Material considerations for thermoelectric enhancement via modulation doping
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Material considerations for thermoelectric enhancement via modulation doping Matt Beekman1 · Grigory Heaton1 · Thomas M. Linker1 · David C. Johnson2 Received: 9 February 2020 / Accepted: 26 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Modulation doping has recently emerged as a method for improving the thermoelectric figure of merit using composite materials. By spatially decoupling charge carriers from their dopant impurities, the average carrier mobility can be improved by reducing the influence of ionized impurity scattering. However, as we show in the present work using a simple parabolic band model and effective medium approach, enhancement in such composites is effective only if ionized impurities dominate the scattering of the charge carriers, which is often not the case in many materials. For example, the enhancement is more significant at lower temperatures (T 𝜎B , the enhanced Seff results in an overall enhanced power factor, and ZTeff is also enhanced above the best possible value for the uniformly doped material (dotted line in Fig. 3d) for f greater than only ≈ 2%. A large enhancement in ZTeff of nearly a factor of 2 is obtained when f is just under 20%. Of course, determination of the enhancement that might be expected in a real material would require solution of the Poisson equation and optimization of the layer thicknesses, which is beyond the scope of the present work. We next evaluate the TE properties of the composite at higher temperature. Figure 4 shows the TE properties of the individual components and the composite at 300 K, calculated as a function of the electron transfer fraction f for a donor impurity density of ND = 2 × 1018 cm−3 in region A (the optimal carrier density for both constituents is higher at high T). The qualitative behaviors of σ and S are similar to the behaviors at 100 K, but the level of enhancement in the power factor and ZT is lessened. For f > 15%, there is a modest enhancement in the power factor and ZT above the maximum possible values in the uniformly doped material, but the level of enhancement is significantly lower than that at 100 K and enhancement also requires higher f. This can be attributed to two compounding effects: (i) the ionized impurity scattering relaxation time (Eq. 8) is only weakly dependent on temperature, tending to produce a mobility
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Fig. 3 Calculated a electrical conductivity, b Seebeck coefficient, c power factor, and d dimensionless figure of merit at 100 K as a function of electron transfer from region A to region B, for the doped region A (dashed curve), undoped region B (dashed-dotted curve), and overall composite (solid curve). The parameters in Table 1 and ND = 9 × 1017 cm−3 were used in the calculation. The horizontal dotted line in (d) indicates the maximum possible (optimized) ZT for the uniformly doped material with the same material parameters (peak value in Fig. 2)
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Fig. 4 Calculated a electrical conductivity, b Seebeck coefficient, c power factor,
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