Measuring anisotropic resistivity of single crystals using the van der Pauw technique

Anisotropy in properties of materials is important in materials science and solid-state physics. Measurement of the full resistivity tensor of crystals using the standard four-point method with bar shaped samples requires many measurements and may be inaccurate due to misalignment of the bars along crystallographic directions. Here an approach to extracting the resistivity tensor using van der Pauw measurements is presented. This reduces the number of required measurements. The theory of the van der Pauw method is extended to extract the tensor from parallelogram shaped samples with known geometry. Methods to extract the tensor for both known and unknown principal axis orientation are presented for broad applicability to single crystals. Numerical simulations of errors are presented to quantify error sources. Several benchmark experiments are performed on isotropic graphite samples to verify the internal consistency of the developed theory, test experimental precision, and characterize error sources. The presented methods are applied to a RuSb_2 single crystal at room temperature and the results are discussed based on the error source analysis. Temperature resolved resistivities along the a and b directions are finally reported and briefly discussed

Phase transition enhanced thermoelectric figure-of-merit in copper chalcogenides

While thermoelectric materials can be used for solid state cooling, waste heat recovery, and solar electricity generation, low values of the thermoelectric figure of merit, zT, have led to an efficiency too low for widespread use. Thermoelectric effects are characterized by the Seebeck coefficient or thermopower, which is related to the entropy associated with charge transport. For example, coupling spin entropy with the presence of charge carriers has enabled the enhancement of zT in cobalt oxides. We demonstrate that the coupling of a continuous phase transition to carrier transport in Cu 2Se over a broad (360–410 K) temperature range results in a dramatic peak in thermopower, an increase in phonon and electron scattering, and a corresponding doubling of zT (to 0.7 at 406 K), and a similar but larger increase over a wider temperature range in the zT of Cu 1.97 Ag .03Se (almost 1.0 at 400 K). The use of structural entropy for enhanced thermopower could lead to new engineering approaches for thermoelectric materials with high zT and new green applications for thermoelectrics

Measurement of the electrical resistivity and Hall coefficient at high temperatures

The implementation of the van der Pauw (VDP) technique for combined high temperature measurement of the electrical resistivity and Hall coefficient is described. The VDP method is convenient for use since it accepts sample geometries compatible with other measurements. The technique is simple to use and can be used with samples showing a broad range of shapes and physical properties, from near insulators to metals. Three instruments utilizing the VDP method for measurement of heavily doped semiconductors, such as thermoelectrics, are discussed

Measuring thermoelectric transport properties of materials

In this review we discuss considerations regarding the common techniques used for measuring thermoelectric transport properties necessary for calculating the thermoelectric figure of merit, zT. Advice for improving the data quality in Seebeck coefficient, electrical resistivity, and thermal conductivity (from flash diffusivity and heat capacity) measurements are given together with methods for identifying possible erroneous data. Measurement of the Hall coefficient and calculation of the charge carrier concentration and mobility is also included due to its importance for understanding materials. It is not intended to be a complete record or comparison of all the different techniques employed in thermoelectrics. Rather, by providing an overview of common techniques and their inherent difficulties it is an aid to new researchers or students in the field. The focus is mainly on high temperature measurements but low temperature techniques are also briefly discussed

Crystal structure across the β to α phase transition in thermoelectric Cu2−xSe

The crystal structure uniquely imparts the specific properties of a material, and thus provides the starting point for any quantitative understanding of thermoelectric properties. Cu2−xSe is an intensely studied high performing, non-toxic and cheap thermoelectric material, and here for the first time, the average structure of β-Cu2−xSe is reported based on analysis of multi-temperature single-crystal X-ray diffraction data. It consists of Se–Cu layers with additional copper between every alternate layer. The structural changes during the peculiar zT enhancing phase transition mainly consist of changes in the inter-layer distance coupled with subtle Cu migration. Just prior to the transition the structure exhibits strong negative thermal expansion due to the reordering of Cu atoms, when approached from low temperatures. The phase transition is fully reversible and group–subgroup symmetry relations are derived that relate the low-temperature β-phase to the high-temperature α-phase. Weak superstructure reflections are observed and a possible Cu ordering is proposed. The structural rearrangement may have a significant impact on the band structure and the Cu rearrangement may also be linked to an entropy increase. Both factors potentially contribute to the extraordinary zT enhancement across the phase transition

Functionally Graded Ge_1–<i>x</i>Si_<i>x</i> Thermoelectrics by Simultaneous Band Gap and Carrier Density Engineering

Exploiting the material gradients inherent to crystal growth techniques, boron doped Ge_1–<i>x</i>Si_<i>x</i> (<i>x</i> = 0 to ∼0.25) samples graded in both band gap and carrier concentration have been prepared by the Czochralski method. Along the length of the Ge_1–<i>x</i>Si_<i>x</i> samples <i>x</i> changes continuously, giving rise to changes in the band gap from 0.87 to 0.65 eV. Similarly, gradients in the boron content results in continuous carrier density changes along the sample. This results in samples graded in several material parameters relevant to thermoelectric performance. The present study thereby demonstrates a one-step method for preparing thermoelectrics graded in both carrier concentration and band gap. By careful matching of dopant and material system, it is demonstrated how the gradient in dopant and band gap can work in synergy and mutually enhance the thermoelectric performance over the individual contributions