Resonator element, resonator, electronic device, electronic apparatus, and mobile object

摘要

A resonator element includes a substrate including a first principal surface and a second principal surface respectively forming an obverse surface and a reverse surface of the substrate, and vibrating in a thickness-shear vibration mode, a first excitation electrode disposed on the first principal surface, and a second excitation electrode disposed on the second principal surface, and being 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, and the energy trap confficient M fulfills 15.5≦M≦36.7.

主权项

1. A resonator element comprising:
a substrate including a first principal surface and a second principal surface respectively forming an obverse surface and a reverse surface of the substrate, and vibrating in a thickness-shear vibration mode; a first excitation electrode disposed on the first principal surface; and a second excitation electrode disposed on the second principal surface, and 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≦M≦36.7where:
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 thickness-shear vibration direction; ts denotes a thickness of the substrate; Δ denotes an amount of frequency drop; fs denotes a cut-off frequency of the substrate; fe denotes a frequency when the excitation electrodes are disposed on the substrate; R denotes a frequency constant of the substrate; te denotes a sum of a thickness of the first excitation electrode and a thickness of the second excitation electrode; te2 denotes the thickness of the second excitation electrode; ρe denotes a density of the excitation electrodes; and ρx denotes a density of the substrate.