Low temperature refrigeration by using thermal-field electron emission in a coaxial cylindrical diode

This paper explores possibility of refrigeration by using thermal-field emission of electrons in a coaxial cylindrical diode with a nanometer scale inner electrode (or cathode). Our calculation shows that it is possible to provide cooling at temperatures down to 200 K if the work function of the cathode is about 1 eV. The limitation on using a low work function cathode can be improved by applying an external axial magnetic field to create an additional potential barrier near the anode, more efficiently restricting the emission of low energy electrons (below the Fermi energy level). Because of this extra filtering process, emitters of arbitrary work functions can be used to provide an improved cooling capability from 300 to 10 K. The optimal conditions to maximize cooling power density are determined both numerically and analytically. The space charge effects of the emitted electrons in the gap are included self-consistently.