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.

Modification of the in vivo four-point loading model for studying mechanically induced bone adaptation

We modified the noninvasive, in vivo technique for strain application in the tibiae of rats (Turner et al,, Bone 12:73-79, 1991), The original model applies four-point bending to right tibiae via an open-loop, stepper-motor-driven spring linkage, Depending on the magnitude of applied load, the model produces new bone formation at periosteal (Ps) or endocortical surfaces (Ec.S). Due to the spring linkage, however, the range of frequencies at which loads can be applied is limited. The modified system replaces this design with an electromagnetic vibrator. A load transducer in series with the loading points allows calibration, the loaders' position to be adjusted, and cyclic loading completed under load central as a closed servo-loop. Two experiments were conducted to validate the modified system: (1) a strain gauge was applied to the lateral surface of the right tibia of 5 adult female rats and strains measured at applied loads from 10 to 60 N; and (2) the bone formation response was determined in 28 adult female Sprague-Dawley rats. Loading was applied as a haversine wave with a frequency of 2 Hz for 18 sec, every second day for 10 days. Peak bending loads mere applied at 33, 40, 52, and 64 N, and a sham-loading group tr as included at 64 N, Strains in the tibiae were linear between 10 and 60 N, and the average peak strain at the Ps.S at 60 N was 2664 +/- 250 microstrain, consistent with the results of Turner's group. Lamellar bone formation was stimulated at the Ec.S by applied bending, but not by sham loading. Bending strains above a loading threshold of 40 N increased Ec Lamellar hone formation rate, bone forming surface, and mineral apposition rate with a dose response similar to that reported by Turner et al, (J Bone Miner Res 9:87-97, 1994). We conclude that the modified loading system offers precision for applied loads of between 0 and 70 N, versatility in the selection of loading rates up to 20 Hz, and a reproducible bone formation response in the rat tibia, Adjustment of the loader also enables study of mechanical usage in murine tibia, an advantage with respect to the increasing variety of transgenic strains available in bone and mineral research. (Bone 23:307-310; 1998) (C) 1998 by Elsevier Science Inc. All rights reserved.

Four-point amplitude from open superstring field theory

An open superstring field theory action has been proposed which does not suffer from contact term divergences. In this paper, we compute the on-shell four-point tree amplitude fi om this action using the Giddings map. After including contributions from the quartic term in the action, the resulting amplitude agrees with the first-quantized prescription. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Pure spinor superspace identities for massless four-point kinematic factors

Using the pure spinor formalism we prove identities which relate the tree-level, one-loop and two-loop kinematic factors for massless four-point amplitudes. From these identities it follows that the complete supersymmetric one- and two-loop amplitudes are immediately known once the tree-level kinematic factor is evaluated. In particular, the two-loop equivalence with the RNS formalism (up to an overall coefficient) is obtained as a corollary.

Four-point one-loop amplitude computation in the pure spinor formalism

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism. © SISSA 2006.

Measurements of fracture toughness applying a four-point-bending technique of ice core B34 from Kohnen Station, Dronning Maud Land, Antarctica

The critical fracture toughness is a material parameter describing the resistance of a cracked body to further crack extension. It is an important parameter to simulate and predict the break-up behaviour of ice shelves from calving of single icebergs to the disintegration of entire ice shelves over a wide range of length scales. The fracture toughness values are calculated with equations that are derived from an elastic stress analysis. Additionally, an X-ray computer tomography (CT scanner) was used to identify the density as a function of depth. The critical fracture toughness of 91 Antarctic inland ice samples with densities between 840 to 870 kg/m**3 has been determined by applying a four-point-bending technique on single edge v-notched beam samples. The examined ice core was drilled 70m north of Kohnen Station, Dronnning Maud Land (75°00' S, 00°04' E, 2882 m).

Temperature-referenced high-sensitivity point-probe optical fiber chem-sensors based on cladding etched fiber Bragg gratings

Point-probe optical fiber chem-sensors have been implemented using cladding etched fiber Bragg gratings. The sensors possess refractive index sensing capability that can be utilized to measure chemical concentrations. The Bragg wavelength shift reaches 8 nm when the index of surrounding medium changes from 1.33 to 1.44, giving maximum sensitivity more than 10 times higher than that of previously reported devices. More importantly, the dual-grating configuration of the point-probe sensors offers a temperature reference function, permitting accurate measurement of refractive index encoded chemical concentrations.

Temperature-referenced high-sensitivity point-probe optical fiber chem-sensors based on cladding etched fiber Bragg gratings

Point-probe optical fiber chem-sensors have been implemented using cladding etched fiber Bragg gratings. The sensors possess refractive index sensing capability that can be utilized to measure chemical concentrations. The Bragg wavelength shift reaches 8 nm when the index of surrounding medium changes from 1.33 to 1.44, giving maximum sensitivity more than 10 times higher than that of previously reported devices. More importantly, the dual-grating configuration of the point-probe sensors offers a temperature reference function, permitting accurate measurement of refractive index encoded chemical concentrations.

A study of ternary Cu2SnS3 and Cu3SnS4 thin films prepared by sulfurizing stacked metal precursors

Thin films of Cu2SnS3 and Cu3SnS4 were grown by sulfurization of dc magnetron sputtered Sn–Cu metallic precursors in a S2 atmosphere. Different maximum sulfurization temperatures were tested which allowed the study of the Cu2SnS3 phase changes. For a temperature of 350 ◦C the films were composed of tetragonal (I -42m) Cu2SnS3. The films sulfurized at a maximum temperature of 400 ◦C presented a cubic (F-43m) Cu2SnS3 phase. On increasing the temperature up to 520 ◦C, the Sn content of the layer decreased and orthorhombic (Pmn21) Cu3SnS4 was formed. The phase identification and structural analysis were performed using x-ray diffraction (XRD) and electron backscattered diffraction (EBSD) analysis. Raman scattering analysis was also performed and a comparison with XRD and EBSD data allowed the assignment of peaks at 336 and 351 cm−1 for tetragonal Cu2SnS3, 303 and 355 cm−1 for cubic Cu2SnS3, and 318, 348 and 295 cm−1 for the Cu3SnS4 phase. Compositional analysis was done using energy dispersive spectroscopy and induced coupled plasma analysis. Scanning electron microscopy was used to study the morphology of the layers. Transmittance and reflectance measurements permitted the estimation of absorbance and band gap. These ternary compounds present a high absorbance value close to 104 cm−1. The estimated band gap energy was 1.35 eV for tetragonal (I -42m) Cu2SnS3, 0.96 eV for cubic (F-43m) Cu2SnS3 and 1.60 eV for orthorhombic (Pmn21) Cu3SnS4. A hot point probe was used for the determination of semiconductor conductivity type. The results show that all the samples are p-type semiconductors. A four-point probe was used to obtain the resistivity of these samples. The resistivities for tetragonal Cu2SnS3, cubic Cu2SnS3 and orthorhombic (Pmn21) Cu3SnS4 are 4.59 × 10−2 cm, 1.26 × 10−2 cm, 7.40 × 10−4 cm, respectively.

Characterization of processed materials by electrical currents: development of equipment and applications

Dissertação para obtenção do Grau de Mestre em Engenharia Mecânica

Untersuchungen zum Dotieren von Silicium aus einer Oberflächenbelegung mit Phosphor in einem Kurzzeitprozess

Silicon, shallow junction, rapid thermal doping, vapour phase doping, atomic-layer doping, phosphorus diffusion, phosphine adsorption, sheet resistance, four-point probe, native oxidation

Medidas de resistividade elétrica DC em sólidos: como efetuálas corretamente

This paper deals with the most common methods for determining the dc electrical resistivity in solid materials. A brief overview of the fundamental concepts related to the electrical resistivity on materials is introduced. Undoubtedly, the most common and useful procedure to determine the electrical resistivity (rho) is the fourpoint probe method. Some crucial mistakes regarding the experimental procedure and the appropriated correction factors are found in the literature. Thus, the correction factor for the most common sample geometries were gathered and revised in order to provide an easy way to use and apply them.

Construção de uma fonte de corrente e de uma sonda para medida de condutividade pelo método da sonda de quatro pontas

This paper describes the construction of an eletrical current source and of a probe to be used in the measurement of eletrical conductivity through a four-point probe method. These pieces of equipments can be obtained at the low price of US$ 50.00 and are adequate for eletrical conductivity measurements in the semiconductor range, that is from 10-1 to 10-6 S cm-1.

Étude de films de nanotubes de carbone dans le domaine de fréquences térahertz : propriété antiréfléchissante

Les expériences de spectroscopie ont été réalisées en collaboration avec Jean-François Allard du groupe de Denis Morris de l'Université de Sherbrooke.

Phosphonsäurehaltige polycyclische aromatische Kohlenwasserstoffe für Anwendungen in Brennstoffzellen

Die vorliegende Arbeit umfasst die Synthese und Charakterisierung phosphonsäurehaltiger, organischer Kristalle als ionenleitende Verbindungen in Brennstoffzellen-Anwendungen. Sie zielt dabei einerseits auf die Darstellung von protonenleitenden Polyphenylenverbindungen und deren Verwendung als Linker für den Aufbau protonenleitender Aluminium-Phosphonat-Netzwerke ab und behandelt andererseits die Einführung stark polarer Phosphonsäuregruppen in einen diskreten Nanographenkern sowie deren Einfluss auf die ionen- und elektronenleitenden Eigenschaften, um diese als gemischt-leitende Kompatibilisatoren an der isolierenden Elektrode/ Membran-Grenzfläche in einer Brennstoffzelle zu verwenden. Am Beispiel eines phosphonsäurefunktionalisierten, phenylenisch-expandierten Hexaphenylbenzols konnte ein solvothermisch stabiler Protonenleiter mit einer Selbstorganisation in kolumnare, supramolekulare Strukturen und hoher, temperaturunabhängiger Leitfähigkeit mit dominierendem Grotthuss-Anteil präsentiert werden. Durch einen Wechsel dieser 1D-radialen Phosphonsäureanordnung in der Molekülhülle hin zu 2D- und 3D-H2PO3-funktionalisierten, dendritischen Stäbchen- bzw. Kugelstrukturen konnte gezeigt werden, dass eine kolumnare Molekülanordnung jedoch kein notwendiges Kriterium für einen Grotthuss-artigen Protonentransport darstellt. Durch die mehrdimensionale Orientierung der Phosphonsäuren in der Außenhülle der Dendrimere garantieren die synthetisierten Strukturen hochaggregierte Phosphonsäurecluster, die als dichtes Säurekontinuum die eigentlichen protonenleitfähigen Kanäle darstellen und somit als entscheidendes Kriterium für das Auftreten eines Grotthuss-artigen Mechanismus definiert werden müssen. Eine signifikante Erhöhung der Leitfähigkeit konnte durch den Aufbau poröser, organisch-anorganischer Netzwerke (Al-HPB-NETs) über Komplexierung einer unterstöchiometrischen Menge an Aluminium-Kationen mit der Polyphosphonsäureverbindung Hexakis(p-phosphonatophenyl)benzol als Linkereinheit erfolgen, die anschließend mit kleinen intrinsischen Protonenleitern wie Phosphonsäure dotiert wurden. Diese dotierten Netzwerke wiesen außergewöhnliche Leitfähigkeit auf, da sie die σ-Werte des Referenzpolymers Nafion® bereits in einem Temperaturbereich oberhalb von 135°C übertrafen, aber gleichzeitig ein sehr gutes Säureretentionsverhalten von einem Gew.-% Säuredesorption über eine Immersionsdauer von 14 h gegenüber wässrigem Medium zeigten. Durch Mischen dieser Aluminiumphosphonate mit einer dotierten Polymermatrix wie PBI konnten synergistische Effekte durch zusätzliche attraktive H-Brückenbindungen zwischen molekular angebundener Phosphonsäure und mobiler H3PO4 an Hand eines signifikanten Leitfähigkeitsanstiegs für die resultierenden Membranen beobachtet werden. Die Protonenleitfähigkeit lag in diesen Materialien in dem gesamten untersuchten Temperaturbereich oberhalb von Nafion®. Durch das Einbringen der NETs in PBI konnte ebenfalls die Säureretention von PBI um etwa 9 % bei kurzen Immersionszeiten (bis 1 min) verbessert werden. Darüber hinaus wurde in der vorliegenden Arbeit die synthetische Kombination eines hydrophoben, elektronenleitenden Nanographenkerns mit einer, durch eine isolierende Peripherie getrennten, stark polaren, protonenleitenden Außenhülle realisiert. Am Beispiel von zwei phosphonsäurefunktionalisierten Triphenylenen, die sich in Länge und Planarität der gewählten Peripheriebausteine unterschieden, sollten polycyclische aromatische Kohlenwasserstoffe mit gemischt protonen- und elektronenleitenden Eigenschaften hergestellt werden, die über Impedanzspektroskopie und Vierpunktmessungen untersucht wurden. Da es sich bei der Anwendung solcher gemischtleitenden Verbindungen um grenz-flächenaktive Substanzen handelt, die das ohne verbesserte Anbindung bestehende Dielektrikum zwischen Elektrode und protonenleitender Membran überbrücken sollen, wurde die Untersuchung eines möglichen Elektronentransportes durch eine Molekülmonolage ebenfalls über kombinatorische STM- und STS-Technik durchgeführt.