Simultaneous Characterization of In-plane and Cross-plane Resistivities in Highly Anisotropic (PbSe)1(VSe2)1 Heterostructures

We present a method to measure and model contact and lead resistances through a series of in-plane measurements with different contact area and at various temperatures. The contact and lead resistances are obtained by fitting the width dependence of the contact end voltages of top and bottom electrodes of different linewidths to a model based on current crowding, which are then used to eliminate the contribution of contacts in cross-plane measurements without needing multiple devices and/or etching steps. The effective contact area of the cross-plane measurements is also corrected for lateral current spreading to obtain the cross-plane resistivity from the cross-plane resistance. This approach was used to measure both in-plane and cross-plane resistivities of a (PbSe)₁(VSe₂)₁ heterostructure containing alternating layers of PbSe and VSe₂ with random in-plane rotational disorder. Several samples measured exhibited a 4 order of magnitude difference between cross-plane and in-plane resistivities over the 6 – 300 K temperature range. The similar temperature dependencies of the resistivities reflect a large difference in the density of states, mobilities, and/or tunneling between metallic VSe₂ layers. The device fabrication process is fully lift-off compatible, and the method developed enables the straightforward measurement of the resistivity anisotropy of most thin film materials with nm thicknesses.