Impact of Anisotropic Conductivity on Current Crowding and Spreading Resistance in Vertical Contacts to 2D Thin Films

Electrical contacts to layered semiconductors often struggle with current crowding at the contact edge, which is intensified in materials, such as layered graphene and transition-metal dichalcogenides (TMDs) with highly anisotropic conductivity. Conventional models for calculating spreading (constriction) resistance typically assume isotropic transport, which may result in an inaccurate determination of spreading resistance, as well as intrinsic transport parameters. Here, we present an exact analytical solution that generalizes the classical two-layer vertical thin film model to anisotropic systems, incorporating in-plane and out-of-plane resistivities, interfacial resistivity, and both planar and cylindrical (disk-shaped) contact geometries. This framework allows for exact quantitative modeling of the spreading resistance over a wide range of contact sizes, film thicknesses, and anisotropy ratios. Our model uncovers high current crowding at the contact edge driven by the high in-plane conductivity of two-dimensional (2D) materials. In materials such as MoS 2 and WSe 2, this high in-plane conductivity causes potential distributions to extend laterally along the contact plane, rather than vertically into the material. The model’s predictions are further validated by finite-element method (FEM) simulations. When applied to experiments on highly oriented pyrolytic graphite (HOPG) and MoS 2 thin films, it matched the spreading resistance data without any fitting parameters and recovered the classical diffusive limit for wide, thick substrates. Notably, we also find that the standard diffusive model approximations for spreading resistance fail for ultrathin films or short channels. This makes it essential to use our full anisotropic model to reliably interpret experimental data and obtain accurate transport parameters. This unified framework provides a robust physics-based tool for designing and optimizing electrical contacts in 2D materials and van der Waals heterostructures.