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

A. Jaakkola, M. Prunnila, T. Pensala, J. Dekker, P. Pekko

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

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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",
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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 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

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KW - micromechanical devices

KW - radiofrequency microelectromechanical systems

KW - temperature dependence

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