Recent research and development of high-temperature thermoelectric materials has demonstrated great potential for converting automobile exhaust heat directly into electricity. Thermoelectrics based on classic bismuth telluride have also started to impact the automotive industry by enhancing air-conditioning efficiency and integrated cabin climate control. In addition to engineering challenges of making reliable and efficient devices to withstand thermal and mechanical cycling, the remaining issues in thermoelectric power generation and refrigeration are mostly materials related. The dimensionless figure of merit, ZT, still needs to be improved from the current value of 1.0 to 1.5 to above 2.0 to be competitive with other alternative technologies. In the meantime, the thermoelectric community could greatly benefit from the development of international test standards, improved test methods, and better characterization tools. Internationally, thermoelectrics have been recognized by many countries as a key component for improving energy efficiency. The International Energy Agency (IEA) group under the Implementing Agreement for Advanced Materials for Transportation (AMT) identified thermoelectric materials as an important area in 2009. This paper is part I of the international round-robin testing of transport properties of bulk thermoelectrics. The main foci in part I are the measurement of two electronic transport properties: Seebeck coefficient and electrical resistivity.

Transport Properties of Bulk Thermoelectrics—An International Round-Robin Study, Part I: Seebeck Coefficient and Electrical Resistivity

Concentration profiles have been determined for phosphorus diffusion into silicon. These have been fitted to the solution of Fick's diffusion equations using a model where a moving boundary separates two distinct phases. Thus, it is concluded that the silicon surface region is part of a different phase from the rest of the diffused layer. For the short diffusion times studied, the phase boundary reaction is the rate limiting process and the phase boundary moves at a nearly constant rate. In the region beyond the phase boundary the transport of phosphorus is controlled by two diffusion species, characterized by two substantially different diffusion coefficients. The slow diffusant is present mainly in a transition region between the phase boundary and the fast diffusant dominated region. The fast diffusant has a maximum concentration at the phase boundary. The linear rates of movement of the phase boundary, the concentrations of the fast diffusant at the phase boundary, and the diffusion constants for the slow and the fast diffusants were obtained over the temperature range from 820 to 1100°C. As the diffusion temperature increases the diffusion constants for the slow and the fast diffusants approach each other. At 1100°C, the diffusion profile can be represented by a single diffusion constant. For long diffusion times the phase boundary became less distinct.

Shallow phosphorus diffusion profiles in silicon

Tungsten-based model alloys were fabricated to simulate compositional changes by neutron irradiation, performed in the JOYO fast test reactor. The irradiation damage range was 0.17–1.54 dpa and irradiation temperatures were 400, 500 and 750 � C. After irradiation, microstructural observations and electrical resistivity measurements were carried out. A number of precipitates were observed after 1.54 dpa irradiation. Rhenium and osmium were precipitated by irradiation, which suppressed the formation of dislocation loops and voids. Structures induced by irradiation were not observed so much after 0.17 dpa irradiation. Electrical resistivity measurements showed that the effects of osmium on the electrical resistivity, related to impurity solution content, were larger than that of rhenium. Measurements of electrical resistivity of ternary alloys showed that the precipitation behavior was similar to that in binary alloys. [doi:10.2320/matertrans.MAW200821]

https://www.jstage.jst.go.jp/article/matertrans/49/10/49_MAW200821/_pdf

Precipitation of Solid Transmutation Elements in Irradiated Tungsten Alloys

Resistivity measurement is a weighted averaging of local resistivities. We develop a formalism to calculate the weighting function, applying it to square van der Pauw samples and to linear and square four‐point probe arrays. In each case, some regions of the sample are negatively weighted, but these regions can be reduced or eliminated by van der Pauw averaging. We discuss negative weighting, which we feel is responsible for spurious reports of superconductivity above room temperature. We show how a square four‐point array can be more effective at measuring local resistivity than a linear one. Finally, we show how to apply our formalism to anisotropic materials.

What do you measure when you measure resistivity

Equations and graphs are presented to aid in the evaluation of resistivity non-uniformities when measured by use of the four-point probe. Both the in-line and square array four-point probes are considered. To enable a circular disc to be probed for non-uniformities, correction factors for a displaced probe are given for an in-line array displaced with points on a diameter, for an in-line array displaced with points perpendicular to a diameter, and for a displaced square array.

Four-point probe measurement of non-uniformities in semiconductor sheet resistivity☆

A new direct-reading ac bridge circuit has been developed to measure semiconductor bulk and sheet resistivity, using a four-point (or other appropriate) probe. The range of resistivity which can be measured is from 0.001 to 10,000 ohm-cm. Resistivity is read directly from resistance decades and a ratio multiplier, eliminating voltmeter and ammeter errors — the final reading being the result of a bridge-balancing operation for each measurement. Stability and sensitivity provide better than 0.5 per cent electrical accuracy, with mechanical point spacing being the controlling limitation on the over-all accuracy of the measurement. The use of ac eliminates the influence of rectification, thermal, or contact potentials on the measurements, and also provides sensitivity more readily than with dc. The four-point probe and test specimen are the only nongrounded elements. An Appendix compiles four-point probe conversion factors for thin circular and rectangular slices of material. New tables are presented for slices having a continuous diffused skin all over, and thus also conducting across the back.

M. A. Logan

Papers

An AC bridge for semiconductor resistivity measurements using a four-point probe