Piezoelectric Silicon Resonator Geometry for Quadratic TCF Reduction
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Solution Overview
Problem
Existing resonators struggle to control quadratic or higher temperature coefficients of resonant frequency (TCF), which are not adequately addressed in current MEMS resonator designs.
Innovation Solution
A resonator design incorporating a silicon substrate with a temperature characteristic correction layer and specific dimensions for the vibrator, where the width-to-thickness ratio of the vibration region is optimized to reduce quadratic TCF, utilizing a laminate structure with piezoelectric thin films and electrodes to achieve stable frequency-temperature characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional MEMS resonator designs are used, then linear TCF can be controlled through doping, but quadratic or higher TCF cannot be adequately reduced
Solution Approach 1:
The patent changes the geometric parameters of the vibrator, specifically setting the width-to-thickness ratio (W/T) to 4 or more, and adjusts the resistivity of the silicon substrate to a specific range. These parameter changes enable the quadratic TCF to be reduced to zero or close to zero, solving the problem of inadequate quadratic TCF control in conventional designs.
Solution Approach 2:
The patent uses a composite structure combining piezoelectric thin films (such as AlN or ScAlN) with silicon substrate. This composite material approach allows for better control of temperature characteristics by leveraging the properties of both materials, enabling reduction of quadratic and higher TCF while maintaining good linear TCF control through doping.
2Measurement precision
If the vibrator dimensions are optimized to reduce quadratic TCF, then frequency-temperature characteristics improve, but manufacturing precision requirements increase
Solution Approach 1:
The patent establishes specific parameter ranges for the vibrator dimensions, particularly W/T ≥ 4 and resistivity between 0.1-1000 mΩ·cm. By defining these parameter ranges rather than single values, the patent balances the need for precise frequency-temperature characteristics with practical manufacturing capabilities, allowing some tolerance while achieving the desired quadratic TCF reduction.
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 effectively reduces quadratic TCF to zero, providing favorable frequency-temperature characteristics and stable vibration modes, enhancing the performance of MEMS resonators.
Implementation Method 1
a piezoelectric thin film that produces in-plane contour vibration in accordance with voltage applied to the electrode
Implementation Method 2
a spring thereof is set in a direction of a spring constant depending mainly on items C11-C12, thereby enabling a variation in the spring constant due to temperature to be reduced by n-type doping
Data Source
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AI summary
A quadratic or higher TCF can be reduced in a resonator. There are included a vibrator including a silicon substrate, at least one electrode having a face facing a surface of the silicon substrate, and a piezoelectric body that is formed between the silicon substrate and the electrode and that produces contour vibration in a plane along the surface of the silicon substrate in accordance with a voltage applied to the electrode; a holder surrounding at least a portion of the vibrator; and a holding arm connecting the vibrator to the holder. The vibrator includes at least one substantially rectangular vibration region having a long side parallel to a node of the contour vibration of the piezoelectric body and a short side orthogonal to the node of the contour vibration of the piezoelectric body and corresponding to a half-wavelength of the contour vibration. The resonator is set within a range that satisfies W/T ≥ 4 and y = -0.85 × (1/T) + 0.57 ± 0.05 where T is the thickness of the silicon substrate in a direction orthogonal to the surface thereof, W is the width of the short side of the vibration region, and y is the resistivity of the silicon substrate.