We report the fabrication of 3 nm NiCr wires on a solid silicon substrate. The process uses conventional 100 keV electron beam lithography and poly(methyl methacrylate) resist. The wires consist of short, continuous, lengths of metal that are attached at either end to 20 nm wide wires. Instead of exposing continuous lines in the resist, we blank the beam for several pixels to leave a gap. The resist in the gap is therefore exposed only by the secondary electrons from the neighboring regions that are directly exposed by the beam. The technique is repeatable and we demonstrate that it is possible to make 3 nm features on demand.

The transverse magnetoresistance of a two-dimensional electron gas in an n-type GaAs/(AlGa)As heterostructure subjected to a square superlattice potential is investigated. Magneto-oscillations are observed at low field (B ⩽ 0.4 T) with period Δ(1/B) = ea/2ℏkF, where a = 145 nm is the superlattice constant. At higher fields the magneto-resistance is dominated by Shubnikov-de Haas oscillations. A comparison is made with experiments on a one-dimensional superlattice.

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narrower (Table I) so that the separation of energy sublevels along the y-direction is increased. This increases the oscillation period when measuring the conductances as functions of the Fermi energy. On the other hand, the increase of the Fermi energy as a function of the lower gate bias is very significant. In the final conductances versus lower gate bias diagram, Fig. 2, the Fermi energy factor dominates, and the oscillation period in the conductance increases, as indicated in the experiments when the upper gate bias is decreased.The calculated oscillation period increases with increasing lower gate bias in Fig. 2. This is due to the square-well approximation in the y-direction used in the model calculation. When parabolic well is used, the energy separations between sublevels are constant, so becomes the oscillation period. Thus, when real band profile is used in the transport calculation, constant oscillation period is expected. ( 3 )When Q = e and t = 13.1 (silicon), we have V = 1.1,'~ V at the surface of the sphere and 5' = 1.65/a V at the center (a is in the unit of A). It is shown that decreasing the upper gate bias makes the conducting channel created by the lower gate narrower so that the separation of the energy sublevels in the y -direction is increased. However, the decrease of the upper gate bias also greatly reduces the Fermi energy. The total effect of decreasing the upper gate bias is the decrease of the oscillation period in the conductance as functions of the lower gate bias. The calculated oscillation period as a function of the lower and upper gate bias explains very well the experimental data.

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