Theory of field emission from dielectric coated surfaces

This paper presents an exact analytical theory for field emission from dielectric coated cathode surfaces, by solving the one-dimensional (1D) Schrodinger equation with a double-triangular potential barrier introduced by the coating. The effects of the cathode material (work function and Fermi energy), dielectric properties (dielectric constant, electron affinity, and thickness), applied dc field strength, and cathode temperature are analyzed in detail. For 1D flat cathode surfaces with coating, it is found that the emission current density can be larger than the uncoated case when the dielectric constant is smaller than a certain value epsilon(diel)th and the dielectric thickness is larger than the threshold value dth[nm] approximate to epsilon W-diel/eF with the dielectric constant epsilon(diel) < epsilon(th)(diel), where W is the work function of the cathode material, F the applied dc field, and e the elementary charge. Our quantum model is also compared with a modified Fowler-Nordheim equation for a double barrier, showing qualitatively good agreement. Our study provides insights for designing field emitters with higher efficiency and better stability.