This paper presents an in-plane sandwich nano-g microelectromechanical systems (MEMS) accelerometer. The proof-mass fabrication is based on silicon etching through technology using inductive coupled plasma (ICP) etching. The capacitive detection system, which employs the area-changing sensing method, combines elementary capacitive pickup electrodes with periodic-sensing-array transducers. In order to achieve a large dynamic range with an ultrahigh resolution, the capacitive detection system employs two periodic-sensing-array transducers. Each of them can provide numbers for the signal period in the entire operating range. The suspended proof-mass is encapsulated between two glass caps, which results in a three dimensional structure. The measured resonant frequency and quality factor (Q) are 13.2 Hz and 47, respectively. The calibration response of a ±0.7 g input acceleration is presented, and the accelerometer system presents a sensitivity of 122 V/g and a noise floor of 30 ng/√Hz (at 1 Hz, and 1 atm). The bias stability for a period of 10 h is 30 μg. The device has endured a shock up to ±2.6 g, and the full scale output appears to be approximately ±1.4 g presently. This work presents a new opportunity for highly sensitive MEMS fabrication to enable future high-precision measurement applications, such as for gravity measurements.

Simultaneously and independently measuring two-dimensional (2D) displacement, one-dimensional (1D) for out-of-plane measurement and 1D for in-plane measurement, is important for practical applications. Although extrinsic fiber Fabry-Perot interferometers (EFPIs) have been reported for highly precise out-of-plane displacement measurements for many years, simultaneous measurement of 2D displacement with sub-micrometer accuracy has not been realized by a monolithic EFPI as far as we know. In this paper, a monolithic dual-cavity EFPI to realize 2D displacement measurement of a target is reported. By quantitatively analyzing and experimentally calibrating the linear dependences of the in-plane displacement sensitivity and interception on the cavity length, the effect of out-of-plane displacement on the in-plane displacement measurement is removed, which is the basis of the 2D displacement detection. 2D random movement detection and the repeatability of the system are investigated experimentally. Within the range of ±7 μm for in-plane displacement, and 352 μm-358 μm for cavity length, demodulation errors better than 96 nm are achieved. The 2D displacement measurement system based on the dual-cavity EFPI with the advantages of noncontact, high accuracy and compact size is promising to be applied in the 2D acceleration measurement, 2D rotor vibration measurement, 2D precise positioning in semiconductor manufacture, thermal expansion coefficient measurement, and so on.

Encoder-like micro area-changed capacitive transducers are advantageous in terms of their better linearity and larger dynamic range compared to gap-changed capacitive transducers. Such transducers have been widely applied in rectilinear and rotational position sensors, lab-on-a-chip applications and bio-sensors. However, a complete model accounting for both the parasitic capacitance and fringe effect in area-changed capacitive transducers has not yet been developed. This paper presents a complete model for this type of transducer applied to a high-resolution micro accelerometer that was verified by both simulations and experiments. A novel optimization method involving the insertion of photosensitive polyimide was used to reduce the parasitic capacitance, and the capacitor spacing was decreased to overcome the fringe effect. The sensitivity of the optimized transducer was approximately 46 pF/mm, which was nearly 40 times higher than that of our previous transducer. The displacement detection resolution was measured as 50 pm/√Hz at 0.1 Hz using a precise capacitance detection circuit. Then, the transducer was applied to a sandwich in-plane micro accelerometer, and the measured level of the accelerometer was approximately 30 ng/√Hz at 1Hz. The earthquake that occurred in Taiwan was also detected during a continuous gravity measurement.

Capacitive sensing is a key technique to measure the test mass movement with a high resolution for space-borne gravitational wave detectors, such as Laser Interferometer Space Antenna (LISA) and TianQin. The capacitance resolution requirement of TianQin is higher than that of LISA, as the arm length of TianQin is about 15 times shorter. In this paper, the transfer function and capacitance measurement noise of the circuit are modeled and analyzed. Figure-of-merits, including the product of the inductance L and the quality factor Q of the transformer, are proposed to optimize the transformer and the capacitance measurement resolution of the circuit. The LQ product improvement and the resonant frequency augmentation are the key factors to enhance the capacitance measurement resolution. We fabricated a transformer with a high LQ product over a wide frequency band. The evaluation showed that the transformer can generate a capacitance resolution of 0.11 aF/Hz^1/2 at a resonant frequency of 200 kHz, and the amplitude of the injection wave would be 0.6 V. This result supports the potential application of the proposed transformer in space-borne gravitational wave detection and demonstrates that it could relieve the stringent requirements for other parameters in the TianQin mission.

A method for automatic compensation of misalignment angles during matching the scale factors of two pairs of the accelerometers in developing the rotating accelerometer gravity gradient instrument (GGI) is proposed and demonstrated in this paper. The purpose of automatic scale factor matching of the four accelerometers in GGI is to suppress the common mode acceleration of the moving-based platforms. However, taking the full model equation of the accelerometer into consideration, the other two orthogonal axes which is the pendulous axis and the output axis, will also sense the common mode acceleration and reduce the suppression performance. The coefficients from the two axes to the output are δ_O and δ_P respectively, called the misalignment angles. The angle δ_O, coupling with the acceleration along the pendulous axis perpendicular to the rotational plane, will not be modulated by the rotation and gives little contribution to the scale factors matching. On the other hand, because of coupling with the acceleration along the centripetal direction in the rotating plane, the angle δ_P would produce a component with 90 degrees phase delay relative to the scale factor component. Hence, the δ_P component coincides exactly with the sensitive direction of the orthogonal accelerometers. To improve the common mode acceleration rejection, the misalignment angle δ_P is compensated by injecting a trimming current, which is proportional to the output of an orthogonal accelerometer, into the torque coil of the accelerometer during the scale factor matching. The experimental results show that the common linear acceleration suppression achieved three orders after the scale factors balance and five orders after the misalignment angles compensation, which is almost down to the noise level of the used accelerometers of 1~2 × 10⁻⁷ g/√Hz (1 g ≈ 9.8 m/s²).

Nano- g accelerometers are widely used in space exploration and measurement of the earth's gravitational field. It is essential to precisely evaluate error effects at high orders such as cross-coupling for applications in a dynamic environment. Nevertheless, it remains challenging to meet the precision requirements using conventional calibration measures. In this article, we propose a method to separate the cross-coupling coefficients of a linear single-axis accelerometer by mounting it on a steadily rotating rate table that is tilted at a fixed deviation angle with respect to the horizontal plane. The gravity component is periodically modulated along the input axis per revolution. Simultaneously, a series of centripetal acceleration is applied along the cross axis in sequence while adjusting the rotation frequency of the rate table by steps. Thus, the cross-coupling coefficient can be separated by its dependence both on the modulated gravity acceleration and the centripetal acceleration. In comparison to the static multipoint angular rotation test on a tilted dividing head, the proposed dynamic modulation method demonstrates improved robustness against corruption from bias drift, with an improved uncertainty. This method to separate the cross-coupling coefficient is suitable for testing high-resolution accelerometers, without requiring high bias stability or sensitive response sustaining at ultralow frequency.