Scanning Force Microscopy (SFM)

Since its invention in 1986 [Bin86], the SFM has become a very successful and widely used tool to study surfaces in various fields. The success is based on a set of advantages of the SFM in comparison to other high resolution real space imaging methods like scanning electron microscopy (SEM) or transmission elec-tron microscopy (TEM). Two of them are the ease of use, i.e. the easy sample preparation and its applicability in different environments like ultra high vacuum, gaseous atmospheres, or liquids.

A scanning force microscope is build as shown in Figure2.1. A tip positioned

x y z

Piezo

Piezo-tube Segmented

Photodiodes

Cantilever

Tip

A

a

Sample

Laser

Figure 2.1: Schematic setup of a scanning force microscope. The tip is located at the end of a cantilever. A laser is reflected from the cantilever onto a segmented photodiode. Either the sample (as shown here) or the tip are positioned in 3d space by piezo elements (here a piezo tube). In a dynamic mode of operation the cantilever is excited by a piezo element causing the cantilever to vibrate at an amplitude A.

at the very end of a cantilever is used as probe. A laser is focussed onto the end of the cantilever and reflected into the center of a segmented photo diode.

Any forces acting on the tip result in a bending (vertical forces) or twisting (lateral forces) of the cantilever and therefore in a different reflection angle. The difference of the output of the photodiodes is used as output signal, which is in good approximation proportional to the deflection of the cantilever. Depending on the mode of operation the photodiode signal is used directly or in another way as a feedback signal as discussed below. A feedback loop continuously checks the feedback signal, compares it to some user defined setpoint value and adjusts the height of the tip over the sample such that the difference is minimized.

Stable operation is possible if the feedback signal is monotonous in the tip-surface distance. The tip is then kept at a height corresponding to a constant interaction over the sample surface.

Either the sample or the cantilever is mounted to piezoelectric elements, which

provide the necessary means to position the tip relative to the sample in three-dimensional space. With the feedback enabled the tip is then scanned relative to the sample surface and the height adjustments to keep the feedback value at its setpoint are recorded as an height image of the surface.

Amplitude

Frequency

wr

wNC

Dw A0

wTM

Amplitude,Phase

Phase

Figure 2.2: Resonance curve of a harmonic oscillator representing the exited can-tilever system. The resonance frequency is ω_r and the width of the resonance curve is ∆ω. The arrows at the bottom of the curves denote the ranges of the typical excitation frequencies for the tapping mode (ω_{T M}) and the noncontact mode (ω_{N C}).

A variety of modes have been established depending on the environment of scanning and the source of forces acting on the tip. To simply measure topo-graphic information, the early used contact mode is more and more replaced by dynamic modes. In the latter the tip is forced to oscillate close to its resonance frequency excited by an additional piezo element positioned at the base of the cantilever. The oscillation is monitored by the photodiodes and converted to an amplitude and a phase signal. A typical resonance curve is shown in Figure 2.2.

The phase signal measures the phase difference between the detected cantilever vibration and the exciting oscillation and scales between 0 and -π.

If the tip experiences any kind of forces from the sample surface, the resonance curves of the tip sample system deviate characteristically form the resonance curve of the tip only. Elastic interactions cause the resonance frequency of the tip-sample system to either decrease or increase in the case of attractive or repulsive

forces. Dissipative interactions decrease the energy in the system and therefore the amplitude of oscillation. See also chapter 3for details.

Two modes of operation have found widespread use. The first one is the so called ”dynamic mode”, which uses the shift of the resonance frequency as feedback parameter. This mode is best suited for ultra high vacuum applica-tion, since in this environment the resonance curve is very small (quality factor Q_{U HV} = ω_r/∆ω ≈ 20000) and the resonance frequency shift is larger than the width of the resonance curve. In ambient conditions the presence of air de-creases the quality factor toQ_ambient ≈400, Therefore either the ”tapping mode”

(also called ”intermittend contact” mode) or the ”noncontact mode” are typically used. These modes use the amplitude signal as feedback signal, which normally decreases monotonous with the tip sample distance. One major obstacle in scan-ning in ambient conditions is the adhesion force between the tip and the sample, which is much larger than in liquid or in vacuum environments due to an absorbed water layer on tip and sample surfaces. Therefore rather stiff cantilevers (spring constants ≈ 40 N/m) and large vibration amplitudes (10-80 nm) are used, such that the restoring force at maximum amplitude exceeds the adhesion force. Only under these conditions a stable operation is possible. Depending on the setpoint amplitude the forces between the tip and the sample are attractive or repulsive.

The noncontact mode operates at very large amplitudes setpoints only slightly below the free amplitude of the tip and at frequencies larger than the resonance frequency in order to establish scanning with only attractive forces between tip and sample. This mode has the advantage of being the least destructive of the two modes. The tapping mode or intermittend contact mode uses lower setpoints at which repulsive forces due to tip sample indentation come into play. Only in this case the phase signal exhibits material contrast. Another advantage to the noncontact mode is the fact that the amplitude distance dependence is steeper at lower setpoints, which in turn enables faster scanning of the sample surface.