5.3 Acoustic versus Magnetic Drive
Two methods for exciting the cantilever are in common use and are illustrated in Figure 8. Acoustic drive (Hansma, Cleveland et al. 1994; Putman, Werf et al. 1994) is illustrated in Fig. 8a. An oscillator (frequency w) supplies a voltage drive to a piezoelectric actuator (PZT) which generates sound waves in the cantilever holder. The frequencies are typically from tens of kHz to MHz, corresponding to long wavelength modes that serve to displace the base of the cantilever. When the driving frequency is near a bending-mode resonance of the cantilever, the cantilever is driven into a bending motion which causes an ac signal to be detected by the segmented photodiode detector. Figure 8b illustrates magnetic drive. In this case an alternating current (frequency w) is supplied to a solenoid in the vicinity of the cantilever. The cantilever is coated with a magnetic film and its base (and the sample) remain stationary. Direct bending of the cantilever is induced either as a consequence of magnetostriction or the magnetic interaction of the moment of the film with the applied field which generates a bending torque (Lantz, O'Shea et al. 1994; Han, Lindsay et al. 1996). Another approach is to glue a magnetic particle onto the end of the cantilever and apply a field gradient (Lindsay, Lyubchenko et al. 1993).
Direct comparison of the two methods as used for imaging in fluid (Lantz, O'Shea et al. 1994) has shown that magnetic drive is less noisy. Results with biological samples suggest that higher resolution is often obtained (Han, Dlakic et al. 1997; Han, Lindsay et al. 1997). The origin of these differences is not completely clear, but magnetic drive has some obvious advantages. One lies in its ability to drive the cantilever at any frequency. In the case of acoustic drive, significant displacement of the cantilever base occurs only at frequencies for which there is a mechanical resonance of this assembly. Secondly (as we shall show) significant bending is obtained only near a cantilever bending resonance. Thus, acoustic drive is limited to those mechanical resonances of the microscope that lie near a bending resonance of the cantilever. The result is a ‘forest of peaks’, only some of which yield a useable signal (Putman, Werf et al. 1994; Schaffer, Cleveland et al. 1996). In contrast, magnetic drive yields a broad response which matches the expected thermal response of the cantilever (Han, Lindsay et al. 1996). Comparative plots of amplitude as a function of frequency are given in Fig 9a (acoustic drive) and Fig. 9b (magnetic drive).A second difference lies with mechanics of the excitation. In acoustic excitation, the long-wavelength sound waves cause displacement of the cantilever holder (Fig 8a)
Figure 7: Showing amplitude decay (heavy curves) as a function of distance from a surface (the zero is arbitrary) together with a trace of the ac bending signal as the tip is swept towards a surface. At low frequency (a) the decay of amplitude follows the advance of the tip (dA/dz=1) in hard contact with the surface. At resonance (b) the slope is increased owing to damping. With a high Q cantilever at resonance (c) dA/dz approaches two as damping becomes symmetrical.
Figure 8: Illustrating (a) acoustic drive for DFM, (b) magnetic drive for DFM and (c) the origin of the residual bending signal when the tip contacts the surface with the base acoustically-driven. The optical detection system (not shown) responds to bending rather than absolute displacement.
so that the net bending signal is the difference between the displacement of the tip and the displacement of the holder. Writing the complex amplitude in this way and solving for the real part of the signal yields the following result
Here A0 is the amplitude of the drive applied to the holder and w0 and Q the resonant frequency and Q of the cantilever. Note that the response, A(w), drops to zero at zero frequency, in contrast to magnetic drive where the response is FM/k (Han, Lindsay et al. 1996). This can be seen in Fig. 9. The response of the acoustically driven cantilever falls to zero at low frequency, but is finite at low frequency in the case of magnetic drive.
Figure 9: (a) Tuning curve for acoustic drive: the sharp peaks correspond to mechanical resonances of the microscope. These are largely eliminated with magnetic drive (b).(From Lantz et al. (Lantz, Liu et al. 1999) with permission.)
This method of driving the cantilever results in a substantial background signal when the cantilever contacts the sample because of its low Q in fluid. In order to achieve a displacement A0 at resonance, the base of the cantilever must be moved by an amount A0/Q. For example, 3nm amplitude would require 1nm drive with Q=3. Thus, the base of the cantilever must be moved by a significant fraction of the desired amplitude, and this results in a substantial background signal when the tip of the cantilever is in contact with the surface, as illustrated in Fig. 8c. The exact amount of the signal will depend on the bending profile and the location of the laser spot. This residual signal is demonstrated in Fig. 10a which shows a plot of the oscillation amplitude for an acoustically driven cantilever as a surface is approached in water. Driven near resonance (25kHz) the signal falls to a little less than 2nm p/p on contact. The origin of the background is clarified by operating well below resonance (5kHz). In this case, the bending signal falls dramatically, approaching zero at zero frequency (Eqn. 14 and Fig. 9). The residual signal on contact is still present, with the result that the control signal is reversed at low frequency (Fig. 10a).
Figure 10: (a) Approach curves for acoustic drive near resonance (solid line) and well below resonance (dashed line). Note inversion of control signal. (b) shows approach (heavy solied line) and retraction (heavy dashed line) for magnetic excitation. Average force is shown as the light lines (solid is approach, dashed is retraction). (From Lantz et al. (Lantz, Liu et al. 1999) with permission.)
This problem is not present with magnetic drive where the cantilever bending signal falls to zero as the surface is contacted (Fig. 10b). Some residual signal is possible with the softest cantilevers because the first bending mode with both ends of the cantilever pinned can have a significant amplitude, but with the cantilever used in this case (k=0.5N/m) this motion was below the level of thermal and other background noise in the instrument. The data for Fig. 10b were obtained well below resonance, so the region labeled "1" where dA/dz<1 corresponds to a region of ‘soft contact’ in which the motion of the tip is not stopped abruptly at the interface. We show below that the tip probably does not contact the surface at all in this region, sensing the interface by changes in the fluid that extend nm away from the surface. The region where dA/dz=1 is labeled "2". The static deflection signal (obtained by filtering the output of the detector) is shown as the thin solid line and this does not begin to rise, indicating contact, until close to the point ("3") where the DFM signal falls to zero. In this experiment, the tip was pushed hard into the surface by continuing the advance many hundreds of nm (not shown) so that, on retraction, the average deflection signal (thin dotted line) showed the hysterysis characteristic of adhesion ("5"). The corresponding DFM signal remained at zero (heavy dashed line) until the tip jumped off the surface ("6") at which point the DFM signal was restored to about half its maximum value, indicating that much (if not all - see below) of the swing is out of contact with the surface in the region labeled "1".
The tuning curve shown in Fig. 9b was obtained from an early instrument and it shows signs of some spurious mechanical resonances (sharp peak near 15kHz). We have found that noise increases significantly with such resonances, suggesting that mechanical excitation of the microscope contributes to the noise background. With care all spurious resonaces can be eliminated, and it is useful to obtain a tuning curve prior to imaging in order to ensure that the cantilever really is magnetically excited.
