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

Abstract

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
Pages442-445
ISBN (Electronic)978-1-4577-1820-5
ISBN (Print)978-1-4577-1819-9, 978-1-4577-1821-2
DOIs
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

Conference

ConferenceIEEE International Frequency Control Symposium, IFCS 2012
Abbreviated titleIFCS 2012
CountryUnited States
CityBaltimore
Period21/05/1224/05/12

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wave propagation
acoustics
temperature
shear
coefficients
free electrons
elastic properties
resonators
propagation
single crystals
silicon
curves
electronics

Cite this

Pensala, T., Prunnila, M., & Jaakkola, A. (2012). Bulk acoustic wave propagation characteristics in degenerately n-doped Si. In Proceedings : International Frequency Control Symposium, IFCS 2012 (pp. 442-445). IEEE Institute of Electrical and Electronic Engineers . https://doi.org/10.1109/FCS.2012.6243713
Pensala, Tuomas ; Prunnila, Mika ; Jaakkola, Antti. / Bulk acoustic wave propagation characteristics in degenerately n-doped Si. Proceedings : International Frequency Control Symposium, IFCS 2012. IEEE Institute of Electrical and Electronic Engineers , 2012. pp. 442-445
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title = "Bulk acoustic wave propagation characteristics in degenerately n-doped Si",
abstract = "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 Lam{\'e} mode which is a pure superposition of shear bulk acoustic waves. Good agreement is found.",
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Pensala, T, Prunnila, M & Jaakkola, A 2012, Bulk acoustic wave propagation characteristics in degenerately n-doped Si. in Proceedings : International Frequency Control Symposium, IFCS 2012. IEEE Institute of Electrical and Electronic Engineers , pp. 442-445, IEEE International Frequency Control Symposium, IFCS 2012, Baltimore, United States, 21/05/12. https://doi.org/10.1109/FCS.2012.6243713

Bulk acoustic wave propagation characteristics in degenerately n-doped Si. / Pensala, Tuomas; Prunnila, Mika; Jaakkola, Antti.

Proceedings : International Frequency Control Symposium, IFCS 2012. IEEE Institute of Electrical and Electronic Engineers , 2012. p. 442-445.

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

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N2 - 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.

AB - 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.

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Pensala T, Prunnila M, Jaakkola A. Bulk acoustic wave propagation characteristics in degenerately n-doped Si. In Proceedings : International Frequency Control Symposium, IFCS 2012. IEEE Institute of Electrical and Electronic Engineers . 2012. p. 442-445 https://doi.org/10.1109/FCS.2012.6243713