Bulk acoustic wave propagation characteristics in degenerately n-doped Si

Tuomas Pensala, Mika Prunnila, Antti Jaakkola

    Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

    1 Citation (Scopus)


    The effect of degenerate level n-type doping on the bulk acoustic wave propagation properties in single crystal silicon is studied.
    Keyes' theory [1] is used to calculate the electronic effect of free electrons on the elastic constants c ij as function of temperature. Slowness curves are calculated for the bulk acoustic wave modes via solution of the Christoffel equation at several doping levels. Variation with respect to temperature is performed in order to extract the linear temperature coefficient of slowness as function of propagation direction.
    It is found that n-type doping has the largest effect on the slow shear mode and that temperature stable wave propagation directions exist with doping levels above 10 19 cm -3 . Comparison to experiment is made via measured temperature coefficients of frequency of square plate resonators vibrating in the Lamé mode which is a pure superposition of shear bulk acoustic waves. Good agreement is found.
    Original languageEnglish
    Title of host publicationProceedings
    Subtitle of host publicationInternational Frequency Control Symposium, IFCS 2012
    PublisherIEEE Institute of Electrical and Electronic Engineers
    ISBN (Electronic)978-1-4577-1820-5
    ISBN (Print)978-1-4577-1819-9, 978-1-4577-1821-2
    Publication statusPublished - 2012
    MoE publication typeNot Eligible
    EventIEEE International Frequency Control Symposium, IFCS 2012 - Baltimore, United States
    Duration: 21 May 201224 May 2012
    Conference number: 66


    ConferenceIEEE International Frequency Control Symposium, IFCS 2012
    Abbreviated titleIFCS 2012
    Country/TerritoryUnited States


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