Analysis and simulation of refrigeration by electron emission

Phenomena based on nanoscale transport processes offer new possibilities for direct refrigeration by electron emission at room temperature. Electron emission is the process by which electrons escape from the surface of a conductor either by overcoming the potential barrier at the surface or by tunnelling through it. Because the average emitted electron energy may be higher or lower than the energy of the replacement electrons, a heating or cooling effect, known as the Nottingham effect, can occur at the emitter. Theoretical studies indicate the possibility of very large ( > 100 W/cm ) cooling rates for low work function emitters; however, nanometer range emission gaps are necessary to produce a device with a sufficiently high coefficient of performance to be useful in most practical cooling applications. In this regime of low work function and narrow emission gap, the traditional approach involving the WKB approximation to solve for electron transmission across the gap breaks down. In this study, a non-equilibrium Green´s function (NEGF) method is employed to model the energy exchange attending field emission for a range of emitter work functions and vacuum gap distances. Predictions indicate that a cooling density of approximately 100 W/cm² is possible for a 0.7 eV work function device emitting across a vacuum gap of approximately 5 nm. Operating under those conditions the cooling mechanism would require an emission current density of approximately 350 A/cm² and could have a coefficient of performance as high as 0.6