Effective medium theory of the space-charge region electrostatics of arrays of nanoscale junctions

Abstract

We develop an Effective Medium Theory for the electrostatics of the Space-Charge Region (SCR) of Schottky and p-n junctions in arrays of nanofilms (NFs), nanowires (NWs), and nanotubes (NTs) in a dielectric ambient. The theory captures the effects of electric fields in both the semiconductor, i.e., NF/NW/NT, and the dielectric media of the array. It shows that the depletion width and the screening length characterizing the SCR tail in the array correspond to those in a bulk junction with an effective semiconductor medium, whose permittivity and doping are their weighted averages over the cross-sectional areas of the semiconductor and dielectric; the shapes of the cross-sections are immaterial. Further, the reverse bias 1/C2-V behavior of junctions in NF/NW/NT arrays is linear, as in bulk junctions, and is useful to extract from measurements the built-in potential, effective doping including the semiconductor-dielectric interface charge, and NF/NW/NT length. The theory is validated with numerical simulations, is useful for the experimentalist, and yields simple formulas for nano-device design which predict the following. In the limiting case of a single sheet-like NF, the junction depletion width variation with potential drop is linear rather than square-root (as in a bulk junction). In arrays of symmetric silicon p-n junctions in oxide dielectric where NF/NW thickness and separation are 5% and 100% of the bulk depletion width, respectively, the junction depletion width and the screening length are scaled up from their bulk values by the same factor of ∼2 for NF and ∼10 for NW array.