The photodiode sensitivity in the atomic force microscope is calibrated by relating the voltage noise to the thermal fluctuations of the cantilever angle. The method accounts for the ratio of the thermal fluctuations measured in the fundamental vibration mode to the total, and also for the tilt and extended tip of the cantilever. The method is noncontact and is suitable for soft or deformable surfaces where the constant compliance method cannot be used. For hard surfaces, the method can also be used to calibrate the cantilever spring constant.

Theoretical calculations and experimental measurements are used to show that hitherto neglected inertial effects can be significant in computer- controlled surface force measurement devices such as the atomic force microscope. The problem is analyzed in detail for the case of the van der Waals attraction in air. It is demonstrated that equating the cantilever deflection to the surface force systematically underestimates the magnitude of the surface force, increasingly so as the speed of approach is increased. It is also shown that the surface separation becomes lost at high accelerations due to a dynamic uncoupling of the cantilever deflection and angle. The effects of elastic deformation of the bodies are taken into account, including the collision-induced elastic vibrations in the solids. Experimental data are obtained for the van der Waals attraction and collision of glass surfaces in air using the measurement and analysis of surface forces device. All of the effects found in the theoretical calculations are identified in the experimental data.

A number of atomic force microscopy cantilevers have been exhaustively calibrated by a number of techniques to obtain both normal and frictional force constants to evaluate the relative accuracy of the different methods. These were of either direct or indirect character—the latter relies on cantilever resonant frequencies. The so-called Sader [Rev. Sci. Instrum. 70, 3967 (1999)] and Cleveland [Rev. Sci. Instrum. 64, 403 (1993)] techniques are compared for the normal force constant calibration and while agreement was good, a systematic difference was observed. For the torsional force constants, all the techniques displayed a certain scatter but the agreement was highly encouraging. By far the simplest technique is that of Sader, and it is suggested in view of this validation that this method should be generally adopted. The issue of the photodetector calibration is also addressed since this is necessary to obtain the cantilever twist from which the torsional force is calculated. Here a technique of obtaining the torsional photodetector sensitivity by combining the direct and indirect methods is proposed. Direct calibration measurements were conducted in liquid as well as air, and a conversion factor was obtained showing that quantitative friction measurements in liquid are equally feasible provided the correct calibration is performed.

Presented here is a novel technique for the in situ calibration and measurement of friction with the atomic force microscope that can be applied simultaneously with the normal force measurement. The method exploits the fact that the cantilever sits at an angle of about 10° to the horizontal, which causes the tip or probe to slide horizontally over the substrate as a normal force run is performed. This sliding gives rise to an axial friction force in the axial direction of the cantilever , which is measured through the difference in the constant compliance slopes of the inward and outward traces. Traditionally, friction is measured through lateral scanning of the substrate, which is time consuming, and requires an ex situ calibration of both the torsional spring constant and the lateral sensitivity of the photodiode detector. The present method requires no calibration other than the normal spring constant and the vertical sensitivity of the detector, which is routinely done in the force analysis. The present protocol can also be applied to preexisting force curves, and, in addition, it provides the means to correct force data for cantilevers with large probes

In an atomic force microscope AFM , the force is normally sensed by measuring the deflection of a cantilever by an optical lever technique. Experimental results show a nonlinear relationship between the detected signal and the actual deflection of the cantileve, which is widely ignored in literature. In this study we have designed experiments to investigate different possible reasons for this nonlinearity and compared the experimental findings with calculations. It is commonly assumed that this nonlinearity only causes problems for extremely large cantilever deflections. However, our results show that the nonlinear detector response might influence many AFM studies where soft or short cantilevers are used. Based on our analysis we draw conclusions of the main reason for the nonlinearity and suggest a rule of thumb for which cantilevers one should use under different experimental conditions.

A technique has been developed for the calculation of torsional spring constants for AFM cantilevers based on the combination of the normal spring constant and plate/beam theory. It is easy to apply and allow the determination of torsional constants for stiff cantilevers where the thermal power spectrum is difficult to obtain due to the high resonance frequency and low signal/noise ratio. The applicability is shown to be general and this simple approach can thus be used to obtain torsional constants for any beam shaped cantilever.