Geometric properties of an embedded electrode structure for an acoustic filter

A method of manufacturing an acoustic filter, the method comprising:

• providing a piezoelectric layer having two opposite surfaces that respectively form a first plane and a second plane;
• and
• providing an electrode structure that is at least partially embedded within the piezoelectric layer, the electrode structure comprising multiple fingers positioned across a first axis, wherein:
• a value of a metallization ratio associated with the multiple fingers is greater than approximately 0.2, wherein the metallization ratio represents an average width of adjacent fingers of the multiple fingers divided by an average distance between the adjacent fingers of the multiple fingers;
• a cross section of each finger of the multiple fingers has a planar surface that is perpendicular to the first plane, the cross section having:
• a first segment that abuts the first plane;
• and
• a second segment that is between the first plane and the second plane;
• and
• a tangent line positioned at a point along an edge of the cross section forms an exterior angle relative to the first axis, a value of the exterior angle having a range approximately from 50° to 120°, the edge of the cross section joining the first segment to the second segment, wherein
• longitudinal axes of the multiple fingers are substantially parallel to a second axis that is perpendicular to the first axis;
• a third axis is normal to the first axis and the second axis;
• an orientation of the first axis, the second axis, and the third axis is relative to a crystalline structure of the piezoelectric layer as defined by Euler angles lambda (λ), mu (μ), and theta (θ);
• and
• providing the piezoelectric layer comprises providing the piezoelectric layer such that a value of Euler angle mu (μ) has a range approximately from −70° to −55° or at least one symmetrical equivalent.

An acoustic filter comprising:

• a piezoelectric layer having two opposite surfaces that respectively form a first plane and a second plane;
• an electrode structure comprising multiple fingers positioned across a first axis, at least a portion of each finger of the multiple fingers extending from the first plane towards the second plane;
• and
• a substrate stack that abuts the second plane,
• a value of a metallization ratio associated with the multiple fingers having a range from approximately 0.3 to 0.6, wherein the metallization ratio represents an average width of adjacent fingers of the multiple fingers divided by an average distance between the adjacent fingers of the multiple fingers;
• and
• a cross section of each finger of the multiple fingers having a quadrilateral shape with a segment that faces the second plane and a sidewall that forms an exterior angle with a line that extends from the segment, a value of the exterior angle having a range approximately from 60° to 90°.

An apparatus comprising:

• a high-quality temperature-compensated surface-acoustic-wave filter comprising:
• a piezoelectric layer having two opposite surfaces that respectively form a first plane and a second plane;
• an electrode structure that is at least partially embedded within the piezoelectric layer, the electrode structure comprising multiple fingers positioned across a first axis,
• a value of a metallization ratio associated with the multiple fingers being greater than approximately 0.2, wherein the metallization ratio represents an average width of adjacent fingers of the multiple fingers divided by an average distance between the adjacent fingers of the multiple fingers;
• a cross section of each finger of the multiple fingers having a planar surface that is perpendicular to the first plane, the cross section having:
• a first segment that abuts the first plane;
• and
• a second segment that is between the first plane and the second plane;
• and
• a tangent line positioned at a point along an edge of the cross section forming an exterior angle relative to the first axis, a value of the exterior angle having a range approximately from 60° to 90°, the edge of the cross section joining the first segment to the second segment.