We calculate the conductance of three-dimensional semiconductor quantum wires considering different effective masses in the contacts and in the channel. We show that, with respect to the case with equal masses in the channel and in the contacts, the amplitude of the conductance oscillations increases if the electron effective mass in the channel is larger and decreases if it is smaller than in the contacts. Effects on the density of probability are also shown. These effects of the effective mass discontinuity are explained in terms of kinetic confinement and transmission coefficient modulation.

The influence of dimensionality on the conductance of semiconductor cross junctions is investigated in the effective mass approximation and quantum ballistic regime. Our calculations exhibit some similar features for both two- and three-dimensional models, namely the conductance peaks before the fundamental eigenenergy of the quantum wire that represents the sidearms and the zero conductance dip. Despite this, we show that, in general, the conductance and the electronic wave function are strongly affected when the third spatial dimension is taken into account. In other words, we prove that two-dimensional models are not suitable for representing this kind of system.