Method for manufacturing a vibrating MEMS circuit

• US 9,369,105 B1
• Filed: 09/02/2008
• Issued: 06/14/2016
• Est. Priority Date: 08/31/2007
• Status: Active Grant

• Current Assignee: Qorvo US, Inc. (Qorvo, Inc.)
• Original Assignee: RF Micro Devices Incorporated (Qorvo, Inc.)
• Inventors: Li, Sheng-Shian, Lee, Seungbae, Bhattacharjee, Kushal
• Primary Examiner(s): Tugbang, A. Dexter
• Application Number:
  US12/202,624
• Time in Patent Office: 2,842 Days
• Field of Search: 29/253.5, 298/42, 298/46, 295/94, 252/62.9 PZ, 310/349, 310/351, 310/353, 310/363, 310/364, 310/366
• US Class Current: 1/1
• CPC Class Codes: H03H 2009/02283 Vibrating means
• CPC Class Codes: H03H 2009/02299 Comb-like, i.e. the beam comprising a plurality of fingers or protrusions along its length
• CPC Class Codes: H03H 2009/155 using MEMS techniques
• CPC Class Codes: H03H 3/0076 for obtaining desired frequency or temperature coefficients
• CPC Class Codes: H03H 3/02 for the manufacture of piezoelectric or electrostrictive resonators or networks H03H3/08 takes precedence
• CPC Class Codes: H03H 9/02015 Characteristics of piezoelectric layers, e.g. cutting angles
• CPC Class Codes: H03H 9/02062 Details relating to the vibration mode
• CPC Class Codes: H03H 9/0207 the vibration mode being harmonic
• CPC Class Codes: H03H 9/0542 consisting of a lateral arrangement H03H9/0566 takes precedence
• CPC Class Codes: H03H 9/0547 consisting of a vertical arrangement H03H9/0566 takes precedence
• CPC Class Codes: H03H 9/17 having a single resonator crystal tuning forks H03H9/21
• CPC Class Codes: H10N 30/06 Forming electrodes or interconnections, e.g. leads or terminals
• CPC Class Codes: H10N 30/071 Mounting of piezoelectric or electrostrictive parts together with semiconductor elements, or other circuit elements, on a common substrate
• CPC Class Codes: H10N 30/87 Electrodes or interconnections, e.g. leads or terminals
• CPC Class Codes: H10N 30/88 Mounts; Supports; Enclosures; Casings
• CPC Class Codes: Y10T 29/42 Piezoelectric device making
• CPC Class Codes: Y10T 29/49005 Acoustic transducer
• CPC Class Codes: Y10T 29/49147 Assembling terminal to base
• CPC Class Codes: Y10T 29/49155 Manufacturing circuit on or in base

Abstract

A method for making a micro-electro-mechanical systems (MEMS) vibrating structure is disclosed. The MEMS is supported by a MEMS anchor system and includes a single-crystal piezoelectric thin-film layer that has a specific non-standard crystal orientation, which may be selected to increase an electromechanical coupling coefficient, decrease a temperature coefficient of frequency, or both. The MEMS vibrating structure may have dominant lateral vibrations or dominant thickness vibrations. The single-crystal piezoelectric thin-film layer may include Lithium Tantalate or Lithium Niobate, and may provide MEMS vibrating structures with precise sizes and shapes, which may provide high accuracy and enable fabrication of multiple resonators having different resonant frequencies on a single substrate.

Claims

1. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

forming a single conducting layer over the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit; and

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body and made from the single conducting layer; and

a second conducting section residing on the second surface of the body and made from the single conducting layer, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section.

2. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 1 wherein the at least one defined characteristic comprises a substantially maximized coupling coefficient of the MEMS vibrating structure.

3. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 1 wherein the at least one defined characteristic comprises a coupling coefficient of the MEMS vibrating structure above a first threshold.

4. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 1 wherein the at least one defined characteristic comprises a substantially minimized temperature coefficient of frequency of the MEMS vibrating structure.

5. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 1 wherein the at least one defined characteristic comprises a temperature coefficient of frequency of the MEMS vibrating structure below a first threshold.

6. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 1 wherein the at least one defined characteristic comprises a coupling coefficient of the MEMS vibrating structure that provides a bandwidth of the MEMS vibrating structure above a first threshold.

7. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 6 wherein the at least one defined characteristic further comprise a substantially minimized temperature coefficient of frequency of the MEMS vibrating structure.

8. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 7 wherein the vibrations comprise dominant lateral vibrations that are about parallel to the substrate surface.

9. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 1 wherein the single-crystal piezoelectric thin-film comprises Lithium Tantalate.

10. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 1 wherein the single-crystal piezoelectric thin-film comprises Lithium Niobate.

11. The method for manufacturing the vibrating micro-electro-mechanical circuit of claim 1 wherein the MEMS vibrating structure is configured to vibrate, such that a dominant mode of vibration of the MEMS vibrating structure comprises one of an inter-digital-transduced mode, a periodically-poled-transduced mode, and a width-extensional mode.

12. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit; and

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body; and

a second conducting section residing on the second surface of the body, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section;

wherein the MEMS vibrating structure is configured to vibrate, such that a dominant mode of vibration of the MEMS vibrating structure is a contour mode of vibration, wherein an outer diameter of the MEMS vibrating structure varies as the MEMS vibrating structure vibrates.

13. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit; and

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body; and

a second conducting section residing on the second surface of the body, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section,

wherein the MEMS vibrating structure is configured to vibrate, such that a dominant mode of vibration of the MEMS vibrating structure is a contour mode of vibration, wherein an outer diameter of the MEMS vibrating structure and an inner diameter of the MEMS vibrating structure vary as the MEMS vibrating structure vibrates.

14. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit; and

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body; and

a second conducting section residing on the second surface of the body, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section,

wherein the MEMS vibrating structure is configured to vibrate, such that a dominant mode of vibration of the MEMS vibrating structure is a thickness-shear mode of vibration, wherein as the MEMS vibrating structure vibrates, a top of the single-crystal piezoelectric thin-film moves laterally in one direction, while a bottom of the single-crystal piezoelectric thin-film layer moves in about an opposite direction.

15. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit; and

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body; and

a second conducting section residing on the second surface of the body, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section,

wherein the MEMS vibrating structure is configured to vibrate, such that a dominant mode of vibration of the MEMS vibrating structure is a thickness-extensional mode of vibration, wherein a thickness of the MEMS vibrating structure varies as the MEMS vibrating structure vibrates.

16. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit; and

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body; and

a second conducting section residing on the second surface of the body, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section, wherein;

the single-crystal piezoelectric thin-film comprises Lithium Tantalate;

the body has;

a length that is about parallel to the first surface;

a width that is about parallel to the first surface and is about perpendicular to the length; and

a thickness that is about perpendicular to the first surface,

wherein the substantially uniform crystalline orientation relative to the first surface and the body is represented with a translation between a Cartesian Coordinate System and a third translated Cartesian Coordinate System, such that;

a uniform crystalline structure of the single-crystal piezoelectric thin-film is about aligned with an x-axis, a y-axis, and a z-axis of the Cartesian Coordinate System;

before translation, the x-axis is about parallel with the width, the y-axis is about parallel with the length, and the z-axis is about parallel with the thickness;

a translation from the Cartesian Coordinate System to a first translated Cartesian Coordinate System is based on keeping the z-axis stationary, and forming a first translated x-axis, a first translated y-axis, and a first translated z-axis by rotating the x-axis toward the y-axis, such that a first angle is formed between the x-axis and the first translated x-axis;

the first translated x-axis, the first translated y-axis, and the first translated z-axis are perpendicular to one another;

a translation from the first translated Cartesian Coordinate System to a second translated Cartesian Coordinate System is based on keeping the first translated x-axis stationary, and forming a second translated x-axis, a second translated y-axis, and a second translated z-axis by rotating the first translated z-axis away from the first translated y-axis, such that a second angle is formed between the first translated z-axis and the second translated z-axis;

the second translated x-axis, the second translated y-axis, and the second translated z-axis are perpendicular to one another;

a translation from the second translated Cartesian Coordinate System to the third translated Cartesian Coordinate System is based on keeping the second translated z-axis stationary, and forming a third translated x-axis, a third translated y-axis, and a third translated z-axis by rotating the second translated x-axis toward the second translated y-axis, such that a third angle is formed between the third translated x-axis and the second translated x-axis;

the third translated x-axis, the third translated y-axis, and the third translated z-axis are perpendicular to one another, and the first angle, the second angle, and the third angle form an angle set; and

the angle set comprises one of a first set, a second set, a third set, a fourth set, a fifth set, a sixth set, a seventh set, an eighth set, a ninth set, a tenth set, an eleventh set, and a twelfth set, such that;

the first set comprises the first angle equal to between about −

10 degrees and about 10 degrees, the second angle equal to between about 25 degrees and about 55 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the second set comprises the first angle equal to between about 170 degrees and about 190 degrees, the second angle equal to between about 115 degrees and about 145 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the third set comprises the first angle equal to between about −

10 degrees and about 10 degrees, the second angle equal to between about 25 degrees and about 55 degrees, and the third angle equal to between about 260 degrees and about 280 degrees;

the fourth set comprises the first angle equal to between about 170 degrees and about 190 degrees, the second angle equal to between about 115 degrees and about 145 degrees, and the third angle equal to between about 260 degrees and about 280 degrees;

the fifth set comprises the first angle equal to between about 110 degrees and about 130 degrees, the second angle equal to between about 25 degrees and about 55 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the sixth set comprises the first angle equal to between about 290 degrees and about 310 degrees, the second angle equal to between about 115 degrees and about 145 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the seventh set comprises the first angle equal to between about 110 degrees and about 130 degrees, the second angle equal to between about 25 degrees and about 55 degrees, and the third angle equal to between about 260 degrees and about 280 degrees;

the eighth set comprises the first angle equal to between about 290 degrees and about 310 degrees, the second angle equal to between about 115 degrees and about 145 degrees, and the third angle equal to between about 260 degrees and about 280 degrees;

the ninth set comprises the first angle equal to between about 230 degrees and about 250 degrees, the second angle equal to between about 25 degrees and about 55 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the tenth set comprises the first angle equal to between about 50 degrees and about 70 degrees, the second angle equal to between about 115 degrees and about 145 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the eleventh set comprises the first angle equal to between about 230 degrees and about 250 degrees, the second angle equal to between about 25 degrees and about 55 degrees, and the third angle equal to between about 260 degrees and about 280 degrees; and

the twelfth set comprises the first angle equal to between about 50 degrees and about 70 degrees, the second angle equal to between about 115 degrees and about 145 degrees, and the third angle equal to between about 260 degrees and about 280 degrees.

17. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit; and

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body; and

a second conducting section residing on the second surface of the body, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section,

wherein;

the single-crystal piezoelectric thin-film comprises Lithium Niobate;

the body has;

a length that is about parallel to the first surface;

a width that is about parallel to the first surface and is about perpendicular to the length; and

a thickness that is about perpendicular to the first surface,

wherein the substantially uniform crystalline orientation relative to the first surface and the body is represented with a translation between a Cartesian Coordinate System and a third translated Cartesian Coordinate System, such that;

a uniform crystalline structure of the single-crystal piezoelectric thin-film is about aligned with an x-axis, a y-axis, and a z-axis of the Cartesian Coordinate System;

before translation, the x-axis is about parallel with the width, the y-axis is about parallel with the length, and the z-axis is about parallel with the thickness;

a translation from the Cartesian Coordinate System to a first translated Cartesian Coordinate System is based on keeping the z-axis stationary, and forming a first translated x-axis, a first translated y-axis, and a first translated z-axis by rotating the x-axis toward the y-axis, such that a first angle is formed between the x-axis and the first translated x-axis;

the first translated x-axis, the first translated y-axis, and the first translated z-axis are perpendicular to one another;

a translation from the first translated Cartesian Coordinate System to a second translated Cartesian Coordinate System is based on keeping the first translated x-axis stationary, and forming a second translated x-axis, a second translated y-axis, and a second translated z-axis by rotating the first translated z-axis away from the first translated y-axis, such that a second angle is formed between the first translated z-axis and the second translated z-axis;

the second translated x-axis, the second translated y-axis, and the second translated z-axis are perpendicular to one another;

a translation from the second translated Cartesian Coordinate System to the third translated Cartesian Coordinate System is based on keeping the second translated z-axis stationary, and forming a third translated x-axis, a third translated y-axis, and a third translated z-axis by rotating the second translated x-axis toward the second translated y-axis, such that a third angle is formed between the third translated x-axis and the second translated x-axis;

the third translated x-axis, the third translated y-axis, and the third translated z-axis are perpendicular to one another, and the first angle, the second angle, and the third angle form an angle set; and

the angle set comprises one of a first set, a second set, a third set, a fourth set, a fifth set, a sixth set, a seventh set, an eighth set, a ninth set, a tenth set, an eleventh set, and a twelfth set, such that;

the first set comprises the first angle equal to between about −

10 degrees and about 10 degrees, the second angle equal to between about 30 degrees and about 60 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the second set comprises the first angle equal to between about 170 degrees and about 190 degrees, the second angle equal to between about 120 degrees and about 150 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the third set comprises the first angle equal to between about −

10 degrees and about 10 degrees, the second angle equal to between about 30 degrees and about 60 degrees, and the third angle equal to between about 260 degrees and about 280 degrees;

the fourth set comprises the first angle equal to between about 170 degrees and about 190 degrees, the second angle equal to between about 120 degrees and about 150 degrees, and the third angle equal to between about 260 degrees and about 280 degrees;

the fifth set comprises the first angle equal to between about 110 degrees and about 130 degrees, the second angle equal to between about 30 degrees and about 60 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the sixth set comprises the first angle equal to between about 290 degrees and about 310 degrees, the second angle equal to between about 120 degrees and about 150 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the seventh set comprises the first angle equal to between about 110 degrees and about 130 degrees, the second angle equal to between about 30 degrees and about 60 degrees, and the third angle equal to between about 260 degrees and about 280 degrees;

the eighth set comprises the first angle equal to between about 290 degrees and about 310 degrees, the second angle equal to between about 120 degrees and about 150 degrees, and the third angle equal to between about 260 degrees and about 280 degrees;

the ninth set comprises the first angle equal to between about 230 degrees and about 250 degrees, the second angle equal to between about 30 degrees and about 60 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the tenth set comprises the first angle equal to between about 50 degrees and about 70 degrees, the second angle equal to between about 120 degrees and about 150 degrees, and the third angle equal to between about 80 degrees and about 100 degrees;

the eleventh set comprises the first angle equal to between about 230 degrees and about 250 degrees, the second angle equal to between about 30 degrees and about 60 degrees, and the third angle equal to between about 260 degrees and about 280 degrees; and

the twelfth set comprises the first angle equal to between about 50 degrees and about 70 degrees, the second angle equal to between about 120 degrees and about 150 degrees, and the third angle equal to between about 260 degrees and about 280 degrees.

18. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit; and

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body; and

a second conducting section residing on the second surface of the body, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section, wherein;

the single-crystal piezoelectric thin-film comprises Lithium Tantalate;

the body has;

a length that is about parallel to the first surface;

a width that is about parallel to the first surface and is about perpendicular to the length; and

a thickness that is about perpendicular to the first surface,

wherein the substantially uniform crystalline orientation relative to the first surface and the body is represented with a translation between a Cartesian Coordinate System and a third translated Cartesian Coordinate System, such that;

a uniform crystalline structure of the single-crystal piezoelectric thin-film is about aligned with an x-axis, a y-axis, and a z-axis of the Cartesian Coordinate System;

before translation, the x-axis is about parallel with the length, the y-axis is about parallel with the width, and the z-axis is about parallel with the thickness;

a translation from the Cartesian Coordinate System to a first translated Cartesian Coordinate System is based on keeping the z-axis stationary, and forming a first translated x-axis, a first translated y-axis, and a first translated z-axis by rotating the x-axis toward the y-axis, such that a first angle is formed between the x-axis and the first translated x-axis;

the first translated x-axis, the first translated y-axis, and the first translated z-axis are perpendicular to one another;

a translation from the first translated Cartesian Coordinate System to a second translated Cartesian Coordinate System is based on keeping the first translated x-axis stationary, and forming a second translated x-axis, a second translated y-axis, and a second translated z-axis by rotating the first translated z-axis away from the first translated y-axis, such that a second angle is formed between the first translated z-axis and the second translated z-axis;

the second translated x-axis, the second translated y-axis, and the second translated z-axis are perpendicular to one another;

a translation from the second translated Cartesian Coordinate System to the third translated Cartesian Coordinate System is based on keeping the second translated z-axis stationary, and forming a third translated x-axis, a third translated y-axis, and a third translated z-axis by rotating the second translated x-axis toward the second translated y-axis, such that a third angle is formed between the third translated x-axis and the second translated x-axis;

the third translated x-axis, the third translated y-axis, and the third translated z-axis are perpendicular to one another, and the first angle, the second angle, and the third angle form an angle set; and

the angle set comprises one of a first set, a second set, a third set, a fourth set, a fifth set, and a sixth set, such that;

the first set comprises the first angle equal to between about −

10 degrees and about 10 degrees, the second angle equal to between about 102 degrees and about 148 degrees, and the third angle equal to between about zero degrees and about 360 degrees;

the second set comprises the first angle equal to between about 170 degrees and about 190 degrees, the second angle equal to between about 54 degrees and about 100 degrees, and the third angle equal to between about zero degrees and about 360 degrees;

the third set comprises the first angle equal to between about 110 degrees and about 130 degrees, the second angle equal to between about 102 degrees and about 148 degrees, and the third angle equal to between about zero degrees and about 360 degrees;

the fourth set comprises the first angle equal to between about 290 degrees and about 310 degrees, the second angle equal to between about 54 degrees and about 100 degrees, and the third angle equal to between about zero degrees and about 360 degrees;

the fifth set comprises the first angle equal to between about 230 degrees and about 250 degrees, the second angle equal to between about 102 degrees and about 148 degrees, and the third angle equal to between about zero degrees and about 360 degrees; and

the sixth set comprises the first angle equal to between about 50 degrees and about 70 degrees, the second angle equal to between about 54 degrees and about 100 degrees, and the third angle equal to between about zero degrees and about 360 degrees.

19. A method for manufacturing a vibrating micro-electro-mechanical circuit comprising:

providing a substrate having a substrate surface;

forming at least one anchor on the substrate surface;

selecting a substantially uniform crystalline orientation of a single-crystal piezoelectric thin-film to provide at least one defined characteristic of the vibrating micro-electro-mechanical circuit;

forming a micro-electro-mechanical systems (MEMS) vibrating structure comprising;

a body suspended from the at least one anchor and comprising;

a first surface and a second surface that are about parallel to the substrate surface; and

the single-crystal piezoelectric thin-film having the substantially uniform crystalline orientation relative to the first surface and the at least one anchor;

a first conducting section residing on the first surface of the body; and

a second conducting section residing on the second surface of the body, such that the MEMS vibrating structure has vibrations when a first electrical signal is applied to the first conducting section and the second conducting section, wherein;

the single-crystal piezoelectric thin-film comprises Lithium Niobate;

the body has;

a length that is about parallel to the first surface;

a width that is about parallel to the first surface and is about perpendicular to the length; and

a thickness that is about perpendicular to the first surface,

wherein the substantially uniform crystalline orientation relative to the first surface and the body is represented with a translation between a Cartesian Coordinate System and a third translated Cartesian Coordinate System, such that;

a uniform crystalline structure of the single-crystal piezoelectric thin-film is about aligned with an x-axis, a y-axis, and a z-axis of the Cartesian Coordinate System;

before translation, the x-axis is about parallel with the length, the y-axis is about parallel with the width, and the z-axis is about parallel with the thickness;

a translation from the Cartesian Coordinate System to a first translated Cartesian Coordinate System is based on keeping the z-axis stationary, and forming a first translated x-axis, a first translated y-axis, and a first translated z-axis by rotating the x-axis toward the y-axis, such that a first angle is formed between the x-axis and the first translated x-axis;

the first translated x-axis, the first translated y-axis, and the first translated z-axis are perpendicular to one another;

a translation from the first translated Cartesian Coordinate System to a second translated Cartesian Coordinate System is based on keeping the first translated x-axis stationary, and forming a second translated x-axis, a second translated y-axis, and a second translated z-axis by rotating the first translated z-axis away from the first translated y-axis, such that a second angle is formed between the first translated z-axis and the second translated z-axis;

the second translated x-axis, the second translated y-axis, and the second translated z-axis are perpendicular to one another;

a translation from the second translated Cartesian Coordinate System to the third translated Cartesian Coordinate System is based on keeping the second translated z-axis stationary, and forming a third translated x-axis, a third translated y-axis, and a third translated z-axis by rotating the second translated x-axis toward the second translated y-axis, such that a third angle is formed between the third translated x-axis and the second translated x-axis;

the third translated x-axis, the third translated y-axis, and the third translated z-axis are perpendicular to one another, and the first angle, the second angle, and the third angle form an angle set; and

the angle set comprises one of a first set, a second set, a third set, a fourth set, a fifth set, and a sixth set, such that;

the first set comprises the first angle equal to between about −

10 degrees and about 10 degrees, the second angle equal to between about 106 degrees and about 139 degrees, and the third angle equal to between about zero degrees and about 360 degrees;

the second set comprises the first angle equal to between about 170 degrees and about 190 degrees, the second angle equal to between about 42 degrees and about 75 degrees, and the third angle equal to between about zero degrees and about 360 degrees;

the third set comprises the first angle equal to between about 110 degrees and about 130 degrees, the second angle equal to between about 106 degrees and about 139 degrees, and the third angle equal to between about zero degrees and about 360 degrees;

the fourth set comprises the first angle equal to between about 290 degrees and about 310 degrees, the second angle equal to between about 42 degrees and about 75 degrees, and the third angle equal to between about zero degrees and about 360 degrees;

the fifth set comprises the first angle equal to between about 230 degrees and about 250 degrees, the second angle equal to between about 106 degrees and about 139 degrees, and the third angle equal to between about zero degrees and about 360 degrees; and

the sixth set comprises the first angle equal to between about 50 degrees and about 70 degrees, the second angle equal to between about 42 degrees and about 75 degrees, and the third angle equal to between about zero degrees and about 360 degrees.