Stacked Beam MEMS Resonator Geometry for Higher Q Anchoring
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Solution Overview
Problem
Microelectromechanical (MEMS) resonators face challenges in maximizing the quality factor Q due to suboptimal anchoring and energy losses from the surrounding gas atmosphere, particularly in silicon MEMS resonators used for frequency reference applications.
Innovation Solution
The geometry of stacked beam resonators is optimized by varying the dimensions and orientations of beam elements and connection elements to position nodal points at the resonator perimeter, coinciding with anchoring points, and by minimizing gas damping through trench design to reduce acoustic resonance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the resonator is anchored at the edge using silicon tethers, then the anchoring is simplified and manufacturing is easier, but the quality factor Q decreases because the anchoring points do not coincide with nodal points
Solution Approach 1:
The resonator structure employs asymmetric beam element designs where outer beam elements have different widths than inner beam elements. This asymmetry shifts the nodal points of the resonance mode shape to coincide with the anchoring points at the resonator perimeter, thereby maximizing the quality factor Q while maintaining edge anchoring configuration
Solution Approach 2:
Different beam elements are designed with different local geometries (widths) to optimize the mode shape distribution. The outer beam elements have reduced widths compared to inner elements, creating localized geometric variations that position nodal points at the anchoring locations without requiring changes to the overall anchoring structure
2Adaptability or versatility
If the resonator operates in a gas atmosphere, then the operating environment is more practical and accessible, but energy losses increase due to gas damping which decreases the quality factor Q
Solution Approach 1:
The resonator design modifies geometric parameters (beam widths, connection element dimensions) to optimize the mode shape and reduce the resonator's interaction with the gas atmosphere. By positioning nodal points at the perimeter and optimizing the beam geometry, the effective surface area exposed to gas damping is reduced, minimizing energy losses while maintaining gas atmosphere operation
3Device complexity
If conventional stacked beam resonator geometry is used with equal width beams and rectangular connection elements, then manufacturing is simpler and design is more straightforward, but the nodal points do not coincide with anchoring points resulting in lower quality factor
Solution Approach 1:
The resonator structure employs asymmetric beam element designs where outer beam elements have different widths than inner beam elements. This asymmetry shifts the nodal points of the resonance mode shape to coincide with the anchoring points at the resonator perimeter, thereby maximizing the quality factor Q while maintaining edge anchoring configuration
Solution Approach 2:
The geometry of beam elements and connection elements is optimized to dynamically position the nodal points of the resonance mode shape. By varying beam widths and connection element dimensions, the mode shape is controlled to ensure nodal points align with anchoring locations, maximizing energy retention
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
This approach enhances the quality factor Q by optimizing the resonator geometry and reducing energy losses, leading to improved performance and efficiency in MEMS resonators.
Implementation Method 1
nodal point(s) of the resonance mode shape
Implementation Method 2
damping due to a gas atmosphere surrounding the resonator
Data Source
AI summary
A microelectromechanical (MEMS) resonator includes a resonator structure having a plurality of beam elements and connection elements with certain geometry, where the plurality of beam elements are positioned adjacent to each other and adjacent beam elements are mechanically connected to each other by the connection elements, where the geometry of the beam elements or the connection elements varies within the resonator structure.