Konstantin Nikiforov

Mathematical model and software complex for computer simulation of field emission electron sources

The software complex developed in MATLAB allows modelling of function of diode and triode structures based on field emission electron sources with complex sub-micron geometry, their volt-ampere characteristics, calculating distribution of electric field for educational and research needs. The goal of this paper is describing the physical-mathematical model, calculation methods and algorithms the software complex is based on, demonstrating the principles of its function and showing results of its work. For getting to know the complex, a demo version with graphical user interface is presented.

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.

Studying Informational Sensitivity of Computer Algorithms

This study is focused on informational sensitivity of an algorithm, defined as impact of different fixed-length inputs on the value of the algorithm’s complexity function. In addition to classic worst-case complexity this characteristic provides a supplementary tool for more detailed and more “real world” approach to studying algorithms. Statistical measure of informational sensitivity is calculated based on statistical analysis of results obtained from multiple runs of the same program implementation of the algorithm in question with random inputs. This theory is illustrated by an example of algorithm that solves the travelling salesman problem by branch and bound method using the concorde package. For a sample of different input graphs with 1,000÷10,000 vertices the statistical measurements of informational sensitivity were found and confidence ranges for complexity function were constructed. It was proven that this particular algorithm is highly sensitive to fixed-size inputs by complexity function.

Informational sensitivity as algorithm’s complexity function characteristic

The main goal of this study is to present technique realized with the numeric experiments, that can come to the aid in algorithm practical characterization. Input data of both varied size and varied values are considered. Informational sensitivity and confidence complexity are calculated.

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.

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.

Modelling of field desorption of monocrystal nanotip

Mathematical and computer model of field desorption process from metal nanocrystal tip is proposed. The radius of curvature on the top of the emitter is about 50 lattice parameters. The model includes initial calculation of intersection between the crystal lattice and emitter shape for bcc and fcc crystal structures. Arbitrary axisymmetric shapes (figures of rotation) can be used for the emitter model. The algorithm for allocation of atoms being desorbed at given time step is based on an analysis of geometric environment with specified local electric field. Polyhedron nanostructured shape of emitter is obtained as result of evaporation. Computer program realization (Matlab stand alone application) is presented.

Studying electric field enhancement factor of the nanostructured emission surface

Mathematical model of nanostructured field emission surface is proposed. In order to determine geometrical parameters of the surface structure digital processing of scanning electron microscopy images was used. Effective value of local electrical field enhancement factor is defined and calculated within the Fowler-Nordheim theory. It was found effective enhancement factor decreases as the applied electrical field increases for a fixed geometry.

Modelling of static mode characteristics of a thin-film vacuum nanotriode

Mathematical modelling and computer simulation is performed for analysis of nanotriode characteristics in static mode. It is shown nanotriode has differential parameters, which significantly (by orders) differ from those characteristics of usual vacuum lamps, which, together with miniaturization significantly expands the possibilities of their use.