Quantum limit of the contact resistance to low-dimensional materials

Abstract

As device dimensions approach the nanoscale, contact resistance increasingly limits performance, particularly in low-dimensional systems where quantum mechanical effects dominate. In this work, we systematically investigate the quantum limit (QL) of contact resistance in 1D, 2D, and 3D semiconductors. Using general analytical expressions derived from ballistic transport theory and Fermi-Dirac statistics, we evaluate the QL across both the non-degenerate (Maxwell-Boltzmann) and degenerate (low-temperature) regimes. These expressions are validated against numerical simulations that incorporate electrostatic effects via the Poisson equation, allowing us to assess both fundamental and practical limits of contact resistance. Our results show that in the non-degenerate limit, all dimensionalities exhibit similar behavior, whereas in the degenerate limit, resistance increases exponentially as dimensionality decreases. When realistic contact electrostatics are included, the intrinsically weaker screening in lower-dimensional systems leads to more extended depletion regions, which influence resistance scaling in the non-degenerate regime. In contrast, in the degenerate limit, contact resistance is primarily governed by the quantum limit.