Employing non-equilibrium quantum transport models, we investigate the
details and operating conditions of nano-structured Peltier coolers embedded
with an energy filtering barrier. Our investigations point out non-trivial
aspects of Peltier cooling which include an inevitable trade-off between the
cooling power and the coefficient of performance, the coefficient of
performance being high at a low voltage bias and subsequently deteriorating
with increasing voltage bias. We point out that there is an optimum energy
barrier height for nanowire Peltier coolers at which the cooling performance is
optimized. However, for bulk Peltier coolers, the cooling performance is
enhanced with the height of the energy filtering barrier. Exploring further, we
point out that a degradation in cooling performance with respect to bulk is
inevitable as a single moded nanowire transitions to a multi-moded one. The
results discussed here can provide theoretical insights for optimal design of
nano Peltier coolers