Hiroshi Tanigawa

Silicon diaphragm pressure sensors fabricated by anodic oxidation etch-stop

Abstract Silicon diaphragm pressure sensors have been fabricated by anodic oxidation etch-stop to reduce the pressure sensitivity variation. The diaphragm thickness is precisely controlled by automatic etch-stop in hydrazine-water solution. p-Type piezoresistive elements are fabricated by boron ion implantation on a (100) orientation n-type epitaxial layer. A 5 V positive voltage is applied to the n-type layer of an n/p epitaxial silicon wafer. The thick p-type substrate is then etched off, etching stopped and a thin n-type diaphragm is left. Diaphragm size is 1 mm × 1 mm and the thickness is 20 ± 2 μm. The pressure sensitivity variation is less than ± 20% from wafer to wafer.

Silicon Beam Resonator Utilizing the Third-Order Bending Mode

A silicon beam resonator utilizing the third-order bending mode is designed and fabricated. It has three driving electrodes for increasing the amplitude of the third-order mode. The mechanical vibration modes of the beam are measured using a laser-Doppler vibrometer, and the electrical characteristic is evaluated with a network analyzer. Because the in-plane vibration is caused by the electrostatic force exerted on a gap between the beam and each driving electrode, the amplitude of the third-order mode in the in-plane vibration can be enhanced by placing three driving electrodes along a resonant beam. The measured resonant frequencies well agree with the simulated ones. From the measurement of the third-order mode in the in-plane vibration with a network analyzer, it has been shown that resonant frequency decreases by 2.3 kHz as DC voltage increases from 30 to 70 V owing to the spring softening effect. The DC bias dependence agrees well between the electrical and mechanical measurements. Finally, the mechanism of inducing an out-of-plane vibration is discussed from a viewpoint of the influence of the electric field generated on a substrate.

Higher-order vibrational mode frequency tuning utilizing fishbone-shaped microelectromechanical systems resonator

Resonators based on microelectromechanical systems (MEMS) have received considerable attention for their applications for wireless equipment. The requirements for this application include small size, high frequency, wide bandwidth and high portability. However, few MEMS resonators with wide-frequency tuning have been reported. A fishbone-shaped resonator has a resonant frequency with a maximum response that can be changed according to the location and number of several exciting electrodes. Therefore, it can be expected to provide wide-frequency tuning. The resonator has three types of electrostatic forces that can be generated to deform a main beam. We evaluate the vibrational modes caused by each exciting electrodes by comparing simulated results with measured ones. We then successfully demonstrate the frequency tuning of the first to fifth resonant modes by using the algorithm we propose here. The resulting frequency tuning covers 178 to 1746 kHz. In addition, we investigate the suppression of the anchor loss to enhance the Q-factor. An experiment shows that tapered-shaped anchors provide a higher Q-factor than rectangular-shaped anchors. The Q-factor of the resonators supported by suspension beams is also discussed. Because the suspension beams cause complicated vibrational modes for higher frequencies, the enhancement of the Q-factor for high vibrational modes cannot be obtained here. At present, the tapered-anchor resonators are thought to be most suitable for frequency tuning applications.

Variable Resonance Frequency Selection for Fishbone-Shaped Microelectromechanical System Resonator Based on Multi-Physics Simulation

In this paper, we present and demonstrate the principle of variable resonance frequency selection by using a fishbone-shaped microelectromechanical system (MEMS) resonator. To analyze resonator displacement caused by an electrostatic force, a multi-physics simulation, which links the applied voltage load to the mechanical domain, is carried out. The simulation clearly shows that resonators are operated by three kinds of electrostatic force exerted on the beam. A new frequency selection algorithm that selects only one among various resonant modes is also presented. The conversion matrix that transforms the voltages applied to each driving electrode into the resonant beam displacement at each resonant mode is first derived by experimental measurements. Following this, the matrix is used to calculate a set of voltages for maximizing the rejection ratio in each resonant mode. This frequency selection method is applied in a fishbone-shaped MEMS resonator with five driving electrodes and the frequency selection among the 1st resonant mode to the 5th resonant mode is successfully demonstrated. From a fine adjustment of the voltage set, a 42 dB rejection ratio is obtained.

Characterization of Four-Points-Pinned Ring-Shaped Silicon Microelectromechanical Systems Resonator

A four-points-inner-pinned ring-shaped microelectromechanical systems (MEMS) resonator has been investigated. The simulated comparison between disk- and ring-shaped resonators indicates that the amplitudes of the ring-shaped resonators are more than ten times larger than those of the disk-shaped ones for modes with the same resonant frequency. Three types of anchor configuration for the ring-shaped resonators, inner-pinned, outer-pinned, and center-fixed, were compared. The results show that, for the inner-pinned ring-shaped resonator, three fundamental resonant modes occur close to each other, although this resonator is the smallest and does not suffer from the effect of misalignment as a result of one mask fabrication. A new method to identify each fundamental resonant mode has been proposed and successfully adapted for evaluating the frequency characteristics of fabricated resonators. The fabricated ring-shaped resonator had a radial-contour-common (RCC) resonant mode at 1.615 MHz with a Q-factor of over 30,000. These values agreed at 98.9% accuracy with those of the simulated resonator.

Microelectromechanical Systems Resonator Utilizing Torsional-to-Transverse Vibration Conversion

A silicon microelectromechanical systems (MEMS) resonator utilizing the torsional-to-transverse vibration conversion is designed, fabricated and evaluated. The resonant frequency for the torsional modes mostly depends on only beam length, providing a large tolerance in the fabrication process. It has been, however, a critical issue to investigate the mechanism for generating the torsional vibration and the reduction of motional resistance. We propose a new beam structure, in which four torsion beams are vibrated by twist force generated by a transverse beam. The novel process for fabricating resonators provides a narrow gap surrounded by flat surfaces, which can reduce the motional resistance. The fabricated resonators are measured with a laser-Doppler (LD) vibrometer. The scanning function of the LD vibrometer confirms the torsional-to-transverse vibration conversion has been successfully achieved. The measured resonant frequency, 10.96 MHz, is in good agreement with the simulated one. The Q-factor has been also measured to be as high as 2.2 ×104 in vacuum. The electrical characteristic is evaluated with an impedance analyzer. At the resonant frequency, the extracted motional resistance for the 0.5-µm-gap resonator is 2.0 MΩ, which is greatly reduced, owing to the narrow gap effect, from that of the 1-µm-gap resonator. The temperature coefficient of the resonant frequency between -40 and 85 °C, has been measured to be -24.4 ppm/deg. The resonant frequency linearly decreases as the temperature rises.

Temperature Dependence of Hyperfine Spectrum of Rb D1 Line

This paper deals with the experimental studies of the rubidium (Rb) spectral lamp for the purpose of getting an excellent pumping light source for a Rb gas cell type frequency standard, or for a Rb microwave maser. Some of Rb lamps containing Ne, Ar, Kr, and Ne-Ar as a carrier gas were made by way of experiment. In order to observe the hyperfine spectrum of D1 line, the Fabry-Perot type scanning interferometer was made, which is driven electrostrictively. The hyperfine components of D1 line were resolved successfully. It was observed that the line which is used as a pumping source became intense as the lamp temperature was raised, and it began to be dipped and decrease, however, over the definite temperature. Also observed was that this optimum temperature differs from the temperature at which the integrated intensity of D1 line shows a maximum.

Silicon Beam Microelectromechanical Systems Resonator with a Sliding Electrode

A silicon beam microelectromechanical systems (MEMS) resonator with a sliding driving electrode (DE) has been investigated. Although the narrow gap between a driving electrode and a resonant beam greatly improves the resonator performance, it has been difficult to fabricate the narrow gap owing to the process limitation. In this study, the gap is decreased by sliding the driving electrode after the resonator process is completed (postprocessed narrow gap formation). The effective gap length for a fabricated resonator was decreased to 0.84 µm after the pull-in, while the initial gap was 3.44 µm. After the pull-in, the fabricated resonator vibrated at the 899.5 kHz resonant frequency (the Q-factor of 6600). The resonant beam displacement amplitude increased 17.5 times compared with that for the as-fabricated (before the pull-in) resonator. In the electrical domain, the magnitude of the impedance largely decreased from ~58 to 3.85 MΩ. The large phase transition, 50°, was also measured. From these results, largely improved resonator characteristics due to the narrow gap effect were confirmed. Moreover, the displacement amplitude ratio of the sliding DE to the resonant beam was found to be less than 4.5×10-5 for the resonator after the pull-in. This implies that the vibration of the sliding DE could affect negligibly the overall beam resonator vibration.

High Quality Factor 80 MHz Microelectromechanical Systems Resonator Utilizing Torsional-to-Transverse Vibration Conversion

A silicon microelectromechanical systems (MEMS) resonator utilizing torsional-to-transverse vibration conversion with quarter-wavelength torsional support beams is designed, fabricated, and evaluated. The resonant frequency for torsional modes mostly depends only on beam length, providing a large tolerance in the fabrication process. However, the following have remained critical issues: the increase in the quality factor (Q-factor) and the reduction in the motional resistance. We propose a new beam structure, in which the MEMS resonator utilizing torsional-to-transverse vibration conversion is anchored by four quarter-wavelength torsional support beams. First, the fabricated resonators are measured with a laser-Doppler (LD) vibrometer. The measured resonant frequency of 78.224 MHz has been in good agreement with the simulated one. The Q-factor has also been measured to be as high as 3.0×104 in vacuum. Then, the electrical characteristic is evaluated with an impedance analyzer. The Q-factor has been electrically measured to be as high as 3.1×104 in vacuum, which agrees well with the mechanically measured one of 3.0×104. The Q-factor has also been electrically measured to be as high as 1.3×104 at atmospheric pressure. In the measurement, a spring softening effect has been clearly observed. By increasing the DC bias voltage from 20 to 40 V, the resonant frequency has decreased by 640 Hz. The extracted motional resistance for a 0.1-µm-gap resonator has been greatly reduced to 0.039 MΩ at 5 V DC, owing to the narrow-gap effect, from that of a 0.25-µm-gap resonator. The tolerance in the fabrication process has also been evaluated and successfully verified from the measurement of the fabricated MEMS resonators.

Evaluation of a Single-Crystal-Silicon Microelectromechanical Systems Resonator Utilizing a Narrow Gap Process

To investigate a higher frequency microelectromechanical systems (MEMS) resonator, mechanical behaviors and electrical characteristics on a single-crystal-silicon MEMS resonator, utilizing a narrow gap process, have been evaluated. The size reduction for the resonators leads to a decrease in output signal. To overcome this problem, an increase in electromechanical coupling coefficient is required. To investigate the effect of the reduction of the gap between a beam and a driving electrode, two types of 100 kHz MEMS resonator with different gaps have been fabricated and compared. It has been observed that the resonator with a narrow gap (1 µm) has a larger displacement amplitude, as well as a larger phase transition, than that with a 4 µm gap, which suggests that the gap reduction is effective. Then, a 10 MHz MEMS resonator has been fabricated by using the narrow gap process with a focused-ion beam (FIB). The resonant vibration for the fabricated device has been observed at 11.262 MHz. To further improve the resonators, it is suggested that the substrate vibration near the beam resonant frequency should be suppressed and that a smooth surface of the gap should be fabricated.