Quantifying the spreading resistance of an anisotropic thin film conductor

Recently, highly anisotropic conductors, such as multilayer graphene, have been attracting much attention. The local resistivity can be determined by measuring the contact resistance; however, the theoretical expressions of contact resistance have been developed for isotropic slabs but have not been well developed for highly anisotropic film conductors. We obtain theoretical expressions of the spreading resistance below the circular contact for a highly anisotropic film on a bulk slab. The film spreading resistance of isotropic conductors deviates from the bulk spreading resistance when the film thickness is smaller than the contact radius. Nevertheless, the spreading resistance of anisotropic conducting films can be approximated by that of the bulk slabs even when the film thickness is smaller than the contact radius if the in-plane electrical conductivity is larger than the out-of-plane electrical conductivity. Owing to the high in-plane conductivity, the spreading resistance of anisotropic bulk conductors can be lowered from that predicted by the Holm's equation obtained using the out-of-plane conductivity and the contact radius. We show that these characteristics are beneficial to use the highly anisotropic film as a cover layer when the in-plane conductivity of the film is high and the conductivity of the base slab is low.