Broadband Vibration-Based Energy Harvesting for Wireless Sensor Applications Using Frequency Upconversion.

Silicon-based kinetic energy converters employing variable capacitors, also known as electrostatic vibration energy harvesters, hold promise as power sources for Internet of Things devices. However, for most wireless applications, such as wearable technology or environmental and structural monitoring, the ambient vibration is often at relatively low frequencies (1-100 Hz). Since the power output of electrostatic harvesters is positively correlated to the frequency of capacitance oscillation, typical electrostatic energy harvesters, designed to match the natural frequency of ambient vibrations, do not produce sufficient power output. Moreover, energy conversion is limited to a narrow range of input frequencies. To address these shortcomings, an impacted-based electrostatic energy harvester is explored experimentally. The impact refers to electrode collision and it triggers frequency upconversion, namely a secondary high-frequency free oscillation of the electrodes overlapping with primary device oscillation tuned to input vibration frequency. The main purpose of high-frequency oscillation is to enable additional energy conversion cycles since this will increase the energy output. The devices investigated were fabricated using a commercial microfabrication foundry process and were experimentally studied. These devices exhibit non-uniform cross-section electrodes and a springless mass. The non-uniform width electrodes were used to prevent pull-in following electrode collision. Springless masses from different materials and sizes, such as 0.5 mm diameter Tungsten carbide, 0.8 mm diameter Tungsten carbide, zirconium dioxide, and silicon nitride, were added in an attempt to force collisions over a range of applied frequencies that would not otherwise result in collisions. The results show that the system operates over a relatively wide frequency range (up to 700 Hz frequency range), with the lower limit far below the natural frequency of the device. The addition of the springless mass successfully increased the device bandwidth. For example, at a low peak-to-peak vibration acceleration of 0.5 g (peak-to-peak), the addition of a zirconium dioxide ball doubled the device's bandwidth. Testing with different balls indicates that the different sizes and material properties have different effects on the device's performance, altering its mechanical and electrical damping.

On the Lateral Instability Analysis of MEMS Comb-Drive Electrostatic Transducers.

This paper investigates the lateral pull-in effect of an in-plane overlap-varying transducer. The instability is induced by the translational and rotational displacements. Based on the principle of virtual work, the equilibrium conditions of force and moment in lateral directions are derived. The analytical solutions of the critical voltage, at which the pull-in phenomenon occurs, are developed when considering only the translational stiffness or only the rotational stiffness of the mechanical spring. The critical voltage in a general case is numerically determined by using nonlinear optimization techniques, taking into account the combined effect of translation and rotation. The influences of possible translational offsets and angular deviations to the critical voltage are modeled and numerically analyzed. The investigation is then expanded for the first time to anti-phase operation mode and Bennet's doubler configuration of the two transducers.

The challenge of distinguishing mechanical, electrical and piezoelectric losses.

Understanding the energy loss in piezoelectric materials is of significant importance for manufacturers of acoustic transducers. The contributions to the power dissipation due to nonzero phase angles of the mechanical, electrical, and piezoelectric constants can be separated in the expression for power dissipation density. However, this division into separate contributions depends on the piezoelectric constitutive equation form used. Thus, it is problematic to identify any of the three terms with a specific physical domain, electric or mechanical, or to a coupling as is common in the discussion of loss in piezoelectric materials. Therefore, assumptions on the phase of the material constants based on this distinction could be erroneous and lead to incorrect piezoelectric models. This study demonstrates the challenge of distinguishing mechanical, electrical, and piezoelectric losses by investigating the power dissipation density and its contributions in a piezoelectric rod for all four piezoelectric constitutive equation forms.

Constitutive Equations of Piezoelectric Layered Beams With Interdigitated Electrodes.

This paper establishes the constitutive equations, or linear two-port models, of piezoelectric layered beams with interdigital electrodes (IDEs). The effect of the nontrivial field on the transduction is analyzed. Based on conformal mapping techniques, we derive new analytic expressions for the capacitance, the electric field, and the electromechanical coupling factor of an anisotropic dielectric with the IDE configuration on top. The IDE capacitance with an anisotropic permittivity can be treated as the one with an isotropic permittivity. The complex expression for the nonuniform field is simplified to a quadratic form. A correction is required for the transducer's coupling constant. All modifications are expressed analytically. The analytic models are verified against the finite element method. Finally, the two-port models help to compare the devices with other electrode configurations, such as beams with a top and bottom electrode.

Actuation of Piezoelectric Layered Beams With and Coupling.

In this paper, we derive and compare the linear static bending of piezoelectric actuators with transversal ( ) and longitudinal ( ) coupling. The transducers are, respectively, structures utilizing top and bottom electrodes (TBEs) and interdigitated electrodes (IDEs). While the theory is well developed for the TBE beam, governing equations for the bending of the piezoelectric beams with IDEs are far less developed. We improve on this by deriving the governing equation for the IDE beam with an arbitrary number of layers and with coupling consistently included. In addition, we introduce a phenomenological quadratic form for the nonuniform field that lets us derive a deflection formula with nontrivial effects of the field accounted for. The theory is applied to derive deflection formulas for both cantilever and clamped-clamped beams. All analytic results are validated with numerical simulations. From the analytic models, two different figures of merit (FOMs) are derived. We show that these FOMs are the same for cantilevers and doubly clamped beams. The analysis indicates the optimal transducer length for clamped-clamped beams and gives a criterion that can be used to determine which design concept ( or ) gives the largest deflection.

Modeling framework for piezoelectrically actuated MEMS tunable lenses.

WWe report a modeling framework for evaluating the performance of piezoelectrically actuated MEMS tunable lenses. It models the static opto-electromechanical coupling for symmetric configurations of piezoelectric actuators based on the laminated-plate theory, linear piezoelectricity, and ray tracing. With these assumptions, it helps to find geometrical parameters for actuators on clamped square or circular diaphragms that give a diffraction-limited tunable lens with minimum F-number. The tunable lens' optical performance and its focusing capability, alone and in combination with a paraxial fixed lens, were calculated in terms of object distance and actuation voltage. Using the modeling framework, we confirmed that the modulation transfer function for objects located at different distances remains the same after voltage adjustment.

Identification of microfluidic two-phase flow patterns in lab-on-chip devices.

This work describes a capacitive sensor for identification of microfluidic two-phase flow in lab-on-chip devices. With interdigital electrodes and thin insulation layer utilized, this sensor is capable of being integrated with the microsystems easily. Transducing principle and design considerations are presented with respect to the microfluidic gas/liquid flow patterns. Numerical simulation results verify the operational principle. And the factors affecting the performance of the sensor are discussed. Besides, a feasible process flow for the fabrication is also proposed.

Fundamental issues in nonlinear wideband-vibration energy harvesting.

Mechanically nonlinear energy harvesters driven by broadband vibrations modeled as white noise are investigated. We derive an upper bound on output power versus load resistance and show that, subject to mild restrictions that we make precise, the upper-bound performance can be obtained by a linear harvester with appropriate stiffness. Despite this, nonlinear harvesters can have implementation-related advantages. Based on the Kramers equation, we numerically obtain the output power at weak coupling for a selection of phenomenological elastic potentials and discuss their merits.

Integration of Carbon Nanotubes in Microsystems: Local Growth and Electrical Properties of Contacts.

Carbon nanotubes (CNTs) have been directly grown onto a silicon microsystem by a local synthesis method. This method has potential for wafer-level complimentary metal-oxide-semiconductor (CMOS) transistor-compatible integration of CNTs into more complex Si microsystems; enabling, e.g., gas sensors at low cost. In this work, we demonstrate that the characteristics of CNTs grown on specific locations can be changed by tuning the synthesis conditions. We also investigate the role of the contact between CNTs and the Si microsystem; observing a large influence on the electrical characteristics of our devices. Different contact modes can render either an ohmic or Schottky-like rectifying characteristics.

Local Synthesis of Carbon Nanotubes in Silicon Microsystems: The Effect of Temperature Distribution on Growth Structure.

Local synthesis and direct integration of carbon nanotubes (CNTs) into microsystems is a promising method for producing CNT-based devices in a single step, low-cost, and wafer-level, CMOS/MEMS-compatible process. In this report, the structure of the locally grown CNTs are studied by transmission imaging in scanning electron microscopy-S(T)EM. The characterization is performed directly on the microsystem, without any post-synthesis processing required. The results show an effect of temperature on the structure of CNTs: high temperature favors thin and regular structures, whereas low temperature favors "bamboo-like" structures.

Piezoelectric MEMS energy harvesting systems driven by harmonic and random vibrations.

Switching power conditioning techniques are known to greatly enhance the performance of linear piezoelectric energy harvesters subject to harmonic vibrations. With such circuits, little is known about the effect of mechanical stoppers that limit the motion or about waveforms other than harmonic vibrations. This work presents SPICE simulations of piezoelectric micro energy harvester systems that differ in choice of power conditioning circuits and stopper models. We consider in detail both harmonic and random vibrations. The nonlinear switching conversion circuitry performs better than simple passive circuitry, especially when mechanical stoppers are in effect. Stopper loss is important under broadband vibrations. Stoppers limit the output power for sinusoidal excitations, but result in the same output power whether the stoppers are lossy or not. When the mechanical stoppers are hit by the proof mass during high-amplitude vibrations, nonlinear effects such as saturation and jumps are present.