Temperature compensated plate resonator
The invention relates to a microelectromechanical resonator device comprising a support structure and a semiconductor resonator plate doped to a doping concentration with an n-type doping agent and being capable of resonating in a width-extensional resonance mode. In addition, there is at least one anchor suspending the resonator plate to the support structure and an actuator for exciting the width-extensional resonance mode into the resonator plate. According to the invention, the resonator plate is doped to a doping concentration of 1.2*10 20 cm −3 or more and has a shape which, in combination with said doping concentration and in said width-extensional resonance mode, provides the second order temperature coefficient of frequency (TCF 2 ) to be 12 ppb/C 2 or less at least at one temperature. Several practical implementations are presented.
1. A microelectromechanical resonator device comprising;
a support structure,
a semiconductor resonator plate doped to a doping concentration with an n-type doping agent and being capable of resonating at least partly in a width-extensional resonance mode,
at least one anchor suspending the resonator plate to the support structure, and
an actuator for exciting said width-extensional resonance mode into the resonator plate,
wherein the resonator plate is doped to a doping concentration of at least 1.2*10 20 cm −3 and has a shape which, in combination with said doping concentration and in said width-extensional resonance mode, provides a second order temperature coefficient of frequency (TCF 2 ) of 12 ppb/C 2 or less at at least one temperature.
2. The resonator device according to claim 1 , wherein the shape of the resonator plate has an aspect ratio of 1.1-1.6.
3. The resonator device according to claim 1 , wherein the shape of the resonator plate has an aspect ratio larger than 1.3, and the resonator plate is provided with a piezoelectric thin film forming part of said actuator.
4. The resonator device according to claim 1 , wherein the shape of the resonator plate is rectangular.
5. The resonator device according to claim 1 , wherein the shape of the resonator plate is elliptical.
6. The resonator device according to claim 1 , wherein the shape and doping concentration of the resonator plate are such that the first order temperature coefficient of frequency (TCF 1 ) of the resonator device is 1 ppm/C or less at said at least one temperature.
7. The resonator device according to claim 1 , wherein the shape of the resonator plate is non-square and non-circular and has an aspect ratio of 2 or less.
8. The resonator device according to claim 1 , wherein the resonator plate has an axis of symmetry which is aligned with, a direction of the semiconductor crystals with 5 degrees accuracy.
9. The resonator device according to claim 8 , wherein said axis of symmetry coincides with a longitudinal axis of the resonator plate.
10. The resonator device according to claim 1 , wherein the resonator plate further comprises a base plate having an aspect ratio of 1.2-1.6 and at least one protrusion extending laterally from the base plate.
11. The resonator device according to claim 10 , wherein the base plate is adapted to resonate in said width-extensional mode and the protrusions in a flexural, torsional or length-extensional mode.
12. The resonator device according to claim 1 , wherein the plate resonator is doped to a doping concentration of 1.25*10 20 cm −3 or more.
13. The resonator device according to claim 1 , wherein the shape and doping concentration of the resonator plate are such that the second order temperature coefficient of frequency (TCF 2 ) is 6 ppb/C 2 or less at said at least one temperature.
14. The resonator device according to claim 1 , wherein the shape and doping concentration of the resonator plate are such that the first order temperature coefficient of frequency (TCF 1 ) of the resonator device is 0.5 ppm/C or less and the second order temperature coefficient of frequency (TCF 2 ) is 3 ppb/C 2 or less at said at least one temperature.
15. The resonator device according to claim 1 , wherein its total temperature drift of frequency is less than 50 ppm over a temperature range spanning at least 125° C.
16. The resonator device according to claim 1 , wherein said actuator further comprises a piezoelectric actuator acoustically coupled with the resonator plate.