Microelectromechanical resonators having offset [100] and [110] crystal orientations
A TPoS resonator includes a substrate and a resonator body suspended over the substrate by at least a first pair of fixed supports (e.g., tethers) that attach to first and second ends of the resonator body. The resonator body includes monocrystalline silicon, which has a [100] crystallographic orientation that is offset by ±α degrees relative to a nodal line of the resonator body (e.g., tether-to-tether axis) when the resonator body is operating at a resonant frequency, where a is a real number in a range from about 5 to about 19 and, more preferably, in a range from about 7 to about 17. The resonator may be an extensional-mode resonator and the resonator body may be rectangular-shaped with unequal length and width dimensions.
1. A thin-film piezoelectric-on-silicon (TPoS) resonator containing a single resonating element therein, comprising:
a substrate; and
a resonator body suspended over said substrate by at least a first pair of fixed tethers that attach to first and second ends of said resonator body, said resonator body comprising monocrystalline silicon having a [100] crystallographic orientation offset by ±α degrees relative to a nodal line of said resonator body when said resonator body is operating at a resonant frequency, where α is a real number in a range from about 5 to about 19 and has a value selected to generally passively minimize a total frequency variation range (TFVR) associated with the TPoS resonator when operating at the resonant frequency, and the nodal line corresponds to the tether-to-tether axis extending between the first and second ends of said resonator body.
2. The resonator of claim 1 , wherein the resonator is an extensional-mode resonator; and wherein said resonator body is a rectangular-shaped resonator body having unequal length and width dimensions.
3. The resonator of claim 1 , wherein said substrate is a [100] silicon-on-insulator substrate.
4. The resonator of claim 1 , wherein the monocrystalline silicon in said resonator body is doped with an N-type or P-type dopant to a level greater than about 1×10 19 cm −3 .
5. The resonator of claim 1 , wherein said resonator body has a thickness in a range from about 8 um to about 40 um.
6. The resonator of claim 1 , further comprising lower and upper metal electrodes and an aluminum nitride layer on said resonator body, said aluminum nitride layer extending between the lower and upper metal electrodes.