High accuracy electron trajectory plotting through finite-element fields

Abstract

Computer programs have been written which plot high accuracy trajectory paths for electrons through irregular finite-element meshes. The technique used to achieve this revolves around mapping irregular regions onto a normalized plane, where the usual operations of locating the electron’s position and interpolating for field information is greatly simplified. Results show that if a method of bi-cubic Hermite interpolation is used to derive field information in the normalized plane, then the resulting error in an electron’s energy can typically be kept to below 20 mV, per 1 kV change in the electron’s kinetic energy, for electrostatic fields created on numerical meshes containing as few as 20 by 20 mesh lines.

The boundary fitted coordinate method to improve the numerical analysis of electron optical systems

“…Experience showed that if the number of meshes within each region are chosen correctly, the discontinuity of the fields at the region edges becomes negligible. The KEOS programs also use an inverse mapping routine to solve for the electron's position in normalized space before high order interpolation is performed (Khursheed and Dinnis 1989).…”

Simulation of geometric effects on double-gate field emission devices

“…Most investigators used Finite Element Method (FEM) 5 and Fowler-Nordheim (F-N) field emission model to simulate FED. However, the FEM consumes computation time of CPU.…”

Curvilinear finite element mesh generation for electron gun simulation

“…Although convenient for modelling the electrode boundary shapes, high-order interpolation on such meshes is a nontrivial problem and is the subject of research. Khursheed and Dinnis (1989) use high-order interpolation on irregular meshes for electron optics problems based upon a technique of applying spline/hermite cubic interpolation in normalised space for separate region blocks and then transforming back the normalised field derivatives to real space. Other attempts are made by Zhu and Munro (1989) who use bi-quartic interpolation and by Chmelik and Bath (1993), who employ a technique of polynomial expansion using basis functions which satisfy Laplace's equation.…”