Temperature-engineered MEMS resonator
Degenerately doped semiconductor materials are deployed within resonant structures to control the first and higher order temperature coefficients of frequency, thereby enabling temperature dependence to be engineered without need for cumulative material layers which tend to drive up cost and compromise resonator performance.
1. A microelectromechanical system (MEMS) resonator comprising:
a single-crystal silicon layer doped with an impurity concentration that renders the single-crystal silicon layer sufficiently conductive to serve as a first electrode;
a conductive layer to serve as a second electrode;
an aluminum nitride piezoelectric layer disposed between the conductive layer and the single-crystal silicon layer;
wherein a resonator axis along which the MEMS resonator exhibits a predominant motion during resonant oscillation is offset from a dominant crystallographic axis of the single-crystal silicon layer by an angle that substantially reduces at least one of first-order or second-order temperature coefficients of frequency (TCFs) of the MEMS resonator relative to first- and/or second-order TCFs that would result without angular offset between the resonator axis and the dominant crystallographic axis; and
wherein the impurity concentration and angular offset are jointly controlled to substantially attenuate the first-order and second-order TCFs.
2. The MEMS resonator of claim 1 wherein the conductive layer comprises polysilicon doped with an impurity concentration that renders the polysilicon sufficiently conductive to serve as the second electrode.
3. The MEMS resonator of claim 1 wherein the single-crystal silicon layer and aluminum nitride piezoelectric layer have respective thicknesses in a predetermined ratio that attenuates at least one temperature coefficient of frequency of the MEMS resonator.
4. The MEMS resonator of claim 1 wherein the single-crystal silicon layer doped with the impurity concentration that renders the single-crystal silicon layer sufficiently conductive to serve as the first electrode comprises single-crystal silicon doped with phosphorus in a concentration that renders the single-crystal silicon sufficiently conductive to serve as the first electrode.
5. The MEMS resonator of claim 1 wherein dopant concentration within the single-crystal silicon layer is, at least in one or more regions thereof, greater than 4 E18 atoms per cubic centimeter.
6. The MEMS resonator of claim 1 wherein the first and second electrodes constitute electrodes to receive resonator drive signals that induce resonant oscillation within the MEMS resonator.
7. The MEMS resonator of claim 1 wherein the conductive layer comprises a metal layer sufficiently thin to avoid appreciable contribution to temperature-dependence of a resonant frequency of the MEMS resonator.
8. A method of fabricating microelectromechanical system (MEMS) resonator, the method comprising:
doping a single-crystal silicon layer with an impurity concentration that renders the single-crystal silicon layer sufficiently conductive to serve as a first electrode;
disposing an aluminum nitride piezoelectric layer on the single-crystal silicon layer;
disposing a conductive layer on the aluminum nitride piezoelectric layer to serve as a second electrode;
offsetting a resonator axis along which the MEMS resonator exhibits a predominant motion during resonant oscillation from a dominant crystallographic axis of the single-crystal silicon layer by an angle that substantially reduces at least one of first-order or second-order temperature coefficients of frequency (TCFs) of the MEMS resonator relative to first- and/or second-order TCFs that would result without angular offset between the resonator axis and the dominant crystallographic axis; and
jointly controlling the impurity concentration and angular offset to substantially attenuate the first-order and second-order TCFs.
9. The method of claim 8 wherein disposing the conductive layer comprises disposing, on the aluminum nitride piezoelectric layer, polysilicon doped with an impurity concentration that renders the polysilicon sufficiently conductive to serve as the second electrode.
10. The method of claim 8 further comprising forming the single-crystal silicon layer and aluminum nitride piezoelectric layer with relative thicknesses chosen to attenuate at least one temperature coefficient of frequency of the MEMS resonator.
11. The method of claim 8 wherein doping the single-crystal silicon layer with the impurity concentration that renders the single-crystal silicon layer sufficiently conductive to serve as the first electrode comprises doping the single-crystal silicon layer with phosphorus.
12. The method of claim 8 wherein doping the single-crystal silicon layer with the impurity concentration that renders the single-crystal silicon sufficiently conductive to serve as the first electrode comprises doping the single-crystal silicon layer with greater than 4 E18 impurity atoms per cubic centimeter.
13. The method of claim 8 wherein disposing the conductive layer on the aluminum nitride comprises disposing on the aluminum nitride a metal layer sufficiently thin to avoid appreciable contribution to temperature-dependence of a resonant frequency of the MEMS resonator.
14. A microelectromechanical system (MEMS) resonator comprising:
a single-crystal silicon layer doped with an impurity concentration that renders the single-crystal silicon layer sufficiently conductive to serve as a first electrode;
a conductive layer to serve as a second electrode;
an aluminum nitride piezoelectric layer disposed between the conductive layer and the single-crystal silicon layer; and
wherein first-order and second-order temperature coefficients of frequency (TCFs) of the MEMS resonator and at least one TCF of the MEMS resonator beyond second-order are substantially attenuated by virtue of (i) angular offset between a dominant crystallographic axis of the single-crystal silicon layer and a resonator axis along which the MEMS resonator exhibits a predominant motion during resonant oscillation, (ii) a chosen impurity concentration of the single-crystal silicon layer and (iii) chosen relative thicknesses of the single-crystal silicon layer and aluminum nitride piezoelectric layer.
15. A method of fabricating microelectromechanical system (MEMS) resonator, the method comprising:
doping a single-crystal silicon layer with an impurity concentration that renders the single-crystal silicon layer sufficiently conductive to serve as a first electrode;
disposing an aluminum nitride piezoelectric layer on the single-crystal silicon layer;
disposing a conductive layer on the aluminum nitride piezoelectric layer to serve as a second electrode; and
wherein the method further comprises (i) offsetting a dominant crystallographic axis of the single-crystal silicon layer from a resonator axis along which the MEMS resonator exhibits a predominant motion during resonant oscillation by a predetermined angle, (ii) doping the single-crystal silicon layer with a predetermined impurity concentration and (iii) forming the single-crystal silicon layer and aluminum nitride piezoelectric layer with relative thicknesses to collectively and substantially attenuate first-order and second-order temperature coefficients of frequency (TCFs) of the MEMS resonator and at least one TCF of the MEMS resonator beyond second-order.