Dept. of Applied Physics
Oregon Graduate Center
The formation of high intensity electron beams by means of field emission is well known. Recently, high intensity ion beams have been formed by the application of electric fields of the order of 1 to 5V/Ã to liquid metal surfaces. Intensities of greater than 20ÂµA/sr have been reported for various metals such as gallium, indium, aluminum and bismuth. In focused beam applications such as scanning microscopy, inspection and testing, ion implantation and mask repair, the energy broadening and angular beam spreading are important parameters which impose fundamental limits on the focused spot size. These parameters depend on both deterministic and randomly produced forces, as well as upon the geometry of the beam. The purpose of this investigation is to study the energy exchange and trajectory perturbations attending the Coulomb interaction between a pair of electrons or ions which happen, by random fluctuation in the emission process to be in close proximity to each other. To this end, a numerical solution of the equations of motion of the particles moving in the external field of an emitter was performed. Two emitter field models were studied: the field produced by a spherical conductor, and the field produced by a conducting sphere whose center is at the apex of a conducting cone. By suitable choices of cone half-angle and sphere radius, an equipotential can be found whose shape closely approximates either a solid field electron emitter or the surface of a liquid metal ion source. Emitter radii r [subscript a] from 10[superscript 2] to 10[superscript 4] Ã and emitter field strengths F [subscript o] from 0.01 to 1.0 V/ Ã were examined. The influence of initial relative position, particle mass m and charge n on the energy and trajectory broadening was investigated for electrons and the ionic species Li+, Al+, Ga+, Bi+, Bi+2and Bi+3. Relationships between the time spacing between emission events and other parameters of interest were obtained. The sphere model was found to predict the following dependencies for the energy spread: ÎE oc l [superscript Â½] (mr [subscript a] F [subscript o]) [superscript Â¼] n [superscript Â¾] where l is the total current. The SOC model was found to predict the same current and mass dependencies, but a more complex relationship for emitter radius, field strength and charge was obtained. The functional relationship for these parameters depends on the emitter shape and on the current. A mechanism for the observed shift in peak energy was also found in these studies: the conversion of the initial Coulomb potential energy between the pair into kinetic energy. In summary, the pairwise Coulomb interaction is able to produce energy and angular beam spreading of the magnitude observed in electron and LMIS experimental data, even in the absence of beam crossovers.
Larson, Dale Lennart, "Pairwise coulomb interactions in diverging electron and ion beams" (1986). Scholar Archive. 218.