4. Correlation between atomic structure and electrical properties of SiO2/SiC interface

Corresponding SiC-MOS capacitors were fabricated with the top aluminum electrode evaporated through a shadow mask after post oxidation annealing at 900ºC in argon ambient. Electrical properties, such as the interface state density (D) and fixed oxide charge density (Qx) of the SiO%SiC interface, were extracted from the high-frequency C-V characteristics of SiC capacitors. The Di, value was extracted with the Terman method, and the Q& was deduced from the flatband voltage (V%) shift that depends on the oxide thickness [21]. Figure 6 summarizes the changes in Da and V .. values. Since post-treatment, such as nitrogen and hydrogen incorporation, was not conducted in this experiment, high Dki over 1022 cm2eV14 was extracted at an energy level of E. - E = 0.36 eV. The high Di, value indicates degradation of the electrical properties of the SiO2/SiC interface, especially for thick thermal oxides. In addition, the positive V " shift in the C-V curves implies the existence of a negative fixed charge within the gate oxides. Assuming that the fixed charge is located at the SiO , SiC interface, the Q , of the SiC-MOS devices estimated from the thickness-V ,, slope was 2.3 x 1011 cm² for oxides thinner than 20 nm and 1.2 x 1012 cm² for thick oxides, meaning that the fixed charges also accumulated at the interface probably due to the suppressed outdiffusion of carbon impurities as dry oxidation progressed.

Figure 6. Summary of electrical properties of SiC-MOS capacitors fabricated by dry oxidation. Horizontal axis represents oxide thickness extracted from measured maximum capacitance. The Da and Q& were estimated using Terman method and Vt shift in C-V curves, respectively.

The correlation between electrical degradation and the atomic bonding feature of the SiO2/SiC interfaces raises the intrinsic problem of SiC oxidation. This is consistent with the common understanding of SiC-MOS devices, whereas our synchrotron XPS analysis excludes the several-nm-thick transition layer having excess carbon as a physical origin of the electrical degradation. Instead, we think that the electrical defects at the interface, such as Du and Q ~ are partly ascribed to the atomic scale roughness and imperfection identified with the intermediate oxide states in the Si 2p spectra. Moreover, considering the significant mobility reduction in SiC-MOSFETs, we should take into account the various forms of carbon interstitials forming local C-C dimers located on the SiC bulk side as a possible origin of the electrical defects [22]. Therefore, it is concluded that, for improving the performance of SiC- /! z
z !2%!/\_z3!z/\$+1( z"+1/z+1.z00!\*0%+\*z+\*z 0\$!z0+)%z+\* %\*#z"!01.!z\* z.¥ bon impurities within the channel region rather than the thick transition layer near the SiO2/SiC interface.

regardless of substrate orientation (8.7 eV) [24]. Considering the high oxidation temperatures +2!.zDCCC~z\* z(+3z+\*!\*0.0%+\*z+"z.!/% 1(z.+\*z%),1.%0%!/z3%0\$%\*z0\$!.)((5z#.+3\*z+4¥

Fundamental Aspects of Silicon Carbide Oxidation

http://dx.doi.org/10.5772/51514

243

/,!0.z - d^z\$!/!z.!/1(0/z !)+\*/0.0! z0\$0z0\$!z2(!\*!z\* z+""/!0z+"z0\$!z%2/SiC for the w"!z/1/0.0!z3/z+10zC^Gz!z(.#!.z0\$\*z0\$0z"+.z0\$!z%w"!^z \*z %0%+\*\_z3!z+\* 10! /%)%(.z/5\*\$.+0.+\*zz\*(5/%/z"+.z0\$%'z+4% !z/),(!/z0+z!4)%\*!z0\$!z!""!0/z+"z%\*0!."!

Figure 8. Measured and deconvoluted valence band spectra for SiO2/SiC structures formed on (0001) Si-face and

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(000-1) C-face 4H-SiC substrates.

ides on SiC [17], these results seem to be quite reasonable.

!"!0/z+\*z!\*!.#5z\* z)+ 1(0%+\*z/z0\$!z+4% !z0\$%'\*!//z%\*.!/! ^

Figure 7. O 1s energy loss spectra for thermal oxides on (0001) Si-face and (000-1) C-face 4H-SiC substrates. The onset G>L@==P;AL9LAGF >JGEL@=N9D=F;=LG;GF<M;LAGF:9F<K :9F<?9H;9F:=<=L=JEAF=< >JGEL@==F=J?QDGKK0@=N9s lence band maximum of SiC substrates and the oxides was determined by the valence spectra taken from SiO2/SiC structures and a reference SiC surface [24]. Figure 8 represents measured and deconvoluted valence spectra obtained after 3-nm oxidation of the Si-face and C-face substrates, in which the valence band maximum of the thermal oxides was estimated by subtracting the reference SiC spectra ( ) from the measured SiO2/SiC spectra ( ) both for the Si- and C-face substrates (see


Meet the editor

Dr. Ambrish Singh is a professor in the School of Materials Science and Engineering, Southwest Petroleum University, China. He leads the Corrosion Research Group with master's students, PhD students, and postdoctoral researchers. His research interests are mainly focused on corrosion, electrochemistry, green chemistry, quantum chemistry, smart coatings, polymers, nanomaterials, composites, and petroleum engineering. He was

invited to the Indian Science Congress 2019 as the only foreign speaker on chemical sciences. Dr. Singh received the prestigious Sichuan 1000 Talent Award from the Sichuan government, China, for his outstanding research contributions as a faculty, and the President's Award for exceptional postdoctoral research work. He also received the Young Scientist Award from UPCST, Lucknow, India. He has published more than 100 SCI peer-reviewed research papers in high-impact journals and acts as a reviewer for more than 40 high-impact journals and editor for a small number of journals. He is included as board member in several journals due to his contributions to the field of corrosion. Dr. Singh has been invited to present his work in several national and international conferences, seminars, and workshops. He has drafted five patents and filed two patents based on his innovative findings in China. He has finished several state and provincial projects in China and India. He is the member of the National Association for Corrosion Engineers, Houston, USA, the Society of Petroleum Engineers, and the American Chemical Society. He collaborates with other corrosion groups in Germany, South Korea, the United Kingdom, Portugal, Italy, and South Africa.

Contents

**Section 1**

Corrosion Inhibitors *by Geethamani Palanisamy*

Protection of Metals in Acid Cleaning Process *by Perumal Kannan and Anitha Varghese*

for Mild Steel Using Factorial Design Method

*Seteno K. Ntwampe and Seide M. Akoro*

*and Suleiman B. Hassan*

Applying EDM

**Section 2**

Green Corrosion Inhibitors

**Preface III**

Inhibitors **1**

**Chapter 1 3**

**Chapter 2 27**

**Chapter 3 41**

**Chapter 4 59**

**Chapter 5 77**

**Chapter 6 95**

Theoretical Studies **119**

**Chapter 7 121**

Formation of Anticorrosive Structures and Thin Films on Metal Surfaces by

Investigation of Corrosion Inhibitors Adsorption on Metals Using Density

*by Ambrish Singh, Kashif R. Ansari, Mumtaz A. Quraishi and Yuanhua Lin*

Structural Effect in Ionic Liquids Is the Vital Role to Enhance the Corrosion

Exploring *Musa paradisiaca* Peel Extract as a Green Corrosion Inhibitor

Green Corrosion Inhibitory Potentials of Cassava Plant (*Manihot esculenta* Crantz) Extract Nanoparticles (CPENPs) in Coatings for Oil and Gas Pipeline

*by Funsho O. Kolawole, Shola K. Kolawole, Oluwamayowa M. Olugbemi*

*by Lipiar K. M. O. Goni and Mohammad A. J. Mazumder*

Functional Theory and Molecular Dynamics Simulation

*by Pavel Topala, Alexandr Ojegov and Vitalie Besliu*

*by Olusola S. Amodu, Moradeyo O. Odunlami, Joseph T. Akintola,*


Preface

Polynomials are well known for their evincing properties and wide applicability in interdisciplinary areas of science. The problems arising in physical sciences and engineering are mathematically framed in terms of differential equations. Most of them can only be solved using special polynomials. Special polynomials and orthogonal polynomials provide new means of analysis for solving large classes of differential equations often encountered in physical problems. In particular, sequences of special polynomials play a fundamental role in applied mathematics. Such sequences can be described in various ways, for example, by orthogonality conditions, as solutions to differential equations, by generating functions, by recurrence relations and by operational formulas.

Written by leading researchers and mathematicians, this book provides an overview of the current research in the field of polynomials. Topics include but are not limited to the following:

Chapter 8 149

The Orthogonal Expansion in Time-Domain Method for Solving

Maxwell Equations Using Paralleling-in-Order Scheme

by Zheng-Yu Huang, Zheng Sun and Wei He

II

This timely book will help fill a gap in the literature on the theory of polynomials and related fields. We hope it will promote further research and development in this important area.

We thank the authors for their creative contributions and the referees for their prompt and careful reviews.

> Cheon Seoung Ryoo Department of Mathematics, Hannam University, Daejeon, Korea

> > Section 1

Theory of Polynomials

1


*2.2. Modeling of LRI*

Modeling of relatively "soft" X-ray radiation of LRI was carried out on an LNK-268 (RAP100-10) X-ray unit (Diagnostika-M LLC, Moscow, Russia) with a radiation exposure mode at a dose of 110 Gy with a 0.1 mm aluminum filter, voltage 30 kV, beam current 6.1 mA, dose rate 21.1 Gy/min for 312 s (dose accuracy ± 5%, dose measurement uncertainty ± 6%) according to the proposed earlier method [10–12], leading to a short latency period and chronic skin ulcer in laboratory animals. After irradiation, the animals were seated in individual sterile boxes with an autonomous Smart Flow ventilation system (Tecniplast Group, Buguggiate, Italy), with free access to water and food.


*5.1.1 Continuum methods*

The different continuum methods of design are as under.

input parameters. This method computes separately the essential information in the solution domains from the information at the boundary, which is achieved by the solution of boundary integral equation rather than direct solution of PDEs [26].

Following are the different Hybrid continuum/discontinuum methods of design:

This method of design was developed by Clough et al., (1950). Due to wide application of this method in mining engineering especially tunneling, it get more attention for solving mining problems and popularity in this field [19]. The FEM divide problem into small parts and connect these parts at a point/nodes at the apexes and at the boundaries of meshing/discretization. The FEM has many applications in modeling in rock engineering design due to dealing with nonlinearity,

The unidentified function over each element in FEM estimated through test function having its nodal values of anonymous system (in polynomial form). This practice is the fundamental supposition of FEM. For experimental function, it is mandatory to satisfy the principal of PDFs. In this research the FEM based software Phase2 was used for analysis of stresses and total displacement around tunnel. For experimental

*j*¼1

*j*¼1 *f e*

*Nij* is the shape function or interpolation function; this must be defined into inherent coordinates for use of Gaussian quadratic integration, *M* is the element order. Using shape function the problem original PDFs can be substituted by the

*Nij*u*e*

*i* (7)

*i or Ku* ¼ *F* (8)

function it must be satisfied the principal of PDFs, which is given in Eq. (7).

u*e i* ¼ X *M*

The different discontinuum methods of design are given below.

*5.1.2 Discontinuum methods*

1.Discrete Element Method (DEM)

*Design Techniques in Rock and Soil Engineering DOI: http://dx.doi.org/10.5772/intechopen.90195*

2.Discrete Fracture Network (DFN)

*5.1.3 Hybrid continuum/Discontinuum*

1.Hybrid FEM/BEM methods

2.Hybrid DEM/DEM methods

3.Hybrid FEM/DEM methods

4.Other hybrid method/models

**6. Finite element method (FEM)**

arithmetical equation as given below.

X *N*

*Ke ij* h i u*e i* � � ¼ X *N*

*j*¼1

Where,

**69**

boundary conditions and heterogeneity problems [26, 27].

**Figure 7.**

*Division of numerical models and methods [24, 25].*

#### *Finite Difference Method (FDM).*

The Finite difference method (FDM) is the direct calculation of PDEs and transmitted the creative PDEs in term of unknown at grid point into a system of algebraic equations by interchange the fractional derivatives with difference at irregular or regular grid forced over problem areas. This system is solved due to establishing the required initial and boundary condition. This method is old but widely applied in the numerical modeling in rock mechanics. This method is based for explicit approach of discreet element method (DEM) [26].

#### *Finite Element Method (FEM).*

The Finite element method (FEM) splits the problem into sub-elements of smaller sizes and shapes with fitting the number of nodes at the vertices and at the side of discretization. FEM is mostly used to estimate the behavior of PDEs at elemental level and for signifying the behavior of elements; it produces the local algebraic equation. After creating the local equation the FEM gathered it according to topographic relation of node and elements and further put it into worldwide system of algebraic equation for receiving the required information after establishing the definite initial and boundary situations.

#### *Boundary Element Method (BEM).*

The Boundary element method is the precise method then FEM and FDM because of its easiness. This method involves the discretization of solution areas at boundary and thus decreases the problem dimension by simplifying the design

input parameters. This method computes separately the essential information in the solution domains from the information at the boundary, which is achieved by the solution of boundary integral equation rather than direct solution of PDEs [26].

*5.1.2 Discontinuum methods*

The different discontinuum methods of design are given below.