Field emitter electrostatics: Efficient improved simulation technique for highly precise calculation of field enhancement factors

When solving the Laplace equation numerically via computer simulation, in order to determine field values at surface of a shape model that represents emitter, it is necessary define simulation box and, within this, domain. This domain must not be so small boundaries have an undesirable influence on predicted values. A recent paper discussed situation cylindrically symmetric emitter models stand one pair well-separated parallel plates. geometry can simulated by using two-dimensional domains. For cylindrical box, formulae previously been presented minimum dimensions (MDD) (height and radius) needed evaluate apex value enhancement factor for this type model, with error-magnitude never larger than "tolerance" $\epsilon_{\rm{tol}}$. MDD criterion helps avoid inadvertent errors oversized The present article discusses (in greater depth previously) significant improvement method; has called Extrapolation Technique (MDDET). By carrying out two simulations relatively values, possible achieve level precision comparable results single much some simulations, could result savings memory requirements computing time. Following brief restatement original method, MDDET method illustrated applying hemiellipsoid-on-plane (HEP) hemisphere-on-cylindrical-post (HCP) models.