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.
Articles you may be interested inFermi resonance distortion of the Ru-CO stretching mode of CO adsorbed on Ru(001) J. Chem. Phys. 108, 5035 (1998); 10.1063/1.475910 CO desorption kinetics from clean and sulfurcovered Ru(001) surfaces J. Chem. Phys. 92, 4483 (1990); 10.1063/1.457759Layer resolved spectroscopy of potassium adsorbed on a Ru(001) surface: Photoemission and thermal desorption study A variety of methods [temperature programmed desorption via pressure rise and via work function changes (.:1~); isothermal desorption via .:1~: quasiequilibrium measurements via isobars monitored by .:1~. in combination with sticking coefficients] has been used to obtain detailed data on the coverage dependence of the adsorption equilibrium and desorption kinetics for CO on the basal Ru(OOI) face. While the deviation from reversibility varies strongly over these methods, no significant influence of the degree of irreversibility on the results has been found. Desorption energies and isosteric heats are constant at 160 kJ/mol for 0 < e < 0.2, then rise slowly up to 175 kJlmol at e = 0.33, where they fall abruptly to 120 kJ/mol and more gradually at higher coverage. The "first order" frequency factor (Arrhenius preexponential normalized by the coverage) is 10'6 s-' at e = 0, rises precipitously, especially in the range 0.2 < e < 0.33, to 1019 s-' at e :::::0.33, where it drops abruptly to :::::10" s-'. The main conclusions drawn are: (1) The dependence on coverage of the desorption energies and preexponentials can be understood in terms of the equilibrium statistical mechanics of the chemisorption layer, governed by lateral adsorbate-adsorbate interactions. In particular, the high preexponentials and their strong increase close to e = 0.33 are due to strong localization in the adlayer. (2) No strong influence of precursor kinetics exists in desorption.(3) Possible dynamic effects have constant influence throughout the range of measurements and can be described by the behavior of the sticking coefficient. These conclusions are discussed in connection with other recent findings.
Understanding the complex behavior of particles at surfaces requires detailed knowledge of both macroscopic and microscopic processes that take place; also certain phenomena depend critically on temperature and gas pressure. To link these processes we combine state-of-the-art microscopic, and macroscopic phenomenological, theories. We apply our theory to the O͞Ru(0001) system and calculate thermal desorption spectra, heat of adsorption, and the surface phase diagram. The agreement with experiment provides validity for our approach which thus identifies the way for a predictive simulation of surface thermodynamics and kinetics. PACS numbers: 68.45.Da, 82.65.Dp, 82.65.My The study of the physical and chemical processes that take place at gas-surface interfaces have long been an area of intense research. This interest is both fundamental as well as driven by the possible discovery of important technological applications, e.g., in the field of heterogeneous catalysis, corrosion, etc. [1,2]. With respect to the field of the theory of adsorption of gases on solid surfaces, advancement in recent years has developed in two distinct, albeit complimentary, directions: (i) electronic structure calculations, at best done by density-functional theory (DFT), to determine the geometries, energetics, and vibrational properties of adsorbate covered surfaces, and (ii) phenomenological models, both for the thermodynamics and the kinetics [3] of the adsorbate. If one can assume that the geometry of the solid surface does not change dramatically and that adsorption occurs at well defined sites, one frequently employs a lattice gas model. A number of parameters enter this type of model, such as the binding energies and vibrational frequencies of a single adparticle in the various adsorption sites, and their mutual lateral interactions with adparticles in close-by sites. Traditionally, these parameters are adjusted in the theory in order to fit a variety of experimental data such as phase diagrams, heats of adsorption, infrared spectra, and thermal desorption data, etc. Such an approach, while useful, is clearly not necessarily predictive in nature, nor the parameters unique, and may not capture the physics of the microscopic processes that are behind the "best-fit" adjusted "effective" parameters.In this Letter, with the aim to improve upon this approach, we combine state-of-the-art procedures of (i) microscopic theories, i.e., DFT electronic structure calculations and (ii) macroscopic phenomenological approaches, i.e., lattice gas and rate equations, and Monte Carlo schemes. On doing this, we present a consistent first-principles-based approach for calculation of the thermodynamic and kinetic properties of an adsorbate, such as heats of adsorption, temperature programmed desorption (TPD) spectra, and the surface phase diagram. We have chosen the system of oxygen at Ru(0001) for which detailed structural [4-9], thermodynamic [10], and kinetic data [11,12] exist. We will show that, with the present approach, a realistic description...
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