Distributed Lamé Mode Beam Resonators for High-Frequency Timing

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Solution Overview

Problem

Silicon MEMS resonators face challenges in temperature stability at high resonance frequencies, with Lamé mode resonators offering high quality factor but low operational frequency, requiring a design that balances frequency, Q factor, transduction area, and motional impedance.

Innovation Solution

A distributed Lamé mode resonator design with elongated beams and multiple electrode pairs, where the length is an integer multiple of the width, increasing transduction area and reducing motional impedance while maintaining temperature stability through a quadratic temperature coefficient of frequency profile.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Speed

If the width of a Lamé mode silicon resonator is decreased to increase operational frequency, then the operational frequency is improved, but the transduction area decreases and motional impedance increases

Engineering Contradiction:

Improveoperational frequencyVSAvoidtransduction area

Core Design Contradiction:

SpeedVSArea of moving object

Solution Approach 1:

The resonator is divided into multiple distributed resonant units along the beam length, each contributing to the overall transduction area while maintaining the high frequency operation through the distributed Lamé mode structure

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The design transitions from a square planar structure to an elongated beam structure where the length is an integer multiple of the width, utilizing the longitudinal dimension to distribute the Lamé mode and increase frequency without proportionally reducing the transduction area

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

2Speed

If the width of a Lamé mode silicon resonator is decreased to increase operational frequency, then the operational frequency is improved, but the motional impedance increases

Engineering Contradiction:

Improveoperational frequencyVSAvoidmotional impedance

Core Design Contradiction:

SpeedVSObject-affected harmful factors

Solution Approach 1:

The resonator is segmented into multiple distributed resonant units that collectively reduce the motional impedance through distributed coupling, allowing high frequency operation with lower impedance than a single narrow resonator

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Multiple resonant units are merged into a single distributed structure that operates in unison, combining their individual contributions to achieve low motional impedance while maintaining high operational frequency

Inventive Principle:

Principle #5Merging (Combining)

3Reliability

If traditional square Lamé mode resonator design is used to achieve high quality factor, then the Q factor is improved, but the operational frequency remains low

Engineering Contradiction:

Improvequality factorVSAvoidoperational frequency

Core Design Contradiction:

ReliabilityVSSpeed

Solution Approach 1:

The resonator employs a distributed dynamic structure where multiple resonant units are coupled along the beam, enabling the system to achieve both high Q factor through resonant coupling and high operational frequency through the distributed Lamé mode configuration

Inventive Principle:

Principle #15Dynamics

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 design achieves high frequency operation up to hundreds of MHz with low motional impedance and high Q factor, overcoming the limitations of traditional square Lamé mode resonators by distributing the Lamé mode across a beam, enabling frequency scaling without compromising transduction efficiency.

Implementation Method 1

The resonator is configured to resonate at a frequency upon application of an input signal

Methodology Applied

Scientific EffectResonance: Resonance

Implementation Method 2

A MEMS resonator comprising a first resonator beam... configured to resonate at a frequency upon application of an input signal

Methodology Applied

Scientific EffectPiezoelectric effect: Piezoelectric Effect

Implementation Method 3

This temperature stability in the Lamé mode is owed to its quadratic temperature coefficient of frequency (TCF) profile

Methodology Applied

Scientific EffectThermal expansion: Thermal Expansion

Data Source

PatentUS11533042B2Distributed-mode beam and frame resonators for high frequency timing circuits

Publication Date: 2022.12.20 GEORGIA TECH RES CORP

AI summary

Embodiments of the present disclosure relate generally to MEMS resonators. An exemplary MEMS resonator comprises a resonator beam having a length and a width. The length can be an integer multiple of the width. The integer multiple can be at least two. The resonator is configured to resonate at a frequency upon application of an input signal. The TCF of this resonator can be made close to zero, thus providing a temperature stable resonator. The exemplary MEMS resonator thereby has the advantages of high Q, low polarization voltage, low motional impedance and temperature stability of low frequency resonators while being able resonate at high frequencies of 30 MHz to 30 GHz.