the inclination of the cantilever, as well as the best resolution (smallest increment) at which the study is carried out, cannot be accepted as reliable, due to the probabilistic character of results thus obtained. Moreover, surface images obtained using AFM without proper justification for the resolution (value of the measurement increment) represent only a qualitative picture, providing an insufficient basis for carrying out computational manipulations. In order to increase the reliability of measurements of nanoscale surface topography measurements using AFM, it is necessary to radically increase probe manufacture precision, as well as to use probes with the smallest possible angle at the apex. In addition, it is necessary to make changes in the design of AFM apparatus. In particular, the microscope stage should be designed to employ automatic rotation. It should provide closeness the probe axis direction to the normal to the average plane of the sample. This “integral” angle of rotation of the microscope stage is easily iteratively determined at the stage of preliminary investigation of the surface topography of the sample. In this case, it will be necessary to geometrically increase the length of the cantilever so that the base extends beyond the limits of the sample.