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 language | English |
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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 |
Keywords
- acoustic waves
- design for manufacture
- micromechanical devices
- radiofrequency microelectromechanical systems
- temperature dependence