scholarly journals Markov jump transport of trapped charge in thin dielectric layers

2020 ◽  
Author(s):  
Andrey Pil'nik ◽  
Andrey Chernov ◽  
Damir Islamov
Keyword(s):  
Charge Transport ◽  
Theoretical Models ◽  
Thin Layers ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Dielectric Layers ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

Abstract In this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley-Read-Hall-like transport equations, which describe 1D transport through dielectric layers, might incorrectly describe the charge flow through the ultra-thin layers with a countable number of traps, taking into account injection-from and extraction-to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for dynamics of system evolution for special cases. These solutions can be used to test the code and for studying of charge transport properties of thin dielectric films.

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

On the Interaction at Anti-Flat Deformation of Stress Concentrators of the Type of Cracks and Stringers with Regard to the Layer Manufactured from Miscellaneous Materials

2019 ◽  
Vol 828 ◽  
pp. 81-88
Author(s):  
Nune Grigoryan ◽  
Mher Mkrtchyan
Keyword(s):  
Integral Transform ◽  
Composite Layer ◽  
Singular Integral Equations ◽  
Original System ◽  
Fourier Integral ◽  
Quadrature Formulas ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Tangential Forces

In this paper, we consider the problem of determining the basic characteristics of the stress state of a composite in the form of a piecewise homogeneous elastic layer reinforced along its extreme edges by stringers of finite lengths and containing a collinear system of an arbitrary number of cracks at the junction line of heterogeneous materials. It is assumed that stringers along their longitudinal edges are loaded with tangential forces, and along their vertical edges - with horizontal concentrated forces. In addition, the cracks are laden with distributed tangential forces of different intensities. The case is also considered when the lower edge of the composite layer is free from the stringer and rigidly clamped. It is believed that under the action of these loads, the composite layer in the direction of one of the coordinate axes is in conditions of anti-flat deformation (longitudinal shift). Using the Fourier integral transform, the solution of the problem is reduced to solving a system of singular integral equations (SIE) of three equations. The solution of this system is obtained by a well-known numerical-analytical method for solving the SIE using Gauss quadrature formulas by the use of the Chebyshev nodes. As a result, the solution of the original system of SIE is reduced to the solution of the system of systems of linear algebraic equations (SLAE). Various special cases are considered, when the defining SIE and the SLAE of the task are greatly simplified, which will make it possible to carry out a detailed numerical analysis and identify patterns of change in the characteristics of the tasks.

UV-Laser Ablation of HFO2 Dielectric Layers on SiO2 for Mask Preparation

1998 ◽  
Vol 526 ◽  
Author(s):  
K. Rubahn ◽  
J. Ihlemann
Keyword(s):  
Single Pulse ◽  
Fused Silica ◽  
Ablation Depth ◽  
Dielectric Films ◽  
Uv Laser ◽  
Substrate Roughness ◽  
Multilayer Systems ◽  
Dielectric Layers ◽  
Dielectric Mirrors ◽  
Thin Dielectric Films

AbstractThe thickness dependence of ablation rates following 193nm UV-laser irradiation of single HfO2 layers on fused silica (SiO2) is investigated using scanning electron microscopy and stylus profilometry to determine quantitatively substrate roughness and ablation depth. Thin dielectric films of the investigated kind build up dielectric mirrors, which are patterned to prepare masks for excimer-laser micromachining. The single pulse ablation thresholds are found to increase approximately linearly with increasing HfO2 thickness and consequently the threshold fluence for obtaining clean ablation of the total HfO2 coating increases exponentially with its thickness. At elevated fluences both ablation of the coating as well as ablation of the substrate are observed. The results provide important quantitative values for a future treatment of more complicated multilayer systems of HfO2/SiO2 bilayers.

Vibration of a Cracked Cylindrical Shell of Rectangular Planform

1985 ◽  
Vol 52 (4) ◽  
pp. 927-932
Author(s):  
R. Solecki ◽  
F. Forouhar
Keyword(s):  
Cylindrical Shell ◽  
Fourier Transformation ◽  
Circular Cylindrical Shell ◽  
Homogeneous System ◽  
Algebraic Equations ◽  
Discontinuous Functions ◽  
Harmonic Vibrations ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Gauss Theorem

Harmonic vibrations of a circular, cylindrical shell of rectangular planform and with an arbitrarily located crack, are investigated. The problem is described by Donnell’s equations and solved using triple finite Fourier transformation of discontinuous functions. The unknowns of the problem are the discontinuities of the slope and of three displacement components across the crack. These last quantities are replaced, using constitutive equations, by curvatures and strain in order to improve convergence and to represent explicitly the singularities at the tips. The formulas for differentiation of discontinuous functions are derived using Green-Gauss theorem. Application of the boundary conditions at the crack leads to a homogeneous system of linear algebraic equations. The frequencies are obtained from the characteristic equation resulting from this system. Numerical results for special cases are provided.

XII.—Studies in Practical Mathematics. I. The Evaluation, with Applications, of a Certain Triple Product Matrix

1938 ◽  
Vol 57 ◽  
pp. 172-181 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Quadratic Form ◽  
Matrix Multiplication ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Product Matrix ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
The Matrix ◽  
Practical Mathematics ◽  
General Operation

The solution of simultaneous linear algebraic equations, the evaluation of the adjugate or the reciprocal of a given square matrix, and the evaluation of the bilinear or quadratic form reciprocal to a given form, are all special cases of a certain general operation, namely the evaluation of a matrix product H′A-1K, where A is square and non-singular, that is, the determinant | A | is not zero. (Matrix multiplication is like determinant multiplication, but exclusively row-into-column. The matrix H′ is obtained from H by transposition, that is, by changing rows into columns.) The matrices H′ and K may be rectangular. If A is singular, the reciprocal A-1 does not exist; and in such a case the product H′(adj A) K may be required. Arithmetically, the only difference in the computation of H′A-1K and H(adj A) K is that in the latter case a final division of all elements by | A | is not performed.

Diffraction of light by ultrasonic waves I. General theory

1953 ◽  
Vol 220 (1142) ◽  
pp. 356-368 ◽  
Keyword(s):  
Integral Equation ◽  
Trial Function ◽  
Plane Waves ◽  
Ultrasonic Waves ◽  
Algebraic Equations ◽  
Approximate Methods ◽  
Trial Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Diffraction Of Light

In this paper, following Darwin's (1924) treatment of the reflexion and refraction of light on a transparent homogeneous medium, the problem of the diffraction of light by ultrasonic waves is formulated in terms of the scattering of electromagnetic waves by a periodically perturbed medium. This leads to an integral equation which has been solved for E-polarization with the help of a trial solution for the electric disturbance in the medium in the form of a double infinity of plane waves. The condition that the trial function be a solution of the integral equation leads to ( a ) the frequencies and the directions of the diffracted spectra and ( b ) three infinite sets of linear algebraic equations for the amplitudes N lm and other unknowns occurring in the trial solution. The expressions for the intensities of the diffracted spectra involve the various unknowns of the trial function and can be immediately written down once these unknowns have been determined from the equations. The solution of the equations ( b ) by approximate methods, calculation of intensities for special cases and comparison of various theoretical results with available experimental data are dealt with in part II which follows. A summary of the main results obtained there is given in the Introduction (§1) of the present paper.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

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