Quantum ballistic conductance of quasi-two-dimensional and three-dimensional semiconductor nanowires

With the solution of the Schrödinger equation for electrons in three-dimensional (3D) hard wall quantum channels, the conductance of semiconductor nanowires is studied as a function of length, size, and contact dimensionality. Within the envelope function approximation, the two-terminal Landauer Büttiker conductance has been calculated in the quantum ballistic regime, using the mode matching technique. The contacts are modeled by semi-infinite regions with hard wall confinement along only one of the transverse directions, so that continuous crossover from quasi-two-dimensional to 3D contacts can be simulated through the increase of this confinement length. The conductance resonances due to the resonant transmission through quasi-bound longitudinal states are shown to get much better resolved with 3D contacts, which leads to larger Fabry Pérot like conductance oscillations within the 2 e² /h quantized plateaus, which are independent of the contact dimension. An effective phase shift due to electron reflection at the exit and entrance of the quantum channel is introduced, which helps the interpretation of the numerical and experimental data on these conductance oscillations.