Vibrator device

1 . A vibrator device comprising:

a vibrator element having a base part, and a plurality of vibrating arms extending along a first direction from the base part;

a base body; and

a support substrate configured to support the vibrator element with respect to the base body, wherein

the support substrate includes

a base-body fixation part to be fixed to the base body,

an element support part configured to support the base part of the vibrator element, and

a beam part configured to couple the base-body fixation part and the element support part to each other,

the support substrate has a plurality of recessed parts in a surface facing the vibrator element,

each of the plurality of recessed parts partially overlaps with each of the plurality of vibrating arms, respectively, in a plan view, and the support substrate, in which each of the plurality of recessed parts is formed, has a first thickness,

an intermediate part of the support substrate between two adjacent recessed parts of the plurality of recessed parts has a second thickness, and

the first thickness is smaller than the second thickness.

2 . The vibrator device according to claim 1 , wherein

each of the plurality of recessed parts overlaps with each tip portion of the plurality of vibrating arms, respectively, in the plan view.

3 . The vibrator device according to claim 1 , wherein

each of a first inner side surface and a second inner side surface of each of the plurality of recessed parts opposed to each other along a second direction crossing the first direction has a tilted surface, and

a distance along the second direction between the first and second inner side surfaces decreases toward a bottom surface of each of the plurality of recessed parts.

4 . The vibrator device according to claim 1 , wherein

the plurality of vibrating arms includes a first vibrating arm and a second vibrating arm, and the second vibrating arm is arranged side by side with the first vibrating arm along a second direction crossing the first direction,

the second vibrating arm is arranged farther from the element support part than the first vibrating arm,

the plurality of recessed parts has a first recessed part arranged so as to be opposed to the first vibrating arm, and a second recessed part arranged so as to be opposed to the second vibrating arm, and

Wa 2 −Wb 2 >Wa 1 −Wb 1 is fulfilled, where a width along the second direction of the first vibrating arm is defined as Wb 1 , a width along the second direction of the second vibrating arm is defined as Wb 2 , a width along the second direction of the first recessed part is defined as Wa 1 , and a width along the second direction of the second recessed part is defined as Wa 2 .

5 . The vibrator device according to claim 1 , wherein

the plurality of vibrating arms includes a first vibrating arm and a second vibrating arm, the second vibrating arm is arranged side by side with the first vibrating arm along a second direction crossing the first direction,

the second vibrating arm is arranged farther from the element support part than the first vibrating arm,

the plurality of recessed parts has a first recessed part arranged so as to be opposed to the first vibrating arm, and a second recessed part arranged so as to be opposed to the second vibrating arm,

the first recessed part has a third inner side surface located closer to the base part along the first direction than a tip portion of the first vibrating arm,

the second recessed part has a fourth inner side surface located closer to the base part along the first direction than a tip portion of the second vibrating arm, and

Lc 2 >Lc 1 is fulfilled, where a first distance along the first direction between the tip portion of the first vibrating arm and the third inner side surface is defined as Lc 1 , and a second distance along the first direction between the tip portion of the second vibrating arm and the fourth inner side surface is defined as Lc 2 .

6 . The vibrator device according to claim 4 , wherein

the first recessed part has a third inner side surface located closer to the base part along the first direction than a tip portion of the first vibrating arm,

the second recessed part has a fourth inner side surface located closer to the base part along the first direction than a tip portion of the second vibrating arm, and

Lc 2 >Lc 1 is fulfilled, where a first distance along the first direction between the tip portion of the first vibrating arm and the third inner side surface is defined as Lc 1 , and a second distance along the first direction between the tip portion of the second vibrating arm and the fourth inner side surface is defined as Lc 2 .

7 . The vibrator device according to claim 1 , wherein

defining a direction perpendicular to the first direction and a second direction as a third direction,

the vibrator element and the support substrate are arranged so as to overlap each other in the third direction, and

the vibrator element includes

a pair of detection arms, as the plurality of vibrating arms, extending toward both sides in the first direction from the base part, the pair of detection arms being fixed to the element support part via a bonding member,

a pair of coupling arms extending toward both sides in the second direction from the base part,

a pair of first drive arms, as the plurality of vibrating arms, extending toward both sides in the first direction from a tip portion of one of the pair of coupling arms, and

a pair of second drive arms, as the plurality of vibrating arms, extending toward the both sides in the first direction from a tip portion of another of the pair of coupling arms.