Low Temperature Cooling by Thermal-Field Electron Emission in a Crossed-Field Gap

A new method of refrigeration using thermal-field electron emission from nano-scale emitters of arbitrary work function in a vacuum crossed-field gap is proposed. A sample potential profile V vs. x for a sharp emitter (cathode) with effective radius R=10 nm, work function phi=4 eV, emitter-collector separation of L=20 mum, dc voltage applied at anode V_g=420 v is shown. For a given emitter (fixed work function and radius), and gap spacing, an optimal magnetic field B₀ can be determined for a given electric field F at various temperatures. To achieve maximum normalized cooling power density eta, a critical electric field F_c is extracted by varying F with its corresponding B₀. It is found that the optimal local cooling power density per emitter is about 600 kW/cm² at 300 K, 2.7 kW/cm² at 50 K and 20 W/cm² at 10 K. To measure the efficiency of the proposed cooling method, Peltier coefficient Pi and COP = Pi/V_g at various conditions are presented. Effects of space-charge effects are also discussed