Surface acoustic wave resonator and surface acoustic wave oscillator
A surface acoustic wave resonator includes: an IDT which is disposed on a quartz crystal substrate with an Euler angle of (−1.5°≦φ≦1.5°, 117°≦θ≦142°, 41.9°≦|ψ|≦49.57°) and which excites a surface acoustic wave in an upper mode of a stop band; and an inter-electrode-finger groove formed by recessing the quartz crystal substrate between electrode fingers of the IDT, wherein the following expression: 0.01λ≦G where λ represents a wavelength of the surface acoustic wave and G represents a depth of the inter-electrode-finger groove, is satisfied and when a line occupancy of the IDT is η, the depth of the inter-electrode-finger groove G and the line occupancy η are set to satisfy the following expression: −2.5× G /λ+0.675≦η≦−2.5× G /λ+0.775.
1. A surface acoustic wave resonator comprising:
an IDT which is disposed on a quartz crystal substrate with an Euler angle of (−1.5°≦φ≦1.5°, 117°≦θ≦142°, 41.9°≦|ψ|≦49.57°) and which excites a surface acoustic wave in an upper mode of a stop band; and
an inter-electrode-finger groove formed by recessing the quartz crystal substrate between electrode fingers of the IDT,
wherein the following expression:
0.01λ≦G
where λ represents a wavelength of the surface acoustic wave and G represents a depth of the inter-electrode-finger groove, is satisfied and
when a line occupancy of the IDT is η, the depth of the inter-electrode-finger groove G and the line occupancy η are set to satisfy the following expression:
−2.5× G/λ+ 0.675≦η≦−2.5× G/λ+ 0.775.
2. The surface acoustic wave resonator according to claim 1 , wherein the depth of the inter-electrode-finger groove G satisfies the following expression:
0.01λ≦G≦0.0695λ.
3. The surface acoustic wave resonator according to claim 1 , wherein the following expression:
0<H≦0.035λ
where H represents an electrode thickness of the IDT, is satisfied.
4. The surface acoustic wave resonator according to claim 3 , wherein the line occupancy η satisfies the following expression:
η=−2.533× G/λ− 2.269× H/λ+ 0.785+±0.04.
5. The surface acoustic wave resonator according to claim 3 , wherein the sum of the depth of the inter-electrode-finger groove G and the electrode thickness H satisfies the following expression:
0.0407λ≦ G+H.
6. The surface acoustic wave resonator according to claim 1 , wherein the ψ and θ satisfy the following expression:
ψ=1.191×10 −3 ×θ 3 −4.490×10 −1 ×θ 2 +5.646×10 1 ×θ−2.324×10 3 ±1.0.
7. The surface acoustic wave resonator according to claim 1 , wherein the following expression:
fr1<ft2<fr2
where ft 2 represents a frequency of the upper mode of the stop band in the IDT, fr 1 represents a frequency of the lower mode of the stop band in reflectors disposed to interpose the IDT therebetween in a propagation direction of the surface acoustic wave, and fr 2 represents a frequency of the upper mode of the stop band in the reflectors, is satisfied.
8. The surface acoustic wave resonator according to claim 1 , wherein an inter-conductor-strip groove is disposed between conductor strips of the reflectors, and
wherein the depth of the inter-conductor-strip groove is smaller than the depth of the inter-electrode-finger groove.
9. A surface acoustic wave oscillator comprising the surface acoustic wave resonator according to claim 1 and an IC driving the IDT.