Piezoelectric resonator and manufacturing method thereof

A method for producing an energy trap piezoelectric resonator which operates in a thickness longitudinal vibration mode and which includes a piezoelectric member and a first vibrating electrode and a second vibrating electrode that are provided on respective major surfaces of the piezoelectric member and that overlap each other at a portion of the piezoelectric member, the method comprising the steps of:

• in the case where C is to be determined so that C=Qe×(R×A) by determining R and A of the piezoelectric member and Qe, where R is the average pore size in micrometers, A is the porosity in percent, Qe is a value at a target resonant frequency of the piezoelectric resonator having the first and second vibrating electrodes on the respective major surfaces thereof, and C is a constant that is uniquely determined by a piezoelectric material of the piezoelectric member, and
• in the case where C (S) is to be determined so that C (S)=Qe (S)×(R×A) by determining Qe (S), where Qe (S) is a Qe value at a frequency of a spurious wave that is in a mode that is higher than a mode of a wave at the resonant frequency, and C (S) is a constant that is uniquely determined by the piezoelectric material of the piezoelectric member,
• when Qe (S) is to be equal to or less than Qe (max) and Qe is to be equal to or greater than Qe (min), where Qe (max) is an upper limit of Qe (S) and Qe (min) is a lower limit of Qe,
• forming the piezoelectric member using a piezoelectric material having an R value and an A value that are such that C (S)/Qe (max)≦(R×A)≦C/Qe (min);
• and
• forming the first and second vibrating electrodes on the respective major surfaces of the piezoelectric member.

An energy trap piezoelectric resonator which operates in a thickness longitudinal vibration mode, the piezoelectric resonator comprising:

• a piezoelectric member in which, in the case where C is to be determined so that C=Qe×(R×A) by determining R and A of the piezoelectric member and Qe, where R is the average pore size in micrometers, A is the porosity in percent, Qe is a value at a target resonant frequency of the piezoelectric resonator having a first vibrating electrode and a second vibrating electrode on respective major surfaces thereof, and C is a constant that is uniquely determined by a piezoelectric material of the piezoelectric member, and
• in the case where C (S) is to be determined so that C (S)=Qe (S)×(R×A) by determining Qe (S), where Qe (S) is a Qe value at a frequency of a spurious wave that is in a mode that is higher than a mode of a wave at the resonant frequency, and C (S) is a constant that is uniquely determined by the piezoelectric material of the piezoelectric member,
• when Qe (S) is to be equal to or less than Qe (max) and Qe is to be equal to or greater than Qe (min), where Qe (max) is an upper limit of Qe (S) and Qe (min) is a lower limit of Qe,
• the piezoelectric member includes a piezoelectric material having an R value and an A value that are such that C (S)/Qe (max)≦(R×A)≦C/Qe (min);
• and
• a first vibrating electrode and a second vibrating electrode provided on the respective major surfaces of the piezoelectric member and that partially oppose each other through the piezoelectric member.