TY - JOUR

T1 - The 100th anniversary of the four-point probe technique

T2 - The role of probe geometries in isotropic and anisotropic systems

AU - Miccoli, Ilio

AU - Edler, Frederik

AU - Pfnür, Herbert

AU - Tegenkamp, Christoph

PY - 2015/5/18

Y1 - 2015/5/18

N2 - 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.

AB - 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.

KW - bulk and surface resistivity

KW - correction factor

KW - four-point probe techniques

KW - nanostructures

UR - http://www.scopus.com/inward/record.url?scp=84930227027&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/27/22/223201

DO - 10.1088/0953-8984/27/22/223201

M3 - Review article

AN - SCOPUS:84930227027

VL - 27

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 22

M1 - 223201

ER -