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The Lorenz function: Its properties at optimum thermoelectric figure-of-merit
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Image of FIG. 1.
FIG. 1.

Lorenz function at different chemical potentials and carrier concentrations for a single parabolic band. Three limiting electron scattering mechanisms are shown: constant relaxation time (solid line), acoustic phonon (dashed line), and ionized impurity (dotted line). The figure-of-merit maximum (for κl  = 1 W/Km, a = −1) is indicated for the three scattering mechanisms: za , zi , and zc for acoustic phonon, ionized impurity, and constant relaxation time scattering, respectively. A mixture of acoustic phonon and ionized impurity scattering (dashed-dotted) is also included with the scattering prefactor defined as . The Sommerfeld limit is illustrated by the thin dashed line. The band onset is at 0 eV.

Image of FIG. 2.
FIG. 2.

Parametrized Lorenz values as a function of temperature. The filled square (Ca2.94Na0.06AlSb3 (Ref. 12), circle (Ce0.9CoFe3Sb12 (Ref. 14), and diamond (Ba8Ga15.5Ge30.5 (Ref. 13) show the Lorenz values calculated from experimental data and used to extract the electronic thermal conductivity at the given temperature. A temperature independent effective mass (a = m */me ) and acoustic phonon scattering are assumed. The carrier concentration nc (in units of 1021 cm−3) is listed, unless it has been extracted from temperature dependent data (see references).

Image of FIG. 3.
FIG. 3.

Lorenz values as a function of carrier concentrations, temperatures (no symbol 300 K, circles 500 K, and squares 800 K) and different scattering mechanisms (see caption of Fig. 1 for additional details).


Generic image for table
Table I.

The Lorenz value L and deviation ΔL = |LL 0|/L from the Sommerfeld value L 0 at the optimized figure-of-merit, zmT for different scattering mechanisms. The combined scattering is calculated for . Fitting coefficients Ai for Eq. (4) are also listed.

Generic image for table
Table II.

Temperature dependence of the Lorenz values (Lc , La and Li for constant, acoustic phonon and ionized impurity scattering, respectively) at zmT.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The Lorenz function: Its properties at optimum thermoelectric figure-of-merit