Force measurement with a scanning tunneling microscope

Abstract

The scanning tunneling microscope STM has proven its unique abilities in imaging surfaces up to atomic resolution. Soon after its invention by Binnig and Rohrer it was realized that, due to its close proximity to the surface atoms the STM tip often influences and modifies the surface. This disadvantage however was used positively by modifying substrate surfaces in a controlled way. Eigler et al.1 showed that even single atoms can be positioned on selected adsorption sites proving the startling possibilities to build up man-designed functional nanostructures atom by atom. The manipulation process itself is a subject of fundamental experiments with single atoms. The data recorded during the positioning with the microscopes tip yields information whether the interaction is attractive or repulsive2 and about the atoms path on the surface.3,4 The nature of the tip-atom interaction for metal atoms was determined recently as a chemical force, dependant only on the tip-atom distance.5 Recent insights into single atom processes on crystal surfaces include friction measurements with atomically sharp cantilever6 and the dynamics of single atom switching.7 The force required to move a single atom across a crystal surface however has not been measured yet and we show here a simple way to measure forces with a STM. A formula is presented and tested with simulated manipulation curves. Atomic manipulation can be described within a simple model where the surface is assumed to have a continuous sinusoidal potential with the amplitude of the diffusion barrier.3 We describe here the tip with a Morse potential and let the atom reside in the local minimum of the combined tip and surface potential. The scheme used here is not dependant on the used potential, other potentials or results from firstprinciple calculations can be used too. The atom moves on a two dimensional surface and the tip is assumed to be spherical. With these assumptions one can realistically describe atomic movements and tip height curves once the tip-atom force and the diffusion barrier are known. A simulation starts by placing the tip above the atom and the height is adjusted with closed feedback loop until the current set point is reached. The local potential minimum of the combined potentials is determined and the atom is shifted to it. Again the tip height is adjusted to reach the set point value of the current. These feedback loop cycles are repeated until the atom stabilizes only then the tip is shifted laterally. Figure 1 shows a description of the potential model where the atom always resides in a local potential minimum of the combined potentials of tip and surface.3 In this equilibrium position the tipatom force is counterbalanced by the surface forces expressed by the migration barrier U0. With this description topography curves or manipulation curves at constant current can be calculated.8 The reverse, namely the tip-atom interaction forces can be determined too. They require experimental manipulation curves. In such case first the atoms position is determined and then the tip-atom interaction force can be calculated. Hereby one uses that the projected lateral force component Flat=Ftip cos needs to be equal to the surfaces force Fsurface. By using an approximate potential for the surface one can follow a simpler way and the force can be determined from a single formula shown in the following. Figure 2 shows simulated tip height or manipulation curves for a quasi-one-dimensional periodic surface potential. Experimental values for the height are typically 4 A and the amplitudes range is 0.1 A.2 The tip moves over the atom and changes thereby the lateral force component which is pulling the atom across the surface plane. Once the lateral force component exceeds the counterforces from the surface the atom will jump to the next local potential minimum. The recorded tip height shows a characteristic shape which can