Peter G. Steeneken

Graphene Squeeze-Film Pressure Sensors

The operating principle of squeeze-film pressure sensors is based on the pressure dependence of a membranes resonance frequency, caused by the compression of the surrounding gas which changes the resonator stiffness. To realize such sensors, not only strong and flexible membranes are required, but also minimization of the membranes mass is essential to maximize responsivity. Here, we demonstrate the use of a few-layer graphene membrane as a squeeze-film pressure sensor. A clear pressure dependence of the membranes resonant frequency is observed, with a frequency shift of 4 MHz between 8 and 1000 mbar. The sensor shows a reproducible response and no hysteresis. The measured responsivity of the device is 9000 Hz/mbar, which is a factor 45 higher than state-of-the-art MEMS-based squeeze-film pressure sensors while using a 25 times smaller membrane area.

Nonlinear dynamic characterization of two-dimensional materials

D. Davidovikj, F. Alijani, S. J. Cartamil-Bueno, H. S. J. van der Zant, M. Amabili, and P. G. Steeneken Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands Department of Precision and Microsystems Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street W. Montreal, Quebec, Canada, H3A 2K6Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator’s material properties has remained elusive. Here we show a method forxa0determining the Young’s modulus of suspended 2D material membranes from their nonlinear dynamic response. To demonstrate the method, we perform measurements on graphene and MoS2 nanodrums electrostatically driven into the nonlinear regime at multiple driving forces. We show that a set of frequency response curves can be fitted using only the cubic spring constant as a fit parameter, which we then relate to the Young’s modulus of the material using membrane theory. The presented method is fast, contactless, and provides a platform for high-frequency characterization of the mechanical properties of 2D materials.The mechanical resonances of atomically thin membranes show nonlinear responses at driving forces in the picoNewton range. Here, the authors develop a contactless method to extract the Young’s modulus of 2D materials from the nonlinear dynamic response of these nanomechanical resonators.

High-quality-factor tantalum oxide nanomechanical resonators by laser oxidation of TaSe2

Controlling the strain in two-dimensional (2D) materials is an interesting avenue to tailor the mechanical properties of nanoelectromechanical systems. Here, we demonstrate a technique to fabricate ultrathin tantalum oxide nanomechanical resonators with large stress by the laser oxidation of nano-drumhead resonators composed of tantalum diselenide (TaSe2), a layered 2D material belonging to the metal dichalcogenides. Before the study of their mechanical properties with a laser interferometer, we verified the oxidation and crystallinity of the freely suspended tantalum oxide using high-resolution electron microscopy. We demonstrate that the stress of tantalum oxide resonators increases by 140 MPa (with respect to pristine TaSe2 resonators), which causes an enhancement in the quality factor (14 times larger) and resonance frequency (9 times larger) of these resonators.

High-Q Tantalum Oxide Nanomechanical Resonators by Laser-Oxidation of TaSe2

Controlling the strain in two-dimensional (2D) materials is an interesting avenue to tailor the mechanical properties of nanoelectromechanical systems. Here, we demonstrate a technique to fabricate ultrathin tantalum oxide nanomechanical resonators with large stress by the laser oxidation of nano-drumhead resonators composed of tantalum diselenide (TaSe2), a layered 2D material belonging to the metal dichalcogenides. Before the study of their mechanical properties with a laser interferometer, we verified the oxidation and crystallinity of the freely suspended tantalum oxide using high-resolution electron microscopy. We demonstrate that the stress of tantalum oxide resonators increases by 140 MPa (with respect to pristine TaSe2 resonators), which causes an enhancement in the quality factor (14 times larger) and resonance frequency (9 times larger) of these resonators.

Spontaneous mechanical oscillation of a DC driven single crystal

A micrometre-scale device that exploits the piezoresistive characteristics of silicon acts like an engine, converting heat into mechanical work in one mode of operation, and, in another, like a refrigerator, suppressing mechanical fluctuations.There is a large interest to decrease the size of mechanical oscillators since this can lead to miniaturization of timing and frequency referencing devices, but also because of the potential of small mechanical oscillators as extremely sensitive sensors. Here we show that a single crystal silicon resonator structure spontaneously starts to oscillate when driven by a constant direct current (DC). The mechanical oscillation is sustained by an electrothermomechanical feedback effect in a nanobeam, which operates as a mechanical displacement amplifier. The displacement of the resonator mass is amplified, because it modulates the resistive heating power in the nanobeam via the piezoresistive effect, which results in a temperature variation that causes a thermal expansion feedback-force from the nanobeam on the resonator mass. This self-amplification effect can occur in almost any conducting material, but is particularly effective when the current density and mechanical stress are concentrated in beams of nano-scale dimensions.

Colorimetry Technique for Scalable Characterization of Suspended Graphene

Previous statistical studies on the mechanical properties of chemical-vapor-deposited (CVD) suspended graphene membranes have been performed by means of measuring individual devices or with techniques that affect the material. Here, we present a colorimetry technique as a parallel, noninvasive, and affordable way of characterizing suspended graphene devices. We exploit Newtons rings interference patterns to study the deformation of a double-layer graphene drum 13.2 μm in diameter when a pressure step is applied. By studying the time evolution of the deformation, we find that filling the drum cavity with air is 2-5 times slower than when it is purged.

Visualizing the Motion of Graphene Nanodrums

Membranes of suspended two-dimensional materials show a large variability in mechanical properties, in part due to static and dynamic wrinkles. As a consequence, experiments typically show a multitude of nanomechanical resonance peaks, which make an unambiguous identification of the vibrational modes difficult. Here, we probe the motion of graphene nanodrum resonators with spatial resolution using a phase-sensitive interferometer. By simultaneously visualizing the local phase and amplitude of the driven motion, we show that unexplained spectral features represent split degenerate modes. When taking these into account, the resonance frequencies up to the eighth vibrational mode agree with theory. The corresponding displacement profiles, however, are remarkably different from theory, as small imperfections increasingly deform the nodal lines for the higher modes. The Brownian motion, which is used to calibrate the local displacement, exhibits a similar mode pattern. The experiments clarify the complicated dynamic behavior of suspended two-dimensional materials, which is crucial for reproducible fabrication and applications.

Direct and parametric synchronization of a graphene self-oscillator

We explore the dynamics of a graphene nanomechanical oscillator coupled to a reference oscillator. Circular graphene drums are forced into self-oscillation, at a frequency f osc, by means of photothermal feedback induced by illuminating the drum with a continuous-wave red laser beam. Synchronization to a reference signal, at a frequency f sync, is achieved by shining a power-modulated blue laser onto the structure. We investigate two regimes of synchronization as a function of both detuning and signal strength for direct ( f sync ≈ f o s c ) and parametric locking ( f sync ≈ 2 f osc ). We detect a regime of phase resonance, where the phase of the oscillator behaves as an underdamped second-order system, with the natural frequency of the phase resonance showing a clear power-law dependence on the locking signal strength. The phase resonance is qualitatively reproduced using a forced van der Pol-Duffing-Mathieu equation.

Graphene gas osmometers

We show that graphene membranes that separate two gases at identical pressure are deflected by osmotic pressure. The osmotic pressure is a consequence of differences in gas permeation rates into a few-layer graphene enclosed cavity. The deflection of the membrane is detected by measuring the tension-induced resonance frequency with an interferometric technique. Using a calibration measurement of the relation between resonance frequency and pressure, the time dependent osmotic pressure on the graphene is extracted. The time dependent osmotic pressure for different combinations of gases shows large differences that can be accounted for by a model based on the different gas permeation rates. In this way, a graphene-membrane based gas osmometer with a responsivity of ~60 kHz mbar–1 and nanoscale dimensions is demonstrated.

Very large scale characterization of graphene mechanical devices using a colorimetry technique

We use a scalable optical technique to characterize more than 21u2009000 circular nanomechanical devices made of suspended single- and double-layer graphene on cavities with different diameters (D) and depths (g). To maximize the contrast between suspended and broken membranes we used a model for selecting the optimal color filter. The method enables parallel and automatized image processing for yield statistics. We find the survival probability to be correlated with a structural mechanics scaling parameter given by D4/g3. Moreover, we extract a median adhesion energy of Γ = 0.9 J m-2 between the membrane and the native SiO2 at the bottom of the cavities.