Abstract
Aliovalent doping is a way to optimize the electrical properties of semiconductors, but its impact on the phonon structure and propagation is seldom considered properly. Here we show that aliovalent doping can be much more effective in reducing the lattice thermal conductivity of thermoelectric semiconductors than the commonly employed isoelectronic alloying strategy. We demonstrate this in the heavy-band NbFeSb system, finding that a reduction of 65% in the lattice thermal conductivity is achieved through only 10% aliovalent Hf doping, compared with the four times higher isoelectronic Ta alloying. We show that aliovalent doping introduces free charge carriers and enhances screening, leading to the softening and deceleration of optical phonons. Moreover, the heavy dopant can induce the avoided crossing of acoustic and optical phonon branches, decelerating the acoustic phonons. These results highlight the significant role of aliovalent dopants in regulating the phonon structure and suppressing the phonon propagation of semiconductors.
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Data availability
All data that support the findings of this study are available from the corresponding authors upon reasonable request. Experimental data from the ISIS Neutron and Muon Source are available at https://doi.org/10.5286/ISIS.E.RB1820186. Source data are provided with this paper.
Code availability
The codes that support the findings of this study are available from the corresponding authors upon reasonable request.
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Acknowledgements
T.Z. thanks the National Natural Science Foundation of China (no. 92163203), the National Science Fund for Distinguished Young Scholars (no. 51725102) and the Fundamental Research Funds for the Central Universities (no. 2021FZZX001) for support. C. Fu thanks the National Natural Science Foundation of China (no. 52101275) and the Fundamental Research Funds for the Central Universities (no. 226-2023-00001). J.Y. thanks the National Natural Science Foundation of China (nos. 52172216 and 92163212) and the Key Research Project of Zhejiang Lab (no. 2021PE0AC02). J.M. thanks the National Science Foundation of China (no. U2032213) for support. C. Felser thanks the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Projektnummer (no. 392228380). Q.R. thanks the project from Guangdong Basic and Applied Basic Research Foundation (grant no. 2021B1515140014). Q.R. also acknowledges the beam time granted by ISIS (RB no. 1820186), SINQ (proposal no. 20181498) and J-PARC/MLF (proposal no. 2018B0144). P.M. thanks the National Natural Science Foundation of China (no. 12005243) and the Guangdong Basic and Applied Basic Research Foundation (grant no. 2022B1515120014).We thank J. Yu and K. Xia for helpful discussions.
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Contributions
C. Fu and T.Z. designed the project. S.H. prepared the samples and carried out the high-temperature transport measurements. C. Fu and C. Felser performed the low-temperature transport measurements. S.D. and J.Y. performed the first-principles calculations. Q.R. and J.M. carried out the INS experiment and high-resolution neutron diffraction studies with input from M.D.L., D.S., P.M., S.T. and T.K. Q.R. and J.M. analyzed the neutron scattering data and Q.R. carried out the Rietveld refinement of the neutron diffraction patterns. S.H. and C. Fu analysed the data and wrote the original manuscript, with input from C.H. and Z.G. T.Z. and C. Felser supervised the project. All the authors reviewed and edited the manuscript.
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Supplementary Figs. 1–13, Tables 1–7 and Discussion.
Source data
Source Data Fig. 1
Optimal carrier concentration data versus DOS effective mass (Fig. 1a) and reduction in lattice thermal conductivity versus doping/alloying concentration (Fig. 1b).
Source Data Fig. 2
Experimental lattice thermal conductivity data (Fig. 2a) and calculated lattice thermal conductivity data (Fig. 2b–d).
Source Data Fig. 3
INS data (Fig. 3a,b), calculated phonon DOS (Fig. 3b) and group velocity data (Fig. 3c).
Source Data Fig. 4
Calculated phonon dispersion data (Fig. 4a,b), integrated partial COHP data (Fig. 4c) and deformation electron density isosurface (Fig. 4d).
Source Data Fig. 5
Calculated group velocity data (Fig. 5a), phonon dispersion data (Fig. 5b) and partial phonon DOS data (Fig. 5c).
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Han, S., Dai, S., Ma, J. et al. Strong phonon softening and avoided crossing in aliovalence-doped heavy-band thermoelectrics. Nat. Phys. 19, 1649–1657 (2023). https://doi.org/10.1038/s41567-023-02188-z
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DOI: https://doi.org/10.1038/s41567-023-02188-z
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