Spectroscopy of multi-electrode tunnel barriers

Despite their ubiquity in nanoscale electronic devices, the physics of tunnel barriers has not been developed to the extent necessary for the engineering of devices in the few-electron regime. This problem is of urgent interest, as this is the specific regime into which current extreme-scale electronics fall. Here, we propose theoretically and validate experimentally a compact model for multielectrode tunnel barriers, suitable for design-rules-based engineering of tunnel junctions in quantum devices. We perform transport spectroscopy at approximately T = 4 K, extracting effective barrier heights and widths for a wide range of biases, using an efficient Landauer-Bilttiker tunneling model to perform the analysis. We find that the barrier height shows several regimes of voltage dependence, either linear or approximately exponential. Effects on threshold, such as metal-insulator transition and lateral confinement, are included because they influence parameters that determine barrier height and width (e.g., the Fermi energy and local electric fields). We compare these results to semiclassical solutions of Poisson's equation and find them to agree qualitatively. Finally, this characterization technique is applied to an efficient lateral tunnel barrier design that does not require an electrode directly above the barrier region in order to estimate barrier heights and widths.