The electrostatic force balance technology is adopted in the circuit, and the application range of vacuum microelectronic accelerometer is greatly extended.2.?Structure and Working PrincipleThe structure diagram of a vacuum microelectronic accelerometer is illustrated in Figure 1. The mechanical components comprise four cantilever beams, a proof mass and a micro-silicon field emission tip array. The electrodes include a cathode, an anode and a feedback electrode. Meanwhile, the protecting chain is designed. It will prevent the damage of the tip array and realize over loading self-protection. When the acceleration exceeds the measurement range, the anode will contact with the protecting chain, and avoid the collision between the anode and the tip array.Figure 1.

Structure diagram of vacuum microelectronic accelerometer.This accelerometer has been designed and fabricated. The dimensions of the accelerometer are obtained. Figure 2 is the SEM diagram of single tip. The bottom pyramid is the tip, and the top plate is the SiO2/Si3N4 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.Figure 2.The SEM diagram of the single tip.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.3.?Mathematical Model and System-Level Analysis3.1. The Mathematical ModelMatlab 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.3.1.1. The Sensing PartThe proof mass is the sensing part of the accelerometer. It can be considered as a suspended mass-spring-damping system [10]. Using Laplace transforms, the dynamic performance of the proof mass can be expressed as:G1(s)=��xm��a=1ms2+bs+k(1)where m, b, and k represent the mass, damping Anacetrapib coefficient, and spring constant of the proof mass, respectively. ��a is the external acceleration, and ��x is the displacement of the proof mass.