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Journal of Electronic Materials

, Volume 48, Issue 2, pp 1031–1043 | Cite as

Using First-Principles Calculations in CALPHAD Models to Determine Carrier Concentration of the Binary PbSe Semiconductor

  • Matthew C. PetersEmail author
  • Jeff W. Doak
  • J. E. Saal
  • G. B. Olson
  • P. W. Voorhees
Article

Abstract

PbSe is a promising thermoelectric that can be further improved by nanostructuring, band engineering, and carrier concentration tuning; therefore, a firm understanding of the defects in PbSe is necessary. The formation energies of point defects in PbSe are computed via first-principles calculations under the dilute-limit approximation. We find that under Pb-rich conditions, PbSe is an n-type semiconductor dominated by doubly-charged Se vacancies. Conversely, under Se-rich conditions, PbSe is a p-type semiconductor dominated by doubly-charged Pb vacancies. Both of these results agree with previously performed experiments. Temperature- and chemical potential-dependent Fermi levels and carrier concentrations are found by enforcing the condition of charge neutrality across all charged atomic and electronic states in the system. The first-principles-predicted charge-carrier concentration is in qualitative agreement with experiment, but slightly varies in the magnitude of carriers. To better describe the experimental data, a CALPHAD assessment of PbSe is performed. Parameters determined via first-principles calculations are used as inputs to a five-sublattice CALPHAD model that was developed explicitly for binary semiconductors. This five sublattice model is in contrast to previous work which treated PbSe as a stoichiometric compound. The current treatment allows for experimental carrier concentrations to be accurately described within the CALPHAD formalism. In addition to the five-sublattice model, a two-sublattice model is also developed for use in multicomponent databases. Both models show excellent agreement with the experimental data and close agreement with first-principles calculations. These CALPHAD models can be used to determine processing parameters that will result in an optimized carrier concentration and peak zT value.

Keywords

Thermoelectrics CALPHAD first-principles DFT defect chemistry 

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Notes

Acknowledgments

The authors gratefully acknowledge thermoelectrics research at Northwestern University through the Center for Hierarchical Materials Design (CHiMaD) and financial support from the DARPA SIMPLEX program through SPAWAR (Contract #N66001-15-C-4036). M. Peters was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

Funding

Funding was provided by Defense Advanced Research Projects Agency and National Institute of Standards and Technology (US).

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Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringNorthwestern UniversityEvanstonUSA
  2. 2.QuesTek Innovations LLCEvanstonUSA

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