天津大学2010届本科生毕业设计（论文）
外文资料
High performance silicon accelerometers with charge controlled
rebalance electronics （provenance：Keith Warren Litton Guidance Control Systems， 5500 Canoga Ave.
MS 87， Woodland Hills. CA 91367）
ABSTRACT
A charge-controlled, force rebalanced accelerometer loop is described, along with its advantages over prior voltage-controlled forcing methods. First generation silicon accelerometers incorporating charge-controlled electronics are performing well in current production systems. A new all silicon accelerometer chip is being developed for higher accuracy applications.
INTRODUCTION Microelectronics has followed a path of ever increasing integration for the last several decades which has resulted in
increased functionality at markedly reduced cost. What makes the progress depicted in Figure 1 possible is the reduction of assembly complexity and labor through rnicrolithography and batch fabrication. Silicon micromechanics holds the same potential for inertial systenis by reducing assembly labor and integrating inertial devices with electronics on a single chip. Miniature metal components, screws, springs, coils, and bearings, as well as the labor necessary to assemble them can be replaced by hundreds of identical microstructures replicated photolithographically on silicon wafers. The cost of each device is low, since the cost of each process step i s divided by the number of devices comprising a batch, typically several thousands. In the near term, high performance, low cost accelerometers and Coriolis angular rate 'sensors can be fabricated, with the longer term possibility that a silicon micromechanical INU on a chip can be realized. First generation silicon
accelerometers developed in the mid 1980s are now being manufactured in production
天津大学2010届本科生毕业设计（论文）
quantities of 400 per month. The inertial sensing element is composed of a silicon proof mass, with flexures and support kame, all anisotropically c:tched from a
single-crystal silicon wafer. The silicon proof mass surfaces are etched to provide a 2.7 pm gap for pendulum freedom. Each wafer containing 109 devices, is iinodically bonded to Pyrex capping wafers which have thin film metal patterns defining
electrode plates on either side of the silicon proof mass for electrostatic forcing. An exploded view of this structure is shown in Figure 2.
ELECTROSTATRIE RBALANCE
The accelerometer chip, along with its force rebalance electronics, operates as a closed loop using capacitive sensing and electrostatic forcing to servo the pendulum to a null position. Electrostatic forcing is especially applicable to micromechanical devices since the force is proportional to the surface area of the proof mass. As devices are made smaller, the volume, and hence the mass, of the pendulum diminishes as the inverse cube of the linear dimensions, while the surface area is
reduced by the inverse square of the linear dimensions. The surface area to mass ratio therefore increases as structures become smaller, allowing practical low voltage electrostatic servo rebalance. The force between the proof mass and an electrode is given by:
Where V is the voltage between electrode and proof mass, li-ee space,
is the permittivity of
is the relative permittivity of the nitrogen gas filling the gap and is
nearly 1. (one), A represents the area of one side of the proof mass, d is the gap between proof mass and electrode. As evident from the equation the force is a square-law function of voltage. Methods have been devised to produce a force linearly proportional to a servoable parameter. One classic method applies a bias voltage to the proof mass, with complimentary control voltages on each electrode linearly
proportional to force or acceleration [2]. Another method utilizes pulse width
modulation of' a constant voltage to the opposing electrodes [3]. Since the voltage is constant, the force is a linear function of the duty cycle. The major drawback that both
天津大学2010届本科生毕业设计（论文）
these approaches suffer froms the presence of a net voltage between proof mass arid electrodes, even at zero G's when no force is required. A strong inverse square law sensitivity to gap remains, which manifests itself as a large negative electrostatic spring. Small changes in the servo null point caused by thermal or aging
effects in the position sensing electronics cause the pendulum to be moved against this large negative spring, thereby producing the bulk of the bias errors in this type of device.
CHARGE CONTROL
Fortunately, charge controlled forcing [4] provides a way to use electrostatic forces without the attendant errors related to negative spring rate. For a parallel plate geometry, substitution of Q/C for V in the force equation yields:
Note that the inverse square law dependence on gap is eliminated, along with the undesirable large negative spring since there is no change in force with pendulum motion. This relationship holds true for parallel motion and the departure from parallel motion due to small rotation angles about the hinge axis does introduce a small spring rate due to charge mobility, but even taking this into account, reduction of the negative spring by a factor of 28 has been achieved, with further improvements possible. The charge controlled forcer loop operates by alternately applying a constant charge on each forcer plate in a pulse width modulated fashion, with the
charge duration controlled as required to hold the pendulum at null. A timing diagram showing typical waveforms is presented in Figure 3. Pendulum position is sensed by sampling the voltage on each plate just after the constant charge is introduced. The servo electronics adjusts the forcer duty cycle and moves the pendulum as required to make these voltages equal. Duty cycle switching is allowed only on precision, clock controlled boundaries resulting in a linear quantized digital output.
The key to implementing the charge controlled forcer is the charge integrator in
Figure 4. The feedback path of an op amp makes a very good current source and if the current is dispensed only during precise time intervals a constant charge is integrated. The closed loop is superior to open loop current generators since the effect of stray capacitance to ground at the input and output is negligible. Also, the same charge generating components (voltage reference, resistor, op amp, reset switch) are used for
天津大学2010届本科生毕业设计（论文）
the charge applied to both plates.
PERFORMANCE
The charge controlled loop electronics has been manufactured in hybrid form with the silicon accelerometer chip included in the 3.3 cm x 2.3 cm x .5 cm package as photographed in Figure 5. Present production units have a
45g full scale range with a
dynamic range. This Silicon Accelerometer exhibits
good overall performance with desirable features not available in non-servoed,
resonant beam type accelerometers. The symmetrical squeeze-film damping provided by the servo gap suppresses structural resonances, and makes the unit rugged and well behaved under high vibration inputs, with a rectification coefficient of 10g/inherent 1g-sec of velocity storage, uncommon in a dry instrument, allows the accelerometer to tolerate short power interruptions without loss of data
. The
The charge controlled electrostatic forcer is stable and predictable as shown by the. thermal model residuals from five representative units in Figure 6. Bias stability versus time is recorded in Figure 7.
天津大学2010届本科生毕业设计（论文）
NEW DEVELOPMENTS
Present production silicon accelerometers are suitable for tactical grade and medium accuracy applications. Future applications require higher g range, lo8
dynamic rangc, navigation grade performance and stability, with low voltage and low power. New micromechanical technologies, principally Silicon Direct Wafer Bonding and Reactive Ion Etching (RE) are being used to develop an all silicon accelerometer to meet these requirements. For high g operation with low voltage, a servo gap
smaller than is easily achievable with an assembled etched gap is needed. Sacrificiail dissolution of a placeholder oxide film of precisely controlled thickness, permits structures to be built up by Silicon Direct Bonding and shaped by RE, while as solid and rugged as conventional silicon wafers. Proofmasses or other suspended structures are released after processing and bonding together complementary half structures, making them easily manufactured [ 5 ] . The final device is stable since it is single crystal silicon, with the pendulum, flexures, and cover plates having identical thermal coeficient of expansion throughout, and low thermal gradient sensitivity due to the high thermal conductivity of silicon. Devices of this type have been fabricated with 1.3 pm gaps, and hwe been successfully servoed after the removal of the oxide layer. Figure 8 is a Scanning Electron Micrograph (SEM) of a Silicon on Insukitor (SOI) Proofmass structure 35 pm thick, photolithographically patterned, and dry etched by ME. A closer detail of the holes used to tailor the proofmass squeeze film damping, and the smooth vertical sidewalls is shown in Figure 9.