Modeling of field emission devices using a conformal finite difference time domain particle-in-cell method

Abstract

This work introduces a conformal finite difference time domain (CFDTD) particle-in-cell (PIC) method to accurately and efficiently study field emission devices such as field emission diodes and triodes [1]. The CFDTD method is based on the Dey-Mittra algorithm or cut-cell algorithm, as implemented in the VORPAL code [2]. Locally distorted cells with edges tangential to the metallic surface are used. The fields in these distorted cells are computed using a modification of the conventional FDTD update equations. For each cell partially within the region of interest, the magnetic field is assumed to be located at the center of that undistorted Cartesian cell and constant over the area of the distorted cell. The electric fields are assumed to have a constant value along the edge of a cell that resides within the cavity and are zero along the metallic surface [3,4]. It is demonstrated that the CFDTD method approximately exhibits a second order accuracy, while the conventional FDTD is just a first order accuracy. Complicated electromagnetic structures can be well described by the cut-cells in the CFDTD method. Field emission of electrons from a cathode surface is based on the Fowler-Nordheim equation. However, the emission behavior is strongly dependent on the surface electric fields. The conventional modeling of field emission tips with a FDTD PIC method may predict wrong field enhancements due to the meshes cannot conform with the tip geometry well, therefore causing incorrect amount of electron emission.