Analytical theory of the space-charge region of lateral p-n junctions in nanofilms

There is growing interest in fabricating conventional semiconductor devices in a nanofilm which could be a 3D material with one reduced dimension (e.g., silicon-on-insulator (SOI) film), or single/multiple layers of a 2D material (e.g., MoS₂), or a two dimensional electron gas/two dimensional hole gas (2DEG/2DHG) layer. Lateral p-n junctions are essential parts of these devices. The space-charge region electrostatics in these nanofilm junctions is strongly affected by the surrounding field, unlike in bulk junctions. Current device physics of nanofilms lacks a simple analytical theory of this 2D electrostatics of lateral p-n junctions. We present such a theory taking into account the film's thickness, permittivity, doping, interface charge, and possibly different ambient permittivities on film's either side. In analogy to the textbook theory of the 1D electrostatics of bulk p-n junctions, our theory yields simple formulas for the depletion width, the extent of space-charge tails beyond this width, and the screening length associated with the space-charge layer in nanofilm junctions; these formulas agree with numerical simulations and measurements. Our theory introduces an electrostatic thickness index to classify nanofilms into sheets, bulk and intermediate sized