(a) The friction force measurement approach. The AFM cantilever exerts a force on a free standing plate resting on a substrate. The AFM piezoelectric scanner moves the substrate (or in alternative configurations, the cantilever) laterally. The resulting twisting of the lever can be used to measure the magnitude of the friction forces acting at the plate-substrate interface, provided the tip-plate contact does not slip. A position sensitive detector (PSD) is used so that the absolute movement of the cantilever deflection can be found. A camera or microscope is used to ascertain whether the tip does or does not slip with respect to the sample plate. (b) The method applied using a triangular Si3N4 cantilever in contact with a microfabricated (300 μm square) Si plate. (c) The implementation of the method in a commercial AFM (Digital Instruments Nanoscope II) showing a Si cantilever in contact with a large (3 mm square) Si plate. The cantilever is mounted on the piezoelectric scanner and is continuously moved in the lateral direction by a triangular waveform. The video shows the movement of the plate as a force curve is undertaken. The plate is initially in contact with the AFM tip and is seen to move with the tip, i.e., the tip sticks on the plate, and the plate slips on the mica surface. At ∼17s the AFM tip pulls off the plate surface and the motion of the plate stops (enhanced online). [URL: http://dx.doi.org/10.1063/1.4773534.1]doi: 10.1063/1.4773534.1.
Schematics showing the basic analytical elements of the method. (a) The case with no adhesion. If the AFM tip slides on the plate the measured friction force is F f = μ t F n . If the plate slides on the substrate the measured friction force is F f = μ s F n . The friction causes the cantilever to twist by an angle θ/2, which is larger for longer AFM tip heights h. (b) The case with adhesion and a rough plate surface. If the AFM tip slides on the plate the measured friction force is F f = τ t A t + μ t F n . If the plate slides on the substrate the measured friction force is F f = τ s A s + μ s F n . Multi-asperity contact occurs between a rough plate and the substrate, with each asperity contact in general having a different value of adhesion force (i F ads).
Scanning electron microscope images of a 6 μm thick square silicon plate used as a sample in the experiments. (a) The plate suspended by two sacrificial connectors before release. The plate is released onto the substrate surface by breaking the connectors. The three plate tips can be observed protruding from the surface. (b) Close up of a plate tip.
Oscilloscope traces showing the raw friction signal (i.e., the PSD signal corresponding to the twisting of the AFM cantilever) at three different applied loads (approximately 2, 8, and 16 μN). The triangular waveform (5 Hz, 100 mVp-p) is the voltage driving the displacement of the AFM piezoelectric scanner. The peak-peak piezoelectric voltage corresponds to a displacement of 670 nm, giving a displacement speed of 3.35 μm/s. The friction signal changes to a new steady state value when the displacement changes direction and half the difference between the two steady state values is the dynamic friction force (F f).
A force curve, i.e., force as a function of piezoelectric displacement in the normal (z) direction, showing the change in friction as a function of the applied load. In this experiment the flat face (i.e., smooth Si; no tips) of a square plate (300 × 300 μm2, 3 μm thick) contacts a mica surface (S/N 4 in Table II ). The AFM tip approaches the plate surface from negative z values and contacts the plate at z = 0 nm. Positive z values correspond to the AFM tip being in contact with the plate. At positive z values, the plate is observed (optically) to move with the cantilever, verifying that the measured friction relates to the sliding of the plate and not the AFM tip. The plate moves linearly with speed 0.33 μm/s and the experiment is undertaken in ambient atmosphere. The AFM cantilever is no. 1 (Table I ) and the magnitude of the friction force shown could be considerably in error because keff is uncertain for this cantilever. Hence, the friction data should be considered as showing the qualitative variation with load.
Approach (dashed line) and retreat (solid line) force curves as a function of piezoelectric displacement in the normal (z) direction, showing, (a) negligible adhesion at the AFM tip-plate contact, and (b) strong adhesion at the AFM tip-plate contact. The AFM tip approaches the plate surface from negative z values and contacts the plate at z = 0 nm. At positive z values, the plate is observed (optically) to be moving with the cantilever, verifying that the measured friction relates to the sliding of the plate and not the AFM tip. In this experiment the 3-plate-tips of a square plate (300 × 300 μm2, 6 μm thick) contact a fluorine-terminated silicon surface (S/N 1 in Table II ). The plate moves linearly with speed 9.5 μm/s and the experiment is undertaken in ambient atmosphere. The AFM cantilever is no. 3 (Table I ).
The calculated friction coefficient (μs = F f/F n) of the plate-substrate contact as a function of load for the low load data corresponding to Fig. 6(a) . Data taken in ambient on a square plate (300 × 300 μm2, 6 μm thick) with the 3-plate-tips in contact with a F-Si surface (S/N 1 in Table II ), and using AFM cantilever no. 3 (Table I ). The plate moves linearly with speed 9.5 μm/s. The dashed line shows the theoretical single asperity relationship μ ∼ F n −1/3.
Approach force curves showing qualitative effects of plate rotation during data acquisition. Optical observations show the measured friction relates to the sliding of the plate and not the AFM tip. Curve A: the plate moves linearly. Curve B: some rotational jiggle is observed superimposed on the linear movement of the plate. Curve C: a large rotational movement occurred during data acquisition giving a step jump in the friction force. In this experiment the 3-plate-tips of a square plate (300 × 300 μm2, 6 μm thick) contact a F-Si surface in ambient atmosphere (S/N 1 in Table I ). The AFM cantilever is no. 3 (Table I ).
Schematics showing the loading of 3 tips (▴) of a plate by a point force applied at position P(xo,yo). The force on each plate tip (F 1, F 2, F 3) depends on the location at which the AFM tip exerts the load. (a) In the general case, the force on each plate tip is not equal. (b) A special case occurs if the 3 plate tips are placed equidistantly on a circle and the normal force acts in the centre of the circle. The reaction forces of the 3 plate tips are equal ( ).
The spring constants kz, kx, and kxT calculated for several commercial rectangular silicon cantilevers and one triangular Si3N4 cantilever. Equation (8) is used with E = 169 GPa and G = 60 GPa for the rectangular cantilevers. The analytical method of Sader 31 is used for the Si3N4 triangular cantilever with E = 150 GPa and G = 50 GPa. 32 All cantilever dimensions (L, w, t, h) are in micrometres and spring constants in N/m.
A summary of the experiments for different plate-substrate combinations undertaken (denoted by the S/N number) showing the conditions under which either the plate-substrate contact slips or the tip-plate contact slips, or both (listed as “variable”). For application of the method we require the plate-substrate to consistently slip, which was only achieved for S/N 1 and S/N 4. Note that the table is not inclusive and simply indicates generalisations. For example, for the low friction interface of fluorine-terminated silicon (F-Si) and a 3 tip contact (S/N 1), the plate will not move if the F-Si surface becomes contaminated.
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