  We propose a thermoelectric cooling device based on an atomic-sized junction.
Using first-principles approaches, we investigate the working conditions and
the coefficient of performance (COP) of an atomic-scale electronic refrigerator
where the effects of phonon's thermal current and local heating are included.
It is observed that the functioning of the thermoelectric nano-refrigerator is
restricted to a narrow range of driving voltages. Compared with the bulk
thermoelectric system with the overwhelmingly irreversible Joule heating, the
4-Al atomic refrigerator has a higher efficiency than a bulk thermoelectric
refrigerator with the same $ZT$ due to suppressed local heating via the
quasi-ballistic electron transport and small driving voltages. Quantum nature
due to the size minimization offered by atomic-level control of properties
facilitates electron cooling beyond the expectation of the conventional
thermoelectric device theory.
