Thermomagnetic Figure of Merit: Bismuth

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Abstract
The asymptotic value of the isothermal thermomagnetic figure of merit is obtained for a two‐band multivalleyed semiconductor or semimetal where the concentration of holes and electrons is equal. The bismuth band structure is used as a specific model. It is shown that at strong magnetic fields the isothermal Nernst coefficient Njii is independent of the magnetic field Bk. The isothermal electrical resistivity is proportional to (Njii)Bk2 and the isothermal thermal conductivity is equal to the sum of the lattice thermal conductivity κii0 and the strong field ambipolar contribution (κiii)amb, where (κiii)amb is proportional to Njii. The isothermal Ettingshausen coefficient Ejii is also obtained and it is shown that κiiiEiji = −NjiiT. The largest figure of merit is obtained when the electron and hole mobilities are large and approximately equal, when the lattice thermal conductivity is small, and when the Fermi energy is approximately equal to +kT.