Applying Statistics to Nano-Circuit Dimensions in Fabrication
A high-resolution microscope with sophisticated imaging software is required to measure nano-circuit component dimensions; accuracies of 1.49 μm/pixel or better can be achieved.Copyright 2015 Wearable Electronics Laboratory, Energy Park Unit, Mechanical Engineering Department, University of Houston
Measuring the dimensions of nano-circuits requires an expensive, high-resolution microscope with integrated video camera and a computer with sophisticated imaging software, but in this activity, students measure nano-circuits using a typical classroom computer and (the free-to-download) GeoGebra geometry software. Inserting (provided) circuit pictures from a high-resolution microscope as backgrounds in GeoGebra's graphing window, students use the application's tools to measure lengths and widths of circuit elements. To simplify the conversion from the on-screen units to the real circuits' units and the manipulation of the pictures, a GeoGebra measuring interface is provided. Students export their data from GeoGebra to Microsoft® Excel® for graphing and analysis. They test the statistical significance of the difference in circuit dimensions, as well as obtain a correlation between average changes in original vs. printed circuits' widths. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note below for details.
Flexible nano-electronics—that is, electronic circuits that bend and take different forms—have seen rapid development during the last few years because of the plentiful range of applications that are difficult if not impossible achieve with conventional rigid electronics. Nano-wearable electronics are composed of millions of circuits arranged in a thin, lightweight, mechanically flexible, stretchable and conformable structure. They enable comfortable, continuous and mobile monitoring on people and animals. Using wearable electronics, engineers are able to find solutions for challenges such as: What if electronics were soft and pliable? What if electronics conformed to us, instead of us conforming to electronics? In this context, students see a real-world applied use for statistical analysis.
After this activity, students should be able to:
- Empirically quantify how much diffraction affects circuit dimensions during the printing process, and determine if these changes are statistically significant.
- Determine linear and non-linear correlations between variables.
- Use the GeoGebra geometry software to obtain indirect measurements of objects that cannot be measured directly.
- Use Excel® functions and capabilities to process, graph and perform statistical analysis on data.
- Use PowerPoint® to present results and conclusions.