A microscopic computer model of electrical conduction and joule heating in nanodevices

A time-dependent method that allows the modelling of the flow of electrons in a nanoscale device in the presence of open boundaries is presented. This method is applied to the simplest possible device (one atom attached to two leads) to investigate steady-state conduction, and the variation of the electric current in the presence of a rapidly varying external potential. The model is then extended to include the heating effect of the current, and we find that both ionic heating and cooling can take place, depending on the bias. Despite its qualitative success, the simplest model is quantitatively in error. The reason for this is described, and the first order corrections to this model are presented.