Resonator element, resonator, electronic device, and electronic apparatus

1. A resonator element comprising at least one resonating arm that vibrates in a torsional mode,

wherein the resonating arm includes a structural portion having a first portion disposed in a first direction in a sectional view in the width direction and a second portion connected to the first portion so that the center of gravity departs from the center of gravity of the first portion in the first direction and a second direction perpendicular to the first direction,

wherein the first portion vibrates in a stretch mode in the length direction of the resonating arm with an application of a voltage, and

wherein the second portion does not substantially vibrate in the stretch mode in the length direction of the resonating arm with the application of the voltage or vibrates in a stretch mode with a phase different from that of the first portion.

2. The resonator element according to claim 1 , wherein the first portion and the second portion each have a long plate shape in the length direction of the resonating arm and ends thereof in the width direction are connected to each other so that plate surfaces thereof are perpendicular to each other.

3. The resonator element according to claim 2 , wherein the resonating arm includes a plurality of the structural portions.

4. The resonator element according to claim 3 , wherein the resonating arm includes the plurality of structural portions so as to be arranged in the length direction.

5. The resonator element according to claim 3 , wherein the resonating arm includes a pair of the structural portions so as to face each other with the center axis along the length direction interposed therebetween.

6. The resonator element according to claim 2 , wherein the resonating arm includes the structural portion which is formed to extend all over the range in the length direction.

7. The resonator element according to claim 2 , wherein the resonating arm is formed to be symmetric about the center axis along the length direction.

8. The resonator element according to claim 1 , wherein the distal end of the resonating arm is provided with a massive portion of which the sectional area in the sectional view along the width direction of the resonating arm is greater than that of the structural portion.

9. The resonator element according to claim 1 , wherein a plurality of the resonating arms are provided.

10. The resonator element according to claim 9 , wherein a pair of the resonating arms vibrating in a torsional mode in the same direction are provided to be parallel to each other.

11. The resonator element according to claim 1 , wherein the resonating arm is formed of a piezoelectric material.

12. The resonator element according to claim 1 , wherein the resonating arm is formed of a non-piezoelectric material and a piezoelectric element having a piezoelectric thin film is disposed on the first portion of the resonating arm.

13. A resonator comprising:

the resonator element according to claim 1 ; and

a package that receives the resonator element therein.

14. An electronic device comprising:

the resonator element according to claim 1 ; and

an electronic component that drives the resonator element.

15. An electronic apparatus comprising:

the resonator element according to claim 1 ; and

an electronic component that drives the resonator element.