N. V. Egorov

Surface Reconstruction of a Field Electron Emitter

The surface and emission images of a metal field’s electron cathode in the form of a tip are simulated. The surface structure is calculated in the thin-shell and broken-bond (local-environment) models for the perfect crystal lattice. The cathode shape and macroscopic electric field are represented by the sphere-on-cone model. The amplification of a local electric field is the adjustable parameter of the model. The method of determination of the emitter tip’s crystal faces based on the analysis of the surface atoms’ environment geometry is proposed. It is shown that it is enough to restrict the consideration of geometric environment by the fifth order of the nearest neighbors for the emitter radius of 100–1000 lattice parameters (31.6–316 nm for the tungsten). The crystallographic model of work function anisotropy in the broken-bond approach is used: the local work function’s value is set in accordance with Miller indices of the face containing this area. The model adequacy is corroborated by the comparison of current-voltage characteristics and emission images with the data of the natural experiment.

Calculation of a triode field-emission system with a modulator

The electrostatic potential of a triode field-emission system with a modulator that represents a circular diaphragm is calculated. A tip field-emission cathode serves as an emitter. The inner part of the system under study is filled with two insulators. In the calculation of the potential distribution, a real field-emission cathode is changed by a virtual cathode whose surface coincides with an equipotential surface, so that the effect of the cathode on the distribution of the electrostatic potential is simulated as the effect of a finite charged wire that is located at the axis of the system. The separation of variables is used to solve the problem. The potential is represented as an expansion in terms of eigenfunctions, and the expansion coefficients are found from the solution to a system of linear algebraic equations.

Calculation of the electrostatic potential of the diode system based on a sharp-edged field cathode

A mathematical model of a diode system based on a sharp-edged field cathode is presented. The surface of the sharp-edged cathode is simulated by two infinitely thin spherical segments, while the anode is modeled by a single infinitely thin spherical segment. The region occupied by the cathode is a lens (lune-shaped region). The problem of the electrostatic potential distribution in the entire domain occupied by the system is solved.

Simulation of specimen structure in atom probe tomography and field electron microscopy

This study presents a mathematical model of a crystal structure of emitter that is the study object of atom probe tomography, field emission electron/ion microscopy and field desorption microscopy. Modern simultaneous use of these methods and its advantages over separate microscopy studies (other than the obvious utility of similarity of samples and mechanisms of constructing the magnified image) is discussed. Intensity of field desorption grows significantly with increase of the surface work function. We present multi-scale modelling of the sample structure: at micro-scale it is an approximation of emitter shape, on meso-scale its construction of crystallographic faces for application of a semi-empirical regression model of work function distribution, on the nano-scale its calculation of surface atom coordinates that serve as base data for all the above mentioned levels of detail.

Mathematical modeling of a diode system based on a field emitter

A mathematical model of a diode system based on a field emitter is considered. The field emitter is modeled in the following way: the tip is a conducting sphere; the “body” is a solid dielectric with a spindle surface of revolution. The anode is a part of the spherical surface and the substrate of the emitter is a spherical surface or a plane. The influence of a space charge is not taken into account. To find the electrostatic potential distribution, the methods of separation of variables and paired equations are used. The problem of finding unknown coefficients in the eigenfunction expansion of the potential is reduced to the solution of the system of equations, which includes linear algebraic equations and the Fredholm equation of the second kind. Thus, the computational problem of the distribution of electrostatic potential in the entire domain of the investigated system is solved.

Field Emission spectroscopy of silicon carbide: Natural modelling

This article discusses the problem of measurement of Field Emission Energy Distribution (FEED) from silicon carbide by the retarding potential method. A description of an natural experiment setting is presented as well as a model of its electrophysical system of field emission current differentiation by modulated retarding potential. It discusses problems of implementations of the measurement on a field emission array (FEA) 6H-SiC.

Mathematical simulation of a diode system with a cylindrical field-emission tip

A diode system with a cylindrical field-emission tip is demonstrated. The cathode on a plane substrate represents a cylinder with a rounded tip, and the anode represents a plane. The effect of the space charge of the beam is disregarded. The geometrical sizes of the diode system serve as parameters of the problem. The distribution of the electrostatic potential over the system is determined using the method of overlapped domains that is based on separation of variables.

Calculation of the electrostatic field of a system of spherical segments

The electrostatic potential distribution is determined for a system of axisymmetric electrodes in the form of nonconcentric spherical segments.

Field emission spectroscopy of SiC

Experimental set up for the natural experiment and measurement model are presented to obtain the feld emission energy distribution spectrum out of silicon carbide in case of the macro-sample having a macroscopic shape of a tip. The prototype of feld emission 6H - SiC monolithic cathode is proposed for spectroscopy measurements, and characterised by current-voltage dependence at macroscale interelectrode distance.

Mathematical simulation of a diode system with a field-emission matrix cathode

A mathematical model of a diode system based on a matrix field-emission cathode with an edge structure of vertical-type emitters is constructed. We calculate the macroscale electrostatic field distribution for the planar and spherical configurations of the anode. In the microscale, the field distribution at the emitter edge is determined for various versions of the arrangement of the matrix cathode relative to the edge.