Atomistic study of the electronic contact resistivity between the half-Heusler alloys (HfCoSb, HfZrCoSb, HfZrNiSn) and the metal Ag

Abstract

Half-Heusler(HH) alloys have shown promising thermoelectric properties in the medium and high temperature range. To harness these material properties for thermoelectric applications, it is important to realize electrical contacts with low electrical contact resistivity. However, little is known about the detailed structural and electronic properties of such contacts, and the expected values of contact resistivity. Here, we employ atomistic ab initio calculations to study electrical contacts in a subclass of HH alloys consisting of the compounds HfCoSb, HfZrCoSb, and HfZrNiSn. By using Ag as a prototypical metal, we show that the termination of the HH material critically determines the presence or absence of strong deformations at the interface. Our study includes contacts to doped materials, and the results indicate that the p-type materials generally form ohmic contacts while the n-type materials have a small Schottky barrier. We calculate the temperature dependence of the contact resistivity in the low to medium temperature range and provide quantitative values that set lower limits for these systems. where h max =(T H -T C )/T H is the Carnot efficiency, T H and T C are the hot and cold side temperatures, and ZT is a dimensionless figure of merit that characterizes the TE performance of materials. For the efficiency of a TE device, ZT is an average of the ZT values for the n-type and p-type TE materials. The material ZT is given by ("#) %&' = * + ,#/. , where σ is the electrical conductivity, S the Seebeck coefficient, and κ the thermal conductivity. Equation 1 is valid in the ideal situation where the thermal and electrical contact resistivity at the hot and cold ends are negligible [2]. In reality, the finite electrical and thermal contact resistivities lead to both temperature and voltage drops at the hot and cold ends, hence reduce the overall device efficiency, which is proportional to the effective figure of merit (ZT) 233 = ZT * [1 + +r 8 9 : ; : ] => , where ZT is the device level figure of merit without contact effects, r C is the contact resistivity, r m and L m are the resistivity and length of the p-type and n-type TE materials for the legs in the TE module. Thus, for optimal device performance, the contact resistivity should be as small as possible; a rule of thumb is that a good module performance requires r C <r*L/10. Half-Heusler (HH) alloys have recently attracted a great deal of attention as promising thermoelectric materials [3-5] for medium and high temperatures (i.e. in the range of 500 to 1000 K) due to their high chemical stability and small lattice thermal conductivity, which is achieved by creating nanostructures, atomic mass differences, and multiple alloys[6-8]. Within the family of HH alloys, the p-type Hf 0.5 Zr 0.5 CoSb 0.8 Sn 0.2 material and the n-type Hf 0.75 Zr 0.25 NiSn 0.99 Sb 0.01 material have shown large ZT values of 0.8 and 1, respectively[9]. In addition, these materials are relatively low-cost and environmentally friendly hence desired for green energy generation. leve...

Atomistic study of an ideal metal/thermoelectric contact: The full-Heusler/half-Heusler interface

“…In particular we are interested in the fundamental limit of the electrical contact resistivity at these interfaces. To this end we employ a previously developed atomistic approach [17,18] that combines first-principles simulations with macroscopic modeling. The approach uses: i) ab initio calculations based on Density Functional Theory (DFT) [19] to obtain the electronic properties near the interface.…”

“…We begin by investigating from first-principles the basic properties of the HH and FH systems in bulk form. In a previous study [18] we calculated the low-temperature properties of Ag contacts to several HH alloys including compounds from the family (Zr,Hf)NiSn. In particular we found that bulk HH properties important for band alignment at the metal interface (such as the electron affinity or the band gap) do not depend significantly on the alloy composition or doping.…”

“…Another bulk property of relevance for interfacial electron transport phenomena is the carrier concentration in the semiconductor as function of the Fermi level E F . Figure 1c) shows the concentration of holes and electrons estimated at room temperature via standard expressions [18] based on DFT eigenvalues calculated for a dense set (36x36x36) of Monkhorst-Pack k-points in the Brillouin zone [27]. N-type doping can be achieved in (Zr,Hf)NiSn compounds via Sn substitution with Sb.…”

“…Having obtained from first-principles the band bending for the undoped semiconductor case we would like to extend the results to non-zero n-type doping levels. This is done in several steps [17,18,41]: i) We obtain the macroscopic total charge density ρ macro (including free carriers, valence and ionic charge) from the one-dimensional Poisson equation satisfied by V macro :…”

“…To calculate the contact resistivity we use an effective mass model [18,35] with the band bending potential serving as input. Good agreement between the effective mass and full ab initio approaches has been demonstrated for other semiconductor contacts [36].…”