High-Accuracy Atomic-Force-Microscope Head For Dimensional Metrology

5th IFAC Symposium on Mechatronic Systems Marriott Boston Cambridge Cambridge, MA, USA, Sept 13-15, 2010

High-Accuracy Atomic-Force-Microscope Head For Dimensional Metrology ? D. Amin-Shahidi ∗ D. Ljubicic ∗ J. Overcash ∗∗ R. Hocken ∗∗ D. Trumper ∗ ∗

Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: d [email protected]) ∗∗ University of North Carolina at Charlotte, Charlotte, NC 28223 USA (e-mail: [email protected])

Abstract: We present the design and experimental results of a high-accuracy atomic force microscope head (HAFM) to be used for dimensional metrology. HAFM uses monolithic flexures which are designed for minimum error motion. A piezoelectric stack drives the head over a range of 20 µm. HAFM uses a self-sensing AFM probe, which is operated in constant-amplitude selfresonance, for frequency-measuring microscopy. A discrete-time surface-tracking controller is implemented on a real-time FPGA board. The controller tracks the surface by maintaining a constant self-resonance period. To avoid spurious mixing, the controller’s sampling is made synchronous to the self-resonance oscillations. Three capacitive displacement sensors directly measure the surface tracking motion. We have experimentally demonstrated surface tracking control with 100 Hz unity-crossover frequency, 70 degrees phase margin, and 0.12 nm RMS noise in a 100 Hz measurement bandwidth. We have also used the HAFM to measure calibration gratings and the surface of freshly cleaved sanded Mica sample. Keywords: Precision measurement, control system design, position accuracy, self-excited oscillations, frequency control. 1. INTRODUCTION

amplitude self-resonance mode in a frequency-measuring AFM configuration.

We have designed and tested a new high accuracy atomic force microscope (HAFM) to be used for dimensional metrology. The HAFM’s mechanical design was completed in the Master’s thesis of Ljubicic (2008). The instrumentation and control of HAFM are the subject of the present work, with the goal of enabling surface tracking with nanometer accuracy and sub-nanometer resolution. The HAFM is specifically designed to be integrated with the Sub Atomic Measurement Machine (SAMM), which has been developed in collaboration with the University of North Carolina at Charlotte in the Doctoral thesis of Holmes (1998). The paper by Hocken et al. (2001) also describes SAMM’s design and dimensional measurements made with a confocal microscope probe. The HAFM will supersede this confocal microscope in order to overcome optical resolution limits. The SAMM stage provides the inplane sample raster within a 25-mm by 25-mm range with 1-nm repeatability and better than 30-nm accuracy. In this configuration, the HAFM measures the sample surface in the out-of plane (Z) direction.

Using the probe’s feedback, HAFM’s closed-loop controller tracks the sample surface at a constant probe-sample gap. A piezoelectric actuator moves the probe over a 20-µm range. For lower error-motion, the HAFM uses monolithic flexures to constrain its moving stage. Three capacitive displacement sensors directly measure the stage’s tracking motion. In this paper, we present the HAFM’s design, dynamics, controller implementation and algorithms, and experimental results, including images of surfaces.

To sense the sample surface, the HAFM uses a commercial self-sensing and self-actuating Akiyama AFM probe, which is described in Akiyama et al. (2003). The probe eliminates the need for an optical lever sensing mechanism and results in a more compact AFM head. For better sensing bandwidth, we operate the probe in controlled? This work was supported by the National Science Foundation under contract DMI-0506898.

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2. MECHANICAL DESIGN The HAFM sits on the SAMM’s metrology frame using three ball-groove kinematic mounts. Fine-pitch threads on the three mounting feet on the HAFM allow adjustment of the tip-sample gap. The HAFM’s moving stage extends down into the SAMM, to reach the plane where the sample is mounted on the SAMM stage. The AFM probe is attached to the end of the HAFM moving stage and senses the sample surface. The HAFM stage moves the probe normal to the sample plane to keep a fixed probesample gap. Three capacitive displacement sensors are used to measure the tracking motion and determine the sample profile. While in principle only one displacement probe would be required to measure the single HAFM axis of motion, we used three probes symmetrically located around the periphery of the HAFM head in order to allow an open central bore for a bore scope which will be used to image the tip and sample. The use of three probes will 10.3182/20100913-3-US-2015.00111

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Fig. 2. Simplified diagram of the self-resonance system.

Fig. 1. Assembled HAFM with overlaid CAD crosssectional view. also allow us to measure two rotational error motions of the HAFM stage. Fig. 1 shows HAFM’s mechanical design. The probe is fixed to the bottom of the moving stage, which is constrained to axial motion by the guide flexure. A piezoelectric stack actuator drives the moving stage over a range of 20 µm. A decoupling flexure connects the piezoelectric actuator to the moving stage. Complimentary to the guide flexure, the decoupling flexure is stiff only in the axial direction, and hence attenuates off-axis error motions of the piezoelectric element by at least a factor of 80. Three ADE8810 capacitive displacement sensors, with a range of 50 µm, are symmetrically spaced around the moving target and measure its motion. To avoid measurement error due to forced deformation, we have designed HAFM with separate force and metrology loops. The components within the metrology loop are manufactured from INVAR to significantly reduce measurement error due to thermal deformations. 3. AFM PROBE Two major advantages of using an AFM probe for metrology are its high resolution (better than 1-nm) and very localized sensing (less than 15-nm tip radius). Typical AFM probes use an optical lever sensing mechanism to sense the tip’s motion. To enable a more compact design for integration with the SAMM, the HAFM uses a selfsensing probe which does not need an optical lever system. We use a commercial Akiyama probe; for more details on the probe operation see Akiyama et al. (2003). The Akiyama probe has a silicon V-shaped cantilever bridging the two legs of a quartz tuning fork. The AFM probe’s sharp tip is located at the apex of the V. The quartz tuning fork is electrically driven into oscillation via the piezoelectric properties of quartz, using electrodes on the tuning fork. The V-shaped cantilever is constructed such that lateral oscillation of the tuning fork legs results in amplified motion at the probe tip in the vertical direction, resulting in a tapping motion of the probe tip. The 228

Fig. 3. Experimentally captured frequency-measuring sensing curves for different oscillation amplitudes. cantilever reflects interaction forces between the tip and the sample into the tuning fork resonator dynamics. These dynamics can be sensed electrically as changes in the tuning fork’s electrical impedance, allowing measurement of the tip-sample separation. In the FM mode which we utilize, the probe resonance frequency is controlled by the feedback loop shown in Fig. 2 so as to maintain oscillation at the instantaneous natural frequency of the probesample system. By this mechanism, the probe-sample gap is maintained at a constant value within the bandwidth of the tracking loop, and the tracking dynamics are not limited by the low damping of the probe resonance. The Akiyama probe has a high quality-factor, which improves the probe’s sensitivity but correspondingly slows the decay rate of transients. Long lasting transients would reduce the probe’s bandwidth if the probe were used in an amplitude-measuring (AM) mode. Albrecht et al. (1991) presents a frequency-measuring (FM) mode which has a bandwidth which is independent of the probe’s qualityfactor, and hence can achieve high sensitivity without sacrificing bandwidth. An FM AFM uses the probe’s resonance frequency, which shifts with the tip-sample gap, as the feedback variable. In this mode, the probe is moved up and down to maintain a constant self-resonance frequency, corresponding to a fixed tip-sample gap. For more details, see Garcia and Perez (2002) which provides a review of frequency-measuring AFM control.

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The specifics of our FM mode implementation are similar to the design in NanoSensors (2009). Fig. 2 shows a schematic of the self-resonance system, which implements a self-excited oscillator in which constructive positive feedback is used to create self-resonance. The electrical terminals of the probe are driven with a sinusoidal voltage V , and the resulting probe current im is amplified by a transimpedance amplifier to yield a voltage Vm . The output signal Vm is phase shifted by an all-pass filter to provide constructive feedback at resonance, that is, to maintain the net loop phase shift at zero degrees at the resonant frequency, which is a first required condition for sustained oscillation. The feedback gain of this loop is set by the amplitude controller input to a multiplier in order to maintain a constant oscillation amplitude. This is accomplished by maintaining the average loop gain equal to unity at the frequency where the net phase shift is zero, which is a second required condition for sustained oscillation. The phase-shifted and scaled signal (V ) is used to excite the probe, thereby closing the loop. The self-resonance frequency of the probe operating in controlled-amplitude self-resonance can be used as feedback on the tip-sample gap. Fig. 3 shows the AFM probe’s sensing curves at different self-resonance amplitudes captured over several approach-retract cycles. The probe’s sensitivity is found to be inversely proportional to the oscillation amplitude. This makes sense, since the tip-sample contact interaction can be most simply modeled as a spring which is added to the stiffness of the probe. The addtional stiffness will increase the natural frequency of the probe. As the tip approaches the sample, the duty cycle of the probe’s contact with the spring, i.e., the proportion of time that the tip is in contact with the sample, increases, and thus has a larger effect in increasing the natural frequency. The duty cycle of the spring depends on the approach distance normalized to the amplitude of oscillation, which explains why the sensitivity is inversely proportional to the oscillation amplitude. However, there is an oscillation amplitude below which stable self-resonance cannot be sustained. In the data of Fig. 3 we see that the lowest current amplitude for stable self-resonance is 24 nA. For the lower value of 22 nA, the probe oscillation is not stable as a function of displacement. We also see that even for stable curves, the retract curve is below the approach curve and contains discontinuities, which become more significant as the minimum oscillation amplitude limit is approached. These effects are likely due to probe-sample adhesion to the surface, and are expected to depend upon adsorbed water on the sample surface. For the probe under test, we found that at the minimum stable oscillation amplitude of 24 nA, the probe has a sensitivity of 0.78 Hz/nm relative to the probe selfoscillation frequency of about 46.65 kHz. 4. SURFACE TACKING CONTROL 4.1 Overall Configuration The surface tracking controller moves the probe to maintain a constant tip-sample gap. Fig. 4 shows the block diagram of the overall HAFM system. The Akiyama probe measures the tip-sample gap. A pre-amplification board, 229

Piezo Driver (PI510.00®)

DAC 16 bits

Capacitive Displacement Sensor (ADE8810)

ADC 20 bits

VP

NI Real-Time Controller HAFM Head Akiyama Probe

X-Y Scan Control

Sample X-Y Scanner (S.A.M.M.)

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VIN Amplification Self-Resonance CLKSR Board VOUT Control Board

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FIFO 200-MHz edge timer

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notch filter

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Fig. 4. Overall HAFM system diagram (top); controller and period estimation blocks (bottom). which is located close to the probe, amplifies and conditions the probe’s output signal and compensates for probe stray capacitance. The self-resonance control board establishes the probe in controlled-amplitude self-resonance. The self-resonance signal CLKSR is a square wave which is obtained by applying the approximately sinusoidal signal representing current passing through the tuning fork to the input of a precision comparator. The comparator output CLKSR is passed to the digital controller. A National Instruments real-time FPGA board is used to implement surface tracking control. The controller commands the piezoelectric actuator to maintain a constant self-resonance period, corresponding to a fixed tip-sample gap. Three ADE8810 capacitive displacement sensors with a range of 50 µm are used to measure the surface tracking motion with 0.18 nm RMS noise at 1-kHz sensor bandwidth. 4.2 Per-Crossing Period Feedback The probe’s resonance frequency changes approximately linearly with the gap, and is used as the feedback variable. More specifically, we use the probe’s self-resonance period as the feedback variable, as measured using a 200 MHz digital counter. This counter is used to measure the period between the zero-crossings of the self-resonance signals with 5-ns resolution. However, at the approximately 96 kHz zero-crossings rate, ±5-ns resolution is equivalent to only 50-Hz resolution, which corresponds to approximately 100 nm uncertainty associated with each raw period measurement. This raw error is unacceptable, given the need for subnanometer resolution. However we recognize that this noise is associated with a single measurement at the 96 kHz loop sample rate. One way to address this noise

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would be to add a filter which averages the periods of multiple zero-crossings. However, such a filter will create an additional measurement phase lag. Instead, the closed loop control system, with about 100 Hz crossover frequency, acts as a 100 Hz low pass filter, and thus the measurement noise is only followed up to about 100 Hz. Said another way, the loop itself acts upon the average of about 1000 samples of the period measurement within the 100 Hz loop bandwidth. This low-pass inherent in the loop bandwidth allows good resolution to be obtained without using additional filtering in the loop, and thus avoiding additional phase lag and reduction in loop stability. A simplified block diagram of the control and period estimation blocks are shown in Fig. 4. To achieve high resolution, it is essential that the high-frequency content of the period measurement error is efficiently filtered. The conversion of the period estimates to a frequency value requires a non-linear division operation which can cause mixing of the frequency content due to the nonlinearity. To prevent this, we instead use period feedback, which is expected to be more closely linear with the tip-sample gap given the small variations. Additionally, we have to address the fact that the edges of the self-resonance signal CLKSR occur asynchronously with respect to the FPGA clock signal CLK200M Hz . Because of this lack of synchronization, if we update the control loop on the basis of a fixed frequency with respect to the FPGA clock, there will result an apparent jitter in the period of CLKSR which will appear as noise in the tip-sample gap. Said another way, the lack of synchronization will result in folding of out-of-band signals in CLKSR into our measurement band. To avoid such mixing, we instead update the tracking control loop period measurement synchronously with the edges (zero-crossings) of CLKSR . Since CLKSR has a frequency of about 48 kHz, we thus update the tracking loop at twice this frequency or about 96 kHz.

4.3 Loop-Shaping Controller Design We have designed a discrete-time surface tracking controller using loop-shaping techniques. Fig. 5 shows the Bode plot of the open-loop plant transfer function from the piezo driver command voltage (Vp ) to the self-resonance period (TSR ). The two resonance peaks at 1.6 and 2.3 kHz are believed to be structural resonances of the head and impose the dynamic limits on closed-loop bandwidth. The probe’s sensing mechanism shows adequate bandwidth up to the resonances, as can be seen by the near-zero plant phase shift through 200 Hz. We use two notch filters in the controller to mask the resonances in the loop. An integrator is used in the controller to create a -1 slope at the unity-gain crossing. A low-pass filter (LPF) is used to further attenuate the high frequency measurement noise above the loop crossover. We have thus achieved a unity gain cross-over frequency of 100 Hz with 70 degrees of phase margin. The 16-bit DAC which commands the piezo driver amplifier is updated at the 96 kHz edge rate. Due to converter data rate limitations, the 20-bit ADC converter which measures the capacitance probe outputs is sampled at a 7 kHz rate to form image data. 230

Fig. 5. Bode plots of the open-loop plant (solid) and compensated loop transmission (dashed).

Fig. 6. HAFM’s response to a 100 nm equivalent step disturbance injected at the piezo-driver input VP , operating with respect to a fixed sample. The probe motion is measured using the capacitive displacement sensors at 1000 Hz and 100 Hz measurement bandwidths as shown in the figure.

Fig. 7. Active tracking of a stationary sample measured using the capacitive displacement sensors at 1000 Hz and 100 Hz measurement bandwidths.

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Charlotte, where it is currently being integrated with the SAMM system. In the near future, the HAFM/SAMM system will be tested for high accuracy dimensional metrology. ACKNOWLEDGEMENTS We wish to thank Dr. Georg Fantner and Mr. Dan Burns at MIT for providing us access to their AFM scanner and helping us with capturing the images. This work was supported by the National Science Foundation under contract DMI-0506898. REFERENCES Fig. 8. Image of TGZ01 and TGX01 gratings captured at 5 µm/s and 10 µm/s scan speeds, respectively. 5. EXPERIMENTAL RESULTS The HAFM can only move in the single degree of freedom normal to the sample plane, and relies on an external stage for in-plane sample scanning. For initial testing, we operated the HAFM with a stationary sample in order to characterize the loop bandwidth, transient response and measurement noise. Fig. 6 shows the HAFM response to a step disturbance added to the piezo-driver input VP . Here the loop acts to reject the applied disturbance with the dynamics shown in the figure. Fig. 7 shows the tracking noise relative to a fixed sample, as the average of the three capacitive displacement sensors’ readings. The tracking noise is 0.12 and 0.24 nm RMS at 100 and 1000 Hz measurement bandwidths, respectively. The noise is dominated by the noise of the capacitive displacement sensors and by mechanical vibration at frequencies corresponding to the structural modes of the HAFM. In order to test the HAFM in imaging, we needed to use an external scanner to move the sample in X and Y , while tracking in Z with the HAFM. We tested the HAFM for imaging by interfacing it with a Veeco MultiMode E piezo-tube scanner with the help of Dan Burns and Dr. Georg Fantner at MIT. We were able to successfully image several samples, including standard gratings and sanded freshly cleaved mica. The tracking noise and bandwidth performance were the same as in the single-point tests presented above. Fig. 8 shows images of TGZ01 and TGX01 gratings scanned at 5µm/s and 10-µm/s scan speeds respectively. The gratings are manufactured by MikroMasch and are commercially available. We measured an average step height of 25.6 nm for TGZ01, which is within the gratings’s specified height of 25.5±1 nm. The TGX01 grating is manufactured with high in-plane accuracy, but is not specified for dimensional accuracy in the normal direction. The TGX01 is shown here as an example of an imaged sample with larger vertical feature sizes. 6. CONCLUSION The high accuracy AFM head (HAFM) is designed to be integrated with the sub-atomic measuring machine (SAMM) and be used for dimensional metrology. We have transferred HAFM to the University of North Carolina at 231

Akiyama, T., Staufer, U., and de Rooji, N. (2003). Symmetrically arranged quartz tuning fork with soft cantilever for intermittent contact mode atomic force microscopy. Review of Scientific Instruments, 74, 112–117. Albrecht, T., Horne, D., and Rugar, D. (1991). Frequency modulation detection using high-q cantilevers for enhanced force microscope sensitivity. Journal of Applied Physics, 69, 668–673. Garcia, R. and Perez, R. (2002). Dynamic atomic force microscopy methods. Surface Science Reports, 47, 197– 301. Hocken, R., Trumper, D., and Wang, C. (2001). Dynamics and control of the uncc/mit sub-atomic measuring machine. CIRP Annals - Manufacturing Technology, 50, 373–376. Holmes, M. (1998). Analysis and Design of MagneticallySuspended Precision Motion Control Stage. Ph.D. thesis, University of North Carolina at Charlotte. Ljubicic, D.L. (2008). Flexural based high accuracy atomic force microscope. Master’s thesis, Massachusetts Institute of Technology. NanoSensors (2009). Akiyama-Probe (A-Probe) technical guide. http://www.akiyamaprobe.com.