Simulation of refrigeration by electron emission across nanometer-scale gaps

Abstract

Nanoscale transport processes offer new possibilities for direct refrigeration by electron emission at room temperature. Because the energy of emitted electrons may be higher or lower than that of their replacement counterparts, a heating or cooling effect, known as the Nottingham effect, can occur at the emitter. Prior theoretical studies indicate the possibility of very large $(>100\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2})$ cooling rates for emitters with low work functions; however, ultrasmall emission gaps are necessary to produce a device with a reasonably high coefficient of performance. In this regime of low work function and narrow emission gap, the traditional approach used to model electron transmission, which is based on the WKB approximation, is not suitable. In this study, a nonequilibrium Green's function method is employed to simulate the energy exchange attending electron emission for a range of emitter work functions and vacuum gap distances, yielding important insights into the thermodynamics associated with electron emission across ultrasmall vacuum gaps. Cooling density and efficiency curves depending on the vacuum gap distance and applied electric field are presented for flat-plate electrodes with work functions ranging from $0.4\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1.7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, and the results indicate that a practical emission device will require that the electrode work function and vacuum gap separation be reduced to approximately $0.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $20\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, respectively.