Design Rules for Temperature Compensated Degenerately n-Type-Doped Silicon MEMS Resonators


The first- and second-order temperature coefficients and the total temperature-induced frequency deviation of degenerately n-sort-doped silicon resonators are modeled. Modeling is predicated on finite part modelling-primarily based sensitivity analysis of numerous resonator geometries combined with the experimental results on doping-dependent elastic constants of n-sort-doped silicon. The analysis covers a doping range from $two.4 times 10^17$ to $7.5 times ten^19~rm cm^-3$ . Families of resonance modes which will be temperature compensated via n-type doping are identified. These embody bulk modes, like the width/length extensional modes of a beam, Lamé/sq. extensional modes of a plate resonator, along with flexural and torsional resonance modes. It's shown that just about all resonance modes of practical importance will reach zero linear temperature coefficient of frequency when correctly designed. Optimal configurations are presented, where a complete frequency deviation of $sim a hundred and fifty$ ppm can be reached. The results counsel that full second-order temperature compensation acquainted from AT cut quartz is not potential in silicon resonators with doping below $7.5 times ten^19~rm cm^-3$ . But, an analysis relying on extrapolated elastic constant information suggests the chance of full second-order temperature compensation for a big selection of resonance modes when doping is extended beyond $ten^20~rm cm^-3$ . [2015-0018]

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