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1.  High-resolution dynamic atomic force microscopy in liquids with different feedback architectures 
The recent achievement of atomic resolution with dynamic atomic force microscopy (dAFM) [Fukuma et al., Appl. Phys. Lett. 2005, 87, 034101], where quality factors of the oscillating probe are inherently low, challenges some accepted beliefs concerning sensitivity and resolution in dAFM imaging modes. Through analysis and experiment we study the performance metrics for high-resolution imaging with dAFM in liquid media with amplitude modulation (AM), frequency modulation (FM) and drive-amplitude modulation (DAM) imaging modes. We find that while the quality factors of dAFM probes may deviate by several orders of magnitude between vacuum and liquid media, their sensitivity to tip–sample forces can be remarkable similar. Furthermore, the reduction in noncontact forces and quality factors in liquids diminishes the role of feedback control in achieving high-resolution images. The theoretical findings are supported by atomic-resolution images of mica in water acquired with AM, FM and DAM under similar operating conditions.
PMCID: PMC3596120  PMID: 23503468
atomic force microscopy; dAFM; high-resolution; liquids
2.  Interpreting motion and force for narrow-band intermodulation atomic force microscopy 
Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip–surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show, by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time-domain perspective, we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip–surface force that are in-phase with the tip motion (F I) and quadrature to the motion (F Q). Traditionally, these force components have been considered as a function of the static-probe height only. Here we show that F I and F Q actually depend on both static-probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of F I and F Q from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe-height dependence of the force components F I and F Q, providing deeper insight into the tip–surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.
PMCID: PMC3566785  PMID: 23400552
atomic force microscopy; AFM; frequency combs; force spectroscopy; high-quality-factor resonators; intermodulation; multifrequency
3.  A measurement of the hysteresis loop in force-spectroscopy curves using a tuning-fork atomic force microscope 
Measurements of the frequency shift versus distance in noncontact atomic force microscopy (NC-AFM) allow measurements of the force gradient between the oscillating tip and a surface (force-spectroscopy measurements). When nonconservative forces act between the tip apex and the surface the oscillation amplitude is damped. The dissipation is caused by bistabilities in the potential energy surface of the tip–sample system, and the process can be understood as a hysteresis of forces between approach and retraction of the tip. In this paper, we present the direct measurement of the whole hysteresis loop in force-spectroscopy curves at 77 K on the PTCDA/Ag/Si(111) √3 × √3 surface by means of a tuning-fork-based NC-AFM with an oscillation amplitude smaller than the distance range of the hysteresis loop. The hysteresis effect is caused by the making and breaking of a bond between PTCDA molecules on the surface and a PTCDA molecule at the tip. The corresponding energy loss was determined to be 0.57 eV by evaluation of the force–distance curves upon approach and retraction. Furthermore, a second dissipation process was identified through the damping of the oscillation while the molecule on the tip is in contact with the surface. This dissipation process occurs mainly during the retraction of the tip. It reaches a maximum value of about 0.22 eV/cycle.
PMCID: PMC3323909  PMID: 22496993
atomic force microscopy; energy dissipation; force spectroscopy; hysteresis loop; PTCDA/Ag/Si(111) √3 × √3
4.  Determining cantilever stiffness from thermal noise 
We critically discuss the extraction of intrinsic cantilever properties, namely eigenfrequency f n, quality factor Q n and specifically the stiffness k n of the nth cantilever oscillation mode from thermal noise by an analysis of the power spectral density of displacement fluctuations of the cantilever in contact with a thermal bath. The practical applicability of this approach is demonstrated for several cantilevers with eigenfrequencies ranging from 50 kHz to 2 MHz. As such an analysis requires a sophisticated spectral analysis, we introduce a new method to determine k n from a spectral analysis of the demodulated oscillation signal of the excited cantilever that can be performed in the frequency range of 10 Hz to 1 kHz regardless of the eigenfrequency of the cantilever. We demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems.
PMCID: PMC3628876  PMID: 23616942
AFM; cantilever; noncontact atomic force microscopy (NC-AFM); Q-factor; thermal excitation; resonance; spectral analysis; stiffness
5.  Force to Rebalance Control of HRG and Suppression of Its Errors on the Basis of FPGA 
Sensors (Basel, Switzerland)  2011;11(12):11761-11773.
A novel design of force to rebalance control for a hemispherical resonator gyro (HRG) based on FPGA is demonstrated in this paper. The proposed design takes advantage of the automatic gain control loop and phase lock loop configuration in the drive mode while making full use of the quadrature control loop and rebalance control loop in controlling the oscillating dynamics in the sense mode. First, the math model of HRG with inhomogeneous damping and frequency split is theoretically analyzed. In addition, the major drift mechanisms in the HRG are described and the methods that can suppress the gyro drift are mentioned. Based on the math model and drift mechanisms suppression method, four control loops are employed to realize the manipulation of the HRG by using a FPGA circuit. The reference-phase loop and amplitude control loop are used to maintain the vibration of primary mode at its natural frequency with constant amplitude. The frequency split is readily eliminated by the quadrature loop with a DC voltage feedback from the quadrature component of the node. The secondary mode response to the angle rate input is nullified by the rebalance control loop. In order to validate the effect of the digital control of HRG, experiments are carried out with a turntable. The experimental results show that the design is suitable for the control of HRG which has good linearity scale factor and bias stability.
PMCID: PMC3252009  PMID: 22247692
Hemispherical Resonator Gyro (HRG); force-to-rebalance control; FPGA; quadrature error; rate sensor
6.  Bimodal atomic force microscopy driving the higher eigenmode in frequency-modulation mode: Implementation, advantages, disadvantages and comparison to the open-loop case 
We present an overview of the bimodal amplitude–frequency-modulation (AM-FM) imaging mode of atomic force microscopy (AFM), whereby the fundamental eigenmode is driven by using the amplitude-modulation technique (AM-AFM) while a higher eigenmode is driven by using either the constant-excitation or the constant-amplitude variant of the frequency-modulation (FM-AFM) technique. We also offer a comparison to the original bimodal AFM method, in which the higher eigenmode is driven with constant frequency and constant excitation amplitude. General as well as particular characteristics of the different driving schemes are highlighted from theoretical and experimental points of view, revealing the advantages and disadvantages of each. This study provides information and guidelines that can be useful in selecting the most appropriate operation mode to characterize different samples in the most efficient and reliable way.
PMCID: PMC3628543  PMID: 23616939
amplitude-modulation; atomic force microscopy; frequency-modulation; phase-locked loop; spectroscopy
7.  Repulsive bimodal atomic force microscopy on polymers 
Bimodal atomic force microscopy can provide high-resolution images of polymers. In the bimodal operation mode, two eigenmodes of the cantilever are driven simultaneously. When examining polymers, an effective mechanical contact is often required between the tip and the sample to obtain compositional contrast, so particular emphasis was placed on the repulsive regime of dynamic force microscopy. We thus investigated bimodal imaging on a polystyrene-block-polybutadiene diblock copolymer surface and on polystyrene. The attractive operation regime was only stable when the amplitude of the second eigenmode was kept small compared to the amplitude of the fundamental mode. To clarify the influence of the higher eigenmode oscillation on the image quality, the amplitude ratio of both modes was systematically varied. Fourier analysis of the time series recorded during imaging showed frequency mixing. However, these spurious signals were at least two orders of magnitude smaller than the first two fundamental eigenmodes. Thus, repulsive bimodal imaging of polymer surfaces yields a good signal quality for amplitude ratios smaller than A 01 /A 02 = 10:1 without affecting the topography feedback.
PMCID: PMC3388370  PMID: 23016150
bimodal AFM imaging; diblock copolymer; polybutadiene; polystyrene
8.  Development of a Prototype Miniature Silicon Microgyroscope 
Sensors (Basel, Switzerland)  2009;9(6):4586-4605.
A miniature vacuum-packaged silicon microgyroscope (SMG) with symmetrical and decoupled structure was designed to prevent unintended coupling between drive and sense modes. To ensure high resonant stability and strong disturbance resisting capacity, a self-oscillating closed-loop circuit including an automatic gain control (AGC) loop based on electrostatic force feedback is adopted in drive mode, while, dual-channel decomposition and reconstruction closed loops are applied in sense mode. Moreover, the temperature effect on its zero bias was characterized experimentally and a practical compensation method is given. The testing results demonstrate that the useful signal and quadrature signal will not interact with each other because their phases are decoupled. Under a scale factor condition of 9.6 mV/°/s, in full measurement range of ± 300 deg/s, the zero bias stability reaches 15°/h with worse-case nonlinearity of 400 ppm, and the temperature variation trend of the SMG bias is thus largely eliminated, so that the maximum bias value is reduced to one tenth of the original after compensation from -40 °C to 80 °C.
PMCID: PMC3291928  PMID: 22408543
silicon microgyroscope (SMG); self-oscillating; dual-channel closed-loop; scale factor; zero bias stability; temperature compensation; miniature prototype
9.  Analysis of force-deconvolution methods in frequency-modulation atomic force microscopy 
In frequency-modulation atomic force microscopy the direct observable is the frequency shift of an oscillating cantilever in a force field. This frequency shift is not a direct measure of the actual force, and thus, to obtain the force, deconvolution methods are necessary. Two prominent methods proposed by Sader and Jarvis (Sader–Jarvis method) and Giessibl (matrix method) are investigated with respect to the deconvolution quality. Both methods show a nontrivial dependence of the deconvolution quality on the oscillation amplitude. The matrix method exhibits spikelike features originating from a numerical artifact. By interpolation of the data, the spikelike features can be circumvented. The Sader–Jarvis method has a continuous amplitude dependence showing two minima and one maximum, which is an inherent property of the deconvolution algorithm. The optimal deconvolution depends on the ratio of the amplitude and the characteristic decay length of the force for the Sader–Jarvis method. However, the matrix method generally provides the higher deconvolution quality.
PMCID: PMC3323913  PMID: 22496997
frequency-modulation atomic force microscopy; force deconvolution; numerical implementation
10.  Intrinsically High-Q Dynamic AFM Imaging in Liquid with a Significantly Extended Needle Tip 
Nanotechnology  2012;23(23):235704.
Atomic force microscope (AFM) probe with a long and rigid needle tip was fabricated and studied for high Q factor dynamic (tapping mode) AFM imaging of samples submersed in liquid. The extended needle tip over a regular commercially-available tapping mode AFM cantilever was sufficiently long to keep the AFM cantilever from submersed in liquid, which significantly minimized the hydrodynamic damping involved in dynamic AFM imaging of samples in liquid. Dynamic AFM imaging of samples in liquid at an intrinsic Q factor of over 100 and an operation frequency of over 200 kHz was demonstrated. The method has the potential to be extended to acquire viscoelastic materials properties and provide truly gentle imaging of soft biological samples in physiological environments.
PMCID: PMC3401635  PMID: 22595833
11.  Noncontact microrheology at acoustic frequencies, using frequency-modulated atomic force microscopy 
Nature methods  2010;7(8):650-654.
We report an atomic force microscopy (AFM) method for assessing elastic and viscous properties of soft samples at acoustic frequencies under non-contact conditions. The method can be used to measure material properties via frequency modulation and is based on hydrodynamics theory of thin gaps we developed here. A cantilever with an attached microsphere is forced to oscillate tens of nanometers above a sample. The elastic modulus and viscosity of the sample are estimated by measuring the frequency-dependence of the phase lag between the oscillating microsphere and the driving piezo at various heights above the sample. This method features an effective area of pyramidal tips used in contact AFM but with only piconewton applied forces. Using this method, we analyzed polyacrylamide gels of different stiffness and assessed graded mechanical properties of guinea pig tectorial membrane. The technique enables the study of microrheology of biological tissues that produce or detect sound.
PMCID: PMC3508509  PMID: 20562866
12.  Self-starting, self-regulating Fourier domain mode locked fiber laser for OCT imaging 
Biomedical Optics Express  2011;2(7):2005-2011.
We present a Fourier domain mode locking (FDML) fiber laser with a feedback loop allowing automatic startup without a priori knowledge of the fundamental drive frequency. The feedback can also regulate the drive frequency making the source robust against environmental variations. A control system samples the energy of the light traversing the FDML cavity and uses a voltage controlled oscillator (VCO) to drive the tunable fiber Fabry-Perot filter in order to maximize that energy. We demonstrate a prototype self-starting, self-regulating FDML operating at 40 kHz with a full width tuning range of 140 nm around 1305 nm and a power output of ~40 mW. The laser starts up with no operator intervention in less than 5 seconds and exhibits improved spectral stability over a conventional FDML source. In OCT applications the source achieved over 120 dB detection sensitivity and an ~8.9-µm axial resolution.
PMCID: PMC3130584  PMID: 21750775
(110.4500) Optical coherence tomography; (140.3600) Lasers, tunable
13.  Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy 
The noise of the frequency-shift signal Δf in noncontact atomic force microscopy (NC-AFM) consists of cantilever thermal noise, tip–surface-interaction noise and instrumental noise from the detection and signal processing systems. We investigate how the displacement-noise spectral density d z at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density d Δ f at the demodulator output in dependence of cantilever properties and settings of the signal processing electronics in the limit of a negligible tip–surface interaction and a measurement under ultrahigh-vacuum conditions. For a quantification of the noise figures, we calibrate the cantilever displacement signal and determine the transfer function of the signal-processing electronics. From the transfer function and the measured d z, we predict d Δ f for specific filter settings, a given level of detection-system noise spectral density d z ds and the cantilever-thermal-noise spectral density d z th. We find an excellent agreement between the calculated and measured values for d Δ f. Furthermore, we demonstrate that thermal noise in d Δ f, defining the ultimate limit in NC-AFM signal detection, can be kept low by a proper choice of the cantilever whereby its Q-factor should be given most attention. A system with a low-noise signal detection and a suitable cantilever, operated with appropriate filter and feedback-loop settings allows room temperature NC-AFM measurements at a low thermal-noise limit with a significant bandwidth.
PMCID: PMC3566860  PMID: 23400758
Cantilever; feedback loop; filter; noncontact atomic force microscopy (NC-AFM); noise
14.  bOptimizing atomic force microscopy for characterization of diamond-protein interfaces 
Nanoscale Research Letters  2011;6(1):337.
Atomic force microscopy (AFM) in contact mode and tapping mode is employed for high resolution studies of soft organic molecules (fetal bovine serum proteins) on hard inorganic diamond substrates in solution and air. Various effects in morphology and phase measurements related to the cantilever spring constant, amplitude of tip oscillations, surface approach, tip shape and condition are demonstrated and discussed based on the proposed schematic models. We show that both diamond and proteins can be mechanically modified by Si AFM cantilever. We propose how to choose suitable cantilever type, optimize scanning parameters, recognize and minimize various artifacts, and obtain reliable AFM data both in solution and in air to reveal microscopic characteristics of protein-diamond interfaces. We also suggest that monocrystalline diamond is well defined substrate that can be applicable for fundamental studies of molecules on surfaces in general.
PMCID: PMC3211425  PMID: 21711846
15.  Atomic force microscopy with sub-picoNewton force stability for biological applications 
Methods (San Diego, Calif.)  2013;60(2):131-141.
Atomic force microscopy (AFM) is widely used in the biological sciences. Despite 25 years of technical developments, two popular modes of bioAFM, imaging and single molecule force spectroscopy, remain hindered by relatively poor force precision and stability. Recently, we achieved both sub-pN force precision and stability under biologically useful conditions (in liquid at room temperature). Importantly, this sub-pN level of performance is routinely accessible using a commercial cantilever on a commercial instrument. The two critical results are that (i) force precision and stability were limited by the gold coating on the cantilevers, and (ii) smaller yet stiffer cantilevers did not lead to better force precision on time scales longer than 25 ms. These new findings complement our previous work that addressed tip-sample stability. In this review, we detail the methods needed to achieve this sub-pN force stability and demonstrate improvements in force spectroscopy and imaging when using uncoated cantilevers. With this improved cantilever performance, the widespread use of nonspecific biomolecular attachments becomes a limiting factor in high-precision studies. Thus, we conclude by briefly reviewing site-specific covalent-immobilization protocols for linking a biomolecule to the substrate and to the AFM tip.
PMCID: PMC3669665  PMID: 23562681
Atomic force microscopy; scanning probe microscopy; single molecule force spectroscopy; drift; overstretching DNA; cantilever; imaging
16.  Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus 
Bimodal atomic force microscopy is a force-microscopy method that requires the simultaneous excitation of two eigenmodes of the cantilever. This method enables the simultaneous recording of several material properties and, at the same time, it also increases the sensitivity of the microscope. Here we apply fractional calculus to express the frequency shift of the second eigenmode in terms of the fractional derivative of the interaction force. We show that this approximation is valid for situations in which the amplitude of the first mode is larger than the length of scale of the force, corresponding to the most common experimental case. We also show that this approximation is valid for very different types of tip–surface forces such as the Lennard-Jones and Derjaguin–Muller–Toporov forces.
PMCID: PMC3323908  PMID: 22496992
AFM; atomic force microscopy; bimodal AFM; frequency shift; integral calculus applications
17.  Exploring the retention properties of CaF2 nanoparticles as possible additives for dental care application with tapping-mode atomic force microscope in liquid 
Amplitude-modulation atomic force microscopy (AM-AFM) is used to determine the retention properties of CaF2 nanoparticles adsorbed on mica and on tooth enamel in liquid. From the phase-lag of the forced cantilever oscillation the local energy dissipation at the detachment point of the nanoparticle was determined. This enabled us to compare different as-synthesized CaF2 nanoparticles that vary in shape, size and surface structure. CaF2 nanoparticles are candidates for additives in dental care products as they could serve as fluorine-releasing containers preventing caries during a cariogenic acid attack on the teeth. We show that the adherence of the nanoparticles is increased on the enamel substrate compared to mica, independently of the substrate roughness, morphology and size of the particles.
PMCID: PMC3896269  PMID: 24455460
AM-AFM in liquid; nanodentistry; nanoparticles
18.  Nanocharacterization of Soft Biological Samples in Shear Mode with Quartz Tuning Fork Probes 
Sensors (Basel, Switzerland)  2012;12(4):4803-4819.
Quartz tuning forks are extremely good resonators and their use is growing in scanning probe microscopy. Nevertheless, only a few studies on soft biological samples have been reported using these probes. In this work, we present the methodology to develop and use these nanosensors to properly work with biological samples. The working principles, fabrication and experimental setup are presented. The results in the nanocharacterization of different samples in different ambients are presented by using different working modes: amplitude modulation with and without the use of a Phase-Locked Loop (PLL) and frequency modulation. Pseudomonas aeruginosa bacteria are imaged in nitrogen using amplitude modulation. Microcontact printed antibodies are imaged in buffer using amplitude modulation with a PLL. Finally, metastatic cells are imaged in air using frequency modulation.
PMCID: PMC3355441  PMID: 22666059
tuning fork; atomic force microscopy; nanocharacterization
19.  Phase imaging of moving DNA molecules and DNA molecules replicated in the atomic force microscope. 
Nucleic Acids Research  1997;25(21):4379-4384.
Phase imaging with a tapping mode atomic force microscope (AFM) has many advantages for imaging moving DNA and DNA-enzyme complexes in aqueous buffers at molecular resolution. In phase images molecules can be resolved at higher scan rates and lower forces than in height images from the AFM. Higher scan rates make it possible to image faster processes. At lower forces the molecules are imaged more gently. Moving DNA molecules are also resolved more clearly in phase images than in height images. Phase images in tapping mode AFM show the phase difference between oscillation of the piezoelectric crystal that drives the cantilever and oscillation of the cantilever as it interacts with the sample surface. Phase images presented here show moving DNA molecules that have been replicated with Sequenase in the AFM and DNA molecules tethered in complexes with Escherichia coli RNA polymerase.
PMCID: PMC147043  PMID: 9336471
20.  Mechanical-Thermal Noise in Drive-Mode of a Silicon Micro-Gyroscope 
Sensors (Basel, Switzerland)  2009;9(5):3357-3375.
A new closed-loop drive scheme which decouples the phase and the gain of the closed-loop driving system was designed in a Silicon Micro-Gyroscope (SMG). We deduce the system model of closed-loop driving and use stochastic averaging to obtain an approximate “slow” system that clarifies the effect of thermal noise. The effects of mechanical-thermal noise on the driving performance of the SMG, including the noise spectral density of the driving amplitude and frequency, are derived. By calculating and comparing the noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude. We observe that the RMS noise frequency can be reduced by increasing the quality factor and the drive amplitude in the closed-loop driving system. The experiment and simulation validate the feasibility of closed-loop driving and confirm the validity of the averaged equation and its stablility criterion. The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and as the driving mass decreases, the mechanical-thermal noise may get bigger than the electrical noise of the closed-loop driving circuitry.
PMCID: PMC3297147  PMID: 22412316
Silicon Micro-Gyroscope (SMG); drive-mode; thermal noise; stochastic averaging
21.  The role of auditory feedback in sustaining vocal vibratoa) 
Vocal vibrato and tremor are characterized by oscillations in voice fundamental frequency (F0). These oscillations may be sustained by a control loop within the auditory system. One component of the control loop is the pitch-shift reflex (PSR). The PSR is a closed loop negative feedback reflex that is triggered in response to discrepancies between intended and perceived pitch with a latency of ~ 100 ms. Consecutive compensatory reflexive responses lead to oscillations in pitch every ~200 ms, resulting in ~5-Hz modulation of F0. Pitch-shift reflexes were elicited experimentally in six subjects while they sustained /u/ vowels at a comfortable pitch and loudness. Auditory feedback was sinusoidally modulated at discrete integer frequencies (1 to 10 Hz) with ±25 cents amplitude. Modulated auditory feedback induced oscillations in voice F0 output of all subjects at rates consistent with vocal vibrato and tremor. Transfer functions revealed peak gains at 4 to 7 Hz in all subjects, with an average peak gain at 5 Hz. These gains occurred in the modulation frequency region where the voice output and auditory feedback signals were in phase. A control loop in the auditory system may sustain vocal vibrato and tremorlike oscillations in voice F0.
PMCID: PMC1769352  PMID: 14514211
22.  “Magnetic Force Microscopy and Energy Loss Imaging of Superparamagnetic Iron Oxide Nanoparticles” 
Scientific Reports  2011;1:202.
We present quantitative, high spatially resolved magnetic force microscopy imaging of samples based on 11 nm diameter superparamagnetic iron oxide nanoparticles in air at room temperature. By a proper combination of the cantilever resonance frequency shift, oscillation amplitude and phase lag we obtain the tip-sample interaction maps in terms of force gradient and energy dissipation. These physical quantities are evaluated in the frame of a tip-particle magnetic interaction model also including the tip oscillation amplitude. Magnetic nanoparticles are characterized both in bare form, after deposition on a flat substrate, and as magnetically assembled fillers in a polymer matrix, in the form of nanowires. The latter approach makes it possible to reveal the magnetic texture in a composite sample independently of the surface topography.
PMCID: PMC3244111  PMID: 22355717
23.  Quantitative multichannel NC-AFM data analysis of graphene growth on SiC(0001) 
Noncontact atomic force microscopy provides access to several complementary signals, such as topography, damping, and contact potential. The traditional presentation of such data sets in adjacent figures or in colour-coded pseudo-three-dimensional plots gives only a qualitative impression. We introduce two-dimensional histograms for the representation of multichannel NC-AFM data sets in a quantitative fashion. Presentation and analysis are exemplified for topography and contact-potential data for graphene grown epitaxially on 6H-SiC(0001), as recorded by Kelvin probe force microscopy in ultrahigh vacuum. Sample preparations by thermal decomposition in ultrahigh vacuum and in an argon atmosphere are compared and the respective growth mechanisms discussed.
PMCID: PMC3304321  PMID: 22428109
FM-AFM; graphene; 6H-SiC(0001); KPFM; SPM
24.  A Unified Picture of Cantilever Frequency-Shift Measurements of Magnetic Resonance 
We report a unified framework describing all existing protocols for spin manipulation and signal creation in frequency-modulation magnetic resonance force microscopy using classical perturbation theory. The framework is well suited for studying the dependence of the frequency shift on the cantilever amplitude via numerical simulation. We demonstrate the formalism by recovering an exact result for a single spin signal and by simulating, for the first time as a function of cantilever amplitude, the frequency shift due to a volume of noninteracting spins inverted by an adiabatic rapid passage. We show that an optimal cantilever amplitude exists that maximizes the signal. Our findings suggest that understanding the amplitude dependence of the spin signal will be important for designing future high-sensitivity experiments.
PMCID: PMC3918878  PMID: 24523575
25.  Two Novel Measurements for the Drive-Mode Resonant Frequency of a Micromachined Vibratory Gyroscope 
Sensors (Basel, Switzerland)  2013;13(11):15770-15784.
To investigate the drive-mode resonance frequency of a micromachined vibratory gyroscope (MVG), one needs to measure it accurately and efficiently. The conventional approach to measure the resonant frequency is by performing a sweep frequency test and spectrum analysis. The method is time-consuming and inconvenient because of the requirements of many test points, a lot of data storage and off-line analyses. In this paper, we propose two novel measurement methods, the search method and track method, respectively. The former is based on the magnitude-frequency characteristics of the drive mode, utilizing a one-dimensional search technique. The latter is based on the phase-frequency characteristics, applying a feedback control loop. Their performances in precision, noise resistivity and efficiency are analyzed through detailed simulations. A test system is implemented based on a field programmable gate array (FPGA) and experiments are carried out. By comparing with the common approach, feasibility and superiorities of the proposed methods are validated. In particular, significant efficiency improvements are achieved whereby the conventional frequency method consumes nearly 5,000 s to finish a measurement, while only 5 s is needed for the track method and 1 s for the search method.
PMCID: PMC3871112  PMID: 24256977
micromachined vibratory gyroscope; drive mode; resonant frequency; one-dimensional search; golden section

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