Research On Capacitive Micro-accelerometers Device Physical Model And Experiment Based On SOI Technology

Due to the small volume, low power, high sensitivity and easily being integrated with circuits, the capacitive micro-accelerometer fabricated by micro-machined process has become key part in civil industry and defense fields as inertia navigation device and therefore, has attracted many attentions and researches recently. In the researches, the residual stress in device layer,the nonlinear model of accelerometer operating in open loop mode, the integrated simulation of the device in mechanic, electric and thermal fields, and the effect of comb fingers gaps'deviation on performance of SOI accelerometers are still in need of being developed.To deal with the current theoretical and technology problems in SOI capacitive micro-accelerometers, an investigation on nonlinear model of open loop operating mode, integrated simulation in multi-physics fields, residual stress in device layer and the relationship between performance and MEMS process error has been carried on.Firstly, after the analysis of various residual stresses in device layer of SOI and the contribution of these stresses to the deformation of proof mass, a support structure is proposed and a maximum deflection model of the structure is investigated. Meanwhile, an experiment with different dimensions of the proof mass on SOI wafer with device layer depth 50μm and dioxide layer depth 5μm is done, in which the maximum deflection is measured. It is indicated by the experiment that the proposed model could basically describe the maximum deflection of proof mass.Secondly, to cope with the nonlinear error of open-loop accelerometers and stresses in SOI device layer, based on the rule of maximum measurand acceleration, initial operating and pull in point changing with the distance between electrodes d and, the variation of spring beams'stiffness due to the stresses, the nonlinear model of micro-machined accelerometer is proposed. It is indicated that, by the model, with the output increasing, the measured acceleration increases roughly linear with the output voltage until it approaches the maximum acceleration amax, then it decrease till the point where electrodes are pulled in. The amax is decided by d andλ, which is the ratio between the spring constant and the mass of the microstructure, and the amax will be increased if the stresses in SOI device layer are taken into account. The accelerometer can not work when d is less than a critical point which is determined by transducer's parameterηand the optimum ofηis from 1×1019 to 2×1019, where the pull in point is beyond 95% of the full travel range of the moveable electrode.Thirdly, to deal with the separated situation of MEMS accelerometer's simulation in multi-physics fields, based on the mechanics, thermal, electrical theories and mechanism of micro-accelerometer, considering the stress gradient in SOI device layer and the relationship between air damping and temperature, the air damping, the stress gradient and the movement of mechanical structure has been transferred into the form of voltage, then, after combined with the electrostatic force and interface circuits, an integrated simulation model is proposed,which can simulate the middle electrode in the whole travel range. Through the comparison of results obtained by proposed model, classic formula and experiments, it is indicated that the model could basically be applied in the integrated simulation of the micro-accelerometers.Finally, due to the deviation between actual comb finger gap and dimension on mask, based on probability and process error theory, the device physical models, which are capacitance and electrostatic force model, sensitivity model and the pulse and step signal response model, are proposed when the deviation is distributed in the adjacent scope of the design value with equal probability.It is indicated that, by the capacitance and electrostatic force model, both the capacitance and electrostatic force distributions are quasi-Gaussian distribution type. Hence the probability for the capacitance and electrostatic force occurring in any interval can be estimated by means of quasi-mean and quasi-variance. The quasi-mean is a little bit different from the value of capacitance or electrostatic force without process error, less than 5%. The quasi-variance depends on the comb finger number and process error degree. When the comb finger number increases from 10 to 60, the quasi-variance of capacitance distribution increases 2 times while is about 1 time for electrostatic force distribution and, as process error degree is from 5% to 20%, the quasi-variance increases 1.5 times for capacitance distribution and is about 2.5 times for electrostatic force distribution.Then, pulse and step acceleration signal response models of capacitive micro-accelerometer with single-sided driving mode and double-sided driving mode are derived respectively. The precision of the models has been verified by the FEA and Monte-Carlo methods with ANSYS software. The deviation between them is less than 10%. It is pointed out by the models that the reliable operation ranges of accelerometers will decrease 10%-15% when the comb gaps deviate 0-20% from ideal value. The models can be used in the estimation of the reliable operation ranges of capacitive accelerometers.Lastly, a model to describe the sensitivity deviation probability is proposed and, is verified by a simulation in a statistical way. The difference between the model and simulation results is less than 10%. According to the model, when the process error is about 25%, the sensitivity will decrease 5-10% with 40-50% probability and increase 5-10% with 25-30% probability. Meanwhile, the smaller the comb finger's number n is, the bigger the deviation probability is. When n is less than 20, the sensitivity decreases 10% with about 30% probability, but when n is close to 50~60, the probability deceases to about 10%. Through the model, a bridge between MEMS process error and the sensitivity is set up and,in the process, a new approach based on probability and statistical theory to study the effect of the process error on performance is presented.