Theory and Experiment
The interplay between theory and experiment is at the heart of science, but it’s easy to neglect experiment when teaching theory is the bulk of most classes’ curriculums. Teaching theory is just so much faster and cheaper. Yet we must recognize that the student reaches a profound appreciation of the power of science through setting up and conducting experiments and measurements. Reading about an experiment is very different from performing it with your own hands.
I’ve come to realize this point over the summer, stimulated by my experience as an undergraduate research assistant to an engineering physics professor. Throughout my work I studied the feasibility of applying nanowires to the construction of a betavoltaic cell, wrote a LabVIEW program to control optical measurement instruments, and examined the effects of annealing on the contact resistance of a metal alloy and semiconductor interface. It was in this last project that I took measurements which gave me insight into the wonderful relationship between theory and experiment.
Here’s the theory part. The solution to the differential equation known as Laplace’s equation, subject to certain constraints given in a particular physical setup, is a potential field. A field is a function that assigns a number to each point in space, where that number tells you something about the point. If you know the potential field inside a conducting solid, you can figure out the magnitude and direction of the electrical current flowing at each point in the material.
To study the effects of annealing, I had to get a sense of the current flow inside the planar device. So I measured the potential at select points on the device and plotted these numbers relative to their spatial positions. I also used FlexPDE, a numerical differential equation solver, to predict the potential based on Laplace’s equation. The results are shown in the image attached to this post: I hope you’ll agree there’s something magical about it.
I head back to begin my third year of schooling with a new appreciation for the need to perform experiments myself, rather than just read about them in a textbook. I experienced a wonderful feeling seeing the theory and experiment line up, the same feeling I’m sure has driven scientists throughout history.