Frequency sensitivity analysis and optimum design for MEMS resonator

• US 20020190607A1
• Filed: 04/02/2002
• Published: 12/19/2002
• Est. Priority Date: 04/03/2001
• Status: Active Grant

• Current Assignee: Regents of the University of California (University of California)
• Original Assignee: Regents of the University of California (University of California)
• Inventors: Liu, Rong, Turner, Kimberly L., Paden, Brad
• Granted Patent: US 6,744,174 B2
• Time in Patent Office: Days
• US Class Current: 310/328
• CPC Class Codes: B81C 99/006 Design; Simulation
• CPC Class Codes: H03H 3/0075 Arrangements or methods specially adapted for testing microelecro-mechanical resonators or networks

Abstract

A frequency stability analysis and design method for frequency robust resonators, such as MEMS resonators, is presented. The frequency characteristics of a laterally vibrating resonator are analyzed. With the fabrication error on the sidewall of the structure being considered, the first and second order frequency sensitivities to the fabrication error are derived. A relationship between the proof mass area and perimeter, and the beam width, is developed for single material structures, which expresses that the proof mass perimeter times the beam width should equal six times the area of the proof mass. Design examples are given for the single material and multi-layer structures. The results and principles presented in the paper can be used to analyze and design other MEMS resonators.

Claims

1. A frequency robust resonator comprising:

at least one beam having a first end, a second end, and a beam width; and

a proof mass having a proof mass area and a perimeter;

wherein the proof mass is affixed to the first end of the beam and the second end of the beam is affixed to a ground and the proof mass perimeter multiplied by the beam width is substantially equivalent to six times the proof mass area.

2. The resonator of claim 1, further comprising a second beam having a first and second end, wherein the first end of the second beam is affixed to the proof mass and the second end of the second beam is affixed to a ground.

3. The resonator of claim 2, wherein the first and second beam are affixed to opposite sides of the proof mass.

4. The resonator of claim 1, wherein the at least one beam is a folded beam including a moving bar.

5. The resonator of claim 1, wherein the resonator is a single material.

6. The resonator of claim 1, wherein the resonator is comb-driven.

7. The resonator of claim 1, wherein proof mass is trussed.

8. The resonator of claim 7, wherein the proof mass further includes a width comprising M+2 row walls, where M is at least one.

9. The resonator of claim 7, wherein the proof mass further includes a length comprising N+2 row walls, where M is at least one.

10. The resonator of claim 1, wherein the resonator is multi-layered.