Numerical simulation of the tunneling current and ballistic electron effects in field emission devices

Using a two-dimensional model, we have considered the effects of spatially changing fields and potentials, stochastic electron emission, and ballistic electron motion on the anode current and on the width of the electron beam in field emission displays. We have solved the electrostatic problem using the boundary element method. Our electron emission model evaluates the current density at the cathode surface from the tunneling transmission coefficient, which is calculated from the solution of the one-dimensional Schrödinger equation using a potential barrier which includes the effect of image charges and nonuniform electric field. The current density is used to calculate the rate of electron emission for each segment of the emitter’s surface. The emission time is assumed to follow a Poisson distribution. The electron’s velocity magnitude and angle with the normal to the surface are also stochastically generated following the probability distribution of field emitted electrons. Ballistic transport is used to propagate electrons through the device. For very sharp tips the electric field changes from its surface value over a very short distance away from the surface, which can be comparable to the tunneling distance. We found that the resulting current density is considerably lower for the calculated barrier profile than for the triangular one, especially at low values of the electric field. We have also shown that the effect of the lateral kinetic energy and emission angle distribution on the electron beam width at the anode is negligible for sharp emitters, where the angular spread is dominated by the curvature of the emitting surface.