Design rules for temperature compensated degerately n-type-doped silicon MEMS resonators

    Research output: Contribution to journalArticleScientificpeer-review

    4 Citations (Scopus)

    Abstract

    The first- and second-order temperature coefficients and the total temperature-induced frequency deviation of degenerately n-type-doped silicon resonators are modeled. Modeling is based on finite element modelling-based sensitivity analysis of various resonator geometries combined with the experimental results on doping-dependent elastic constants of n-type-doped silicon. The analysis covers a doping range from 2.4 * 1017 to 7.5 * 1019 cm-3. Families of resonance modes that can be temperature compensated via n-type doping are identified. These include bulk modes, such as the width/length extensional modes of a beam, Lame /square extensional modes of a plate resonator, as well as flexural and torsional resonance modes. It is shown that virtually all resonance modes of practical importance can reach zero linear temperature coefficient of frequency when correctly designed. Optimal configurations are presented, where a total frequency deviation of ~150 ppm can be reached. The results suggest that full second-order temperature compensation familiar from AT cut quartz is not possible in silicon resonators with doping below 7.5 * 1019 cm-3. However, an analysis relying on extrapolated elastic constant data suggests the possibility of full second-order temperature compensation for a wide range of resonance modes when doping is extended beyond 1020 cm-3.
    Original languageEnglish
    Pages (from-to)1832-1839
    JournalJournal of Microelectromechanical Systems
    Volume24
    Issue number6
    DOIs
    Publication statusPublished - 2016
    MoE publication typeA1 Journal article-refereed

    Fingerprint

    MEMS
    Resonators
    Silicon
    Doping (additives)
    Elastic constants
    Temperature
    Sensitivity analysis
    Quartz
    Geometry
    Compensation and Redress

    Keywords

    • acoustic waves
    • design for manufacture
    • micromechanical devices
    • radiofrequency microelectromechanical systems
    • temperature dependence

    Cite this

    @article{921e33ccd61b470a9823d8a9902d4765,
    title = "Design rules for temperature compensated degerately n-type-doped silicon MEMS resonators",
    abstract = "The first- and second-order temperature coefficients and the total temperature-induced frequency deviation of degenerately n-type-doped silicon resonators are modeled. Modeling is based on finite element modelling-based sensitivity analysis of various resonator geometries combined with the experimental results on doping-dependent elastic constants of n-type-doped silicon. The analysis covers a doping range from 2.4 * 1017 to 7.5 * 1019 cm-3. Families of resonance modes that can be temperature compensated via n-type doping are identified. These include bulk modes, such as the width/length extensional modes of a beam, Lame /square extensional modes of a plate resonator, as well as flexural and torsional resonance modes. It is shown that virtually all resonance modes of practical importance can reach zero linear temperature coefficient of frequency when correctly designed. Optimal configurations are presented, where a total frequency deviation of ~150 ppm can be reached. The results suggest that full second-order temperature compensation familiar from AT cut quartz is not possible in silicon resonators with doping below 7.5 * 1019 cm-3. However, an analysis relying on extrapolated elastic constant data suggests the possibility of full second-order temperature compensation for a wide range of resonance modes when doping is extended beyond 1020 cm-3.",
    keywords = "acoustic waves, design for manufacture, micromechanical devices, radiofrequency microelectromechanical systems, temperature dependence",
    author = "A. Jaakkola and M. Prunnila and T. Pensala and J. Dekker and P. Pekko",
    year = "2016",
    doi = "10.1109/JMEMS.2015.2443379",
    language = "English",
    volume = "24",
    pages = "1832--1839",
    journal = "Journal of Microelectromechanical Systems",
    issn = "1057-7157",
    publisher = "Wiley",
    number = "6",

    }

    Design rules for temperature compensated degerately n-type-doped silicon MEMS resonators. / Jaakkola, A.; Prunnila, M.; Pensala, T.; Dekker, J.; Pekko, P.

    In: Journal of Microelectromechanical Systems, Vol. 24, No. 6, 2016, p. 1832-1839.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

    T1 - Design rules for temperature compensated degerately n-type-doped silicon MEMS resonators

    AU - Jaakkola, A.

    AU - Prunnila, M.

    AU - Pensala, T.

    AU - Dekker, J.

    AU - Pekko, P.

    PY - 2016

    Y1 - 2016

    N2 - The first- and second-order temperature coefficients and the total temperature-induced frequency deviation of degenerately n-type-doped silicon resonators are modeled. Modeling is based on finite element modelling-based sensitivity analysis of various resonator geometries combined with the experimental results on doping-dependent elastic constants of n-type-doped silicon. The analysis covers a doping range from 2.4 * 1017 to 7.5 * 1019 cm-3. Families of resonance modes that can be temperature compensated via n-type doping are identified. These include bulk modes, such as the width/length extensional modes of a beam, Lame /square extensional modes of a plate resonator, as well as flexural and torsional resonance modes. It is shown that virtually all resonance modes of practical importance can reach zero linear temperature coefficient of frequency when correctly designed. Optimal configurations are presented, where a total frequency deviation of ~150 ppm can be reached. The results suggest that full second-order temperature compensation familiar from AT cut quartz is not possible in silicon resonators with doping below 7.5 * 1019 cm-3. However, an analysis relying on extrapolated elastic constant data suggests the possibility of full second-order temperature compensation for a wide range of resonance modes when doping is extended beyond 1020 cm-3.

    AB - The first- and second-order temperature coefficients and the total temperature-induced frequency deviation of degenerately n-type-doped silicon resonators are modeled. Modeling is based on finite element modelling-based sensitivity analysis of various resonator geometries combined with the experimental results on doping-dependent elastic constants of n-type-doped silicon. The analysis covers a doping range from 2.4 * 1017 to 7.5 * 1019 cm-3. Families of resonance modes that can be temperature compensated via n-type doping are identified. These include bulk modes, such as the width/length extensional modes of a beam, Lame /square extensional modes of a plate resonator, as well as flexural and torsional resonance modes. It is shown that virtually all resonance modes of practical importance can reach zero linear temperature coefficient of frequency when correctly designed. Optimal configurations are presented, where a total frequency deviation of ~150 ppm can be reached. The results suggest that full second-order temperature compensation familiar from AT cut quartz is not possible in silicon resonators with doping below 7.5 * 1019 cm-3. However, an analysis relying on extrapolated elastic constant data suggests the possibility of full second-order temperature compensation for a wide range of resonance modes when doping is extended beyond 1020 cm-3.

    KW - acoustic waves

    KW - design for manufacture

    KW - micromechanical devices

    KW - radiofrequency microelectromechanical systems

    KW - temperature dependence

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    DO - 10.1109/JMEMS.2015.2443379

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