CONSIDERATIONS FOR CRYOGENIC AFM OPERATION

Transcription

1 White Paper MK-WP101_01 Sept 2017 CONSIDERATIONS FOR CRYOGENIC AFM OPERATION Authors: Ryan A. Murdick, Ph.D. Product Development Scientist at Montana Instruments Cryogenic environments increase the Q-factor of an AFM dramatically, which can amount to an enhanced sensitivity if correctly implemented. This typically requires the operator to understand how the resonator s properties (amplitude, phase, resonance frequency) change in both magnitude and polarity, the pitfalls that can occur, and how they are manifest in the measurement. While an increase in sensitivity seems desirable, things that were literally in the noise in ambient conditions can become formidable at low temperatures Montana Instruments Corporation, All Rights Reserved

2 Considerations for Cryogenic AFM Operation 2 Considerations for Cryogenic AFM Operation Ryan A. Murdick, Ph.D. Product Development Scientist at Montana Instruments AFM RESONATORS - A BRIEF HISTORY An Atomic Force Microscope (AFM), at its core, is a resonator under feedback. Cantilevers and Quartz Tuning Forks (QTFs) are examples of commonly used mechanical resonators for AFMs. By adhering a nano-sized tip on the end of the resonator and manipulating the tip into close proximity with a surface, the mechanical resonator will sense the surface in the form of a change in its oscillation amplitude, phase, and resonance frequency. Monitoring the resonator s changes and adjusting the tip-sample distance in response to them defines the basic AFM. While ambient AFM is now a well established technique, this paper aims to highlight some of the key considerations in operating an AFM at cryogenic temperatures. Specifically, an overview of resonator choices is given (cantilevers VS Quartz Tuning Forks), and high Q-factor AFM operation is discussed at a basic level, including noise considerations, feedback methods, and sample characteristics. CANTILEVERS VS QUARTZ TUNING FORKS Cantilevers (or Microcantilevers) Monitoring the resonator has come a long way since the mid 1980 s when the various Stanford/Zurich/IBM groups were pioneering their way through SPM. 1,2 The first batch of fabricated silicon based microcantilevers for AFM were fabricated by Tom Albrecht in the clean rooms at Stanford. 3,4 Albrecht s efforts paved the way for the AFM breakthrough that occurred in the late 80 s 2,5,6, as they became available on a much grander scale to the various researchers involved with AFM at that time. Back then, they actually used Scanning Tunneling Microscopy (STM) as a means to monitor the tip position by tunneling into the back of the cantilever! 6 Today, ambient AFMs generally employ a diode laser reflected off the back of the cantilever and captured by a 4-quadrant photodetector, which can very precisely monitor changes in the cantilever s oscillation. As the sale of commercial AFMs boomed through the 1990 s through companies like Digital Instruments, Park Scientific, and Molecular Imaging, the necessity for AFM cantilevers would naturally spawn the industry associated with their fabrication. Today it is very easy to purchase AFM cantilevers off-the-shelf with sharp tips and extremely well-defined mechanical resonances from many sources. Quartz Tuning Forks The first microscopy paper involving a QTF was from Gunther, Fischer, and Dransfeld in Khaled Karrai et al. pioneered some of the early QTF discovery by employing the QTF as a height sensor for near-field measurements. 8,9 In addition there has been a great deal of UHV/low temperature measurements with QTFs, 10,11 which is primarily where QTFs are used today, though not exclusively. QTFs are also frequently employed in ambient conditions in experiments where a constant tip-sample gap is desired. In those conditions, there are two good options: STM or a QTF oriented in shear-force (SF) geometry (oscillation parallel to sample surface). STM carries the requirement of conductive samples, but AFM does not, which is why SF-AFM is commonly chosen in those situations. 8 an AFM consists of four things: a scanner, approach motor, resonator (with a tip), and electronics. Broken down into the simplest pieces, an AFM consists of four things: a scanner, approach motor, resonator (with a tip), and electronics. Signals that are sent into the mechanical AFM apparatus include high voltages for scanning, high frequency drive signals with very clean sinusoidal oscillation for exciting the resonator, along with bias voltages for tip/sample and power supply voltages for the preamplifiers. All need to carry low noise. Signals that are coming from the AFM into the controller are voltages from the preamplifiers and possibly other triggers from external devices. The AFM controller will operate a feedback loop that controls tip-sample distance by interpreting input signals from the preamplifiers and acting on the tip-sample distance via high voltage outputs, which collectively control the tip-sample relative motion in 3D. The feedback loop typically only acts on the Z-axis high voltage output to control the tip-sample distance. The XY-axes high

3 Considerations for Cryogenic AFM Operation 3 voltage outputs are typically for raster scanning. LOW TEMPERATURE AFM - HIGH Q-FACTORS Q-Factor in Cryogenic Environment Anything that suppresses the damping of the AFM mechanical resonator makes for a higher Q-factor. Examples include vacuum and cryogenic environments. Mathematically the measured Q-factor, Q eff, is 17 where Q 0 is the intrinsic damping of the resonator, Q mount is that of the fixing mechanism in the AFM (e.g. a clamp, epoxy, etc.), and Q air is the air damping. Vacuum conditions below 10-2 mbar are sufficient to eliminate the damping contribution from 1/Q air. 18 The cryogenic contribution to raising the Q-factor is through the intrinsic properties of the resonator (the 1/Q 0 term). In practice, a firm tip mounting mechanism and a rough vacuum allow simplification to, Q eff Q A cryogenic environment will increase Q 0, and in turn, the measured Q-factor, Q eff. A high Q-factor can translate into a large increase in signal sensitivity if the electronics are setup properly for this. 12,13 As discussed above, there are measurable changes to the QTF when the tip interacts with the surface. Which observable one chooses for input to the Z-feedback loop determines the speed and sensitivity when using a high-q resonator. The difference between fast and slow for this discussion is dramatic. If QTF amplitude is chosen, this becomes problematic because it takes a long time τ = 2Q ω 0 to settle to a new steady-state value after experiencing a force gradient. In other words, the height change between two pixels while scanning, which amounts to a force gradient that the tip experiences, scales with Q to properly discern the changes. The Q-factor for a QTF can increase by several orders of magnitude in going from 300 K/air to 4K/vacuum conditions. The delays associated with amplitude feedback in cryogenic conditions are generally considered to be intolerable for most experiments. Frequency Modulation AFM One way to circumvent this delay and also take advantage of the bolstered sensitivity due to the high Q-factor is through Frequency Modulation AFM (FM-AFM), which was first demonstrated in a landmark publication by Albrecht et al. in The smallest event that the tip can sense (or minimum detectable force gradient) is given by 12 where k R is the resonator force constant, k B Boltzmann s constant, T is temperature, B is the measurement bandwidth, ω 0 is the resonance frequency, and A is the resonator amplitude. Increasing the Q-factor allows smaller force gradients to be detectable. When feeding back off the amplitude though, Q and B are not independent. The measurement bandwidth, B, is decreased when feeding back off the amplitude, somewhat offsetting the benefit. However, with FM-AFM that dependence is broken, 12 and one can increase the Q-factor as high as possible and still have an acceptable measurement bandwidth. Intuitively one can think of this as follows: the change in the amplitude of a high-q resonator takes a long time to discern because the oscillator is so efficient. When a sudden force gradient acts on the tip, it takes a significantly high number of tip oscillations to settle to a new steady-state amplitude in the absence of air damping. Typically ~ 5τ per pixel is adequate time to discern changes from a force gradient between adjacent pixels. Consider a QTF in ambient conditions with a Q-factor of 500 and f₀ = 32.8 khz; in that case τ~4.8 ms, which means a 256 x 256 pixel image might take about 30 minutes to complete. In cryogenic conditions, it is very common to see a 100x increase in Q, which would mean that same image would take roughly 2 days if amplitude feedback is still used. Phase Locked Loop A phase-locked loop (PLL) is commonly used today for FM-AFM. The compliance change of a resonator is instantaneous, so if it is measurable, then we can side-step the amplitude oscillation problem described above. 12,14 To extract the resonator s change in compliance the PLL fixes the phase between the AC drive signal and the oscillation amplitude. 14 The drive frequency is varied so-as-to maintain a constant phase. (1)

4 Considerations for Cryogenic AFM Operation 4 A probe interacting with a surface will experience a resonance frequency shift f, which the PLL detects and can readily feed to the Z-feedback loop that controls the tip-sample distance. There are limitations to how large a frequency shift is permitted, 13 but for the most part this is a highly effective way to use the high Q-factor for high sensitivity and still have acceptable measurement bandwidths. Note that a PLL is not the only way to incorporate phase into the feedback, but it is the most popular method today for high Q-factor AFM feedback. Sample Considerations Modern FPGA based control electronics enable a wide dynamic range, 15,16 which allows operation on samples that are not necessarily atomically flat. However, PLL locking is vulnerable to both a polarity inversion of f and an abrupt force gradient from a sample feature. When the PLL unlocks, f (no longer a meaningful quantity) will jump by orders of magnitude. Since the Z-feedback loop is still operating on it with proportional and integral gains, tip damage is likely to occur. In general, there are fewer risks associated with f feedback if the sample is largely free of debris. However, modern SPM controllers have widened the error margin for operating in this modality. Noise Sources There are four sources of noise that are of practical concern for an AFM with a high Q-factor: deflection detector noise, oscillator drive signal noise, thermal noise, and frequency drift noise. 19 The smallest force gradient that one can measure will depend on the noise floor of the preamplifier detecting the AFM resonator oscillation, which is deflection detector noise. Since the preamplifier feeds its signal to the AFM controller that subsequently sends the drive signal back to the resonator, that noise is propagated through, which is the oscillator noise. 20 Thermal noise is strongly suppressed in cryogenic conditions making the minimum detectable force gradient much smaller as can be seen in Eqn. (1) above. The frequency drift noise can be especially problematic in cryogenic conditions if precautions are not taken to mitigate its effects. As the temperature is changed in either direction between 4 K and 300 K there is a nonlinear change in the resonator eigenfrequency. Stabilizing the measurement through a temperature controlled feedback scheme is strongly recommended in this case. Once the eigenfrequency is stabilized, one can lock the PLL at this frequency and image as usual. Provided that the temperature of the system stays stable throughout the image, the frequency drift noise can be adequately suppressed. It is important when operating a high-q AFM that temperature control is considered even in ambient temperature conditions to keep the eigenfrequency from meandering. Note that this can be especially troubling because it may not immediately be obvious there is a problem, and the tip begins interacting in a regime that was not defined by the user. Consider a f that meanders and the drive is now off resonance. For a high Q cantilever or QTF, there still may be enough signal-to-noise to where the PLL can still adequately stay phase-locked. Depending on which direction f meanders (toward or away from the f set point), the Z-feedback loop can force a very strong or very weak interaction, which may not be evident until an undesirable outcome is encountered. This effect can be easily observed in a quick experiment. Simply put an AFM head in a vacuum chamber and pull a rough vacuum to increase the Q-factor. Run a frequency sweep and verify the higher Q, and then lock the PLL. Apply heat to the chamber with a heat gun. The f will begin running away monotonically and the PLL should stay locked. Note, if the AFM preamplifier is on the AFM head, a heating source is probably not needed, as the quiescent current in the op-amps will cause the runaway heating in the absence of radiant cooling in vacuum. Thermal control of the environment is essential for a high-q AFM to prevent Δf from running away The great thing about a high-q resonator for AFM is that it s an extraordinarily sensitive sensor the bad thing is that you don t get to decide what else it can sense. Thermal control of the environment is essential for a high-q AFM to prevent f from running away. Sensor Feedback Methods in Cryogenic Environment Cantilevers The conventional way of monitoring an AFM cantilever position is with a diode laser reflected off the back of the lever into a 4-quadrant photodiode, sometimes called a position sensitive detector (PSD). These PSDs are

5 Considerations for Cryogenic AFM Operation 5 predominantly Si based, which makes them inoperable below about 20K. Consequently, the Rugar style interferometer is commonly employed for cryogenic AFM feedback The Rugar interferometer is formed by aligning a fiber optic above the cantilever to set up a Fabry-Perot cavity between the fiber-air interface and the cantilever. Distributed feedback (DFB) lasers are commonly used today to ensure a flat intensity output, which is necessary for effective AFM feedback. In this scheme, the preamplifier is fiber coupled and lives outside the cold environment. The disadvantage with interferometry is that it s generally more difficult to use since every tip change requires realignment to the fiber optic. One advantage of interferometry is that it s a true metrology measurement because the cantilever oscillation may be calculated as λ/4π multiplied by the ratio of oscillation detection voltage to the maximum peak-to-peak fringe height voltage. Quartz Tuning Forks Quartz is a piezoelectric material, so as the tines oscillate an oscillatory charge is generated between the tines, which can be read out by a preamplifier and used for feedback. As mentioned above, a Si based preamplifier is generally inoperable in cryogenic environments. Reading this AC voltage is non-trivial because it is strongly susceptible to parasitic capacitive coupling. Coaxial lines as short as 1 meter long that run between the QTF and a feedthrough will have a significant impact on the signal quality. Therefore, it s generally favorable if the preamplifier can be situated very close to the QTF, which can be difficult in practice at low temperature. CONCLUSIONS High Q-factors enabled with cryogenic AFM operation offer increased sensitivity, but it comes with a higher barrier to entry in terms of necessities to understand how to operate the system and how to construct the system. Sensor feedback and an effective temperature control scheme are subtle points that require attention. Both cantilevers and QTFs will exhibit a higher Q-factor in a cryogenic environment that can be exploited for enhanced sensitivity. QTFs tend to have higher spring constants than cantilevers, which makes them less susceptible to snapping into contact when trying to do non-contact AFM. Optimal feedback schemes for QTFs and cantilevers can be quite diverse from one another. The choice of QTF or cantilever likely depends on what the user s larger research goals are. An ideal workhorse system would consist of a low temperature platform with separate cantilever and QTF AFM heads to enable a diverse range of experimental possibilities. Dr. Karrai had an early implementation of a first stage source follower based on a GaAs MESFET scheme followed by a voltage amplifier that could be positioned outside the cryogenic chamber. 24 Unlike Si, GaAs does not suffer the same carrier freezeout effects, so the source follower portion of the circuit was cryo-compatible. The Sony MESFET used in that implementation has since gone obsolete. For a preamplifier situated outside the cryogenic volume, a standard current amplifier can be used to amplify the signal from the tine with tip while grounding or biasing the other tine. An additional method is to use an AC coupled charge amplifier. 19,25

6 REFERENCES Considerations for Cryogenic AFM Operation 6 1. Binnig, G., Rohrer, H., Gerber, C. & Weibel, E. Surface studies by scanning tunneling microscopy. Phys. Rev. Lett. 49, 57 (1982). 2. Binnig, G., Gerber, C., Stoll, E., Albrecht, T. & Quate, C. Atomic resolution with atomic force microscope. EPL Europhys. Lett. 3, 1281 (1987). 3. Albrecht, T. R., Akamine, S., Carver, T. & Quate, C. F. Microfabrication of cantilever styli for the atomic force microscope. J. Vac. Sci. Technol. Vac. Surf. Films 8, (1990). 4. Mody, C. Instrumental community: Probe microscopy and the path to nanotechnology. (MIT Press, 2011). 5. Albrecht, T. R. & Quate, C. F. Atomic resolution with the atomic force microscope on conductors and nonconductors. J. Vac. Sci. Technol. Vac. Surf. Films 6, (1988). 6. Albrecht, T. R. & Quate, C. Atomic resolution imaging of a nonconductor by atomic force microscopy. J. Appl. Phys. 62, (1987). 7. Günther, P., Fischer, U. C. & Dransfeld, K. Scanning near-field acoustic microscopy. Appl. Phys. B Lasers Opt. 48, (1989). 8. Karrai, K. & Grober, R. D. Piezoelectric tip-sample distance control for near field optical microscopes. Appl. Phys. Lett. 66, (1995). 9. Karraï, K. & Grober, R. D. Piezo-electric tuning fork tip sample distance control for near field optical microscopes. Ultramicroscopy 61, (1995). 10. Giessibl, F. J. Advances in atomic force microscopy. Rev. Mod. Phys. 75, 949 (2003). 11. Giessibl, F. J. Atomic resolution on Si (111)-7x7 by noncontact atomic force microscopy with a force sensor based on a quartz tuning fork. Appl. Phys. Lett. 76, (2000). 12. Albrecht, T., Grütter, P., Horne, D. & Rugar, D. Frequency modulation detection using high-q cantilevers for enhanced force microscope sensitivity. J. Appl. Phys. 69, (1991). 13. Grober, R. D. et al. Fundamental limits to force detection using quartz tuning forks. Rev. Sci. Instrum. 71, (2000). 14. Atia, W. A. & Davis, C. C. A phase-locked shear-force microscope for distance regulation in near-field optical microscopy. Appl. Phys. Lett. 70, (1997). 15. RHK Technology. Troy, MI, USA. 16. Nanonis/SPECS Zurich. Zurich, Switzerland. 17. Lübbe, J. et al. Achieving high effective Q-factors in ultra-high vacuum dynamic force microscopy. Meas. Sci. Technol. 21, (2010). 18. Lübbe, J., Temmen, M., Schnieder, H. & Reichling, M. Measurement and modelling of non-contact atomic force microscope cantilever properties from ultra-high vacuum to normal pressure conditions. Meas. Sci. Technol. 22, (2011). 19. Giessibl, F. J., Pielmeier, F., Eguchi, T., An, T. & Hasegawa, Y. Comparison of force sensors for atomic force microscopy based on quartz tuning forks and length-extensional resonators. Phys. Rev. B 84, (2011). 20. Kobayashi, K., Yamada, H. & Matsushige, K. Reduction of frequency noise and frequency shift by phase shifting elements in frequency modulation atomic force microscopy. Rev. Sci. Instrum. 82, (2011). 21. Rugar, D., Mamin, H., Erlandsson, R., Stern, J. & Terris, B. Force microscope using a fiber-optic displacement sensor. Rev. Sci. Instrum. 59, (1988). 22. Rugar, D., Mamin, H. & Guethner, P. Improved fiber-optic interferometer for atomic force microscopy. Appl. Phys. Lett. 55, (1989). 23. Albrecht, T., Grütter, P., Rugar, D. & Smith, D. Low-temperature force microscope with all-fiber interferometer. Ultramicroscopy 42, (1992). 24. Karrai, K. & Manus, S. Scanning probe microscope head with signal processing circuit. (US Patent 6,006,594, 1999). 25. FEMTO High Frequency Charge Amplifier, HQA-15M-10T. FEMTO Messtechnik GmbH. Klo sterstrasse 64, Berlin, Germany. About the Author: Ryan Murdick earned a Ph.D. in physics in 2009 from Michigan State University where he investigated interfacial dynamics via Ultrafast Electron Diffraction in the group of Chong-Yu Ruan. He was a postdoctoral researcher at the University of Washington and University of Colorado in the Nano-Optics group headed by Markus Raschke. He has since worked for several years in industry for companies including RHK Technology and Molecular Vista, before joining Montana Instruments in 2017 as a Product Development Scientist. info@montanainstruments.com Evergreen Drive Bozeman, MT 59715, USA 2017 Montana Instruments Corporation, All Rights Reserved