Statistical Coulomb interactions in cold field emitters

Statistical Coulomb interactions significantly reduce beam quality. For low voltage applications this may be the limiting factor, as the current in a probe of fixed size scales directly with the reduced brightness and the inverse square of the energy spread - I ∝ B_r/(ΔE.²). We examined statistical Coulomb effects in the gun region of cold field emitters. Two methods are presented a full N body simulation and an approximation called the extended 2 body method [1], adapted for regions of rapidly changing potential -the slice method [2]. We find that for the two tip sizes studied, 10nm and 50nm it is the reduction in brightness that is most serious, not ΔE, and in our set-up for both tips a field of around 4.25V/nm would maximize probe current.