## Pulsed Laser Deposition

This summer after returning from Germany, I spent the rest of my time back at William & Mary doing research for one of my physics professors. One of the areas in which she does experiments is using ultrafast laser pulses to ablate or deposit materials. The basic idea is this: if you have a little chunk of some metal, say nickel, you can shoot it with a laser pulse. If this laser pulse is fast enough and powerful enough, it can actually excite the electrons in the metal so much that they vaporize and form a plasma plume that shoots off the surface of the metal. This is called laser ablation.

You can also repeat this process in quick succession using a laser that generates, say, 1000 pulses that each last for 150 nanoseconds. Each pulse will generate a plasma plume. Now, if you take some kind of substrate or gridwork and place it directly in front of the material, then whenever a plume shoots off the surface of the material, some of that vapor plume is going to recondense on the substrate. By using several thousands laser pulses, it’s possible to build up a film of material that’s only a few atoms thick. This is called pulsed laser deposition, and the sorts of films you generate are apparently useful in fields such as superconductor research.

Although the idea is pretty straightforward, the process itself becomes very complicated when you try to do one of these experiments in reality. There are a tremendous number of interactions that need to be considered- what kind of atmosphere should the experiment be conducted in, how should you set up the laser pulse so that it vaporizes the material without melting it, how do the characteristics of the plume change as you whittle away a hole where the laser is impacting, how do successive laser pulses interact with the gas from the previous plume, and so on. The work I did this summer was kind of a basic first step in coming up with a computational model for one of these experiments.

I spent the last few weeks of summer looking at how the temperature of the material is affected by the laser pulse. Mathematically, this is modeled with a system of differential equations by considering the temperature of the electrons in the material and the temperature of the lattice in which they are held to be two separate but related quantities; it’s referred to as the two-temperature model. In very special, restricted cases, it’s possible to solve this system analytically, but these solutions are not of much practical use. I put together a Mathematica notebook that numerically models the initial laser pulse as well as the period of time during which the heat diffuses throughout the material. Although this project was mostly a chance for me to learn a bit about using Mathematica, it was also an interesting twist on the classic heat diffusion boundary problem, as one side of the material is not held at a fixed temperature. The solution turns out to be using an “insulation” condition for that boundary, which amounts to setting the first derivative of the temperature function with respect to space equal to zero; this represents the fact that heat is not passing through that boundary; it’s insulated. Although this wouldn’t be strictly true in practice, we didn’t get around to including heat loss to radiation in this model before college got rolling again.

Anyhow, for your viewing pleasure, below you can take a look at what I came up with, both as a Mathematica notebook if you’ve got the program, and as a pdf. If anything I’ve done would actually be of help to you on a project of your own, feel free to use whatever you find, but please, credit where credit is due. Additionally, if you have any suggestions for improving the code in this notebook, I would love to hear them.

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