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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A novel high-precision vacuum microelectronic accelerometer has been successfully fabricated and tested in our laboratory. This accelerometer has unique advantages of high sensitivity, fast response, and anti-radiation stability. It is a prototype intended for navigation applications and is required to feature micro-g resolution. This paper briefly describes the structure and working principle of our vacuum microelectronic accelerometer, and the mathematical model is also established. The performances of the accelerometer system are discussed after Matlab modeling. The results show that, the dynamic response of the accelerometer system is significantly improved by choosing appropriate parameters of signal detecting circuit, and the signal detecting circuit is designed. In order to attain good linearity and performance, the closed-loop control mode is adopted. Weak current detection technology is studied, and integral T-style feedback network is used in I/V conversion, which will eliminate high-frequency noise at the front of the circuit. According to the modeling parameters, the low-pass filter is designed. This circuit is simple, reliable, and has high precision. Experiments are done and the results show that the vacuum microelectronic accelerometer exhibits good linearity over -1 g to +1 g, an output sensitivity of 543 mV/g, and a nonlinearity of 0.94 %.

High precision accelerometers find many applications such as acoustic measurement, seismology and navigation. Micro-machined accelerometers have been developed with different working principles [

Since the vacuum microelectronic technology was proposed in 1988, the possibility of producing a high precision, good performance vacuum microelectronic sensor has been actively explored. The study of vacuum microelectronic sensors started in 1991, and since then many new types of sensors have appeared [

The signal detecting circuit is another essential part for high precision micro accelerometers, and considerable research work has been done in this area too. Analog Devices Company has designed a modulation and demodulation circuit for capacitive accelerometers since the 1990s [

The objectives of the present research are to design a signal detecting circuit for a high precision vacuum microelectronic accelerometer, which will ensure good linearity, high sensitivity and fast response of the accelerometer system. In this paper, first the structure and working principles of a vacuum microelectronic accelerometer are introduced, and then the mathematical model is established. We plot and discuss some simulation results of the dynamic performance and stability of the system, and confirm the circuit parameters. The electrostatic force balance technology is adopted in the circuit, and the application range of vacuum microelectronic accelerometer is greatly extended.

The structure diagram of a vacuum microelectronic accelerometer is illustrated in

This accelerometer has been designed and fabricated. The dimensions of the accelerometer are obtained. _{2}/Si_{3}N_{4} cap protecting the tip from being eroded. Finally, the cap will be removed after the tip acuity. When a big enough DC voltage is added between the tip and the anode electrode, the tip will emit electrons under high electric field.

The vacuum microelectronic accelerometer works in electrostatic force balance mode. The working principle is that by applying a forward bias voltage between the anode and cathode, when the bias voltage is large enough, the tip array begins to emit electrons under high electric field, and then the electrons form a diode forward current. When the bias voltage is constant and there is an acceleration acting on the accelerometer, the proof mass will produce a displacement, and result in the change of emission current. Using current detecting circuit and electrostatic negative feedback system can make the proof mass maintain the balance position, and then the acceleration is obtained by measuring the output voltage.

Matlab was used to build the mathematical model of the vacuum microelectronic accelerometer. The model is composed of different function blocks based on Laplace transforms. In general, a vacuum microelectronic accelerometer with a feedback control system is not a linear system. Assumptions and approximations are used to linearize the system.

The proof mass is the sensing part of the accelerometer. It can be considered as a suspended mass-spring-damping system [

According to field emission theory and the prior modeling results [_{0}

The emission current goes through I/V conversion circuit, and compared with a reference voltage _{ref}

_{1}(s)

For an electrostatic force balance accelerometer, the effect of a feedback control loop is to give a static force which is opposite to the acceleration, and make the proof mass maintain the balance position. Ideally, when the acceleration is zero, the proof mass would be at the balance position and the distance between the anode and the cathode is _{0}

_{0}_{f}_{dc}_{ac}_{0}

Since _{dc}_{ac}

The first item is used to set the operation point, and the second item is related to the feedback force applied to the proof mass. At small signal analysis,

So we obtained the overall transfer function diagram of the system, as shown in

As analysis above, when the acceleration acts on the accelerometer, the proof mass will move beyond a balance position. According to force balance theory, the relationship can be given by:
_{f}_{f}

Based on the linearized mathematical model, the system can be simulated and the characteristics of the accelerometer can be evaluated. The system-level analysis can effectively instruct the design of signal detecting circuit, and enhance the performance of the accelerometer system. Under current encapsulation, the vacuum micro cavity is not under an absolute vacuum condition, so a damping coefficient is exists. It is determined by the structure of vacuum microelectronic accelerometer. When the structure is determined, all the design parameters are obtained.

The root locus of the system is shown in ^{3}, and it will be easily accomplished in the actual circuit.

In order to improve the linearity characteristic of the output, the signal detecting circuit works on close-loop mode, as shown in

A vacuum microelectronic accelerometer emits electrons by cathode tip array, and then the electrons form a weak emission current. For weak acceleration, the current change value is only nA level, and it is sensitive to the emission voltage (an exponential relationship). The main problem of weak current detection is the noise and drift, so this paper focuses on a high-precision, low-noise I/V conversion. A low noise prepositive amplifier OP27 is chosen, and the maximum equivalent input noise voltage is 3.8 nV/rtHz at 1 kHz. But the amplifier will bring additional resistance thermal noise and active noise which are both random smooth noise, and in accord with Gauss' rule. An integral I/V conversion circuit will eliminate high frequency noises by integral effect. Otherwise, the large gain and high precision are needed in I/V conversion circuit, and the integral T-style feedback network is chosen, as shown in _{1}, and the noise infection will be controlled by the integration time [_{7} is a compensating resistance, which can eliminate temperature drift. C_{3} and C_{4} are decoupling capacitor used to reduce the interference of power lines, as well as prevent the amplifier from producing self-oscillation. R_{i1}, R_{i2}, R_{i3} are used to adjust the offset voltage of OP27. The I/V conversion voltage is given by:

As analysed in [

When a vacuum microelectronic accelerometer meets emission conditions, the tip array begins to emit electrons and then the electrons form an emission current, even if there is no acceleration. After I/V conversion, the deflection voltage appears. For precision control, a differential amplification is used to eliminate this deflection voltage. The differential amplification circuit is shown in _{ref} is obtained by the distribution of high precision resistors.

In the light of the modeling parameters analyzed by Matlab, the infinite gain multi-channel feedback 2-order low-pass filter is chosen, as illustrated in

The denominator shows that, the filter can't generate self-oscillation, even if the pass band amplification is too large; the filter has good stability. Otherwise, the transfer function will correlate with

For the sake of enhancing output linearity and dynamic response range of vacuum microelectronic accelerometer, the electrostatic force balance technology is adopted, and it forms a servo accelerometer. The feedback network uses linear technology which is constituted of resistors and capacitances, as shown in _{dc} is the DC deflection voltage and V_{out4} is a negative output voltage of forward circuit. Thus a negative feedback control loop is obtained. It has two effects: first, it adjusts the distance between proof mass and anode plate, and makes the cathode tip array emit electrons; second, when there is acceleration acting on the proof mass, the feedback voltage _{f}

In addition, a series of measures are adopted to reduce the interferences, such as accessing decoupling capacitor between power and ground, laying out ground wire reasonably, adding shielding enclosures while testing, and so on. We also utilize zero adjusting resistors to decrease zero drift. This circuit is consistent with the analysis results in Part 3.

The simulation and debugging of signal detecting circuit are done.

The static rolling experiment in ±1 g gravitational field is done.

It shows that the output sensitivity is 543 mV/g, and the nonlinearity is 0.94 % in ±1 g measurement range.

The noise of the accelerometer was measured.

After verifying the fundamental performance of the vacuum microelectronic accelerometer, a rough comparison with a tunneling accelerometer is done. The deflection voltage of a tunneling accelerometer is a high DC voltage of 100 V, but in our design it's only several volts. Therefore the energy consumption will be greatly reduced. In general, the emission distance between the anode and cathode of tunneling accelerometer is only several angstroms. For a vacuum microelectronic accelerometer this distance can reach 0.1 μm, and the motion range of proof mass is broadened. Besides, a vacuum microelectronic accelerometer emits electrons by cathode tip array which contains thousands of single tips, so the output current will be much larger than tunneling accelerometer, and the signal detecting circuit is easier to be achieved.

For high sensitivity and good performance, the system analysis and a high precision signal detecting circuit of a vacuum microelectronic accelerometer were studied in this paper. Based on the structure and working principles, a simple but effective mathematical model is established. Matlab is used for system-level analysis. The step response and root locus of the system are also studied and discussed. A 2-order low-pass filter is needed in the circuit so that the accelerometer system has good performance. Otherwise, in order to attain high precision and good linearity, weak signal detecting theory and closed-loop control mode are adopted. Compared to previous examples, this circuit is simply and reliable. Experiments are carried out to verify the characteristics of our vacuum microelectronic accelerometer system. The results show that the output sensitivity of vacuum microelectronic accelerometer is 543 mV/g, and the nonlinearity is 0.94 % in ±1 g measurement range. Work on an application specific integrated vacuum microelectronic accelerometer circuit is underway. The system noise will be evidently reduced and the performance of accelerometer will be improved. Other experimental results will be reported when they become available.

The authors would like to thank the National Key Laboratory of Micro/Nano Technology of Peking University for the fabrication process. The authors also would like to thank the two anonymous reviewers for their constructive comments which helped improve the manuscript.

Structure diagram of vacuum microelectronic accelerometer.

The SEM diagram of the single tip.

Bottom electrode of vacuum microelectronic accelerometer.

Transfer function diagram of vacuum microelectronic accelerometer system.

Step response of the accelerometer system with and without low-pass filter.

Root locus of accelerometer system

Structure diagram of detecting circuit.

The integral T-style feedback I/V conversion circuit.

The circuit of differential amplification.

The circuit of low-pass filter and feedback control loop.

Photograph of accelerometer with signal processing circuit.

Output curve of static rolling experiment in ±1g gravitational field.

Output fitting curve of vacuum microelectronic accelerometer.

Output voltage of the accelerometer at 42 Hz, 0.5 g input sine acceleration.

Noise spectrum density of vacuum microelectronic accelerometer.

Design parameters of vacuum microelectronic accelerometer.

Design parameters | Values |
---|---|

Mass, |
904 μg |

Spring constant, |
88 N/m |

Damping coefficient, |
6.58×10^{-3} N·S/m |

Feedback coefficient, _{f} |
3.39×10^{-5} N/V |

Static emission current, _{0} |
0.1 μA |