Surface acoustic wave resonator, surface acoustic wave oscillator, and electronic instrument

1. A surface acoustic wave resonator provided on a quartz crystal substrate with Euler angles (−1.5°≦φ≦1.5°, 117°≦θ≦142°, and 42.79°≦|ψ|≦49.57°), comprising:

an IDT which excites a stop band upper end mode surface acoustic wave; and

inter-electrode finger grooves hollowed out of the substrate positioned between electrode fingers configuring the IDT, wherein

when the wavelength of the surface acoustic wave is λ and the depth of the inter-electrode finger grooves is G, λ and G satisfy the relationship of

0.01 λ≦G

and wherein,

when the line occupation rate of the IDT is η, the inter-electrode finger groove depth G and line occupation rate η satisfy the relationships of

−2.0000 ×G/λ+ 0.7200≦η≦−2.5000 ×G/λ+ 0.7775

provided that

0.0100.1λ ≦G≦ 0.0500λ

−3.5898 ×G/λ+ 0.7995≦η≦−2.5000 ×G/λ+ 0.7775

provided that

0.0500λ< G≦ 0.0695λ.

2. The surface acoustic wave resonator according to claim 1 , wherein

the inter-electrode finger groove depth G satisfies the relationship of

0.01λ≦ G≦ 0.0695λ.

3. The surface acoustic wave resonator according to claim 1 , wherein

when the electrode film thickness of the IDT is H, H satisfies the relationship of

0 <H≦ 0.035λ.

4. The surface acoustic wave resonator according to claim 3 , wherein

the line occupation rate η satisfies the relationship of

η=−1963.05×( G /λ) 3 +196.28×( G /λ) 2 −6.53×( G /λ)

−135.99×( H /λ) 2 +5.817×( H /λ)+0.732

−99.99×( G /λ)×( H /λ).

5. The surface acoustic wave resonator according to claim 3 , wherein

the sum of the inter-electrode finger groove depth G and electrode film thickness H satisfies the relationship of

0.0407λ≦ G+H.

6. The surface acoustic wave resonator according to claim 1 , wherein

ψ and θ satisfy the relationship of

Ψ=1.191×10 −3 ×0 3 −4.490×10 −1 ×0 2 +5.646×10 1 ×0−2.324×10 3 ±1.0.

7. The surface acoustic wave resonator according to claim 1 , wherein

when a stop band upper end mode frequency in the IDT is ft 2 , a stop band lower end mode frequency in reflectors disposed in such a way as to sandwich the IDT in the propagation direction of the surface acoustic wave is fr 1 , and a stop band upper end mode frequency of the reflectors is fr 2 , ft 2 , fr 1 , and fr 2 satisfy the relationship of

fr 1 <ft 2 <fr 22.

8. The surface acoustic wave resonator according to claim 1 , wherein

inter-conductor strip grooves are provided between conductor strips configuring the reflectors, and

the depth of the inter-conductor strip grooves is less than that of the inter-electrode finger grooves.

9. A surface acoustic wave oscillator comprising:

the surface acoustic wave resonator according to claim 1 ; and

an IC for driving the IDT.

10. An electronic instrument comprising the surface acoustic wave resonator according to claim 1 .

11. An electronic instrument comprising the surface acoustic wave resonator according to claim 3 .

12. An electronic instrument comprising the surface acoustic wave resonator according to claim 4 .

13. An electronic instrument comprising the surface acoustic wave resonator according to claim 5 .

14. An electronic instrument comprising the surface acoustic wave resonator according to claim 6 .

15. An electronic instrument comprising the surface acoustic wave resonator according to claim 7 .

16. An electronic instrument comprising the surface acoustic wave resonator according to claim 8 .

17. An electronic instrument comprising the surface acoustic wave resonator according to claim 9 .

18. The surface acoustic wave resonator according to claim 2 , wherein

when the electrode film thickness of the IDT is H, H satisfies the relationship of

0 <H≦ 0.035λ.

19. The surface acoustic wave resonator according to claim 4 , wherein

the sum of the inter-electrode finger groove depth G and electrode film thickness H satisfies the relationship of

0.0407λ≦ G+H.

20. An electronic instrument comprising the surface acoustic wave resonator according to claim 2 .