Producing Macroscopic Behaviors of the Free Electron Model Using N-Body Random Walks. - Kemp, Jordan T. (Tufts Archival Research Center, 2018)
The electrical resistivity of a substance deviates from the intrinsic bulk resistivity given by the free electron model as its physical dimensions approach nanometer scales. In this paper, we produce these results given by the Fuchs/Sondheimer and the free electron random point scattering models of electron conduction using a classical Python simulation of electrons moving throughout and interacting with a thin metal crystal lattice with an applied electric field. We reproduced the theoretical relationships between changes in resistivity from the expected bulk value and characteristic scattering time, crystal thickness, surface scattering probability, and surface scatterer density for both uniform and ordered distribution of scatterers. We also examine the heat transfer by the electrons, as well as how temperature dependence of scattering affects the electron distribution during equilibration processes.