Wafer Resonator Stiffness Dispersion Correction
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Solution Overview
Problem
The manufacturing of mechanical resonators on a wafer, such as hairsprings for mechanical timepieces, faces significant geometric dispersion in dimensions and stiffness, leading to a wide variation in natural frequency, which affects the pairing with balance wheels and reduces the functional yield.
Innovation Solution
A method that modifies the lithography step to adjust the dimensions of resonators by dividing the wafer into fields, measuring the stiffness dispersion, and implementing corrections during the lithography process to reduce the standard deviation of stiffness across the wafer, ensuring that most resonators fall within a predefined pairing interval.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If collective manufacturing of resonators is performed on a wafer using standard lithography and machining processes, then productivity is improved by fabricating several hundred resonators simultaneously, but manufacturing precision deteriorates due to significant geometric variation between resonators on the same wafer
Solution Approach 1:
The patent applies local quality by dividing the wafer into multiple fields and assigning different lithography exposure doses to each field. This creates spatially varying resonator dimensions across the wafer, allowing the stiffness distribution to be tailored to match the pairing interval requirements. Each field receives a customized dose that compensates for the Gaussian stiffness dispersion, transforming a uniform manufacturing process into a locally optimized one.
Solution Approach 2:
The patent changes the lithography exposure dose parameter across different fields of the wafer. By modifying the exposure dose, the critical dimensions of resonators in each field are adjusted, which directly controls their stiffness. This parameter variation allows the mean stiffness of each field to be positioned optimally within the pairing interval, converting a single-parameter process into a multi-parameter optimized process.
2Manufacturing precision
If the lithography exposure dose is increased to reduce resonator dimensions and decrease stiffness, then manufacturing precision is improved by centering the stiffness distribution, but productivity is reduced due to the need for field-by-field optimization
Solution Approach 1:
The patent applies preliminary action by pre-calculating the optimal exposure dose for each field before the lithography process. The method determines the Gaussian distribution parameters (mean and standard deviation) for each field in advance, then computes the required dose modification to center each field's stiffness distribution within the pairing interval. This pre-planning eliminates the need for iterative adjustments during manufacturing, maintaining productivity while achieving precision.
Solution Approach 2:
The patent implements feedback by using measured stiffness data from reference wafers to inform the lithography dose settings for production wafers. The method measures the actual stiffness distribution on reference wafers, determines the Gaussian parameters, and uses this information to calculate the optimal exposure doses for subsequent production runs. This closed-loop approach ensures that the lithography process is continuously optimized based on actual process variation data.
Data Source
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AI summary
A method for manufacturing a plurality of mechanical resonators (100) in a manufacturing wafer (10), the resonators being intended to be fitted to an adjusting member of a timepiece, the method comprising the following steps: (a) manufacturing a plurality of resonators in at least one reference wafer according to reference specifications, such manufacture comprising at least one lithography step to form patterns of the resonators on or above the reference wafer and a step of machining in the reference plate using the patterns; (b) for the at least one reference plate, establishing a map indicative of the dispersion of stiffnesses of the resonators relative to an average stiffness value; (c) dividing the map into fields and determining a correction to be made to the dimensions of the resonators for at least one of the fields in order to reduce the dispersion; (d) modifying the reference specifications for the lithography step so as to make the corrections to the dimensions for the at least one field in the lithography step; (e) manufacturing resonators in a manufacturing wafer using the modified specifications.