Miccoli I, Edler F, Pfnür H, Tegenkamp C
Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstrasse 2, D-30167 Hannover, Germany. Dipartimento di Ingegneria dell'Innovazione, Università del Salento, Via Monteroni, I-73100 Lecce, Italy.
J Phys Condens Matter. 2015 Jun 10;27(22):223201. doi: 10.1088/0953-8984/27/22/223201. Epub 2015 May 18.
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.
固态物质的电导率是一种基本物理性质，可以通过四点探针技术测量的电阻精确推导得出，排除寄生接触电阻的影响。随着时间的推移，这种方法已成为材料科学、半导体工业、地质学、物理学等领域的跨学科表征工具，用于基础研究和应用驱动的研究。然而，电导率的正确推导是一项艰巨的任务，面临着几个困难，例如样品的均匀性或相的各向同性。此外，这些特定于样品的特性与诸如探针几何形状和样品尺寸等技术限制密切相关。特别是，后者对于现在可以在非常小的长度尺度上进行技术探测的纳米结构非常重要。在弗兰克·温纳（Frank Wenner）引入四点探针技术100周年之际，在这篇综述中，我们重新审视并讨论了从测量电阻准确推导电阻率所需的各种校正因子。其中包括样品厚度、维度、各向异性以及样品相对于接触组件的相对尺寸和几何形状等因素。我们还能够推导具有可变探针间距的圆形有限区域上二维各向异性系统的校正因子。所有这些方面都通过使用四尖端STM/SEM系统进行的最新实验进行了说明。我们意识到这篇综述文章只能涵盖一些最重要的主题。关于进一步的方面，例如技术实现、不均匀性或不同传输机制的影响等，我们参考该领域的其他综述文章。
