RESONATOR ELEMENT, RESONATOR, ELECTRONIC DEVICE, ELECTRONIC APPARATUS, AND MOBILE OBJECT

摘要

A resonator element includes a substrate having first and second regions. A first region has a vibration region that vibrates with a thickness shear vibration. The first region has first and second surfaces opposite to each other. The second region is integrated with a peripheral area of the first region. The second region has a thickness larger than a thickness of the first region. A first excitation electrode is disposed on the first surface. A second excitation electrode is disposed on the second surface and is larger than the first excitation electrode in a plan view. The first excitation electrode is disposed so as to fit into an outer edge of the second excitation electrode in the plan view. The energy trap coefficient M fulfills 15.5≦M≦36.7.

主权项

1. A resonator element comprising:
a substrate that includes a first region having a vibration region that vibrates with a thickness shear vibration, the first region having first and second surfaces opposite to each other, the substrate including a second region that is integrated with a peripheral area of the first region, and the second region having a thickness larger than a thickness of the first region; a first excitation electrode disposed on the first surface; and a second excitation electrode disposed on the second surface, the second excitation electrode being larger than the first excitation electrode in a plan view, wherein the first excitation electrode fits into an outer edge of the second excitation electrode in the plan view, and the following relational expressions are fulfilled:
M=K×(hx/2×ts)×√ΔΔ=(fs−fe)/fs fs=R/[ts+te2×(ρe/ρx)]fe=R/[ts+te×(ρe/ρx)]15.5≦M36.7where:
M denotes an energy trap coefficient; K denotes an anisotropy factor of the substrate; hx denotes a length of the first excitation electrode along a vibration direction of the thickness shear vibration; ts denotes a thickness of the vibration region; Δ denotes an amount of frequency drop; fs denotes a cut-off frequency of the vibration region; fe denotes a frequency when the first and second excitation electrodes are disposed on the vibration region; R denotes a frequency constant of the vibration region; te denotes a sum of a first thickness of the first excitation electrode and a second thickness of the second excitation electrode; te2 denotes the second thickness of the second excitation electrode; ρe denotes a density of the first and second excitation electrodes; and ρx denotes a density of the vibration region.