Analysis of the emission performance of field emitter with Laplace interpolation method

Abstract

It is well-known that the electric field changes largely around the tip of the field emitter. Since the emission current density is very sensitive to the electric field, it is important to analyse the distribution of electric field and emission current density across the emitter tip accurately. Usually, the interpolation method is used to estimate the electric field at arbitrary point around the tip. However, some errors may be introduced in the interpolation of the electric field. These errors cause a large deviation in the calculation of current density. In order to analyse the emission performance of the field emitter precisely, this paper proposes a new interpolation method to estimate the electric field at any point. In this method, the basis functions satisfy the Laplace equation automatically. Therefore, it can be used to calculate the electric field and emission current density of the field emitter accurately. A spherical capacity and a diode emitter are analysed with the Laplace interpolation and Lagrange interpolation, respectively. As shown in the results, the electric field and emission current density calculated with Laplace interpolation are more accurate than the one calculated with Lagrange interpolation.