Anisotropic MEMS Resonator Shape Design for Uniform Displacement

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Solution Overview

Problem

MEMS resonators made from anisotropic materials suffer from shape distortions in resonant modes, leading to non-uniform edge displacement and increased likelihood of exciting unwanted resonance modes, which affects their performance and efficiency.

Innovation Solution

Designing the resonator with a shape that matches the directional characteristics of the anisotropic material, specifically selecting dimensions based on the modulus of elasticity to achieve uniform displacement in the quasi-longitudinal extensional mode, and using electrodes shaped to maintain a constant actuation gap, thereby reducing distortions and enhancing linearity and efficiency.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If a standard geometry resonator is used with anisotropic material, then the resonator can be manufactured with simple processes, but the resonator suffers from shape distortions and non-uniform edge displacement during resonance

Engineering Contradiction:

Improvemanufacturing simplicityVSAvoidshape uniformity

Core Design Contradiction:

Ease of manufactureVSManufacturing precision

Solution Approach 1:

The patent applies asymmetry by designing a resonator geometry that is specifically tailored to compensate for the anisotropic properties of the material. The resonator dimensions are adjusted in different directions based on the directional elasticity characteristics, creating an asymmetric shape that counterbalances the material's inherent asymmetry in elastic properties. This results in uniform edge displacement during resonance despite using anisotropic material.

Inventive Principle:

Principle #4Asymmetry

2Speed

If the resonator dimensions are reduced to achieve higher frequencies, then the resonant frequency increases, but the resonator becomes more susceptible to unwanted mode excitations due to shape distortions

Engineering Contradiction:

Improveresonant frequencyVSAvoidmode purity

Core Design Contradiction:

SpeedVSReliability

Solution Approach 1:

The patent applies local quality by adjusting the resonator dimensions locally in different directions based on the directional elasticity characteristics of the material. Each dimension is optimized independently to compensate for the anisotropic properties in that specific direction, ensuring uniform stress distribution and edge displacement across the entire resonator structure during high-frequency operation.

Inventive Principle:

Principle #3Local quality

3Power

If electrodes are positioned close to the resonator to maximize actuation force, then the actuation efficiency increases, but the electrodes may contact the resonator during vibration due to non-uniform displacement

Engineering Contradiction:

Improveactuation forceVSAvoidoperational stability

Core Design Contradiction:

PowerVSReliability

Solution Approach 1:

Inventive Principle:

Principle #4Asymmetry

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

The solution results in improved linearity and reduced energy loss by ensuring uniform displacement and minimizing the excitation of unwanted modes, maximizing actuation force and output current, while maintaining the mechanical advantages of anisotropic materials.

Implementation Method 1

a first distance in a first direction from a centroid of the resonator to a first point on a peripheral edge of the resonator is greater than a second distance in a second direction from the centroid to a second different point on the edge, for every first direction and every second direction wherein the material has a lesser modulus of elasticity in the first direction than the second direction

Methodology Applied

Scientific EffectElastic deformation: Elasticity

Implementation Method 2

a shape of the resonator is such that a first distance in a first direction from a centroid of the resonator to a first point on a peripheral edge of the resonator is greater than a second distance in a second direction from the centroid to a second different point on the edge, for every first direction and every second direction wherein the material has a lesser modulus of elasticity in the first direction than the second direction

Methodology Applied

Scientific EffectAnisotropic elasticity: Anisotropy

Implementation Method 3

the mechanical vibration is excited by electrostatic forces resulting from an electrical signal applied via one or more electrodes spaced a small distance apart from the resonator

Methodology Applied

Scientific EffectElectrostatic force: Electrostatics

Implementation Method 4

When the input signal is at or near the resonant frequency of the device, resonance occurs, effectively amplifying the output signal at this frequency by the gain factor Q of the device

Methodology Applied

Scientific EffectResonance: Resonance

Data Source

PatentUS8680951B2MEMS resonator

Publication Date: 2014.03.25 III HOLDINGS 12 LLC

AI summary

A micro-electromechanical resonator comprising a material having anisotropic directional elasticity characteristics. A shape of the resonator is such that a first distance in a first direction from a centroid of the resonator to a first point on a peripheral edge of the resonator is greater than a second distance in a second direction from the centroid to a second different point on the edge. This is true for every first direction and every second direction wherein the material has a lesser modulus of elasticity in the first direction than the second direction.