COMPUTER SIMULATION OF SPACE CHARGE EFFECTS IN ELECTRON GUNS FOR E-BEAM TESTING

Abstract

The development of electron gun simulation is required to understand the mechanism of various existing sources as well as to exploit new ones. The basic difficulty of the numerical simulation of electron sources comes from the space charge problem. Several kinds of electron guns used in the Scanning Electron Microscope are outlined, and the numerical approach for the space charge effect computation in electron guns is given. An investigation into the numerical accuracy, stability of convergence and computation speed of simulation is analyzed with a simple test example. The potential with space charge using a 50 node grid is computed to an accuracy of 2.5%.

A novel two dimensional simulation program is presented, which is based on a quasi-conformal finite element method developed by Dr. Anjam Khursheed. A conformal mesh is generated by using the equipotential and flux lines of a trial field solution in two dimensional Cartesian coordinates. The potential on the top boundary of a near cathode conformal mesh region can be found by interpolation from the background quasi-conformal mesh, and the space charge calculation can be carried out on the conformal mesh.

A parabolic capacitor structure for the gun tip has been analyzed and used in the simulation of a conventional low voltage LaB6 gun, neglecting the thermal effect. The potential distribution and current density distribution as well as the trajectories are all presented. The beam crossover computation is also discussed.

The effect of the finite energy spectrum for electrons emitted from the cathode is investigated. An iterative method is applied to calculate the voltage barrier and the anode current density. The sensitivity of the output results to the input cathode current density is studied. The concept of an equivalent velocity is introduced to improve the speed of simulation. The accuracy, speed and convergence property of the program is presented for a cylindrical capacitor structure.