Optimized Peltier cooling via an array of quantum dots with stair-like ground-state energy configuration

Highlights: • Peltier refrigeration can be optimized using an array of n quantum dots. • The optimal number depends on the scattering energy and kT. • When $\hslash \omega <kT$, the maximal cooling power is almost independent of ℏω. • When $\hslash \omega >kT$, the optimal value of n reaches the limiting value $n=2$. • Elastic scattering deteriorates the performance of the refrigerator. - Abstract: With the advancement in fabrication and scaling technology, the rising temperature in nano devices has attracted special attention towards thermoelectric or Peltier cooling. In this paper, I propose optimum Peltier cooling by employing an array of connected quantum dots with stair-like ground-state eigen energy configuration. The difference in ground state eigen energy between two adjacent quantum dots in the stair-like configuration is chosen to be identical with the optical phonon energy for efficient absorption of lattice heat. I show that in the proposed configuration, for a given optical phonon energy, one can optimize the cooling power by tuning the number of stages in the array of quantum dots. A further analysis demonstrates that the maximum cooling power at a given potential bias under optimal conditions does not depend strongly on the optical phonon energy or the number of stages at which the maximum cooling power is achieved, provided that the optical phonon energy is less than kT. The proposed concept can also be applied to $2-D$ or bulk resonant tunnel and superlattice structures with stair-like resonant energy configuration.