This quick little video shows a simulated density sweep in our TDCS experiment, with the densities and electrostatic potential calculated by a program I wrote to solve the coupled Schrodinger and Poisson equations. Here we're using a simple-minded Landau level density of states in the quantum well. This program is similar to 1d poisson, but with a few extra specialized features that are handy for our structures.

Among other things, this program is able to maintain regions of the simulation at fixed charge density rather than fixed chemical potential, which is useful for simulated the moments immediately after we have applied a large AC pulse to the device, and it is able to use the transfer matrix formalism to compute tunneling currents in the device. Finally, it can solve the Schrodinger equation in large regions, allowing 3D electrodes to be included realistically as very thick quantum wells without resorting to the Thomas-Fermi approximation.