The simplest geometry in which one

The simplest geometry in which one might expect to observe transmission resonances is formed by a single potential barrier across a 2DEG channel. Such a geometry was studied by Washburn et al.394 in a GaAs-AlGaAs heterostructure containing a 2-μm-wide channel with a 45-nm-long gate on top of the heterostructure. At low temperatures (around 20mK) an irregular set of peaks was found in the conductance as a function of gate voltage in the region close to the depletion threshold. The amplitude of the peaks was on the order of e2/h. The origin of the effect could not be pinned down. The authors examine the possibility that transmission resonances associated with a square potential barrier are responsible for the oscillations in the conductance, but also note that the actual barrier is more likely to be smooth on the scale of the wavelength. For such a smooth barrier the transmission probability as a function of energy does not show oscillations. It seems most likely that the effect is disorder-related. Davies and Nixon395 have suggested that some of the structure observed in this experiment could be due to potential fluctuations in the region under the gate. These fluctuations can be rather pronounced close to the depletion threshold, due to the lack of screening in the low-density electron gas. A quantum mechanical calculation of transmission through such a fluctuating barrier has not been performed. As discussed below, conductance peaks of order e2/h occur in the case of resonant tunneling via localized states in the barrier (associated with impurities), a mechanism that might well play a role in the experiment of Washburn et al.394