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“…To evaluate the various derivatives, we rewrite the expressions forσ , η and e λ in terms of polylogs, as the Fermi integrals are a subset of the polylogs [14,29]:…”

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The polylogarithm and the Lambert W functions in thermoelectrics

2011

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In this work, we determine the conditions for the extremum of the figure of merit 2 θ , in a degenerate semiconductor for thermoelectric (TE) applications. We study the variation of the function 2 θ with respect to the reduced chemical potential * µ using relations involving polylogarithms of both integral and non-integral orders. We present the relevant equations for the thermopower, thermal, and electrical conductivities that result in optimizing  2 and obtaining the extremum equations. We discuss the different cases that arise for various values of r, which depends on the type of carrier scattering mechanism present in the semiconductor. We also present the important extremum conditions for  2 obtained by extremizing the TE power factor and the thermal conductivity separately. In this case, simple functional equations, which lead to solutions in terms of the Lambert W function, result. We also present some solutions for the zeros of the polylogarithms. Our analysis allows for the possibility of considering the reduced chemical potential and the index r of the polylogarithm as complex variables.

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Analytical treatment of Trivich–Flinn and Shockley–Queisser photovoltaic efficiency limits using polylogarithms

Green

2011

Progress in Photovoltaics

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Solutions for the Trivich–Flinn and Shockley–Queisser formulations of the limiting efficiency of photovoltaic conversion are derived in terms of polylogarithms. Earlier Trivich–Flinn limits are shown to be zero temperature limits of the Shockley–Queisser approach. The limiting efficiency of an infinite stack of tandem cells was also investigated with an analytically based solution derived, the limit on photovoltaic conversion for a time‐symmetric system, which is compared to the time‐asymmetric limit. Copyright © 2011 John Wiley & Sons, Ltd.

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Cited by 18 publications

References 7 publications

A unified look at the use of successive differentiation and integration in MOSFET model parameter extraction

A unified look at the use of successive differentiation and integration in MOSFET model parameter extraction

The polylogarithm and the Lambert W functions in thermoelectrics

Analytical treatment of Trivich–Flinn and Shockley–Queisser photovoltaic efficiency limits using polylogarithms

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