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a) Oscillation amplitude at the resonance frequency of the cantilever induced by sub-harmonic excitation at half the resonance (f el = f 0 /2 = 173.765 kHz). U ac is varied from 1 V to 5 V and U dc is constant at 5 V. The inset shows the quadratic increase in the peak amplitude with increasing U ac. b) The oscillation amplitude is independent on U dc .
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Abstract
Background: Encased cantilevers are novel force sensors that overcome major limitations of liquid scanning probe microscopy. By trapping air inside an encasement around the cantilever, they provide low damping and maintain high resonance frequencies for exquisitely low tip–sample interaction forces even when immersed in a viscous fluid. Q...
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Context 1
... Figure 4a shows the measured ampli- tude using sub-harmonic electrostatic excitation for constant U dc = 5 V and U ac varying from 1 to 5 V. As predicted, the electrostatic force and resulting amplitude increase quadrati- cally with U ac . ...
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... predicted, the electrostatic force and resulting amplitude increase quadrati- cally with U ac . Figure 4b confirms that the oscillation ampli- tude is independent of U dc . Sweeping U dc from −3.75 V to +3.75 V leaves the amplitude unaffected. ...
Context 3
... sub-harmonic excitation the drive frequency is set to half of the mechanical resonance (ω el = ω 0 /2) such that the second-order force is actuating the cantilever at resonance (f el = f 0 /2 = 173.765 kHz). Figure 4a shows the measured ampli- tude using sub-harmonic electrostatic excitation for constant U dc = 5 V and U ac varying from 1 to 5 V. As predicted, the electrostatic force and resulting amplitude increase quadrati- cally with U ac . Figure 4b confirms that the oscillation ampli- tude is independent of U dc . Sweeping U dc from −3.75 V to +3.75 V leaves the amplitude unaffected. Through fitting of our results we find that the resulting amplitude is best expressed by . When compared to harmonic excita- tion, the same electrical potential results in a four-times smaller force (see Equations Equation 1 and Equation 2). For instance at |U dc − U CPD | = U ac = 4 V the oscillation amplitude induced by sub-harmonic excitation is approx. 400 pm, whereas it is approx. 1.60 nm using harmonic actuation (see blue cross in Figure 3b.). ...
Context 4
... sub-harmonic excitation the drive frequency is set to half of the mechanical resonance (ω el = ω 0 /2) such that the second-order force is actuating the cantilever at resonance (f el = f 0 /2 = 173.765 kHz). Figure 4a shows the measured ampli- tude using sub-harmonic electrostatic excitation for constant U dc = 5 V and U ac varying from 1 to 5 V. As predicted, the electrostatic force and resulting amplitude increase quadrati- cally with U ac . Figure 4b confirms that the oscillation ampli- tude is independent of U dc . Sweeping U dc from −3.75 V to +3.75 V leaves the amplitude unaffected. Through fitting of our results we find that the resulting amplitude is best expressed by . When compared to harmonic excita- tion, the same electrical potential results in a four-times smaller force (see Equations Equation 1 and Equation 2). For instance at |U dc − U CPD | = U ac = 4 V the oscillation amplitude induced by sub-harmonic excitation is approx. 400 pm, whereas it is approx. 1.60 nm using harmonic actuation (see blue cross in Figure 3b.). ...
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Citations
... Multiple peaks with similar mode shapes were observed across all experiments, but only the peak with a mode shape containing minimum displacement at the anchor point(s) was selected to be the fundamental resonant frequency. Multiple resonant peaks with similar modal shapes is also known as "forest of peaks" and has been reported before by others 29 . Coupling of the resonators with each other through the substrate could be argued to cause multiple peaks. ...
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... Microcantilever mass sensors consist of a rectangular shaped beam, normally composed of silicon [2], which is clamped at one end to the substrate forming a flexible electrode. The unclamped end of the beam is suspended above the substrate where a second electrode is deposited [3], by a fixed and designed distance, as shown in Figure 3. Microcantilever mass sensor dimensions are typically up to 50 µm, 500 µm, and 2 µm for width, length, and thickness, respectively. However, dimensions ranging in the hundreds of nanometers have been achieved with emerging nanotechnology fabrication techniques [4]. ...
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... For example, the piezoelectric [23][24][25][26] , electrothermal [27][28][29][30][31] , and Lorentz force 32 excitation methods require specially designed microfabricated cantilevers. Compared to them, the electrostrictive 33 and electrostatic [34][35][36][37] excitation methods have a wider applicability as they only require metal coatings on a cantilever. However, an application of a bias voltage in liquid can induce serious problems such as uncontrolled electrochemical reactions and diffusion of surface charges. ...
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Micro-cantilever beams interact with fluids in static or dynamic modes for several applications with different research purposes. Various theoretical studies are performed based on mathematical dynamic models for fluid-cantilever relationships. Outputs of relevant experimental studies are revealed and evaluated with the consideration of the interactions of micro-cantilevers with fluids. Oscillating micro-cantilevers are used to measure the rheological properties of the Newtonian and non-Newtonian fluids. Oscillation observables such as amplitude, frequency, and phase shift at different eigenmodes of the micro-cantilevers might exhibit notable sensitivities to variations in fluid properties. By considering resonance frequencies and quality factors of micro-cantilevers, densities, and viscosities of fluids can be determined simultaneously. Moreover, AFM micro-cantilevers are driven by using single- and multi-frequency excitation schemes to image the cells and biological specimens with high sensitivity in surrounding liquid environments. Several variations of AFM modes are utilized to visualize the surfaces of samples with high atomic resolution. Investigating interaction force sensitivity in a viscous environment, multi-frequency excitations might provide highly responsive observables at higher eigenmodes. Additionally, micro-fluidic micro-cantilevers are regarded as well-known significant tools to characterize liquids with high selectivity. Monitoring deflections of hollow micro-cantilevers enables the characterization of picoliter liquids with high sensitivity. Therefore, this study covers a comprehensive review on the dynamic responses of micro-cantilevers to varied fluidic conditions. Thorough analysis and discussions are performed to demonstrate the roles of micro-cantilevers in versatile fluidic applications.
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