Temperature compensated resonance modes of degenerately n-doped silicon MEMS resonators
A Jaakkola, M Prunnila… - 2012 IEEE International …, 2012 - ieeexplore.ieee.org
A Jaakkola, M Prunnila, T Pensala
2012 IEEE International Frequency Control Symposium Proceedings, 2012•ieeexplore.ieee.orgWe model the temperature coefficients of resonance modes of degenerately n-type doped
silicon resonators. By combining results from FEM-based sensitivity analysis and modelling
of elastic constants of silicon with free carrier theory we are able to identify classes of
resonance modes that can be temperature compensated via n-type doping. These include
bulk modes such as the width/length extensional modes of a beam, Lamé/square
extensional modes of a plate resonator, as well as flexural and torsional resonance modes …
silicon resonators. By combining results from FEM-based sensitivity analysis and modelling
of elastic constants of silicon with free carrier theory we are able to identify classes of
resonance modes that can be temperature compensated via n-type doping. These include
bulk modes such as the width/length extensional modes of a beam, Lamé/square
extensional modes of a plate resonator, as well as flexural and torsional resonance modes …
We model the temperature coefficients of resonance modes of degenerately n-type doped silicon resonators. By combining results from FEM-based sensitivity analysis and modelling of elastic constants of silicon with free carrier theory we are able to identify classes of resonance modes that can be temperature compensated via n-type doping. These include bulk modes such as the width/length extensional modes of a beam, Lamé/square extensional modes of a plate resonator, as well as flexural and torsional resonance modes. Our results show that virtually all resonance modes of practical importance can reach zero TCF when the resonator is aligned to a correct crystallographic orientation and when the n-dopant concentration is suitably selected.
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