Interferometer*** ** Electrical connection to the piezos through Fisher plugs.
*** Gain/Filter stage is controlled by switches.
USB connection
* Ideally, for AFM/MFM applications, the connection from the piezos to sample/cantilever is purely mechanical.
Figure 4.11: Electronic schematic of the experimental setup. The MFM is build up of two systems that can be controlled separately. For a detailed description about the setup, see the text.
The low temperature magnetic force microscope that was optimized, is based on the attoAFM–I design. As with all low temperature scanning microscopes, our MFM is a fairly complicated instrument. The functional completed instrument is a powerful tool for characterizing materials through high resolution magnetic imaging.
In this section, we will discuss the most complicated part of the setup, the electronic components. In Fig. 4.11 the electronic schematic is shown. It consists of two systems: The attocube setup and the RHK setup, indicated by the two purple boxes. In the attocube setup the SPM control unit is the ASC500. In the RHK setup the ASC500 is replaced by the SPM1000 SPM control unit and the PLLPro2 lock–in amplifier, and an additional power source is added to control the dither piezo. In the following paragraphs, we shall discuss the various components of both electronic setups and discuss the differences between both setups.
4.4.1 The attocube setup
The attoAFM–I consists of a control unit, which is the ASC500 and two piezo controllers, the ANC150 and the ANC300 to control the positioners and the scanners, respectively. The ANC150 controls the piezo positioners that are used for the coarse approach. The ANC300 controls the piezo scanners and provides an additional amplification of ×15 to the output voltage. The controller is equipped with an input second order low–
pass filter, which in normal operation filters out voltages above 160 Hz. Before the voltage is applied to the piezos, the signal is submitted to an additional low–pass filter, which filters out all of the frequencies above 1600 Hz. The ANC300 has an additional axis, which is used to control the dither piezo. In the attoAFM–I setup, both ac (excitation) and dc (setpoint) voltages for controlling the dither are supplied by the control unit. The attocube system is mainly used for alignment and calibration of the cantilever. In this case, the interferometer operates in dc mode, in full bandwidth (FBW) with an amplification of 106(Low Noise). If the photodetector is operated in ac mode, the user does not have control over the working point (the ‘sweet spot’) of the interferometer. The working point of the interferometer can be calculated from the dither spectroscopy, as can be seen in Fig. 4.12. For best results, the interferometer has to be tuned (and repeatedly retuned) to the quadrature point, i.e. in the middle between minimum and maximum, since this point provides the highest sensitivity. Without the dc component of the detector signal, this cannot be done.
dV
dd
l/2
Working point
Intensity[a.u.]
Distance d [a.u.]
Figure 4.12: Schematic drawing of the interference signal. When the cantilever is placed in the working point, the sensitivity is the highest, since the cantilever displacement gives the largest change in intensity. The position of the cantilever with respect to the working point is controlled by the dc voltage that is applied to the dither piezo.
There are a few drawbacks in using the attoAFM–I setup for high–sensitivity measurements. First of all, the control unit is not as stable as the SPM1000/PLLPro2 combination and it does not deliver the low–level noise voltages that are necessary for these kind of experiments. Furthermore, the attoAFM–I only allows for indirect adjustment of the tilting of sample (slope correction). Since topographic features of flat samples usually are much smaller than the tilting of the sample, this puts a constraint on spatial resolution. On top of this, the RHK setup is equipped with a broad range of gain and filtering stages and different modes of operation.
This can be very useful when switching from ambient conditions to low temperatures. On top of this, the PLLPro2 is capable of very precise determination of the resonance frequency, which is particularly useful for frequency–modulation operation. The attoAFM–I setup however, is particularly useful for mounting of the cantilever and can be used to verify results of the RHK setup.
4.4.2 The RHK setup
The RHK setup consists of the SPM1000 universal SPM controller and the PLLPro2 phase–locked–loop am-plifier. In Fig. 4.11, four lines are drawn from the PLLPro2 to the SPM1000, these lines represent the DAC1–4 channels of the PLLPro2‡‡. The DAC1 channel serves as a feedback (FB) channel for the SPM1000, whereas the DAC2–3 channels provide the additional parameters which are used by the SPM1000 to control
‡‡DAC means digital–to–analog converter, whereas ADC means analog–to–digital converter
the movement of the scanner piezos. Depending on the mode of operation, the DAC1 represents the change in amplitude ∆A (amplitude modulation), the change in frequency ∆f (frequency modulation) or the change in phase ∆ϕ (phase modulation). When operating the RHK setup, it is advised to monitor the different channels of both SPM1000 and PLLPro2. This can be done with an oscilloscope, for instance with the LeCroy 9400 Dual 125 MHz digital oscilloscope, which has been added to the setup. It operates at sample frequencies up to 125 MHz, which is much higher than the frequencies that are relevant under normal SPM operation (∼ 80 kHz) or the operating frequencies of the PLLPro2 components (≤ 20 MHz).
Similar to the attoAFM–I setup, the output voltage of the interferometer serves a feedback input channel for the PLLPro2. In this case however, the interferometer has be operated in ac mode, since the feedback input channel of the PLLPro2 cannot handle voltages ≥ 1.0 V. The dc voltages for the dither piezo are supplied by a δ–Electronics ES015–10, which produces up to 15 V in continuous volt (CV) mode and up to 10 A in continuous current (CC) mode. Since the PLLPro2 does not control the dc–component of the feedback signal input, it is of utmost importance that the dither voltage is very stable, to prevent the working point of the interferometer from drifting away from the point of maximum sensitivity. Also thermal fluctuations, e.g.
internal heating, and/or mechanical fluctuations, e.g. drift or creep, can result in a shift of the working point of the interferometer. This can be troublesome when scanning at high resolution (≥ 1024 pixels/line) over small topographic areas (≤ 1.0 µm) with slow scan speed parameters (≤ 500 nm/s). In this case, it is important to correctly set up the feedback parameters on the SPM1000. A possible solution might be to employ what is called closed loop scanning. In this case, both lateral and normal force deviations of the cantilever are monitored by positioning scanners. The PLLPro2 can be upgraded with a four quadrant position sensitive detector (PSD) that monitors the light intensity and converts these signals into normal force, lateral force and total force and then normalizes them. By subsequently re–adjusting the z scanner position in combination with excitation parameters, such as phase and amplitude, deviations from the point of maximum sensitivity can be compensated. If stable operation is achieved, the parameters that control the resolution can be enhanced.
The SPM1000 has a DT3016 board with a programmable gain that can acquire 16 bit resolution data that is spread over a 20 Volt range (0.305 mV least significant bit (LSB)) or as small as 2.5 Volt (0.0381 mV LSB). For a detailled description on how to enhance the resolution by means of gain adjustment, the reader is referred to [71].
Both RHK and attoAFM–I setup make use of the ANC150 for coarse approaching. The method of ap-proaching is done by auto–apap-proaching the tip (in our setup the sample is moving) in what is called the tip
‘retract–mode’, which means that the z scanner is repeatedly being extended after the approach step has been made and retracted before the next approach step is engaged. The approach speed depends on the amount of time is takes to extend and retract the z scanner and the distance that is being traveled per approach step.
From table 4.2, one can see that the distance traveled in one approach step under ambient conditions is 290 nm in the upward direction, which is much smaller than half of the maximum extension length of the z scanner piezo. The total time of approaching of course also depends on the tip–sample distance, but as a result of the optical control system this distance can be shortened quite easily.
4.4.3 Modes of operation
The RHK setup offers a variety of possible modes of operation in combination with a wide range gain/filter stages [76, 71], which shall be discussed in the proceeding paragraphs. The type of operation mode for the acquisition should be set in the settings/operating modes to correctly set the feedback and output channels between the SPM1000 and the PLLPro2. The mode of operation under discussion here is the PLLPro Master acquisition configuration suitable for noncontact AFM and MFM applications.
Lock–in mode
This mode of operation uses the amplitude modulation scheme, as explained in detail in chapter 2.2.1. This mode of operation is most frequently used when working under ambient conditions. This mode of operation is especially useful for coarse approaching and determination of the cantilever properties, in particular the resonance peak. In this mode the PLLPro2 acts like a lock–in amplifier and measures the amplitude of the cantilever oscillation and the phase shift between excitation signal and detection signal. In order to perform closed loop scanning, as discussed in section 4.4.2, the lock–in mode also makes available the normal (IPSD) and the quadrature (QPSD) signals of the phase detector. The relationships that exist between the amplitude A, the phase ϕ, the normal signal IPSDand quadrature signal QPSDare displayed Fig. 4.13 and can be expressed
Normal
Figure 4.13: Various modes of operation for the RHK setup. The purple colored components are all integrated in the PLLPro2 and are controlled by the software. Three possible modes of operation are displayed, the lock–in mode, the self–oscillation mode and the PLL mode. The lock–in mode uses the same components of the PLLPro2 as in PLL mode, but the output parameters are different as indicated in the figure (also see table 4.4). Points where the phase is shifted with respect to the detected phase are indicated in red.
mathematically by A = p
IPSD2 + Q2PSD and ϕ = tan−1(Q/I)PSD. In table 4.4, the output parameters for the different mode of operations are listed. The DAC1 output parameter is always the parameter for the feedback (FB) and the other 3 DACs, of which DAC2 is the most important, are fed to the channels 4–6 of the SPM1000. All of the various modes are able of switching between constant excitation (CE) mode and constant signal (CS) mode. In CE mode, the probe drive amplitude (Aexc) is kept constant, whereas in CS mode the amplitude of the detector signal (Aosc) is kept constant, also see section 2.2.3. This is done by the proportional integral and derivative (PID) controller, which allows the user to adjust the proportional gain value, and integral and derivative cutoff frequencies§§. In lock–in mode, only the values for the amplitude modulation can be adjusted. In general, the proportional gainVp/Vrms] accounts for fast modulations in the feedback signal and the integral cutoff [Hz] controls the slow deviations in the feedback signal. The value for the proportional gain can be estimated from the excitation amplitude, typically ∼ 2 − 3. Higher proportional gain factors should be avoided since this would cause unstable operation. The integral cutoff value can be estimated from the resonance peak value divided by the Q factor of the cantilever, which corresponds to the 3 dB width of the cantilever amplitude resonance peak. The derivative cutoff frequency should be much larger than the resonance peak frequency (∼ 80 Hz). As mentioned before, the lock–in mode is unfavorable when working at low temperatures and/or low pressure when high Q values are apparent (chapter 2.1 and chapter 2.2.1) as this would imply long measurement times. Another disadvantage is that a high Q factor implies a narrow resonance peak. If the resonance peak is shifted due to sample–tip interaction, the cantilever would be driven off resonance very rapidly and imaging becomes impossible.
Self–oscillation mode
Both self–oscillation and PLL mode use the frequency modulation scheme, as explained in chapter 2.2.2. In self–oscillation mode the PLLPro2 phase shifts and amplifies the detector signal and feeds it back into the probe drive output for cantilever excitation. The PLL is not part of the excitation loop this way, it is only used as a device for detecting amplitude and frequency of the cantilever oscillation. This amplitude signal serves
§§In literature, the PID controller is often referred to as the APIC or DPIC, which stands for amplitude proportional integral controller and distance proportional integral controller, respectively, see for instance Nony et al. [77] for a detailed description of phase–locked–loop excitation and detection methods.
Table 4.4: Output parameters for different modes of operation, although both the self–oscillation and the PLL mode use the same parameters, the operation is completely different.
Mode of operation DAC1 DAC2 DAC3 DAC4
Lock–in mode A ϕ IPSD QPSD
Self–oscillation mode ∆f A fexc ϕ
PLL mode ∆f A fexc ϕ
as an input for a PID controller for CE and CS mode operation. The proportional gain is then expressed in terms of [Hz/Hzrms], here Hzrms denotes the root mean square value of the detected frequency. 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 scanner feedback signal. Running the PLLPro2 in self–oscillation mode also has the advantage of a fast feedback of cantilever oscillation disturbances into the probe drive. The disadvantage is that the user has little influence on what resonance the system oscillates at. This means that if two resonance peaks of the cantilever are relatively close together, the drive frequency can jump between these peaks. Another 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. It is therefore not advisable to run a cantilever with multiple resonances in self–oscillation mode.
PLL mode
In PLL mode the PLL is an essential part of the cantilever excitation loop. The digital PLL consists of three subblocks; a numerical controlled oscillator (NCO), a phase detector (PD), and a filtering stage consisting of a decimation filter and a finite impulse response (FIR) low–pass filter in series that is discussed in the next paragraph. The probe drive signal is derived from the PLL reference oscillator. The PLL receives the signal of the oscillation divided by Arms(t) plus an external parameter the ‘center frequency’, fcent= ωcent/2π. fcent
specifies the frequency to which the input signal has to be compared to for the demodulation frequency stage.
The NCO generates the digital sine and cosine wave forms of the time–dependent phase ϕPSNCO(t) + ϕPLL(t), ideally identical to the one of the input signal. ϕNCO(t) is correlated to the error that is potentially produced while the frequency demodulation, upon operating conditions. The sine and cosine wave forms are then send to a digital phase shifter which shifts the incoming phase ϕNCO(t) + ϕPLL(t) by a constant amount ϕPSset by the user. Since the cantilever is usually driven at f0, ϕPSis adjusted to make that condition fulfilled, namely ϕNCO(t) + ϕPLL(t) + ϕPS= fω0t, (4.19) in which fω0(t) denotes the fundamental bending resonance frequency, slightly shifted by the tip–sample in-teractions. At optimally operation ϕPLL ≃ 0 and the PLL produces the phase locked to the input, that is, ϕNCO(t) + ϕPLL(t) ≃ fω0t − π/2. Therefore, ϕPS has to be set equal to +π/2 rad to maintain the excitation at the resonance frequency prior to starting the experiments, consequently ϕ = −π/2 rad. The block output sin [ϕNCO(t) + ϕPLL(t) + ϕPS] is converted into an analog signal and then multiplied by the PID output, thus generating the full ac excitation applied to the piezoelectric actuator to drive the cantilever. Running the PLLPro2 in PLL mode has the advantage that the cantilever is driven with a clean sinusoidal wave that virtually has no distortions. Also the system can be limited to oscillate only on one resonance peak, even if another one is in the vicinity. The disadvantage of this mode is that due to the bigger group delay along the signal path through the PLL it takes longer for distortions of the cantilever oscillation to propagate through the PLL and then back to the probe drive signal.
Gain– and filter stages
In all three different modes, the user can apply different gain– and filter stages for the PLL. The first gain–
filter stage is a low–pass filter for the A/D channel, which default is set to 1 kHz at a gain–factor of 8. This
filter–stage is mainly used for static mode of operation. For dynamic mode of operation, the PLL uses two different gain stages, one for the input and one for the output signal. For all three modes of operation, the output–gain is controlled automatically by the software. It can be controlled manually as well, but this often imposes additional noise levels. The input–gain stage can only be controlled manually in lock–in mode, but both in self–oscillation and PLL mode is done automatically. In Fig. 4.11 theNsymbol represents the variable loop gain filter stage for the lock–in and PLL mode operation. The front panel for the PLLPro2 has a number of pre–set choices to select the PLL loop filter. These filters differ in their bandwidth and in their frequency resolution. Each filter has a name that contains the cutoff frequency and, separated by a colon, the system clock division rate. For each cutoff frequency, ranging from 10 Hz to 4 kHz, the user can choose between zero–, first– and second–order filters. Zero–order filters attenuate the input power by half or 3 dB. First–order filters will reduce the signal amplitude by half (so the power is reduced by 6 dB) every time the frequency doubles (goes up one octave), or more precisely, the power rolloff approaches 20 dB per decade in the limit of high frequency. Third– and higher–order filters are defined similarly. In general, the final rate of power rolloff for an order–n all–pole filter is 6n dB per octave (i.e., 20n dB). Generally a narrower bandwidth lowers the noise but is slower and has a narrower PLL catch range. Besides the low–pass filters, the PLLPro2 also has a finite impulse response (FIR) filter, which is a type of a discrete–time filter. The impulse response, the filter’s response to a Kronecker delta input, is finite because it settles to zero in a finite number of sample intervals.
The difference equation that defines the output of an FIR filter in terms of its input is¶¶
The difference equation that defines the output of an FIR filter in terms of its input is¶¶