Magnetotransport in multiple narrow silicon inversion channels opened electrostatically into a two-dimensional electron gas

Abstract

We study electrical transport in a dual-gate metal-oxide-semiconductor field-effect transistor. The bottom gate is a grating which allows the inversion-layer geometry to be controlled electrostatically. We compare the magnetoconductance of many parallel narrow-inversion channels, a modulated potential, and a uniform two-dimensional electron gas all formed in the same Si crystal. Electron weak localization becomes much more pronounced as the device is electrostatically pinched from a two-dimensional inversion layer into many narrow wires in parallel, proving that the wire width can be reduced below the electron phase coherence length. For magnetic fields greater than 1 T normal to the sample surface there is a large drop in the current, which persists to room temperature, as electrons are added to the device so that it opens electrostatically from many narrow inversion layers in parallel into a two-dimensional electron gas. This large negative transconductance results from electrostatically changing the dominant boundary condition on the classical Drude magnetoconductance tensor from that of a long and narrow to a short and wide conductor. Quantum edge states form at high magnetic fields, giving a high-field magnetoconductance of opposite sign for the parallel wires and wide electron gas. Thus, the evolution from Shubnikov--de Haas oscillations to the quantum Hall effect depends strongly and qualitatively on the device aspect ratio. At a magnetic field of 30 T the two-terminal conductance versus gate voltage of the narrow wires evolves into quantum Hall steps having a height of 2${\mathit{e}}^{2}$/h multiplied by the number of wires in parallel. In contrast to a wide device the conduction-band valley degeneracy is not resolved, giving rise to Hall steps of twice the expected size.