  Theoretical thermoelectric nanophysics models of low-dimensional electronic
heat engine and refrigerator devices, comprising two-dimensional hot and cold
reservoirs and an interconnecting filtered electron transport mechanism have
been established. The models were used to numerically simulate and evaluate the
thermoelectric performance and energy conversion efficiencies of these
low-dimensional devices, based on three different types of electron transport
momentum-dependent filters, referred to herein as: kx, ky and kr filters.
Assuming the Fermi-Dirac distribution of electrons, expressions for key
thermoelectric performance parameters were derived for the resonant transport
processes, in which the transmission of electrons has been approximated as a
Lorentzian resonance function. Optimizations were carried out and the
corresponding optimized design parameters have been determined, including but
not limited to the universal theoretical upper bound of the efficiency at
maximum power for heat engines, and the maximum coefficient of performance for
refrigerators. From the results, it was determined that kr filter delivers the
best thermoelectric performance, followed by the kx filter, and then the ky
filter. For refrigerators with any one of three filters, an optimum range for
the full width at half maximum of the transport resonance was found to be <2kT .
