Home Search Collections Journals About Contact us My IOPscience Measurement of the gold–gold bond rupture force at 4 K in a single-atom chain using photonmomentum-based force calibration This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Meas. Sci. Technol. 26 025202 (http://iopscience.iop.org/0957-0233/26/2/025202) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 176.9.124.142 This content was downloaded on 29/12/2014 at 13:27 Please note that terms and conditions apply. Measurement Science and Technology Meas. Sci. Technol. 26 (2015) 025202 (8pp) doi:10.1088/0957-0233/26/2/025202 Measurement of the gold–gold bond rupture force at 4 K in a single-atom chain using photon-momentum-based force calibration D T Smith and J R Pratt National Institute of Standards and Technology, Gaithersburg, MD 20899-8520, USA E-mail: [email protected] Received 7 August 2014, revised 12 November 2014 Accepted for publication 24 November 2014 Published 22 December 2014 Abstract We present instrumentation and methodology for simultaneously measuring force and displacement at the atomic scale at 4 K. The technique, which uses a macroscopic cantilever as a force sensor and high-resolution, high-stability fiber-optic interferometers for displacement measurement, is particularly well-suited to making accurate, traceable measurements of force and displacement in nanometer- and atomic-scale mechanical deformation experiments. The technique emphasizes accurate co-location of force and displacement measurement and measures cantilever stiffness at the contact point in situ at 4 K using photon momentum. We present preliminary results of measurements made of the force required to rupture a single atomic bond in a gold single-atom chain formed between a gold flat and a gold tip. Finally, we discuss the possible use of the gold–gold bond rupture force as an intrinsic force calibration value for forces near 1 nN. Keywords: atomic force, bond strength, interferometry, force metrology, length metrology (Some figures may appear in colour only in the online journal) 1. Introduction the specimen surface and the interaction force between the tip and the surface. This interaction is typically attractive when the tip is close to, but not yet in contact with, the surface and becomes repulsive if the tip continues to advance and penetrate the surface. As these instruments improve their ability to test smaller and smaller specimens, the forces and displacements involved shrink accordingly, and accurate measurement of these quantities becomes increasingly difficult. Measurement of force in this regime is often based on the deflection of some elastic mechanical transducer, and accurate determination of force requires measurement of both transducer deflection and transducer stiffness at the location where the force is being applied. Many experiments that study forces at the molecular and atomic scale use the deflection of a cantilever to measure that force. Cantilevers, particularly those with low stiffness, can be extremely sensitive force transducers, and it is not unusual for cantilever-based transducers to have force sensitivity in the piconewton range. However, both deflection and stiffness must be measured with an accuracy equal to, or better than, the desired accuracy in force, and displacements well below As microelectromechanical systems and nanoelectromechanical systems become increasingly common in technology applications, designers of these systems need reliable mechanical property data on the wider and wider range of materials used in fabrication. Those mechanical property measurements often must be made on structures and components that are only tens of micrometers or smaller in size, either because the material cannot be fabricated in larger sizes or, when larger test specimens are available, tests on those larger specimens will not accurately predict the mechanical performance of micrometer-scale components. As a result, a range of test instruments are now commercially available to measure the mechanical properties of very small volumes of material. The two most common instrument classes are low-force instrumented indenters [1] and atomic force microscopes (AFMs) [2]. Both techniques are based on measuring the mechanical interaction of a probe tip, which is part of the test instrument, with the surface of a specimen, and both characterize that interaction by measuring the displacement of the tip relative to 0957-0233/15/025202+8$33.00 1 © 2015 IOP Publishing Ltd Printed in the UK D T Smith and J R Pratt Meas. Sci. Technol. 26 (2015) 025202 1 nm must be measured, both to monitor the motion of the probe tip relative to the specimen surface, and also to monitor the deflection of the force sensor. Interferometry techniques exist that achieve the requisite displacement resolution, but the most sensitive of those use displacement modulation methods that do not provide position or displacement information with the long-term stability necessary for quasistatic mechanical property measurement. Accurate force measurement is even more problematic. Calibration traceable to the International System of Units (SI) [3] using deadweight masses extends only down to a force of 5 µN, although for forces in the micronewton and nanonewton range, techniques have been developed recently for realizing force traceably using electrostatic methods involving the units of capacitance, length and time [4–8]. Even when an accurate realization of force in the micronewton range or below is available, however, using a calibrated force to determine a cantilever stiffness is not always straightforward, because of issues related to locating loading points and the fact that the contact between a probe and a cantilever typically involves friction and other contact mechanics complications that can change the mechanical boundary conditions of the cantilever and introduce additional sources of uncertainty in the stiffness calibration [9–14]. In response to these issues surrounding force calibration at the micronewton level and below, we consider the possibility of identifying and using reproducible, intrinsic forces that occur in nature as potential ‘reference forces’ for the calibration of very-low-force transducers. In this work, we present an experimental observation of the force required to rupture a gold–gold atomic bond in a single-atom chain (SAC) of gold atoms in a break junction experiment [15] using a cantilever whose stiffness was measured in situ using a non-contact method based on photon momentum. ferrule at the face closest to the cantilever, taking care not to get glue on either the end of the fiber or the tip of the Au wire. The glue wicks into the space between the two ferrule bores and the Au wire and optical fiber to form a stiff mechanical assembly, ensuring that the motion of the Au wire tip is accurately measured by the motion of the cleaved optical fiber end. The fiber/wire/ferrule assembly is mounted to a nanopositioning stage [17] that is compatible with use both in vacuum and at cryogenic temperatures. A second optical fiber is positioned behind the cantilever (the right side in figure 1). This fiber is used both as part of a second interferometer system to measure force on the break junction via cantilever deflection and also, by changing laser sources, for making an in situ measurement of cantilever stiffness using photon momentum, as described below. Both the wire tip and the rear optical fiber are aligned with the longitudinal axis of the cantilever, and wire tip and both optical fibers are positioned such that they all are the same distance (approximately 7 mm) from the clamped base of the cantilever. This positioning ensures that cantilever and tip displacement will be measured at the same distance from the cantilever base that forces between the Au tip and cantilever are occurring, and the alignment of the tip with the longitudinal axis of the cantilever prevents unwanted torque on the cantilever. The two optical fibers are deliberately offset laterally to prevent the possibility of (very weak) optical cross-talk through the Au-coated glass cantilever. The entire assembly in figure 1(b) is suspended from springs in a vacuum-cryogenic chamber capable of operation between 4 and 400 K. Braided straps of very-fine-gauge Cu wire are connected between the suspended assembly and the chamber’s main sample cooling platform, both to damp spring motion and to connect the experiment thermally to the platform. The experimental assembly is thermally isolated from the room-temperature walls of the vacuum chamber by two layers of radiation shields. The chamber, which is supported by a pneumatic vibration isolation system, is cooled using a continuous flow of liquid He in a ‘split-flow’ configuration that allows independent cooling and temperature control of the experimental stage and the radiation shields. In performing an experiment, the vacuum chamber is first pumped down to a pressure of ≈10−4 Pa (≈10−6 Torr), and then the radiation shields and experimental area are cooled, with care being taken to ensure that the radiation shields always cooled faster, so that any residual gas in the chamber condenses on them rather than on the components of the experiment system. Once temperatures in the experimental chamber approach 4 K, a gate valve between the chamber and the vacuum pumping system is closed and the pumps are turned off, to reduce mechanical vibrations near the chamber. The entire experiment is housed in a metrology laboratory with 0.1 K temperature control located 12 m underground. This environment improves the stability of the interferometer and ancillary electronic equipment and reduces the effects of building-born vibrations. 2. Experimental design 2.1. Basic break junction and force sensor design The basic arrangement of the break junction instrumentation is shown schematically in figures 1(a) and (b). At the heart of the system is a vertically mounted, Au-coated glass cantilever approximately 2 mm wide, 8 mm long and 100 µm thick, clamped at its base in an electrically insulating mount. The Au coating, which is deposited on both sides of the cantilever, is 100 nm thick, and a thin (10 nm) Cr layer is used between the glass and Au to ensure good adhesion of the Au to the cantilever. On the front side of the cantilever (the left side in figure 1), a nanopositioning stage holds both a Au wire tip and an optical fiber with a cleaved end facing the cantilever, where it forms a Fabry–Perot (FP) interferometer cavity [16] between the cleaved fiber end and the cantilever. The fiber and Au wire are held parallel by feeding them through a doublebore glass ferrule. The Au tip and fiber end are positioned such that when the Au tip touches the cantilever, the length of the FP cavity formed between the cleaved fiber end and the cantilever is approximately 100 µm. After setting the relative positions of the Au wire and optical fiber, a very small amount of cyanoacrylate glue is applied to the end of the double-bore 2.2. Fiber optic interferometer The design and performance of the fiber optic interferometer system has been described in detail elsewhere [18], but its basic 2 D T Smith and J R Pratt Meas. Sci. Technol. 26 (2015) 025202 Figure 1. (a) Schematic representations of the entire Au break junction experimental design. Two complete fiber interferometer systems are employed, one to measure the position of the Au probe tip relative to the cantilever surface, and the other to measure the deflection of the cantilever, for the determination of force. The bias voltage source and current amplifier are located outside of the cryostat. (b) An enlarged side view of the cantilever assembly. The cantilever is Au coated on both sides and held at its base with an electrically insulating clamp. The entire assembly is suspended from damped springs in a vacuum chamber, and is cooled to 4 K via thermal anchoring to a continuous-flow liquid helium cryostat. features will be presented here. It is essentially a simple fiberoptics-based homodyne interferometer designed to measure changes in length of a low-finesse Fabry–Perot cavity formed between the cleaved end of an optical fiber and an opposing parallel reflecting surface. The configuration is in general the same as that described in Rugar et al [19], but with the emphasis placed on maximizing long-term stability in low-frequency and dc applications. The laser source is a wavelength-tunable infrared (IR) laser with a center wavelength of 1550 nm and a tuning range of approximately ±50 nm about 1550 nm. This tuning capability is critical in our application; for maximum sensitivity, the FP cavity must be operated near a quadrature, or inflection, point of an interference fringe, either by adjusting cavity length or laser wavelength. Although we set the approximate length of both FP cavities when assembling the instrument (cavity lengths are typically in the range 50–200 µm), we cannot fine-tune the length of either cavity in situ during an experiment, and therefore must tune the wavelength for each interferometer so as to optimize sensitivity. This requires two separate tunable laser sources for the experiment. The interferometer system described above has previously been applied successfully to the study of atomic-scale break 3 D T Smith and J R Pratt Meas. Sci. Technol. 26 (2015) 025202 4 K, cantilever dimensions change, clamping conditions at the base of the cantilever may change, and even the elastic moduli of the cantilever materials change. We therefore make use of features of the experimental configuration to measure directly k in situ during an experiment. One common method for in situ calibration of cantilever stiffness that is particularly convenient for AFM cantilevers is based on the equipartition theorem and involves measuring the vibrational spectrum of a cantilever that results purely from the thermal motion of the cantilever, independent of any external vibrational driving forces [24, 25]. When employed in an AFM system, this thermal method makes use of the AFM’s cantilever deflection measurement method (whether it be optical lever, interferometer, or another) to measure the frequencies and amplitudes of cantilever resonances (primarily the fundamental, or lowest, resonance) that are being driven purely by the thermal energy of the cantilever. We made these measurements on our cantilever, the fundamental resonant frequency of which was approximately 1.15 kHz at 4 K, but the oscillation amplitude of the fundamental resonance was significantly larger than expected from thermal energy, and the resulting calculated stiffness was 3.1 N m−1, or more than ten times lower than we knew the approximate stiffness to be from simple calculations based on cantilever dimensions. This error was almost certainly due to the fundamental resonance being driven by other forces in addition to thermal energy, most likely seismic vibration transferred from the floor through the pneumatic support system and from acoustic room vibrations coupled from the chamber walls through the mechanical support for the experimental platform in the chamber. In order for thermal calibration methods to be accurate, it must be the case that the only forces exciting the cantilever modes are thermal fluctuations. In our system, this was not the case and as a result, we were unable to use this method for in situ stiffness calibration. However, the fact that we had two optical fibers directed at the cantilever, both at the same distance out from the cantilever base as the location where the Au contact was being made, gave us another method of in situ stiffness calibration, based on photon momentum [26]. To implement this method, we used the interferometer on the front (Au break junction) side of the cantilever to measure its deflection, but temporarily replaced the tunable IR laser system that comprised the rear interferometer with a fiber-optic-coupled incoherent superluminescent diode (SLD) light source with center wavelength 1550 nm. The output power of this light source was measured independently using an Agilent 81634B power sensor with a stated total uncertainty of ±4.5%, and could be modulated by an external voltage. This enabled us to apply an oscillating force of known amplitude to the rear of the cantilever, through change in momentum of reflected photons, while simultaneously measuring the amplitude of the resulting cantilever oscillation. For this case, the optical force applied to the cantilever for normal photon incidence is simply: junctions, although without the inclusion of a force sensor. In that work [20], a Au tip and optical fiber were mounted in a configuration similar to the left side of arrangement in figure 1, but a rigidly mounted Au flat was used in place of the cantilever. The interferometer signal was used to measure the motion of the Au tip relative to the Au flat, but also was used in a feedback-control loop to the nanopositioner that canceled any drift in separation of tip and flat, in what was termed a feedback-stabilized break junction (FSBJ) configuration. Total noise in the interferometer system corresponded to an equivalent noise in cavity length of 2 pm (measurement bandwidth 0.1 Hz to 1 kHz), and changes in cavity length of 5 pm, initiated by changes in the setpoint of the feedback control loop, were clearly visible. This same arrangement is used in the current work to measure and control the position of the Au tip relative to the cantilever. Absolute drift in the interferometer and feedback system was checked by operating two completely independent interferometer systems simultaneously against a common Au flat. The use of one interferometer to lock the position of the Au flat resulted in the complete cancellation of any observed drift in the second, independent interferometer. In previous work, this level of stability allowed the creation of individual Au SACs that could be maintained for 30 min or longer while electron transport through them was studied in detail [20, 21]. 3. Experimental results 3.1. In situ measurement of cantilever stiffness In order to obtain accurate force data for the Au break junction, the stiffness of the cantilever at the location of the junction must be known. The selection of an optimal stiffness, or spring constant, k, for the cantilever used in the break junction experiment represents a trade-off between mechanical stability and force sensitivity. Force resolution is determined by the resolution with which its displacement can be measured; force sensitivity will suffer if an unnecessarily stiff cantilever is used. However, in the presence of attractive forces between the Au tip and the Au-coated cantilever, the cantilever must be stiffer than the Au contact; otherwise, the system will be mechanically unstable, with the tip snapping into contact on approach when the gradient of the attractive interaction is greater that the cantilever stiffness, and pulling off unstably on retraction when the contact breaks under tensile force. We estimated that a cantilever force sensor with a stiffness in the approximate range k = 10 to 100 N m−1 would provide the required mechanical stiffness without unnecessarily sacrificing sensitivity, and this range became our target stiffness for the cantilever at the Au point of contact. This range was based on experimental observations [22, 23] that the stiffness of a Au SAC is expected to of the order of 1 N m−1. To ensure that we know the correct value of k for the cantilever during an experiment, we align the Au tip and back FP cavity as described above. We could measure k at the same distance from the base at room temperature before beginning an experiment. However, we do not want to assume that that stiffness is correct when we are performing a Au break junction experiment at 4 K. In cooling down from room temperature to Fphoton = 2PR / c, (1) where P is the optical power, R is the reflection coefficient of the Au-coated cantilever surface and c = 3.0 × 108 m s−1 is 4 D T Smith and J R Pratt Meas. Sci. Technol. 26 (2015) 025202 3.5 3.0 25 Hz Cantilever Displacement (pmrms) 2.5 2.0 1.5 50 Hz 1.0 100 Hz 0.5 0.0 200 Hz 0 50 100 150 200 Time (s) Figure 2. The response of the cantilever to a photon driving force modulated at the frequencies shown and applied to the back side of the cantilever via the same optical fiber used for the rear FP interferometer. These data were used to characterize photothermal effects resulting from photon driving of the cantilever. Photothermal effects were observed to drop approximately as 1/frequency, but represented a small source of error which had to be included in our photon momentum calibration of cantilever stiffness. the speed of light. R for 1550 nm light incident on a smooth Au surface is taken to be R ≈ 0.97 [27]. The assumption of normal incidence neglects the fact that the beam exiting the cleaved fiber end is diverging slightly, but for the approximately 100 µm spacing between the fiber and the cantilever, we have estimated that the cosine error in momentum transfer will be less than 1%. The fact that R for our system is 0.97 and not unity means that 3% of the optical power incident on the cantilever is being absorbed and converted to heat. The SLD source was modulated such that the optical power being delivered to the cantilever varied sinusoidally between a minimum of 1.66 mW and a maximum of 12.45 mW. This resulted in an equivalent steady-state incident power of 7.06 mW, an incident rootmean-square (rms) ac oscillation amplitude of 3.81 mW, and 0.21 mW of heat delivered to the cantilever. This heating resulted in detectable but unquantifiable changes in the average cantilever deflection, as evidenced by drifts in the average position of the cantilever, and hence average or quasistatic cantilever deflection was not used to calculate cantilever stiffness. Instead, only the ac component of the optical drive, Prms, is used to calculate stiffness: the applied rms ac optical power, in units of mW, is related to the rms amplitude of the ac displacement response, in pm, as measured by the front interferometer system using a lock-in amplifier locked to the SLD modulation signal. Even when only the ac component of the optical driving force is considered, at low frequencies the cantilever still displayed a frequency-dependent heating response, in addition to quasistatic bending. However, this component of the thermal response drops rapidly with increasing drive frequency as the cantilever loses its ability to respond in phase to the thermal oscillations. This behavior is shown in figure 2, where the rms amplitude of the displacement oscillation, d, as measured by the front interferometer, is seen to drop steeply as the modulation frequency is increased from 25 to 200 Hz. (At 400 Hz and above, the drive frequency began to interact weakly with the cantilever’s lowest resonance at 1.15 kHz, and d began to rise.) The drop in the ac thermal response for frequencies up to 200 Hz allowed us to quantify and correct for it, and we were able to determine that at 200 Hz, the cantilever response for an incident ac optical power of 3.81 mW in the absence of an ac thermal response was 0.57 pm. Using equation (1), this then gives a cantilever stiffness, k: k = Fphoton / d rms = 2PrmsR /(c ⋅ d rms) = 43 N m −1 ± 3 N m −1 (2) at the break junction location at 4 K. Here, the uncertainty of 3 N m−1 is dominated by the uncertainty in the absolute accuracy of the power sensor, as stated by the manufacturer, as noted above. 3.2. Au–Au bond rupture force The electronic and mechanical properties of SACs have been of great interest for many years [15], due in no small part to the fact that they are one of the closest approximations to a true 1D physical system that is experimentally accessible. The 5 D T Smith and J R Pratt Meas. Sci. Technol. 26 (2015) 025202 Conductance Quantum, G0 quantization of ballistic electron transport through a variety of SACs has been predicted theoretically [28–30], observed and studied in detail experimentally [31], and calculated using a variety of ab initio computational methods [32–35]. The quantum of conductance, G0, is given by 2e2/h, where e is the charge on the electron and h is Planck’s constant. This conductance is 77.5 µS, which corresponds to a resistance of 12.9 kΩ. In addition, several experimental groups have used AFM-based techniques to measure chain breaking forces [22, 36, 37], and a particularly thorough set of density-functionaltheory (DFT) calculations have predicted [34] that the bond rupture force for a Au contact that has been drawn down to a SAC has a remarkably consistent value of 1.54 ± 0.06 nN at temperatures near 0 K, independent of the initial crystallographic orientation or tensile axis along which the SAC is drawn. This remarkably narrow range of force makes the rupture of a gold SAC a promising candidate for a reproducible intrinsic force calibration point in the nanonewton range at low temperatures. Therefore, as one application of the experimental system described in this manuscript, we use it to measure the tensile force required to rupture a 1D chain of Au atoms in a break junction, e.g. the force associated with breaking a single Au–Au bond in a chain, at 4 K. A typical measurement begins by bringing the Au tip into a firm, low resistance contact with the flat Au-coated cantilever surface. A constant 5.0 mV bias voltage is maintained across the junction. This low value of bias voltage is used to keep the energy of electrons passing through the junction low, thereby maintaining transport that is predominantly ballistic by minimizing the probability of electron-phonon interactions. Motion of the Au tip relative to the Au flat is measured using the FP interferometer on the front side of the cantilever; that signal can, if desired, be used to lock the tip position relative to the flat under servo control, as described earlier in the discussion of the FSBJ work. At the same time, the deflection of the cantilever, relative to the base where it is clamped, is measured by the second FP, or the rear of the cantilever, and provides the determination of the tip/flat interaction force using cantilever deflection dc, and stiffness k. We then retract the Au tip, while monitoring the current through the junction, until electrical continuity across the junction is lost. This process is repeated many times. Initially, we often find that junction does not form a SAC with conductivity 1G0, but instead breaks abruptly from a high-conductivity state (10G0 or more). In those cases, a large-area contact has formed that is stiffer than the cantilever, and the system is mechanically unstable. However, by repeatedly working or ‘training’ the junction [38], we routinely are able to ‘sharpen’ the contact region such that we can draw SACs with conductivity at, or just under, 1G0, and can then measure the tensile force at which they break. Typical data from such an experiment are shown in figure 3, for three discrete breaking events. For each event, both the conductivity of the junction, in units of G0, and the quasistatic cantilever deflection, are shown as a function of time. In each of these events, a high-conductivity junction (G > 3G0) was formed and then drawn out until a long plateau at 1G0 was observed, indicating the formation of a SAC that then broke. At each break, a clear relaxation of the cantilever position is 4 a 3 2 1 0 0 5 0 5 10 15 10 15 Cantilever Position (pm) 120 100 80 60 40 20 0 Conductance Quantum, G0 Time (s) 4 b 3 2 1 0 0 2 4 0 2 4 6 8 10 12 6 8 10 12 Cantilever Position (pm) 200 150 100 50 0 Conductance Quantum, G0 Time (s) 4 c 3 2 1 Cantilever Position (pm) 0 0 5 0 5 10 15 10 15 100 50 0 Time (s) Figure 3. Three typical observations (out of more than 30) of Au SACs breaking from the 1G0 (single-atom-chain) quantized conduction state at 4 K. Abrupt changes in cantilever position of 30–50 pm are observed when the chain breaks. Cantilever stiffness is measured in situ at 4 K at the location of the junction, and is found to be 43 N m−1. 6 D T Smith and J R Pratt Meas. Sci. Technol. 26 (2015) 025202 observed. Not all junctions broke from a SAC configuration; some breaks occurred when the conductivity was greater than 1G0. While these observations are interesting, it is assumed that in those cases the observed breaking force resulted from the rupture of more than one Au bond (and in fact the observed breaking force was higher in those cases), and they are not included in the present analysis. For those cases where the junction broke following the creation of an extended 1G0 plateau like those shown in figure 3, we observe an abrupt relaxation in the cantilever position of 41 ± 10 pm (one standard deviation in the experimentally observed values) when the SAC breaks. Using the value of k = 43 N m−1 for the cantilever stiffness at the contact point, this implies a breaking force of 1.8 ± 0.4 nN, an average value that is slightly higher than, but not inconsistent with, earlier experimental values and DFT calculations. Just after the SAC breaks, there may still be a residual force interaction between the tip and cantilever, particularly given that the cantilever position relaxes by only ≈50 pm or less. We believe, however, that this possible interaction does not affect the accuracy of our breaking force measurement, for several reasons. First, if we continue to withdraw the tip after the chain breaks, we typically do not see any further relaxation of the cantilever position. Second, when a chain breaks after the drawing of a SAC, we believe that the resulting gap is significantly larger than the 50 pm cantilever relaxation distance because the Au atoms that had been in the SAC collapse back onto either the tip or flat. This belief is reinforced by our observation that, after breaking a SAC, we typically have to move the tip forward again, toward the cantilever, by at least 1 nm before we reestablish electrical contact. And finally, even if we did have some long-range force interaction between the tip and flat that we are not able to detect or quantify, it is reasonable to assume that the abrupt change in cantilever position when the SAC breaks still represents the chain breaking force, since a long-range force would not be expected to vary significantly as a result of a 50 pm cantilever movement. movements of the Au tip at the front of the cantilever, but is a limiting factor when measuring 40 pm changes in cantilever deflection. Raising the finesse of the rear FP cavity by coating the cleaved end of the optical fiber with reflective dielectric multilayer coatings can raise the sensitivity of the rear FP cavity dramatically. The trade-offs are that (1) cavity alignment must be more exacting as finesse goes up, and (2) the total range of travel that can be measured is reduced, but neither of these represent significant obstacles in this application. Second, correction for the thermal effects that result from the Au coating absorbing 3% of the SLD power when performing the stiffness calibration limits the accuracy of that calibration. Here again, multilayer dielectric coatings offer a significant potential benefit. Dielectric coatings are commercially available that have reflectivity greater than 99.9% at 1550 nm, significantly reducing the amount of heat being pumped into cantilever during the stiffness calibration. A next-generation instrument could use a cantilever with a Au coating on the break junction side, and a high-reflectivity dielectric coating on the back. Finally, it will be easy to replace the single fiber in the single-bore ferrule behind the cantilever with two parallel fibers in a double-bore ferrule like the one used on the front side of the cantilever to hold a fiber and Au wire. It would then be possible to use one rear fiber in a high-finesse FP interferometer while simultaneously driving the cantilever with a SLD source. Not only would this facilitate the cantilever stiffness calibration, and improve its precision, but it would also provide the possibility of using damping, or ‘feedback cooling’, to reduce undesired vibrations of the cantilever through the application of phase-shifted optical force feedback derived from measured cantilever velocity. Acknowledgments The authors wish to thank Paul Wilkinson for useful discussions on optical power and photon momentum measurements, and George Jones for assistance with laboratory instrumentation. Certain commercial equipment, instruments, or materials are identified here to specify the experimental procedure adequately. Such identification does not imply recommendation or endorsement by NIST, nor is it intended to imply that the equipment, instruments or materials identified are necessarily the best available for the purpose. 4. Discussion We have developed an instrument and associated methodology for measuring the Au–Au bond breaking force that uses photon momentum to enable in situ calibration of the force sensor, and have used it to obtain a value for that breaking force that is consistent both with previous experimental work and DFT calculations. There are, however, several ways in which both the accuracy and the precision of the technique could be improved, and we plan to continue to make refinements. First, the resolution with which cantilever deflection, and hence force, can be measured can be improved by increasing the finesse of the FP cavity that measures that deflection. 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