The 100th anniversary of the four-point probe technique: the role of probe geometries in isotropic and anisotropic systems

The electrical conductivity of solid-state matter is a fundamental physical property and can be precisely derived from the resistance measured via the four-point probe technique excluding contributions from parasitic contact resistances. Over time, this method has become an interdisciplinary characterization tool in materials science, semiconductor industries, geology, physics, etc, and is employed for both fundamental and application-driven research. However, the correct derivation of the conductivity is a demanding task which faces several difficulties, e.g. the homogeneity of the sample or the isotropy of the phases. In addition, these sample-specific characteristics are intimately related to technical constraints such as the probe geometry and size of the sample. In particular, the latter is of importance for nanostructures which can now be probed technically on very small length scales. On the occasion of the 100th anniversary of the four-point probe technique, introduced by Frank Wenner, in this review we revisit and discuss various correction factors which are mandatory for an accurate derivation of the resistivity from the measured resistance. Among others, sample thickness, dimensionality, anisotropy, and the relative size and geometry of the sample with respect to the contact assembly are considered. We are also able to derive the correction factors for 2D anisotropic systems on circular finite areas with variable probe spacings. All these aspects are illustrated by state-of-the-art experiments carried out using a four-tip STM/SEM system. We are aware that this review article can only cover some of the most important topics. Regarding further aspects, e.g. technical realizations, the influence of inhomogeneities or different transport regimes, etc, we refer to other review articles in this field.

Electronic Packaging of Paper-Based Anisotropic Magnetoresistive Sensors

This report investigates adaptations of electronic packaging methods used to create stacks of these sensors. Four methods were developed and tested to determine the best option in terms of mechanical stability and electrical conductivity of the system. For the first method, a stack is created by way of through paper vias (TPVs), a hole that is cut in the pads of the sensors and then filled with electrically conductive adhesive through the openings on the two sensors to be joined. The second method is called mechanical caulking and connects sensors through pads which have been lined with copper tape backed with conductive adhesive. The connection is created with a small copper rivet which is flattened in place by compressive force. The third method is the stitching method which is inspired by sewing of fabric. A pattern of thin copper wire is stitched on the pad of a sensor that is lined with copper tape backed with conductive adhesive. The wire is then stitched through a second sensor that is treated similarly with copper tape and the stack receives the same pattern through the two layers as was applied to the first sensor alone. The final method is the collapsed daisy chain which is the linear connection of sensors to their neighboring sensors via copper tape backed with conductive adhesive. The row of sensors is then collapsed in an alternating orientation into a single stack.