Analysis of the interaction mechanisms in dynamic mode SFM by means of experimental data and computer simulation

Abstract

The performance of a scanning force microscope (SFM) operated in the dynamic mode at high oscillation amplitudes is determined by the response of the system to a given set of interaction forces between the probing tip and the sample surface. To clarify the details of the cantilever/tip dynamics two different aspects were investigated in experiment and computer simulation. First, the interaction forces dominating the oscillatory motion of the probe were varied by applying an additional electrostatic force field. It is shown that such variations in the attractive part of the interaction potential can cause a switching between two different oscillation states and thereby significantly contribute to the contrast obtained from phase imaging. Secondly, the interaction forces were kept constant but the system response itself was varied by modifying the effective quality factor of the oscillating cantilever with an active feedback circuit. This provides a means to influence the transition from the attractive to the partly repulsive interaction regime, i.e. the onset of the intermittent contact or tapping mode. Operating an SFM in the dynamic mode at high amplitudes (> 10 nm) offers the possibility of minimizing the contact time of the probing tip with the sample surface and thereby reduce lateral or friction forces involved in the scanning process. It also allows the collection of additional data related to different sample properties by recording the phase shift between the force driving the cantilever and its oscillation. In the last few years these features of operating the SFM in the dynamic mode [1, 2] were shown to be very useful to characterize several different kinds of sample surfaces, e.g. thin organic films, polymers, biological samples or even liquid droplets [3]. Although this has led to a steady increase in the number of possible applications, there are still several details of the interaction process between the tip and the sample that need further clarification. The overall goal must be to relate the experimentally accessible data, such as the amplitude and ∗ Corresponding author phase signal, more or less directly to specific sample properties, such as topography, elasticity and viscoelasticity. Because highly nonlinear interaction forces are involved when the oscillating tip is in close proximity to a solid surface, the analysis of the dynamic system becomes quite complex. Therefore supplementary computer simulations based on proper mathematical models are useful to investigate the details of the interaction process. Basically, the equation of motion describing the dynamic properties of the probing tip has to be solved in such a way that the influence of different parameters characterizing the probe as well as the sample surface can be examined. There have been several reports recently on different approaches to this problem, providing analytical [4] as well as numerical [5–11] solutions. Most of them are based on the point-mass model, but there are also approaches which describe the complete flexural motion of the cantilever beam supporting the probing tip, as this becomes more relevant when the system is driven well above its resonance frequency [12]. Thus by simulating the dynamic system one can gain useful information on the complex interaction process of the oscillating tip and the sample surface. 1 Experimental and simulation methods The simulation results presented here are all based on the point-mass model with the interaction forces being derived from MYD/BHW calculations [11, 13, 14] and applying the Verlet algorithm [15] to solve the equation of motion numerically. All experiments were performed with a NanoScope III MultiMode stage (Digital Instruments) equipped with an additional lock-in amplifier (EG&G Instruments, Princeton Applied Research, Model 5302) to measure the phase lag between the driving force and the cantilever response quantitatively. Rectangular cantilevers made of doped silicon (Nanosensors) with a nominal length of L = 125 μm were used. By analogy with measurements of quasistatic forcedistance curves in contact mode, the amplitude and phase shift as a function of the z-position were quantitatively investigated in the dynamic mode by means of simulation and