2.6.1 Amplitude Modulation
As was discussed in the previous section a good alternative for static mode is the lock-in mode, an amplitude modulation mode. In amplitude modulation mode the difference in amplitude is used as a measure for the force between tip and sample. The amplitude is kept constant by adjusting the z-scanner during scanning in the x- and y-direction. A schematic view of this mode can be seen in figure 2.17. The red color indicates a phase shift with respect to the detected phase, which is in this case 90 degrees at resonance. The dither is driven with a fixed amplitude and frequency. The detector signal is AC coupled into a gain to get a pure AC signal with the desired amplitude. The analog signal is then converted to a digital signal that enters the PLL unit. In lock-in mode the PLL unit is only used as a lock-in amplifier to extract the amplitude and the phase.
These signals can be used for the feedback loop to move the z-piezo. The raw signal is also filtered and can be monitored. Under ambient conditions this is the most used mode to operate an AFM.
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Figure 2.17: Schematic view of the lock in mode. The red color indicates a phase shift with respect to the detected phase.
2.6.2 Frequency Modulation
If the cantilever operates at low temperatures and at low pressures the quality factor will increase. This increase in Q gives a higher sensitivity but also has two drawbacks. First of all the amplitude used as a measure for the tip-sample force needs a long measuring time to become stationary, as was shown in the previous paragraph. This leads to a low scanning speed in amplitude modulation mode.
Another disadvantage is that the resonance peak becomes very narrow. If the cantilever is now driven with a fixed frequency and the resonance frequency changes due to tip-sample interactions the peak will shift and the cantilever is driven off resonance and imaging becomes impossible. The best way to solve this is to add an additional feedback loop to the system to constantly change the drive frequency in order to match the resonance frequency. This is the principle of the two frequency modulation modes.
Self Oscillation Mode
In self oscillation mode the detector signal is phase shifted and used to drive the dither. The variable loop gain is used to make sure the drive amplitude remains the same. In resonance the phase difference between the dither and the tip of the cantilever is 90 degrees. The detected signal of the cantilever is used to drive the dither directly. Therefore a phase shift is needed in order to match the new and the old drive oscillation in a continuous fashion, see figure 2.18. On average the frequency of the tip is equal to the frequency of the dither but on short time scales the frequency changes a bit to adjust to the new resonance frequency. The new resonance frequency will get amplified and then gets fed back into the system as the new drive signal. This means that the drive frequency shifts together with the resonance frequency and the cantilever always oscillates in resonance. In this way it is possible to image with high Q. A constant height distance between your tip and sample can be achieved if
∆f , the frequency shift, is used for z-feedback. There are two disadvantages in this mode. If two resonance peaks of the cantilever are relatively close together the drive frequency can jump between these peaks. A second disadvantage is that the movement of the tip is not completely sinusoidal. This means that the drive amplitude is also not completely sinusoidal and this can enhance itself and distort the signal.
Phase Locked Loop Mode
The phase locked loop mode (PLL mode) solves the problems of the self oscil-lation mode. In figure 2.19 the schematic view of the PLL loop can be seen. In the PLL mode the drive oscillation is determined by an external oscillator. This gives a perfect sinusoidal drive oscillation. The signal of the tip oscillation is then analyzed to give the frequency and the phase. The sinusoidal drive signal is forced to oscillate with the measured frequency and the phase is now shifted by a predetermined amount to force the cantilever to oscillate at the right reso-nance peak. As for self oscillation mode the feedback to the z-piezo is governed by the change in resonance frequency. In figure 2.20 the narrow resonance peak can be seen. As the tip-sample force increases the peak shifts. In AM mode the peak was broader and the amplitude difference was used to measure. This can not be done with the narrow peak since there would be no amplitude left
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Figure 2.18: Schematic view of the self oscillation mode. The red color indicates a phase shift with respect to the detected phase.
even after a small frequency shift. Instead the PLL mode shifts the phase of the detected signal to make sure that the drive signal is on the new resonance frequency. The cantilever is thus always driven on resonance and the amplitude of the detected signal is thus almost constant for different tip-sample forces.
The NCO, numerically-controlled oscillator, is used to make the detected signal phase continuous. The phase shift is determined by doing a resonance sweep and checking what phase corresponds to the maximum amplitude. And because the phase shift is always the same in resonance the cantilever always oscillates at the right resonance peak. This is the most stable mode for high Q factors but it is also a bit slower because the signal has to be analyzed before a change in drive signal can be made.
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Figure 2.19: Schematic view of the PLL loop. The red color indicates a phase shift with respect to the detected phase.
Dw
Dw
Amplitude(a.u.) Phase(a.u.)
Frequency (a.u.)
Figure 2.20: Amplitude and phase shift as a result of the repulsive tip-sample interaction. The PLL loop forces the drive signal to drive the cantilever near resonance with a phase of 90o. As the tip-sample interaction changes the res-onance frequency changes and thus the phase changes. By keeping the phase locked at 90o the cantilever always oscillates on resonance.
Chapter 3
Experimental Setup and Problems
3.1 The AFM
The AFM that was used in this thesis is the AttoAFM-I. This AFM is designed by Attocube to work at low temperatures. The setup can be divided in four different elements: the scan head, the optics, the extension stick and the elec-tronics. The scan head as well as the extension stick are made of non-magnetic materials allowing operation in an externally applied magnetic field at cryogenic temperatures.