Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 1832-1839 |
| Journal | Journal of Microelectromechanical Systems |
| Volume | 24 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2016 |
| MoE publication type | A1 Journal article-refereed |
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Keywords
- acoustic waves
- design for manufacture
- micromechanical devices
- radiofrequency microelectromechanical systems
- temperature dependence
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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 journal › Article › Scientific › peer-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
U2 - 10.1109/JMEMS.2015.2443379
DO - 10.1109/JMEMS.2015.2443379
M3 - Article
VL - 24
SP - 1832
EP - 1839
JO - Journal of Microelectromechanical Systems
JF - Journal of Microelectromechanical Systems
SN - 1057-7157
IS - 6
ER -