Studying field emission characteristics of point and wedge–shaped surface defects

Electric field distribution and field emission current over the surface of point (sphere-on-cone) and wedge-shaped defects on a plane substrate are studied. It is found emission current due to wedge-shaped defects is more sensitive to emitter-anode distance than in case of point conical defects. This property is consequence of greater emission area of wedge-shaped defects and has important practical applications. The computer model in Matlab of field electron emission from emitter-defects arrays is used. Electrostatic simulation of electron transport processes with PDE Toolbox finite element solutions is implemented. The effects of the variations in defects geometrical structure and parameters on its potential distribution, electric field, and emission current are discussed. It is found that with increase of distance from the tip or the edge of defect the current density falls very fast and greater part of emission current is in fact produced by a very small area near the emitter tip. The closer the emitter and collector are to each other, the less significant the inter-defect distance becomes. Field electron emitters are generally characterized by surface non-uniformity, because field emission is process in intensive electric field and surface protrusions or defects are necessary for field enhancement. For example classical field emitter tip from metal or semiconductor wire have different crystal faces on the surface with steps, kinks and edges. Its shape can be very different: ball-models for atomistic surface structure of monocrystal tip and analysis of crystal faces forms and sizes were presented in [1]. Field emitters array can also be imaged as regular grid of surface defects or protrusions on substrate plane. Emitter in unit cell of the array might have sphere-on-cone shape (like Spindt-cathodes [2]) or edged straight line shape (or circular/cylinder edge shape [3]) and etc. In this paper we study two types of multiemitter systems – models for point and wedge-shaped defects on the surface: ones with conic and straight-edge emitters. Employing the methods of mathematical and computer modeling, we analyze interactions between defects in the array and the influence its geometrical features have on the emission current value. We take in account such geometrical properties as distance between emitter and collector d, curvature radius of emitter surface r, distance between the emitters b, as shown on figure 1 and figure 2. SPbOPEN2014 IOP Publishing Journal of Physics: Conference Series 541 (2014) 012009 doi:10.1088/1742-6596/541/1/012009 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 Figure 1. (a) SEM image of nanostructure of emitter surface relief [3]. (b) Results of Sobel-mask filtering, defects with spherical tops are shown. The relation between field emission current density and strength of the field that generates the current is calculated within the framework of Fawler-Nordheim theory. Multiemitter system is regarded as a periodically structured emitter array. The tip of conic emitter is approximated with a spherical surface, and the edge of a straight-blade one with a orthogonal cylinder surface (figure 2). Figure 2. Scheme of conical and edge-shaped emitters. The cells for modelling with conditions of symmetry (periodicity) on the side surfaces are shown. Program complex [4] is used for computer simulation. Non-uniformity of physical conditions on defects surface (variance of work function etc.) is accounted for with a local field enhancing coefficient [1]. The influence of the space charge is neglected and electrostatic approximation is used. The results of electrostatic field calculation are shown on figure 3. SPbOPEN2014 IOP Publishing Journal of Physics: Conference Series 541 (2014) 012009 doi:10.1088/1742-6596/541/1/012009