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

Abstract

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.

What is claimed is: 
     
         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 )×√Δ
 
   Δ=( fs−fe )/ fs  
 
     fs=R/[ts+te 2×(ρ e/ρx )]
 
     fe=R/[ts+te ×(ρ e/ρx )]
 
   15.5≦M36.7
 
   
       where:
 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; 
 te 2  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. 
 
     
     
         2 . The resonator element according to  claim 1 , wherein
 the peripheral area of the first region includes
 a first outer edge and a second outer edge that respectively extend in a first direction perpendicular to the vibration direction, and the first outer edge is located away from the second outer edge in the vibration direction, and 
 a third outer edge and a fourth outer edge that respectively extend in the vibration direction, and the third outer edge is located away from the fourth outer edge in the first direction, 
   the second region includes
 a first thick section that includes a first inclined section having a thickness increasing as the first inclined section separates further away from one end edge connected to the first outer edge of the first region toward other end edge and that includes a first thick main body connected to the other end edge of the first inclined section, 
 a second thick section that includes a second inclined section having a thickness increasing as the second inclined section separates further away from one end edge connected to the second outer edge of the first region toward other end edge and that includes a second thick main body connected to the other end edge of the second inclined section, and 
 a third thick section that includes a third inclined section having a thickness increasing as the third inclined section separates further away from one end edge connected to the third outer edge of the first region toward other end edge and that includes a third thick main body connected to the other end edge of the third inclined section. 
   
     
     
         3 . The resonator element according to  claim 2 , wherein
 one surface of the first thick section, one surface of the second thick section and one surface of the third thick section respectively project from the first surface of the first region, and   the other surface of the first thick section, the other surface of the second thick section and the other surface of the third thick section are even with the second surface of the first region.   
     
     
         4 . The resonator element according to  claim 3 , wherein
 when an electrical axis, a mechanical axis and an optical axis that are crystal axis of a quartz crystal are respectively represented as an X axis, a Y axis and a Z axis, and when an axis obtained by inclining the Z axis so that a +Z side is rotated in a −Y direction of the Y axis is represented as a Z′ axis and an axis obtained by inclining the Y axis so that a +Y side is rotated in a +Z direction of the Z axis is represented as a Y′ axis, using the X axis as a rotation axis, the substrate is a quartz crystal plate in which a surface including the X axis and the Z′ axis corresponds to a main surface and a direction of the Y′ axis corresponds to a thickness.   
     
     
         5 . The resonator element according to  claim 4 , wherein
 the one surfaces of the first through third thick sections project from the first surface of the first region in a +Y direction of the Y′ axis.   
     
     
         6 . The resonator element according to  claim 4 , wherein
 the third thick section is located in a +Z′ direction of the Z′ axis.   
     
     
         7 . The resonator element according to  claim 4 , wherein
 the second thick section is located in a +X direction of the X axis.   
     
     
         8 . The resonator element according to  claim 2 , wherein
 the following relational expression is fulfilled:
   17.1≦M≦35.7.
 
   
     
     
         9 . The resonator element according to  claim 1 , wherein
 When hz denotes a length of the first excitation electrode along first direction perpendicular to the vibration direction, the following relational expression is fulfilled:
   1.25≦ hx/hz≦ 1.31.
 
   
     
     
         10 . The resonator element according to  claim 4 , wherein
 the quartz crystal substrate is an AT-cut quartz crystal substrate.   
     
     
         12 . A resonator comprising:
 the resonator element according to  claim 1 ; and   a package adapted to house the resonator element.   
     
     
         13 . A resonator comprising:
 the resonator element according to  claim 2 ; and   a package adapted to house the resonator element.   
     
     
         14 . An electronic device comprising:
 the resonator element according to  claim 1 ; and   an oscillator circuit adapted to drive the resonator element.   
     
     
         15 . An electronic device comprising:
 the resonator element according to  claim 2 ; and   an oscillator circuit adapted to drive the resonator element.   
     
     
         16 . An electronic apparatus comprising:
 the resonator element according to  claim 1 .   
     
     
         17 . An electronic apparatus comprising:
 the resonator element according to  claim 2 .   
     
     
         18 . A mobile object comprising:
 the resonator element according to  claim 1 .   
     
     
         19 . A mobile object comprising:
 the resonator element according to  claim 2 .