A Further Comparison of Solid-State Thermionic and Thermoelectric Refrigeration
NEW SOUTH WALES UNIV SYDNEY (AUSTRALIA) SCHOOL OF PHYSICS
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We show that the expressions for current and heat current calculated via the non-linearized ballistic and diffusive transport formalisms reduce to the same form for solid-state devices one electron mean free path in length. The materials parameters for thermionic and thermoelectric devices are also shown to be equal, rather than differing by a multiplicative constant. We derive a simple transport equation that includes both ballistic and diffusive contributions to the current, and, as an example, use this to calculate the maximum temperature difference obtainable for a piece of Bi2Te3 as a function of its length, from less than an electron mean-free path to much greater than a mean-free path. Finally we briefly discuss similarities and differences between thermionic and thermoelectric devices in the regime where device length is of the order of a mean-free path length.
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