Length-extensional Resonators Research Articles

Stiffness calibration of qPlus sensors at low temperature through thermal noise measurements.

Non-contact atomic force microscopy (nc-AFM) offers a unique experimental framework for topographical imaging of surfaces with atomic and/or sub-molecular resolution. The technique also permits to perform frequency shift spectroscopy to quantitatively evaluate the tip-sample interaction forces and potentials above individual atoms or molecules. The stiffness of the probe, k, is then required to perform the frequency shift-to-force conversion. However, this quantity is generally known with little precision. An accurate stiffness calibration is therefore mandatory if accurate force measurements are targeted. In nc-AFM, the probe may either be a silicon cantilever, a quartz tuning fork (QTF), or a length extensional resonator (LER). When used in ultrahigh vacuum (UHV) and at low temperature, the technique mostly employs QTFs, based on the so-called qPlus design, which actually covers different types of sensors in terms of size and design of the electrodes. They all have in common a QTF featuring a metallic tip glued at the free end of one of its prongs. In this study, we report the stiffness calibration of a particular type of qPlus sensor in UHV and at 9.8 K by means of thermal noise measurements. The stiffness calibration of such high-k sensors, featuring high quality factors (Q) as well, requires to master both the acquisition parameters and the data post-processing. Our approach relies both on numerical simulations and experimental results. A thorough analysis of the thermal noise power spectral density of the qPlus fluctuations leads to an estimated stiffness of the first flexural eigenmode of ≃2000 N/m, with a maximum uncertainty of 10%, whereas the static stiffness of the sensor without tip is expected to be ≃3300 N/m. The former value must not be considered as being representative of a generic value for any qPlus, as our study stresses the influence of the tip on the estimated stiffness and points towards the need for the individual calibration of these probes. Although the framework focuses on a particular kind of sensor, it may be adapted to any high-k, high-Q nc-AFM probe used under similar conditions, such as silicon cantilevers and LERs.

Critical shear stress of gold nanocontacts estimated by in situ transmission electron microscopy equipped with a quartz length-extension resonator

The critical shear stress (CSS) of gold nanocontacts (NCs) was estimated using a home-made in situ transmission electron microscopy holder equipped with a quartz length-extension resonator (LER) as a force sensor. The LER was being oscillated at its resonance frequency utilizing frequency modulation method, enabled us to measure the dissipative energy in the NCs. From the LER amplitude dependence of dissipative energy, we determined the value of CSS to be 0.94 GPa. The dissipation was reproduced by applying this CSS value to a simple slip model with a hysteretic force–displacement curve, suggesting the possibility of elucidating the plastic deformation mechanism.

Peculiar Atomic Bond Nature in Platinum Monatomic Chains.

Metal atomic chains have been reported to change their electronic or magnetic properties by slight mechanical stimulus. However, the mechanical response has been veiled because of lack of information on the bond nature. Here, we clarify the bond nature in platinum (Pt) monatomic chains by our in situ transmission electron microscope method. The stiffness is measured with sub-N/m precision by quartz length-extension resonator. The bond stiffnesses at the middle of the chain and at the connection to the base are estimated to be 25 and 23 N/m, respectively, which are higher than the bulk counterpart. Interestingly, the bond length of 0.25 nm is found to be elastically stretched to 0.31 nm, corresponding to a 24% strain. Such peculiar bond nature could be explained by a novel concept of "string tension". This study is a milestone that will significantly change the way we think about atomic bonds in one-dimension.

Atomic scale mechanics explored by in situ transmission electron microscopy with a quartz length-extension resonator as a force sensor

An in situ transmission electron microscopy (TEM) holder equipped with a quartz length-extension resonator (LER) as a force sensor was developed to examine the elastic properties of atomic-scale materials. This holder is a useful means of studying the effects of size and crystal orientation on the properties of nanomaterials via measurements of mechanical responses while simultaneously observing atomic structures. The spring constants of nanocontacts (NCs) were determined based on shifts in the resonance frequency of the LER during TEM observations. The LER spring constant and sensitivity (the ratio of the LER induced charge to its oscillation amplitude), both of which are crucial to mechanical evaluation of NCs, were precisely calibrated from an analysis of TEM images along with the output of the electronics attached to the holder. The mechanical stability of the newly developed TEM holder was sufficient to allow chains of Pt atoms in the NC to be maintained for at least several seconds. The minimum measurable NC spring constant was on the order of 1 N m−1, comparable to that associated with a single atomic bond. The spring constant of a NC composed of a single-bonded chain of two Pt atoms was found to be 13.2 N m−1. This holder therefore has significant potential with regard to the characterization of nanoscale mechanical properties.

Force spectroscopy using a quartz length-extension resonator

Frequency modulation atomic force microscopy detects the interaction force between the tip and the sample by measuring the change in the resonance frequency of an oscillating force sensor. Short-range interaction force can be selectively detected by a small oscillation amplitude. A quartz length-extension resonator (LER) offers the advantage of small-amplitude operation by virtue of its ultrahigh stiffness. Here, we demonstrate that an LER can accurately measure the short-range interaction force at cryogenic temperature even under a high magnetic field. We derive a formula for calculating the effective stiffness of an oscillating LER by using the theory of elasticity. The obtained dynamic stiffness is 1.23 times greater than the static stiffness, and this difference significantly affects the estimation of the interaction force. Using a properly calibrated LER, force curves are measured on Si(111)-(7 × 7) surfaces. The maximum attractive short-range forces above Si adatoms using several tip apex states are in the ranges of the values previously obtained by Si cantilevers.

Calibration of the oscillation amplitude of electrically excited scanning probe microscopy sensors.

Atomic force microscopy (AFM) is an analytical surface characterization tool which can reveal a sample's topography with high spatial resolution while simultaneously probing tip-sample interactions. Local measurement of chemical properties with high-resolution has gained much popularity in recent years with advances in dynamic AFM methodologies. A calibration factor is required to convert the electrical readout to a mechanical oscillation amplitude in order to extract quantitative information about the surface. We propose a new calibration technique for the oscillation amplitude of electrically driven probes using the principle of energy balance. Our technique relies on the measurement of the energy input to maintain the oscillation amplitude constant. With the measurement of the energy input to the probe, a mechanical oscillation amplitude is calculated and a calibration factor to convert the electrical readout in volts to a mechanical oscillation amplitude in Ångströms is obtained. We demonstrate the application of the new technique with a quartz tuning fork including the qPlus configuration, while the same principle can be applied to other piezoelectric resonators such as length extension resonators or piezoelectric cantilevers. The calibration factor obtained by this technique is found to be in agreement with using the thermal noise spectrum method for capsulated and decapsulated tuning forks and tuning forks in the qPlus configuration.

Contributed Review: Quartz force sensing probes for micro-applications.

As self-sensing and self-exciting probes, quartz sensors present many advantages over silicon cantilevers for microscopy, micro-robotics, and other micro-applications. Their development and use is further bolstered by the fact that they can be manufactured from common quartz components. This paper therefore reviews applications of the increasingly popular quartz tuning fork probes as force sensors in the literature and examines the options for higher-frequency quartz probes using the other available types of flexional, thickness-shear or length-extensional resonators.

Length-extension resonator as a force sensor for high-resolution frequency-modulation atomic force microscopy in air

Frequency-modulation atomic force microscopy has turned into a well-established method to obtain atomic resolution on flat surfaces, but is often limited to ultra-high vacuum conditions and cryogenic temperatures. Measurements under ambient conditions are influenced by variations of the dew point and thin water layers present on practically every surface, complicating stable imaging with high resolution. We demonstrate high-resolution imaging in air using a length-extension resonator operating at small amplitudes. An additional slow feedback compensates for changes in the free resonance frequency, allowing stable imaging over a long period of time with changing environmental conditions.

Piezoelectric oscillation sensor based noncontact atomic force microscope for imaging in both ambient and liquid environments

A new design of a noncontact atomic force microscope (AFM) is introduced in this paper, based on a piezoelectric oscillator sensor (PEOS) for ambient and liquid environments. Because of the recent development of quartz technology, the PEOS sensor operates independently from conventional laser alignments. The sensor is based on the length extension resonator, which has high force sensitivity and can deliver high resolution AFM images in ultrahigh vacuum. The oscillator design was tested in different gas compositions and liquids to determine its oscillation stability. The scan performance was investigated in both air and liquid on the topography of an inorganic hard material, graphite. The usability of PEOS for soft organic materials was further proven by imaging biological samples of DNA origami.

Application of Scanning Probe Microscopy with Length Extension Resonator to Investigate Sample Morphologies

Application of Scanning Probe Microscopy with Length Extension Resonator to Investigate Sample Morphologies

Comparison of force sensors for atomic force microscopy based on quartz tuning forks and length-extensional resonators

The force sensor is key to the performance of atomic force microscopy (AFM). Nowadays, most AFMs use micro-machined force sensors made from silicon, but piezoelectric quartz sensors are applied at an increasing rate, mainly in vacuum. These self sensing force sensors allow a relatively easy upgrade of a scanning tunneling microscope to a combined scanning tunneling/atomic force microscope. Two fundamentally different types of quartz sensors have achieved atomic resolution: the 'needle sensor' that is based on a length extensional resonator and the 'qPlus sensor' that is based on a tuning fork. Here, we calculate and measure the noise characteristics of these sensors. We find four noise sources: deflection detector noise, thermal noise, oscillator noise and thermal drift noise. We calculate the effect of these noise sources as a factor of sensor stiffness, bandwidth and oscillation amplitude. We find that for self sensing quartz sensors, the deflection detector noise is independent of sensor stiffness, while the remaining three noise sources increase strongly with sensor stiffness. Deflection detector noise increases with bandwidth to the power of 1.5, while thermal noise and oscillator noise are proportional to the square root of the bandwidth. Thermal drift noise, however, is inversely proportional to bandwidth. The first three noise sources are inversely proportional to amplitude while thermal drift noise is independent of the amplitude. Thus, we show that the earlier finding that quoted optimal signal-to-noise ratio for oscillation amplitudes similar to the range of the forces is still correct when considering all four frequency noise contributions. Finally, we suggest how the signal-to-noise ratio of the sensors can be further improved and briefly discuss the challenges of mounting tips.

Langasite as a piezoelectric material for near-field microscopy resonant cantilevers

Quartz length-extension resonators have already been used to obtain atomically-resolved images by frequency-modulation atomic force microscopy. Other piezoelectric materials such as gallium orthophosphate (GaPO(4)), langatate (LGT), and langasite (LGS) could be appropriate for this application. In this paper, the advantages of langasite crystal are presented and the fabrication of similar microsensors in langasite temperature-compensated cuts by chemical etching is proved. A monolithic length extension resonator, with a tip at its end, is obtained which constitutes a real advantage in regard to the existing quartz devices.

Amplitude saturation of MEMS resonators explained by autoparametric resonance

This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators.

Ferroelectric and electromechanical property characterization of single Pb(ZrTi)O3 fiber resonator

Piezoelectric fibers and fiber composites have attracted much attention for anisotropic sensing and actuation applications in recent year. Complete property characterization for piezoelectric fibers is essential for material and device design and fabrication. In this work, ferroelectric and electromechanical properties of single piezoelectric Pb(ZrTi)O3 (PZT) fiber were characterized by polarization–electric field hysteresis loop measurement using single PZT fiber/polymer 1–3 composite approach, and by direct measurement of the complex impedance spectrum of single PZT fiber resonator. A normalized electrical impedance spectrum method developed recently was used to determine the complex piezoelectric, elastic, and dielectric coefficients, mechanical quality factor and electromechanical coefficient from the complex electrical impedance-frequency spectrum measurement. The results were compared with those determined by the IEEE standard method for the pure length extensional resonator. The permittivity of PZT fiber was found larger than PZT bulk materials, which was attributed for the core-shell structure of the fibers.

A comparison of vibrating beam resonators in Quartz, GaPO 4, LGS and LGT

The present paper reviews and compares the properties of vibrating beam resonators in length-extensional, flexural and cylindrical-torsional modes; resonators are designed and built with new piezoelectric materials: Gallium orthophosphate (GaPO 4), Langasite (LGS) and Langatate (LGT). Their characteristics are compared with the results obtained with the same structures built in classical Quartz crystal. For all 3 new crystals, temperature-compensated cuts have been found for length-extensional and flexural modes by a theoretical analysis. Experiments have been made on test beams fabricated by conventional precision lapping/machining and photolithography to deposit electrodes. The existence of temperature-compensated cuts for length-extensional resonators is experimentally confirmed. The possibilities of using temperature-compensated cylindrical resonators in the torsional modes are analysed and their temperature sensitivity is computed.

Atomically resolved imaging by low-temperature frequency-modulation atomic force microscopy using a quartz length-extension resonator

Low-temperature ultrahigh vacuum frequency-modulation atomic force microscopy (AFM) was performed using a 1 MHz length-extension type of quartz resonator as a force sensor. Taking advantage of the high stiffness of the resonator, the AFM was operated with an oscillation amplitude smaller than 100 pm, which is favorable for high spatial resolution, without snapping an AFM tip onto a sample surface. Atomically resolved imaging of the adatom structure on the Si(111)-(7x7) surface was successfully obtained.

Publisher's Note: “Atomically-resolved imaging by frequency-modulation atomic force microscopy using a quartz length-extension resonator”[Appl. Phys. Lett. 87, 133114 (2005)

Publisher's Note: “Atomically-resolved imaging by frequency-modulation atomic force microscopy using a quartz length-extension resonator”[Appl. Phys. Lett. 87, 133114 (2005)

Surface Potential Measurement by Atomic Force Microscopy Using Quartz Resonator

Scanning Kelvin probe microscopy (SKPM) is demonstrated using a 1 MHz quartz length extension resonator as a force sensor. A tungsten probe tip glued onto the end of the quartz rod is electrically connected to the electrode of the resonator for the detection of Coulomb force between the tip and the surface. To detect Coulomb force, a frequency shift signal is used instead of the oscillation amplitude of the resonator. Surface potential mapping is measured on a Au(111) single crystal with nanoscale carbon dots. A potential difference of 100 mV is observed between the Au surface and the carbon dots. The resolution of surface potential mapping is discussed in terms of sharpness of tip, tip–sample separation and Kelvin probe measurement technique.

Atomically-resolved imaging by frequency-modulation atomic force microscopy using a quartz length-extension resonator

Using a 1MHz length-extension type of quartz resonator as a force sensor for frequency-modulation atomic force microscopy (AFM), atomically resolved images of the Si(111)-(7×7) surface was obtained. Fabrications of a tip attached at the front end of the resonator by focused ion beam, and removal of the native oxide layer on the tip by in-situ field ion microscopy are found effective for achieving the highly-resolved AFM imaging.

Finite element modelling of nanostructured piezoelectric resonators (NAPIERs)

A new modification to the traditional piezoelectric thin film bulk acoustic wave resonator (FBAR) and solidly mounted acoustic wave resonator (SMR) is proven to significantly improve their performances. The proposed design involves the surface micro/nano structuring of planar piezoelectric thin films to realize an array of a large number of rod-like structures. In contrast to the plate-like thickness extensional resonance in traditional FBAR and SMR devices, the rod-like structures can be excited in their length extensional resonance, yielding a higher electromechanical coupling factor and effectively eliminating the spurious resonances from lateral modes of vibration. The designs have been investigated by two and three-dimensional finite element analyses and one-dimensional transmissionline modelling. The results show that significant increases in the electromechanical coupling factor of ca. 40% can be achieved by using the rod-like length extensional resonances as compared with the plate-like thickness extensional resonances in traditional devices. Simulations show that rod width-to-thickness aspect ratios of less than 0.5 could result in an electromechanical coupling factor (k2eff) of over 10% for a zinc oxide device, compared with approximately 7% for a conventional design.