Flexural vibration piece and oscillator using the same
A flexural vibration piece includes a flexural vibrator that has a first region on which a compressive stress or a tensile stress acts due to vibration and a second region having a relationship in which a tensile stress acts thereon when a compressive stress acts on the first region and a compressive stress acts thereon when a tensile stress acts on the first region, and performs flexural vibration in a first plane. The flexural vibration piece also includes a heat conduction path, in the vicinity of the first region and the second region, that is formed of a material having a thermal conductivity higher than that of the flexural vibrator and thermally connects between the first region and the second region.
1. A flexural vibration piece comprising:
a flexural vibrator that has a first region on which a compressive stress or a tensile stress acts due to vibration and a second region having a relationship in which a tensile stress acts thereon when a compressive stress acts on the first region and a compressive stress acts thereon when a tensile stress acts on the first region, and performs flexural vibration in a first plane; and
a heat conduction path, in the vicinity of the first region and the second region, that is formed of a material having a thermal conductivity higher than that of the flexural vibrator and thermally connects between the first region and the second region, wherein
when m is the number of heat conduction paths, α th is the thermal conductivity of the heat conduction path, α v is the thermal conductivity of the flexural vibrator, t v is the thickness of the flexural vibrator in a direction orthogonal to the first plane, and t th is the thickness of the heat conduction path, a relationship of t th ≧(t v /m)×(α v /α th ) is satisfied.
2. The flexural vibration piece according to claim 1 , wherein
the flexural vibrator is formed so as to extend from one end of a base, and the heat conduction path is formed so as to pass over the base near the root of the flexural vibrator at the base.
3. The flexural vibration piece according to claim 2 , wherein
a first electrode is formed in at least part of the first region, a second electrode is formed in at least part of the second region, and the heat conduction path is connected to the first electrode and the second electrode.
4. The flexural vibration piece according to claim 1 , wherein
when l th is the length of the heat conduction path, and l v is the distance between the first region and the second region of the flexural vibrator, a relationship of t th ≧(t v /m)×(α v /α th )×(l th /l v ) is satisfied.
5. The flexural vibration piece according to claim 1 , wherein
when fr is a mechanical oscillation frequency of the flexural vibrator, f 20 is a thermal relaxation frequency of the flexural vibration piece, π is a ratio of the circumference of a circle to its diameter, k is a thermal conductivity of a material used for the flexural vibrator in a vibration direction, ρ is a mass density of a material used for the flexural vibrator, C p is a heat capacity of the material used for the flexural vibrator, a is a width of the flexural vibrator in the vibration direction, and f 0 =πk/(2ρC p a 2 ), a relationship of 1>fr/(f 0 +(f 20 −f 0 )/3) is satisfied.
6. The flexural vibration piece according to claim 1 , wherein
when fr is a mechanical oscillation frequency of the flexural vibrator, π is a ratio of the circumference of a circle to its diameter, k is a thermal conductivity of a material used for the flexural vibrator in a vibration direction, ρ is a mass density of a material used for the flexural vibrator, C p is a heat capacity of the material used for the flexural vibrator, a is a width of the flexural vibrator in the vibration direction, and f 0 =πk/(2ρC p a 2 ), a relationship of 1≧fr/f 0 is satisfied.
7. The flexural vibration piece according to claim 1 , wherein
when τ 0 is a thermal relaxation time required for a temperature between the first region and the second region reaching a state of equilibrium in the case where the heat conduction path is not disposed, and τ 1 is the thermal relaxation time in the case where the heat conduction path is disposed, a relationship of τ 1 <τ 0 is satisfied.
8. The flexural vibration piece according to claim 1 , wherein
all or a part of the heat conduction path is formed by burying a material having a thermal conductivity higher than that of the flexural vibrator into a through hole that penetrates from the first region to the second region of the flexural vibrator or a through hole that penetrates in the vicinity of the first region and the second region.
9. An oscillator at least comprising:
the flexural vibration piece according to claim 1 ; and
an oscillator circuit that drives the flexural vibration piece.