Universal Scaling Laws in Schottky Heterostructures Based on Two Dimensional Materials.
We identify a new universality in the carrier transport of two dimensional (2D) material based Schottky heterostructures. We show that the reversed saturation current (J) scales universally with temperature (T) as log(J/T^{b} 1/T, with b=3/2 for lateral Schottky heterostructures and b=1 for vertical Schottky heterostructures, over a wide range of 2D systems including nonrelativistic electron gas, Rashba spintronic systems, single and few layer graphene, transition metal dichalcogenides, and thin films of topological solids. Such universalities originate from the strong coupling between the thermionic process and the in plane carrier dynamics. Our model resolves some of the conflicting results from prior works and is in agreement with recent experiments. The universal scaling laws signal the breakdown of b=2 scaling in the classic diode equation widely used over the past sixty years. Our findings shall provide a simple analytical scaling for the extraction of the Schottky barrier height in 2D material based heterostructures, thus paving the way for both a fundamental understanding of nanoscale interface physics and applied device engineering.
Physical review letters