Noise Analysis of a Tunneling Accelerometer Based on State Space Stochastic Theory

This paper presents noise analysis of a lateral tunneling accelerometer, considering Brownian motion, Nyquist-Johnson and shot noise. The tunneling accelerometer has been fabricated; a low noise differential transresistance amplifier and a digital integral controller have been designed and implemented. Noise analysis has been made based on state space models and compared with experimental results. INTRODUCTION The measurement of acceleration, in addition to being a central element of inertial guidance systems, has application to a wide variety of commercial problems (including automotive, medical, industrial, aeronautics and defense sectors). Different transducer mechanisms have been used in micro fabricated accelerometers [1]. Tunneling is a highly sensitive method for measuring position, which was inspired by the early work on scanning tunneling microscope. An electrostatic actuator is used, which has the advantage over capacitive, piezo-resistive and piezoelectric displacement transducers that the critical sensing area is reduced, and sensitivity and bandwidth are higher. The tunneling current is also largely independent of temperature. Motivation An understanding of the effects of noise is important to determine the factors that limit sensor resolution. There has been considerable work on tunneling accelerometers [2-8]. The analysis presented by Gabrielson [10] concludes that thermal noise is the main factor for most of the tunneling accelerometers. Work from JPL and Stanford reported large amounts of noise at low frequencies (below 100 Hz), and their origin is still under investigation. A mathematical model to simulate the 1/f noise related to surface adsorption-desorption process is presented in [9]. In this paper, we use a different theoretical approach that makes it very easy to investigate the effects of different noise sources on a tunneling accelerometer. The analysis is compared the experimental data using a simple integrating controller. Principle In tunneling displacement transducers, the theoretical relationship between the tunneling electrode gap and the tunneling current is given by o x b t e V I Φ − ∝ α (1) where It is the tunneling current, Vb is tunneling bias across the tunneling electrode gap; a is the tunneling constant; F is the effective height of the tunneling barrier or the effective work function and xo is the shortest tunneling gap between tunneling tip and the proof-mass electrode. Electron tunneling can only be observed when the gap between a pair of clean metal electrodes is nearly on the order of 1 nm. When the micro machined tunneling accelerometer is accelerated, the proof-mass experiences an inertial force that causes its motion (see Figure1). Because of the strong exponential dependence of current distance, it is necessary to use force feedback with the tip to keep a constant tunneling current. In this case, an electrostatic force is used to control the position of the proof mass. Comparing the tunneling current to a reference signal, the feedback control adjusts the electrostatic rebalance force that maintains a constant tunneling electrode separation, as is represented by the block diagram in Figure2. The feedback force is the measurement of the external acceleration. comb-drive actuator Tunneling current It