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Validity of the scattering exponent approximation for materials with a complex electronic structure

Yuji Go*, Rajeev Dutt, Bhawna Sahni, and Neophytos Neophytou

  • *Contact author: yuji.go@warwick.ac.uk
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Phys. Rev. B 114, 235201 – Published 6 October, 2026

DOI: https://doi.org/10.1103/zywf-jxy9

Abstract

A common method to identify the dominant internal material electronic scattering processes that limit transport and conductivity in experimental measurements is to use the scattering exponent approximation. It assumes that the carrier relaxation time follows τ=τ0Er, where r is a value that depends on a specific scattering mechanism. The exponential trend is also reflected in the temperature dependence for parameters like mobility, following μ∝Ts. Literature r and s values are defined using simplified assumptions, the most important being single-band parabolic electronic structures. Typical materials beyond simple semiconductors, however, involve complex electronic structures and many scattering processes of various strengths acting simultaneously. Here, we consider transport simulations for a series of electronic structure models, from single parabolic band models, two-band models, and the full band structure of half-Heusler materials, as well as all important scattering mechanisms such as acoustic phonons, optical phonons, polar optical phonons, and ionized impurity scattering through ab initio calculation methods. We show that, in general, the r values that describe transport in such complex cases do not follow the nominal literature values; thus their ability to provide transport characteristics is limited. We also explore the feasibility of using these exponents to extract thermoelectric transport characteristics from the commonly used Pisarenko relation for the Seebeck coefficient in half-Heusler materials. In this case as well, the scattering exponents used to compute the Seebeck coefficient do not correspond to the internal transport processes due to the complexity of the electronic structures. However, despite the band complexities, we have identified a significant negative correlation between the exponents and the material's optical phonon energy.

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Phys. Rev. B 114, 235201– Published 6 October, 2026
  • Received 27 March 2026
  • Revised 17 July 2026
  • Accepted 27 August 2026
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