Silicon Beam Research Articles

A theoretical and experimental comparison of 3-3 and 3-1 mode piezoelectric microelectromechanical systems (MEMS)

Two piezoelectric transducer modes applied in microelectromechanical systems are (i) the 3-1 mode with parallel electrodes perpendicular to a vertical polarization vector, and (ii) the 3-3 mode which uses interdigitated (IDT) electrodes to realize an in-plane polarization vector. This study compares the two configurations by deriving a Norton equivalent representation of each approach – including expressions for output charge and device capacitance. The model is verified using a microfabricated device comprised of multiple epitaxial silicon beams with sol–gel deposited lead zirconate titanate at the surface. The beams have identical dimensions and are attached to a common moving element at their tips. The only difference between beams is electrode configuration – enabling a direct comparison. Capacitance and charge measurements verify the presented theory with high accuracy. The Norton equivalent representation is general and enables comparison of any figure of merit, including electromechanical coupling coefficient and signal-to-noise ratio. With respect to coupling coefficient, the experimentally validated theory in this work suggests that 3-3 mode IDT-electrode configurations offer the potential for modest improvements compared against 3-1 mode devices (less than 2×), and the only geometrical parameter affecting this ratio is the fill factor of the IDT electrode.

Fracture Dynamics during the Silicon Layer Transfer of the Smart Cut™ Process

The Smart Cut™ technology [1] is currently the industry standard for manufacturing Silicon-On-Insulator (SOI) wafers. The implantation of relatively high doses of hydrogen ions in a silicon substrate leads to the formation of a buried weakened layer. This wafer is bonded onto a host substrate using direct wafer bonding. Under annealing, the implanted species evolve into microcracks lying parallel to the surface, and finally, a controlled fracture process occurs along the implanted layer. While Si/SiO2 direct wafer bonding statics and dynamics have been extensively studied [2],[3], the fracture dynamics during Smart Cut™ remains largely a field to be explored. Since the SOI standard thickness for microelectronics devices is always decreasing, the detailed understanding of the fracture becomes of greater interest e.g. to improve the post-split SOI wafer surfaces.In this paper, the crack propagation during the silicon layer transfer of the Smart Cut™ process is studied using an original patented optical bench[4] (Fig.1). The measurements are based on the transmission monitoring of infrared laser beams through the sample when the fracture wave front crosses the beams. The crack can be mechanically initiated by inserting a blade between the two wafers or thermally initiated by putting the sample into an appropriate oven. Combination of the two split modes is also possible. This set up allows the determination of the crack propagation velocity which is typically in the km.s-1 range. An in-depth study of the post wave front signal oscillations (Fig.2) enabled us to recover the deformation profile of the sample just after the fracture front has gone through it (Fig.3). At first, the two newly separated wafers drift away because of the strong internal pressure of the gas filled microcracks. The energy released during the crack opening separates the silicon beams by several micrometres, until reaching a maxima where the external atmospheric pressure becomes large enough to stop the two silicon arms diverging movement. Subsequently the motion will invert and the wafers will get closer again and reach a minima where the internal pressure will enable the two beams to pull away. Therefore, the wave crack "wake" is made of series of oscillations until the internal pressure equilibrates to the atmospheric one. The typical wavelength of such deformations is about several centimetres, while the vertical speed of displacement is quite slow, around 1µm.µs-1. The dynamics of this motion has been successfully modelled using beam elasticity and thermodynamics. From the modelling, it is e.g. possible to recover the amount of gas trapped inside the microcracks and better understand the driver of Smart Cut™ splitting technique.

High-sensitivity linear piezoresistive transduction for nanomechanical beam resonators.

Highly sensitive conversion of motion into readable electrical signals is a crucial and challenging issue for nanomechanical resonators. Efficient transduction is particularly difficult to realize in devices of low dimensionality, such as beam resonators based on carbon nanotubes or silicon nanowires, where mechanical vibrations combine very high frequencies with miniscule amplitudes. Here we describe an enhanced piezoresistive transduction mechanism based on the asymmetry of the beam shape at rest. We show that this mechanism enables highly sensitive linear detection of the vibration of low-resistivity silicon beams without the need of exceptionally large piezoresistive coefficients. The general application of this effect is demonstrated by detecting multiple-order modes of silicon nanowire resonators made by either top-down or bottom-up fabrication methods. These results reveal a promising approach for practical applications of the simplest mechanical resonators, facilitating its manufacturability by very large-scale integration technologies.

Plasticization of a polymer layer harnessed to a silicon microcantilever as a highly sensitive and selective means to detect nitroaromatic derivatives

A new approach to the chemo-mechanical detection of trace amounts of nitroaromatics, even in the presence of high concentrations of background materials, is presented. The detection scheme is based on the plasticization of an aminopropyl silane layer that is harnessed to a silicon beam following its reaction with nitroaromatic systems. The reactioninduced plasticization attenuates the temperature induced bending of the polymer-beam sandwich, offering a simple and very sensitive tool for the detection of nitroaromatic systems. Using this approach, it was possible to detect a sample of 100 pg TNT even in the presence of a 10 fold excess of a background material such as acetonitrile. VC 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014, 52, 2124–2130

Design and Modelling of a Silicon Optical MEMS Switch Controlled by Magnetic Field Generated by a Plain Coil

Optical switches can be made as a silicon cantilever with a magnetic layer. Such a structure is placed in a magnetic field of a planar coil. There is a torque deflecting the silicon beam with NiFe layer depending on a flux density of the magnetic field. The study shows an analysis of ferromagnetic layer parameters, beam's dimensions on optical switch characteristics. Different constructions of the beams were simulated for a range of values of magnetic field strength from 100 to 1000 A/m. An influence of the actuators parameters on characteristics was analysed. The loss of stiffness of the beam caused by specific constructions effected in displacements reaching 85 nm. Comsol Multiphysics 4.3b was used for the simulations.

Smoothness Control of Wet Etched Si{100} Surfaces in TMAH+Triton

The effect of galvanic interaction between the evolving facets of the etch front on the Si {100} surface smoothness during wet anisotropic etching in surfactant-added tetramethylammonium hydroxide (TMAH) is studied by etching different mask patterns. Triton X-100, with formula C14H22O(C2H4O)n, where n=9-10, is used as the surfactant. The different smoothness of wet etched Si {100} surfaces, evaluated by atomic force microscope (AFM) and optical microscope, indicates that the wet etched Si {100} surfaces could become extremely smooth after the onset of the electrochemical etching contribution. A model to account for the galvanic interaction between the evolving facets is proposed, demonstrating that the chemical etching can be significantly surpassed by the electrochemical etching when the relative area of the exposed {100} surfaces are relatively small in comparison to that of the developed {111} sidewalls. Additionally, silicon beams with smooth surfaces are presented in the fabrication of a sandwich micro accelerometer to avoid the risk of device invalidation. This study is useful for engineering applications where the fabrication of microstructures for high quality devices should contain smooth surfaces.

Precision control of thermal transport in cryogenic single-crystal silicon devices

We report on the diffusive-ballistic thermal conductance of multi-moded single-crystal silicon beams measured below 1 K. It is shown that the phonon mean-free-path ℓ is a strong function of the surface roughness characteristics of the beams. This effect is enhanced in diffuse beams with lengths much larger than ℓ, even when the surface is fairly smooth, 5–10 nm rms, and the peak thermal wavelength is 0.6 μm. Resonant phonon scattering has been observed in beams with a pitted surface morphology and characteristic pit depth of 30 nm. Hence, if the surface roughness is not adequately controlled, the thermal conductance can vary significantly for diffuse beams fabricated across a wafer. In contrast, when the beam length is of order ℓ, the conductance is dominated by ballistic transport and is effectively set by the beam cross-sectional area. We have demonstrated a uniformity of ±8% in fractional deviation for ballistic beams, and this deviation is largely set by the thermal conductance of diffuse beams that support the micro-electro-mechanical device and electrical leads. In addition, we have found no evidence for excess specific heat in single-crystal silicon membranes. This allows for the precise control of the device heat capacity with normal metal films. We discuss the results in the context of the design and fabrication of large-format arrays of far-infrared and millimeter wavelength cryogenic detectors.

Quantitative characteristics of clustered DNA damage in irradiated cells by heavy ion beams

Heavy ion beam as typical high linear energy transfer (LET) radiation produces more expanding ionization domain around their tracks than low LET radiation such as X-rays and gamma rays. Thus, heavy ion beam can cause more densely accumulated damage cluster in the target DNA, termed clustered DNA damage. This damage exhibits difficulty for repair and inhibition of DNA replication with its complex structure [ 1]. So, clustered DNA damage is thought to be strongly involved in the biological effectiveness of heavy ion beam. However, a lot of studies have presented no certain correlation between yields of clustered DNA damage and severity of radiation effect. We previously indicated that the yields of clustered DNA damage decreased with increasing LET in the DNA molecules irradiated in test tubes with gamma rays, and carbon and iron ion beams whose showed different LET, respectively [ 2]. In this study, we aimed to reveal correlation between clustered DNA damage and the LET of heavy ion beam in the irradiated cells.In the experiments, Chinese hamster ovary AA8 cells growing exponentially were irradiated by carbon, silicon, argon and iron ion beams from Heavy Ion Medical Accelerator in Chiba (HIMAC) of the National Institute of Radiological Sciences, Japan. These LETs were 13, 55, 90 and 200 keV/µm, respectively. For comparison, we used gamma rays from 137Cs-gamma source, Gammacell 40 (Atomic Energy of Canada Ltd), at Saga University. The irradiated cells were subjected by static-field gel electrophoresis to quantify clustered DNA damage of the genomic DNA. For this analysis, we used Fpg and endonuclease III for clustered DNA damage including oxidative purine and pyrimidine lesions, respectively. We also analysed the corresponding isolated DNA damages by aldehyde reactive probe method [ 3], and the surviving fractions of the irradiated cells in this study.The electrophoretic results indicated that total yields of clustered DNA damage in the irradiated cells decreased with increasing LET, including the double-strand break (DSB) and the respective clustered base damages (Fig. 1). This result conforms to our previous study with the irradiated DNA molecules [ 2]. The damage kinetics is thought to be mainly derived from two reasons: decreasing fluxes and increasing reaction with reactive oxygen species each other in increase in LET. In the clustered DNA damage induced by each radiation, the most decremental fraction was clustered base damage, but not DSB. The isolated DNA damages decreased with increasing LET like clustered DNA damage in this study (data not shown). These results make us realize the degree of contribution of direct and indirect effects of ionizing radiation. The certain amount of DSB were derived from the direct effect and showed less reactivity to LET. In contrast, oxidative base lesions were mainly generated by indirect effect with reactive oxygen species, which sensitively responded to LET change. We also found seemingly conflicted result of the relationship between LET and RBE (data not shown). We need further study to elucidate act of clustered DNA damage in radiobiological effect with heavy ion beams. Fig. 1.The yields of clustered DNA damages in the cells irradiated with respective ionizing radiations. Each clustered DNA damage consists of DSB (open bar) and clustered base damage (closed bar), and calculated from the strength of released band on electrophoretic gel.Clinical trial registration number if required: None.

Linearity of Piezoresistive Nano-gauges for MEMS Sensors

The work discusses the mechanical properties and the response linearity of sub-micrometric crystalline Silicon beams used as piezoresistive sensing elements (nano-gauges) in MEMS sensors. The study is based on a suitably developed test structure that allows applying bidirectional stresses to a gauge with a cross-section of (250 nm)2, and to monitor the displacement both through a reference linear capacitive sensor and through the nano-gauge piezoresistive variation.Experimental measurements estimate a nominal strength of 6.6 GPa, and a linear range of 2.3 GPa and 1.1 GPa under tensile and compressive stresses respectively, the latter value being limited by buckling effects.

Modeling the Boron-Doping Silicon Beam by a Multilayer Model

The boron-doping silicon beam commonly used in microdevices exhibits a nonuniform material property along its thickness or width because of the gradient of boron concentration induced by diffusion process. The constant of rigidity, one of the most important parameters of microbeam, needs to be accurately calculated and designed in the development of high precise sensors and actuators. Current design methods, mainly depending on the analytical solutions derived under the assumption of a uniform material property or some commercial software for a varied property, are not adequate and time consuming to calculate the constant of rigidity of boron-doping silicon beam. A multilayer model is proposed in this paper to replace the continuous solid model by dividing the beam into separated layers glued together. The finite element lamination method is utilized to acquire the equivalent Young modulus and moment of inertia of cross section of multilayer model. The equivalent values are calculated from double-layer structures to multilayer ones based on the small deformation theory and the material mechanics theory. The proposed method provides an effective method to design the stiffness or frequency of microdevice and its results are validated by COMSOL simulation.

Experimental comparison of 3-3 and 3-1 mode piezoelectric microelectromechanical systems

A common architecture for piezoelectric MEMS sensors and actuators is a thin piezoelectric film patterned atop a much thicker passive bending structure (e.g., a silicon beam or plate). In a first common configuration, parallel plate electrodes reside above and below the piezoelectric film to realize a 3-1 mode device. In a second configuration, a top electrode is patterned in the form of an interdigitated transducer (IDT) to realize a parallel network of 3-3 mode cells. A theoretical comparison of figures-of-merit for each configuration has been presented by research teams in the past. Figures-of-merit include coupling coefficient, actuator strength, and signal to noise ratio for sensing applications. Less work has been performed directly comparing these configurations experimentally using micro-processed thin films. In this presentation, a micromachined accelerometer structure employing a set of multiple springs is used to experimentally compare the two configurations. Each silicon spring contains a 1micron thick lead zicronate titanate (PZT) film along the top surface. Aside from electrode type, the springs are identical in dimension—providing an opportunity for direct comparison.

Accurate spring constant calibration for very stiff atomic force microscopy cantilevers

There are many atomic force microscopy (AFM) applications that rely on quantifying the force between the AFM cantilever tip and the sample. The AFM does not explicitly measure force, however, so in such cases knowledge of the cantilever stiffness is required. In most cases, the forces of interest are very small, thus compliant cantilevers are used. A number of methods have been developed that are well suited to measuring low stiffness values. However, in some cases a cantilever with much greater stiffness is required. Thus, a direct, traceable method for calibrating very stiff (approximately 200 N/m) cantilevers is presented here. The method uses an instrumented and calibrated nanoindenter to determine the stiffness of a reference cantilever. This reference cantilever is then used to measure the stiffness of a number of AFM test cantilevers. This method is shown to have much smaller uncertainty than previously proposed methods. An example application to fracture testing of nanoscale silicon beam specimens is included.

Modifications induced by silicon and nickel ion beams in the electrical conductivity of zinc nanowires

This paper presents the modification in electrical conductivity of Zn nanowires under swift heavy ions irradiation at different fluences. The polycrystalline Zn nanowires were synthesized within polymeric templates, using electrochemical deposition technique and were irradiated with 80 MeV Si7+ and 110 MeV Ni8+ ion beams with fluence varying from 1 × 1012 to 3 × 1013 ions/cm2. I–V characteristics of exposed nanowires revealed a decrease in electrical conductivity with increase in ion fluence which was found to be independent of applied potential difference. But in the case of high fluence of Ni ion beam (3 × 1013 ions/cm2), electrical conductivity was found to increase with potential difference. The analysis found a significant contribution from grain boundaries scattering of conduction electrons and defects produced by ion beam during irradiation on flow of charge carriers in nanowires.

Comparison of lead zirconate titanate thin films for microelectromechanical energy harvester with interdigitated and parallel plate electrodes.

Lead zirconate titanate (PZT) thin films on insulator- buffered silicon substrates with interdigitated electrodes (IDEs) have the potential to harvest more energy than parallel plate electrode (PPE) structures because the former exploit the longitudinal piezoelectric effect, which is about twice as high as the transverse piezoelectric effect used by PPE structures. In this work, both options are compared with respect to dielectric, ferroelectric, and piezoelectric properties, leakage currents, and figure of merit (FOM) for energy harvesting. The test samples were silicon beams with {100} PZT thin films in the case of the PPE geometry, and random PZT thin films for the IDE geometry. Both films were obtained by an identical sol-gel route. Almost the same dielectric constants were derived when the conformal mapping method was applied for the IDE capacitor to correct for the IDE geometry. The dielectric loss was smaller in the IDE case. The ferroelectric loops showed a higher saturation polarization, a higher coercive field, and less back-switching for the IDE case. The leakage current density of the IDE structure was measured to be about 4 orders of magnitude lower than that of the PPE structure. The best FOM of the IDE structures was 20% superior to that of the PPE structures while also having a voltage response that was ten times higher (12.9 mV/μ strain).

Modeling of CH<sub>4</sub> Adsorption-Induced Curvature of a Nanocantilever

In this paper, a simulation model is proposed to describe CH4 adsorption-induced curvature of a nanocantilever, based on the energy transfer between potential energy of adsorbates and elastic energy of the bending cantilever. For most cantilever sensors, the basic structure is a silicon beam coated with a metal layer on the top, and aluminum is chosen here. Because the native oxide is usually formed during the fabrication of silicon beams, we have to describe the effect of native oxide on the elastic modulus of the silicon nanobeam in this model based on the semi-continuum method. This model gives a way to predict the curvature of the composite cantilever with native oxide when adsorbing a single layer of CH4 molecules.

Design and fabrication of a high-aspect-ratio parylene-based comb-drive actuator for large displacements at a low driving force

This paper presents a comb-drive actuator integrated with parylene-based flexible beams for large displacements at a low driving force. Single-crystal silicon and polysilicon are the traditional materials used for comb-drive actuators in the microeletromechanical systems industry. However, the larger Young's modulus limits the displacement at a low applied voltage. This study uses the parylene beams with the characteristic of a low modulus of the elastic comb-drive actuator as a compliant suspension to create a larger displacement (>50 µm) with smaller driving forces than that of silicon. High-aspect-ratio parylene beams can be fabricated through the deposition and removal of parylene in multiple stages on a silicon micro-trench. The proposed process uses a silicon-on-insulator wafer as the substrate to fabricate suspended silicon and parylene beams as rigid and compliant structures, respectively. The test devices of parylene- and silicon-based comb-drive actuators were fabricated with 100 pairs of comb fingers with gaps of 5 µm, and compliant beams of 15 µm in width, 2000 µm in span and 50 µm in thickness. When a driving voltage of 40 V dc was applied, the parylene-based comb-drive actuator generated a displacement of up to 55 µm, whereas the silicon-based comb-drive actuator generated a displacement of 2 µm. The parylene-based comb-drive actuator can generate about 27 times of displacement than that of silicon. This design is suitable for application in devices with large in-plane displacement and low switching speed.

Design and modeling of a novel microsensor to detect magnetic fields in two orthogonal directions

In this paper, we present the design and modeling of the electrical–mechanical behavior of a novel microsensor to detect magnetic fields in two orthogonal directions (2D). This microsensor uses a simple silicon resonant structure and a Wheatstone bridge with small p-type piezoresistors (10 × 4 × 1 μm) to improve the microsensor resolution. The resonant structure has two double-clamped silicon beams (1000 × 28 × 5 μm) and an aluminum loop (1 μm thickness). The microsensor design allows important advantages such as small size, compact structure, easy operation and signal processing, and high resolution. In addition, the microsensor design is suitable to fabricate using silicon on insulator (SOI) wafers in a standard bulk micromachining process. An analytical model is developed to predict the first bending resonant frequency of the microsensor structure using Macaulay and Rayleigh methods, as well as the Euler–Bernoulli beam theory. Air and intrinsic damping sources of the microsensor structure are considered for its electrical–mechanical response. The mechanical behavior of the microsensor is studied using finite element models (FEMs). For 10 mA of root mean square (RMS) excitation current and 10 Pa air pressure, this microsensor has a linear electrical response, a fundamental bending resonant frequency of 52,163 Hz, and a high theoretical resolution of 160 pT.

Micromachined piezoelectric microphones with in-plane directivity

Micromachined piezoelectric microphones with in-plane directivity are introduced. A beam rotates about center torsional pivots and is attached to piezoelectrically active end-springs. Rotation of the beam in response to sound pressure gradients produces spring deflections, which, in turn, produce an open-circuit voltage at the piezoelectric films. Prototypes are presented that contain a 20-μm-thick silicon beam and end-springs with 900-nm-thick chemical solution deposited lead zirconate titanate atop the surface of the end-springs. Acoustic directivity measurements are presented that confirm device functionality.

Simulation of the different position on the E-type round diaphragm and the length of the beam,

singhania university Abstract: This paper studies a resonant silicon sensor whose elementary sensing component is the E-type round diaphragm, and the final sensing component is the silicon beam resonator is attached to the E-type round diaphragm. the relationship between the basic natural frequency of the beam resonator and the measured acceleration are calculated and simulated by using the above finite element modeling in detail. Because of the fact that beam is located on the different position on the E-type round diaphragm and the length of the beam, the outer radius of the E-type round diaphragm are varied respectively. The related analyses and investigations are carried out. Some important results on the relationship between the basic natural frequency of the beam resonator and the measured acceleration are obtained. Finally, based on the differential output scheme of the resonant sensor and some related criteria, a set of appropriate parameters for the above sensing structure of the

Electrodynamic MEMS: Application to Mobile Phone Loudspeakers

This paper presents an electrodynamic MEMS for mobile phone loudspeaker applications. The whole structure of the loudspeaker is a new conception to reach higher performances than in existing devices: a linear behavior to ensure a high acoustic fidelity and a high efficiency to increase the power autonomy. So, the motor is ironless, constituted of permanent magnet only. Several electrodynamic structures are presented and studied with analytical formulations of the magnetic field. The emissive part is a plane silicon surface, very rigid and light, the suspension is achieved by silicon beams, which are not sensitive to mechanical fatigue, the electroplated copper coil is thick and requires a specialist technique to be deposited. The moving part displacements are in a range far larger than in existing MEMS (600 μ m). The trends for dimensioning the structure are investigated and prototypes realized and tested, with NdFeB ring magnets. As a result, the 70 dB SPL at 10 cm bandwidth reaches up to 100 kHz, and the behavior is particularly linear.