Theory of enhancement of thermoelectric properties of materials with nanoinclusions

Sergey V. Faleev and François Léonard

Phys. Rev. B 77, 214304 – Published 12 June 2008

Abstract

Based on the concept of band bending at metal/semiconductor interfaces as an energy filter for electrons, we present a theory for the enhancement of the thermoelectric properties of semiconductor materials with metallic nanoinclusions. We show that the Seebeck coefficient can be significantly increased due to a strongly energy-dependent electronic scattering time. By including phonon scattering, we find that the enhancement of $Z T$ due to electron scattering is important for high doping, while at low doping it is primarily due to a decrease in the phonon thermal conductivity.

Received 19 March 2008

DOI:https://doi.org/10.1103/PhysRevB.77.214304

Authors & Affiliations

Sergey V. Faleev and François Léonard^*

Sandia National Laboratories, Livermore, California 94551, USA

^*sfaleev@gmail.com

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Issue

Vol. 77, Iss. 21 — 1 June 2008

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Images

Figure 1
(Color online) (a) Schematic of the semiconductor host with metallic nanoinclusions. Panel (b) shows an example of the calculated potential $V (r)$ and the energy diagram for PbTe at $T = 300 K$ , $n = 2.5 \times 10^{19} {cm}^{- 3}$ , $V_{B} = - 0.11 eV$ , and $R = 1.5 nm$ . Panel (c) illustrates the concept of energy filtering: low energy electrons scatter strongly with the potential, but high energy electrons are unaffected. The calculated electronic relaxation time for the potential of panel (b) is also shown.Reuse & Permissions
Figure 2
(Color online) Calculated Seebeck coefficient for PbTe with metallic nanoinclusions as a function of the doping for several different values of the nanoinclusion radius.Reuse & Permissions
Figure 3
Panel (a) shows the calculated Seebeck coefficient and conductivity for PbTe as a function of the interface potential $V_{B}$ . Panel (b) shows the resulting power factor. Parameters are $R = 1.5 nm$ , $T = 300 K$ , $x = 5 %$ , and $n = 2.5 \times 10^{19} {cm}^{- 3}$ .Reuse & Permissions
Figure 4
(Color online) Thermoelectric coefficients as a function of temperature calculated for $n = 2.5 \times 10^{19} {cm}^{- 3}$ , $x = 5 %$ , and $R = 1.5 nm$ . (a) The optimized $Z T$ factor, with the optimal values of $V_{B}$ , is shown in the inset. (b) The Seebeck coefficient. (c) The electrical conductivity. Inset shows optimized (filled circles) and bulk PbTe (solid line) power factor $S^{2} σ$ . (d) The thermal conductivity. In all panels, solid circles include electron and phonon scattering on the inclusions; open circles include electron scattering on the inclusions but with bulk PbTe values of $κ_{ph}$ ; solid lines and filled squares are the calculated and measured (Ref. 15) values for bulk PbTe.Reuse & Permissions
Figure 5
Calculated ZT factor for PbTe illustrating the relative effects of electronic and phonon scattering on nanoinclusions. In both panels $R = 1.5 nm$ , $x = 5 %$ , and $T = 300 K$ . (a) High doping $n = 5 \times 10^{19} {cm}^{- 3}$ . (b) Low doping $n = 5 \times 10^{18} {cm}^{- 3}$ . Dotted lines are calculated using the bulk phonon thermal conductivity. Filled circles correspond to the bulk PbTe system. Stars include only the phonon scattering on nanoinclusions.Reuse & Permissions
Figure 6
(Color online) Temperature dependence of the optimized $Z T$ factor for PbTe. (a) low doping $n = 5 \times 10^{18} {cm}^{- 3}$ and (b) high doping $n = 5 \times 10^{19} {cm}^{- 3}$ . In both panels filled circles denote the optimized $Z T$ calculated with both electron and phonon scattering on nanoinclusions, open circles denote $Z T$ calculated with electron scattering on nanoinclusions and with bulk PbTe values of $κ_{ph}$ , and the solid line is for bulk PbTe. The inset in (a) shows the values of $V_{B}$ that maximize $Z T$ . In (b) the bottom inset shows the optimal values of $V_{B}$ that maximize $Z T$ (filled circles) and $V_{B}^{Pb}$ for Pb nanoinclusions. The top inset shows the calculated power factor.Reuse & Permissions

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