A non-degenerate, -type semiconductor thermoelectric at has an effective…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Electronic transport in solids · Semiconductor physics and devices

Solid State Physics, Ch Two currents, two forces: Wiedemann-Franz and thermoelectricity

Problem

A non-degenerate, nn-type semiconductor thermoelectric at T=300 KT=300\,\mathrm{K} has an effective conduction-band density parameter Nc=2.8×1019 cm−3N_c=2.8\times10^{19}\,\mathrm{cm^{-3}}, an electron mobility μn=100 cm2 V−1s−1\mu_n=100\,\mathrm{cm^2\,V^{-1}s^{-1}} (1.0×10−2 m2 V−1s−11.0\times10^{-2}\,\mathrm{m^2\,V^{-1}s^{-1}}), a scattering exponent r=−12r=-\tfrac12 (acoustic-phonon scattering), and a lattice thermal conductivity κlat=1.5 W m−1K−1\kappa_{\rm lat}=1.5\,\mathrm{W\,m^{-1}K^{-1}} fixed by the phonon spectrum, independent of the doping. For a non-degenerate band the Seebeck coefficient is S=−kBe[ln⁡ ⁣(Ncn)+r+52],S=-\frac{k_B}{e}\left[\ln\!\left(\frac{N_c}{n}\right)+r+\frac52\right], the conductivity is σ=neμn\sigma=ne\mu_n, and the electronic thermal conductivity is κel=LσT\kappa_{\rm el}=L\sigma T with the non-degenerate Lorenz number L=(r+52)(kB/e)2=1.49×10−8 W Ω K−2L=(r+\tfrac52)(k_B/e)^2=1.49\times10^{-8}\,\mathrm{W\,\Omega\,K^{-2}}, the counterpart of L0L_0 for carriers on the Boltzmann tail. ((a)) Take electron density n=1.0×1018 cm−3n=1.0\times10^{18}\,\mathrm{cm^{-3}}. Compute SS, σ\sigma, κel\kappa_{\rm el}, the total κ=κel+κlat\kappa=\kappa_{\rm el}+\kappa_{\rm lat}, and ZTZT. ((b)) Repeat for n=1.0×1019 cm−3n=1.0\times10^{19}\,\mathrm{cm^{-3}}. ((c)) State which density gives the larger ZTZT, and explain the trend by identifying which of SS, σ\sigma, κel\kappa_{\rm el} and κlat\kappa_{\rm lat} change with nn and which does not.

Browse the problem library