# Calculation of electrical mean free path in nanomaterials?

• ProfessorMoreRight
ProfessorMoreRight
TL;DR Summary
Seeking information on how to predict the electrical mean free path for nanoscale materials based on shape, composition, temperature, and electrical conditions.
How does one roughly predict the mean free path for electrical conduction in a nanostructure at different temperatures and under different electrical conditions such as different voltages and amperages based on the composition and dimensions of the structure?

For instance in carbon single and multilayer nanotubes vs graphene ribbons vs silicon nanowires, and all of slightly different sizes.

In other words how do I predict the average range of electrical ballistic conduction in a described structure under different power and temperature conditions?

I am trying to model out these structures and their electrical properties as I hope to in turn model out some simple circuits using them and see how they might behave.

I am hoping there is a convenient formula or combined set of formulas I can use.

I asked and searched around and was told the the mean free path increases proportional to conductivity which makes sense however I also know that the shape, size, and temperature of the material is important, see:
https://en.wikipedia.org/wiki/Ballistic_conduction

I need to be able to figure out how a nanoribbon or film, nanowire, and a nanotube will behave differently.

I know that obviously colder is better but I want to figure out what performance if any can be had at temperatures closer to room temperature.

I was initially trying to figure out how great of a distance I could reasonably obtain but could not get a solid figure beyond 28 micrometers which while impressive and useful if it checks out is limiting for my research.

https://physics.stackexchange.com/q...-electrons-can-travel-in-ballistic-conduction

My searching around and some lousy results from a chatbot I tossed out a while back due to the formulas not matching the claims led me to first to the Drude model, then to the Einstein Solid Model, and finally to the Debye model which seems like it might be able to model out the behaviors and factors I am interested in if I make sure everything is either 2D or near 1D but I am not sure how to properly apply it and based on how it looks if I figure it out then I might just try writing out a crude JavaScript program for it that I can enter my parameters into.
See:
https://en.wikipedia.org/wiki/Debye_model

My apologies if this question is poorly worded for I am far from an expert in this matter and the closest I have physically come to handling such things is in my use of microwave etching and off the shelf electronics components.

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