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

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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.

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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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Authors and Affiliations

  1. Department of Materials Science and Engineering, Northwestern University, Evanston, IL, USA

    Matthew C. Peters, G. B. Olson & P. W. Voorhees

  2. QuesTek Innovations LLC, Evanston, IL, USA

    Jeff W. Doak, J. E. Saal & G. B. Olson

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  1. Matthew C. Peters
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  2. Jeff W. Doak
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  3. J. E. Saal
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Correspondence to Matthew C. Peters.

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Peters, M.C., Doak, J.W., Saal, J.E. et al. Using First-Principles Calculations in CALPHAD Models to Determine Carrier Concentration of the Binary PbSe Semiconductor. J. Electron. Mater. 48, 1031–1043 (2019). https://doi.org/10.1007/s11664-018-6819-z

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