Compensation of second order temperature dependence of mechanical resonator frequency
Apparatus and methods for control of the second order temperature dependence of the frequency of a mechanical resonating structure are described. The second order temperature dependence of frequency of the mechanical resonating structure may be non-linear. Control may be provided by doping of a semiconductor layer of the mechanical resonating structure.
1. A mechanical resonating structure, comprising:
a plurality of stacked layers, comprising
a piezoelectric material active layer;
a plurality of electrodes configured to actuate the piezoelectric material active layer by applying thereto an excitation signal; and
a doped semiconductor layer coupled to the piezoelectric material active layer and coupled to a substrate by at least one anchor,
wherein thicknesses of the plurality of stacked layers combine to provide a first order temperature coefficient of frequency (TCF) that is approximately zero for a mode of vibration, and
wherein the doped semiconductor layer has a doping concentration with a value configured to provide the mechanical resonating structure with a second order TCF that is substantially zero for the mode of vibration.
2. The mechanical resonating structure of claim 1 , wherein the doped semiconductor layer is a silicon layer.
3. The mechanical resonating structure of claim 1 , wherein the plurality of electrodes comprises an interdigitated transducer (IDT) on an upper surface of the piezoelectric material active layer.
4. A mechanical resonating structure, comprising:
a piezoelectric material active layer;
a plurality of electrodes configured to actuate the piezoelectric material active layer by applying thereto an excitation signal; and
a semiconductor layer coupled to the piezoelectric material active layer and coupled to a substrate by at least one anchor,
wherein the semiconductor layer is doped so that a mode of vibration of the mechanical resonating structure has a second order temperature coefficient of frequency (TCF) that is substantially zero, and
wherein the plurality of electrodes comprises an interdigitated transducer (IDT) on an upper surface of the piezoelectric material active layer, wherein the plurality of electrodes further comprises a ground electrode, wherein the piezoelectric material active layer is configured between the IDT and the ground electrode, and wherein the mechanical resonating structure further comprises a first oxide layer and a second oxide layer, wherein the semiconductor layer is disposed at least partially between the first oxide layer and the second oxide layer, wherein the first oxide layer is disposed at least partially between the semiconductor layer and the ground electrode.
5. The mechanical resonating structure of claim 1 , wherein the mode of vibration is a primary mode of vibration of the mechanical resonating structure.
6. The mechanical resonating structure of claim 1 , wherein the plurality of electrodes are configured to actuate the piezoelectric material active layer to exhibit lateral vibration in a lateral direction.
7. The mechanical resonating structure of claim 6 , wherein the doped semiconductor layer has a thickness substantially perpendicular to the lateral direction, and wherein the doped semiconductor layer has a doping pattern which varies across the thickness.
8. The mechanical resonating structure of claim 7 , wherein the doping pattern defines a pn junction.
9. The mechanical resonating structure of claim 6 , wherein the doped semiconductor layer has a thickness substantially perpendicular to the lateral direction and a lateral dimension substantially parallel to the lateral direction, and wherein the doped semiconductor layer has a doping pattern which varies across the lateral direction.
10. The mechanical resonating structure of claim 1 , wherein the piezoelectric material active layer and/or the plurality of electrodes are doped.
11. The mechanical resonating structure of claim 1 , wherein the mechanical resonating structure further comprises a first oxide layer and a second oxide layer, wherein the doped semiconductor layer is disposed at least partially between the first oxide layer and the second oxide layer.
12. The mechanical resonating structure of claim 1 , wherein the doping concentration has a value between 10 19 and 10 21 donors/cm 3 .
13. The mechanical resonating structure of claim 1 , wherein the doping concentration has a value between 10 19 and 10 21 acceptors/cm 3 .
14. The mechanical resonating structure of claim 1 , wherein the doped semiconductor layer has a doping concentration with a value configured to provide the mechanical resonating structure with a second order TCF that is substantially zero for the mode of vibration over an entire range from −40° C. to 85° C.
15. The mechanical resonating structure of claim 4 , wherein the semiconductor layer is doped to a concentration between 10 19 and 10 21 donors/cm 3 .
16. The mechanical resonating structure of claim 4 , wherein the semiconductor layer is doped to a concentration between 10 19 and 10 21 acceptors/cm 3 .
17. The mechanical resonating structure of claim 4 , wherein the plurality of electrodes are configured to actuate the piezoelectric material active layer to exhibit vibration in a lateral direction.