Statistical Analysis of Flexible Circuits
Printed circuits are created using equipment with integrated high-resolution microscopes for the alignment process. UV light is passed through a previously imprinted mask to transfer a pattern to the conductor.Copyright 2015 Wearable Electronics Laboratory, Energy Park Unit, Mechanical Engineering Department, University of Houston
Students are introduced to the technology of flexible circuits, some applications and the photolithography fabrication process. They are challenged to determine if the fabrication process results in a change in the circuit dimensions since, as circuits get smaller and smaller (nano-circuits), this could become very problematic. The lesson prepares students to conduct the associated activity in which they perform statistical analysis (using Excel® and GeoGebra) to determine if the circuit dimension sizes before and after fabrication are in fact statistically different. A PowerPoint® presentation and post-quiz are provided. This lesson and its associated activity are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.
Wearable electronics, that is, electronics that are highly bendable and conformable, have attracted a great deal of attention and development in the last decade because they enable classes of applications that are impossible to be addressed with wafer-based technologies (for example, Google Smart Lens). Among their great advantages, wearable electronics are relatively large in area, thin, lightweight, mechanically flexible, stretchable and conformable. They can also enable continuous mobile health-monitoring on animal bodies. With wearable electronics, engineers are able to design solutions for challenges such as: What if electronics were soft and pliable? What if electronics conformed to us, instead of us conforming to electronics? Within this context, students see a real-world applied use for statistical analysis.
Photolithography is the process used to fabricate flexible wearable electronics—a process that resembles the film photographic process used years ago. A very thin conductor foil is adhered on a glass substrate coated with a thin layer of polyimide; then the conductor is covered with a layer of photoresist (a photo-sensitive polymer). Upon exposing to UV light through a mask containing various patterns, chemical reactions happen on the light-exposed regions. The exposed photoresist is selectively washed away with a chemical solution and the conductor foil is exposed for further processing. Because of light diffraction phenomena in the photoresist coating, errors occur in the pattern transfer process, producing changes in the circuit dimensions that might affect the strain and stress properties (such as conductivity and resistivity) of conductors. While no evidence exists that these changes in circuit dimensions affect the reliability or performance of the circuits, determining if these changes are the same for any circuit or if the changes depend on the original circuit size, has the potential to be used as part of a procedure to determine what could be the smallest reliable circuit produced via photolithography.
Due to the complexity of mathematically computing the change in dimensions due to diffraction, students use an empirical method in the associated activity. Using the free GeoGebra application, students determine dimension changes in printed circuits, comparing measurements on circuit images taken before and after the manufacturing process. The data obtained is exported to Excel® for analysis. A statistical test for the circuit width differences is performed to verify whether the changes during the fabrication process are statistically significant. Relative dimensions changes are estimated for different circuits, and a correlation between the circuits' relative dimension change and circuits' original size, is obtained.
After this lesson, students should be able to:
- Explain all steps of the photolithography process in the correct order.
- Use technology and a scale factor to obtain indirect measurements of physical objects using images of them.
- Create a procedure to collect, clean and prepare data for hypothesis testing using students' T-distributions.
- Apply logarithmic-exponential functions, and linear correlation analysis to find relationships between experimental data.