This document describes an approach to optimize technological processes to decrease the dimensions of integrated circuits, specifically XOR circuits, manufactured using field-effect heterotransistors. The approach involves manufacturing a heterostructure with specific material sections that are then doped via diffusion or ion implantation. Analytical modeling of the technological process is used to analyze redistribution of dopants and radiation defects during annealing, in order to formulate recommendations to decrease circuit dimensions. Equations are presented to model the diffusion and redistribution of dopants, point defects, and defect complexes over space and time during the annealing process.
Optimization of technological process to decrease dimensions of circuits xor ...ijfcstjournal
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of dopant
and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
On Approach to Increase Integration rate of Elements of a Circuit Driver with...BRNSS Publication Hub
In this paper, we introduce an approach to increase the integration rate of elements of a driver with 2-tap de-emphasis and impendence matching. Framework the approach, we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect heterotransistor. Based on analytical solution of the considered boundary problems some recommendations have been formulated to optimize technological processes.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect
heterotransistor. Based on analytical solution of the considered boundary problems some recommendations
have been formulated to optimize technological processes.
ON OPTIMIZATION OF MANUFACTURING PLANAR DOUBLE-BASE HETEROTRANSISTORS TO DECR...ijaceeejournal
In this paper we consider an approach of manufacturing of double-base hetero transistors to decrease their
dimensions. Framework the approach it should be manufactured a heterostructure with specific configuration.
Farther it is necessary to dope certain areas of the hetero structure by diffusion or by ion implantation.
After finishing of the doping process the dopant and/or radiation defects should be annealed. We consider
an approach of optimization of dopant and/or radiation defects for manufacturing more compact double base
heterotransistors.
Optimization of technological process to decrease dimensions of circuits xor ...ijfcstjournal
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of dopant
and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
On Approach to Increase Integration rate of Elements of a Circuit Driver with...BRNSS Publication Hub
In this paper, we introduce an approach to increase the integration rate of elements of a driver with 2-tap de-emphasis and impendence matching. Framework the approach, we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect heterotransistor. Based on analytical solution of the considered boundary problems some recommendations have been formulated to optimize technological processes.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect
heterotransistor. Based on analytical solution of the considered boundary problems some recommendations
have been formulated to optimize technological processes.
ON OPTIMIZATION OF MANUFACTURING PLANAR DOUBLE-BASE HETEROTRANSISTORS TO DECR...ijaceeejournal
In this paper we consider an approach of manufacturing of double-base hetero transistors to decrease their
dimensions. Framework the approach it should be manufactured a heterostructure with specific configuration.
Farther it is necessary to dope certain areas of the hetero structure by diffusion or by ion implantation.
After finishing of the doping process the dopant and/or radiation defects should be annealed. We consider
an approach of optimization of dopant and/or radiation defects for manufacturing more compact double base
heterotransistors.
Optimization of Dopant Diffusion and Ion Implantation to Increase Integration...ijrap
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION...ijrap
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
On Approach to Increase Integration Rate of Elements of an Operational Amplif...BRNSS Publication Hub
In this paper, we introduce an approach to optimize manufacturing of an operational amplifier circuit based on field-effect transistors. Main aims of the optimization are (i) decreasing dimensions of elements of the considered operational amplifier and (ii) increasing of performance and reliability of the considered field-effect transistors. Dimensions of considered field-effect transistors will be decreased due to manufacture of these transistors framework heterostructure with specific structure, doping of required areas of the heterostructure by diffusion or ion implantation, and optimization of annealing of dopant and/or radiation defects. Performance and reliability of the above field-effect transistors could be increased by optimization of annealing of dopant and/or radiation defects and using inhomogeneity of properties of heterostructure. Choosing of inhomogeneity of properties of heterostructure leads to increasing of compactness of distribution of concentration of dopant. At the same time, one can obtain increasing of homogeneity of the above concentration. In this paper, we also introduce an analytical approach for prognosis of technological process of manufacturing of the considered operational amplifier. The approach gives a possibility to take into account variation of parameters of processes in space and at the same time in space. At the same time, one can take into account nonlinearity of the considered processes.
An Approach to Analyze Non-linear Dynamics of Mass Transport during Manufactu...BRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a hybrid comparator with the first dynamic amplifying stage and the second quasi-dynamic latching stage. Framework the approach, we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized
On Approach to Increase Integration Rate of Elements of a Current Source CircuitBRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a current source circuit.
Framework the approach, we consider a heterostructure with special configuration. Several specific
areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/
or radiation defects should be optimized.
MODIFICATION OF DOPANT CONCENTRATION PROFILE IN A FIELD-EFFECT HETEROTRANSIST...msejjournal
In this paper we consider an approach of manufacturing more compact field-effect heterotransistors. The
approach based on manufacturing a heterostructure, which consist of a substrate and an epitaxial layer
with specific configuration. After that several areas of the epitaxial layer have been doped by diffusion or
ion implantation with optimized annealing of dopant and /or radiation defects. At the same time we introduce
an approach of modification of energy band diagram by additional doping of channel of the transistors.
We also consider an analytical approach to model and optimize technological process.
MODIFICATION OF DOPANT CONCENTRATION PROFILE IN A FIELD-EFFECT HETEROTRANSIST...msejjournal
In this paper we consider an approach of manufacturing more compact field-effect heterotransistors. The
approach based on manufacturing a heterostructure, which consist of a substrate and an epitaxial layer
with specific configuration. After that several areas of the epitaxial layer have been doped by diffusion or
ion implantation with optimized annealing of dopant and /or radiation defects. At the same time we introduce an approach of modification of energy band diagram by additional doping of channel of the transistors. We also consider an analytical approach to model and optimize technological process.
On Approach to Increase Integration Rate of Elements of a Switched-capacitor ...BRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a switched-
capacitor step-down DC–DC converter. Framework the approach, we consider a heterostructure with
special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion
implantation. Annealing of dopant and/or radiation defects should be optimized.
ON OPTIMIZATION OF MANUFACTURING OF AN AMPLIFIER TO INCREASE DENSITY OF BIPOL...ijoejournal
In this paper we consider a possibility to increase density of bipolar heterotransistor framework an amplifier
due to decreasing of their dimensions. The considered approach based on doping of required areas of
heterostructure with specific configuration by diffusion or ion implantation. The doping finished by optimized
annealing of dopant and/or radiation defects. Analysis of redistribution of dopant with account redistribution
of radiation defects (after implantation of ions of dopant) for optimization of the above annealing
have been done by using recently introduced analytical approach. The approach gives a possibility
to analyze mass and heat transports in a heterostructure without crosslinking of solutions on interfaces
between layers of the heterostructure with account nonlinearity of these transports and variation in time of
their parameters.
On optimization ofON OPTIMIZATION OF DOPING OF A HETEROSTRUCTURE DURING MANUF...ijcsitcejournal
We introduce an approach of manufacturing of a p-i-n-heterodiodes. The approach based on using a δ-
doped heterostructure, doping by diffusion or ion implantation of several areas of the heterostructure. After
the doping the dopant and/or radiation defects have been annealed. We introduce an approach to optimize
annealing of the dopant and/or radiation defects. We determine several conditions to manufacture more
compact p-i-n-heterodiodes
ON APPROACH TO DECREASE DIMENSIONS OF FIELD-EFFECT TRANSISTORS FRAMEWORK ELE...ijfcstjournal
In this paper we consider manufacturing of elements SRAM with increased density of field-effect transistors
consisting these elements. The approach based on manufacturing of the elements in heterostructure with
specific configuration. We consider doping of several required areas of the heterostructure by diffusion or
by ion implantation. After that dopant and radiation defects have been annealed framework optimized
scheme.
ON APPROACH TO DECREASE DIMENSIONS OF FIELD-EFFECT TRANSISTORS FRAMEWORK ELEM...ijfcstjournal
In this paper we consider manufacturing of elements SRAM with increased density of field-effect transistors
consisting these elements. The approach based on manufacturing of the elements in heterostructure with
specific configuration. We consider doping of several required areas of the heterostructure by diffusion or
by ion implantation. After that dopant and radiation defects have been annealed framework optimized
scheme.
OPTIMIZATION OF MANUFACTURE OF FIELDEFFECT HETEROTRANSISTORS WITHOUT P-NJUNCT...ijrap
It has been recently shown, that manufacturing p-n-junctions, field-effect and bipolar transistors, thyristors
in a multilayer structure by diffusion or ion implantation under condition of optimization of dopant and/or
radiation defects leads to increasing of sharpness of p-n-junctions (both single p-n-junctions and p-njunctions,
which include into their system). In this situation one can also obtain increasing of homogeneity
of dopant in doped area. In this paper we consider manufacturing a field-effect heterotransistor without pn-
junction. Optimization of technological process with using inhomogeneity of heterostructure give us
possibility to manufacture the transistors as more compact.
MODELING OF MANUFACTURING OF A FIELDEFFECT TRANSISTOR TO DETERMINE CONDITIONS...antjjournal
In this paper we introduce an approach to model technological process of manufacture of a field-effect
heterotransistor. The modeling gives us possibility to optimize the technological process to decrease length
of channel by using mechanical stress. As accompanying results of the decreasing one can find decreasing
of thickness of the heterotransistors and increasing of their density, which were comprised in integrated
circuits.
Optimization of Manufacturing of Circuits XOR to Decrease Their Dimensionsijrap
We analyzed possibility to increase density of elements of integrated circuits. We illustrate the possibility
by example of manufacturing of a circuit XOR. Framework the paper we consider a heterostructure which
includes into itself a substrate and an epitaxial layer with specific configuration. Several required areas of
the heterostructure have been doped by diffusion and/or ion implantation. After that we consider optimized
annealing of dopant and/or radiation defects.
ENHANCING ENGLISH WRITING SKILLS THROUGH INTERNET-PLUS TOOLS IN THE PERSPECTI...ijfcstjournal
This investigation delves into incorporating a hybridized memetic strategy within the framework of English
composition pedagogy, leveraging Internet Plus resources. The study aims to provide an in-depth analysis
of how this method influences students’ writing competence, their perceptions of writing, and their
enthusiasm for English acquisition. Employing an explanatory research design that combines qualitative
and quantitative methods, the study collects data through surveys, interviews, and observations of students’
writing performance before and after the intervention. Findings demonstrate a beneficial impact of
integrating the memetic approach alongside Internet Plus tools on the writing aptitude of English as a
Foreign Language (EFL) learners. Students reported increased engagement with writing, attributing it to
the use of Internet plus tools. They also expressed that the memetic approach facilitated a deeper
understanding of cultural and social contexts in writing. Furthermore, the findings highlight a significant
improvement in students’ writing skills following the intervention. This study provides significant insights
into the practical implementation of the memetic approach within English writing education, highlighting
the beneficial contribution of Internet Plus tools in enriching students' learning journeys.
A SURVEY TO REAL-TIME MESSAGE-ROUTING NETWORK SYSTEM WITH KLA MODELLINGijfcstjournal
Messages routing over a network is one of the most fundamental concept in communication which requires
simultaneous transmission of messages from a source to a destination. In terms of Real-Time Routing, it
refers to the addition of a timing constraint in which messages should be received within a specified time
delay. This study involves Scheduling, Algorithm Design and Graph Theory which are essential parts of
the Computer Science (CS) discipline. Our goal is to investigate an innovative and efficient way to present
these concepts in the context of CS Education. In this paper, we will explore the fundamental modelling of
routing real-time messages on networks. We study whether it is possible to have an optimal on-line
algorithm for the Arbitrary Directed Graph network topology. In addition, we will examine the message
routing’s algorithmic complexity by breaking down the complex mathematical proofs into concrete, visual
examples. Next, we explore the Unidirectional Ring topology in finding the transmission’s
“makespan”.Lastly, we propose the same network modelling through the technique of Kinesthetic Learning
Activity (KLA). We will analyse the data collected and present the results in a case study to evaluate the
effectiveness of the KLA approach compared to the traditional teaching method.
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by ion implantation. After that dopant and radiation defects have been annealed framework optimized
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enthusiasm for English acquisition. Employing an explanatory research design that combines qualitative
and quantitative methods, the study collects data through surveys, interviews, and observations of students’
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integrating the memetic approach alongside Internet Plus tools on the writing aptitude of English as a
Foreign Language (EFL) learners. Students reported increased engagement with writing, attributing it to
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class and category. The people of the farming community are unaware of the new techniques and Agromachines, which would direct the world to greater heights in the field of agriculture. Though the farmers
work hard, they are cheated by agents in today’s market. This serves as a opportunity to solve
all the problems that farmers face in the current world. The eAgro crop marketing will serve as a better
way for the farmers to sell their products within the country with some mediocre knowledge about using
the website. This would provide information to the farmers about current market rate of agro-products,
their sale history and profits earned in a sale. This site will also help the farmers to know about the market
information and to view agricultural schemes of the Government provided to farmers.
EDGE-TENACITY IN CYCLES AND COMPLETE GRAPHSijfcstjournal
It is well known that the tenacity is a proper measure for studying vulnerability and reliability in graphs.
Here, a modified edge-tenacity of a graph is introduced based on the classical definition of tenacity.
Properties and bounds for this measure are introduced; meanwhile edge-tenacity is calculated for cycle
graphs and also for complete graphs.
COMPARATIVE STUDY OF DIFFERENT ALGORITHMS TO SOLVE N QUEENS PROBLEMijfcstjournal
This Paper provides a brief description of the Genetic Algorithm (GA), the Simulated Annealing (SA)
Algorithm, the Backtracking (BT) Algorithm and the Brute Force (BF) Search Algorithm and attempts to
explain the way as how the Proposed Genetic Algorithm (GA), the Proposed Simulated Annealing (SA)
Algorithm using GA, the Backtracking (BT) Algorithm and the Brute Force (BF) Search Algorithm can be
employed in finding the best solution of N Queens Problem and also, makes a comparison between these
four algorithms. It is entirely a review based work. The four algorithms were written as well as
implemented. From the Results, it was found that, the Proposed Genetic Algorithm (GA) performed better
than the Proposed Simulated Annealing (SA) Algorithm using GA, the Backtracking (BT) Algorithm and
the Brute Force (BF) Search Algorithm and it also provided better fitness value (solution) than the
Proposed Simulated Annealing Algorithm (SA) using GA, the Backtracking (BT) Algorithm and the Brute
Force (BF) Search Algorithm, for different N values. Also, it was noticed that, the Proposed GA took more
time to provide result than the Proposed SA using GA.
PSTECEQL: A NOVEL EVENT QUERY LANGUAGE FOR VANET’S UNCERTAIN EVENT STREAMSijfcstjournal
In recent years, the complex event processing technology has been used to process the VANET’s temporal
and spatial event streams. However, we usually cannot get the accurate data because the device sensing
accuracy limitations of the system. We only can get the uncertain data from the complex and limited
environment of the VANET. Because the VANET’s event streams are consist of the uncertain data, so they
are also uncertain. How effective to express and process these uncertain event streams has become the core
issue for the VANET system. To solve this problem, we propose a novel complex event query language
PSTeCEQL (probabilistic spatio-temporal constraint event query language). Firstly, we give the definition
of the possible world model of VANET’s uncertain event streams. Secondly, we propose an event query
language PSTeCEQL and give the syntax and the operational semantics of the language. Finally, we
illustrate the validity of the PSTeCEQL by an example.
CLUSTBIGFIM-FREQUENT ITEMSET MINING OF BIG DATA USING PRE-PROCESSING BASED ON...ijfcstjournal
Now a day enormous amount of data is getting explored through Internet of Things (IoT) as technologies
are advancing and people uses these technologies in day to day activities, this data is termed as Big Data
having its characteristics and challenges. Frequent Itemset Mining algorithms are aimed to disclose
frequent itemsets from transactional database but as the dataset size increases, it cannot be handled by
traditional frequent itemset mining. MapReduce programming model solves the problem of large datasets
but it has large communication cost which reduces execution efficiency. This proposed new pre-processed
k-means technique applied on BigFIM algorithm. ClustBigFIM uses hybrid approach, clustering using kmeans algorithm to generate Clusters from huge datasets and Apriori and Eclat to mine frequent itemsets
from generated clusters using MapReduce programming model. Results shown that execution efficiency of
ClustBigFIM algorithm is increased by applying k-means clustering algorithm before BigFIM algorithm as
one of the pre-processing technique.
A MUTATION TESTING ANALYSIS AND REGRESSION TESTINGijfcstjournal
Software testing is a testing which conducted a test to provide information to client about the quality of the
product under test. Software testing can also provide an objective, independent view of the software to
allow the business to appreciate and understand the risks of software implementation. In this paper we
focused on two main software testing –mutation testing and mutation testing. Mutation testing is a
procedural testing method, i.e. we use the structure of the code to guide the test program, A mutation is a
little change in a program. Such changes are applied to model low level defects that obtain in the process
of coding systems. Ideally mutations should model low-level defect creation. Mutation testing is a process
of testing in which code is modified then mutated code is tested against test suites. The mutations used in
source code are planned to include in common programming errors. A good unit test typically detects the
program mutations and fails automatically. Mutation testing is used on many different platforms, including
Java, C++, C# and Ruby. Regression testing is a type of software testing that seeks to uncover
new software bugs, or regressions, in existing functional and non-functional areas of a system after
changes such as enhancements, patches or configuration changes, have been made to them. When defects
are found during testing, the defect got fixed and that part of the software started working as needed. But
there may be a case that the defects that fixed have introduced or uncovered a different defect in the
software. The way to detect these unexpected bugs and to fix them used regression testing. The main focus
of regression testing is to verify that changes in the software or program have not made any adverse side
effects and that the software still meets its need. Regression tests are done when there are any changes
made on software, because of modified functions.
GREEN WSN- OPTIMIZATION OF ENERGY USE THROUGH REDUCTION IN COMMUNICATION WORK...ijfcstjournal
Advances in micro fabrication and communication techniques have led to unimaginable proliferation of
WSN applications. Research is focussed on reduction of setup operational energy costs. Bulk of operational
energy costs are linked to communication activities of WSN. Any progress towards energy efficiency has a
potential of huge savings globally. Therefore, every energy efficient step is an endeavour to cut costs and
‘Go Green’. In this paper, we have proposed a framework to reduce communication workload through: Innetwork compression and multiple query synthesis at the base-station and modification of query syntax
through introduction of Static Variables. These approaches are general approaches which can be used in
any WSN irrespective of application.
A NEW MODEL FOR SOFTWARE COSTESTIMATION USING HARMONY SEARCHijfcstjournal
Accurate and realistic estimation is always considered to be a great challenge in software industry.
Software Cost Estimation (SCE) is the standard application used to manage software projects. Determining
the amount of estimation in the initial stages of the project depends on planning other activities of the
project. In fact, the estimation is confronted with a number of uncertainties and barriers’, yet assessing the
previous projects is essential to solve this problem. Several models have been developed for the analysis of
software projects. But the classical reference method is the COCOMO model, there are other methods
which are also applied such as Function Point (FP), Line of Code(LOC); meanwhile, the expert`s opinions
matter in this regard. In recent years, the growth and the combination of meta-heuristic algorithms with
high accuracy have brought about a great achievement in software engineering. Meta-heuristic algorithms
which can analyze data from multiple dimensions and identify the optimum solution between them are
analytical tools for the analysis of data. In this paper, we have used the Harmony Search (HS)algorithm for
SCE. The proposed model which is a collection of 60 standard projects from Dataset NASA60 has been
assessed.The experimental results show that HS algorithm is a good way for determining the weight
similarity measures factors of software effort, and reducing the error of MRE.
AGENT ENABLED MINING OF DISTRIBUTED PROTEIN DATA BANKSijfcstjournal
Mining biological data is an emergent area at the intersection between bioinformatics and data mining
(DM). The intelligent agent based model is a popular approach in constructing Distributed Data Mining
(DDM) systems to address scalable mining over large scale distributed data. The nature of associations
between different amino acids in proteins has also been a subject of great anxiety. There is a strong need to
develop new models and exploit and analyze the available distributed biological data sources. In this study,
we have designed and implemented a multi-agent system (MAS) called Agent enriched Quantitative
Association Rules Mining for Amino Acids in distributed Protein Data Banks (AeQARM-AAPDB). Such
globally strong association rules enhance understanding of protein composition and are desirable for
synthesis of artificial proteins. A real protein data bank is used to validate the system.
International Journal on Foundations of Computer Science & Technology (IJFCST)ijfcstjournal
International Journal on Foundations of Computer Science & Technology (IJFCST) is a Bi-monthly peer-reviewed and refereed open access journal that publishes articles which contribute new results in all areas of the Foundations of Computer Science & Technology. Over the last decade, there has been an explosion in the field of computer science to solve various problems from mathematics to engineering. This journal aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals. Topics of interest include, but are not limited to the following:
Because the technology is used largely in the last decades; cybercrimes have become a significant
international issue as a result of the huge damage that it causes to the business and even to the ordinary
users of technology. The main aims of this paper is to shed light on digital crimes and gives overview about
what a person who is related to computer science has to know about this new type of crimes. The paper has
three sections: Introduction to Digital Crime which gives fundamental information about digital crimes,
Digital Crime Investigation which presents different investigation models and the third section is about
Cybercrime Law.
DISTRIBUTION OF MAXIMAL CLIQUE SIZE UNDER THE WATTS-STROGATZ MODEL OF EVOLUTI...ijfcstjournal
In this paper, we analyze the evolution of a small-world network and its subsequent transformation to a
random network using the idea of link rewiring under the well-known Watts-Strogatz model for complex
networks. Every link u-v in the regular network is considered for rewiring with a certain probability and if
chosen for rewiring, the link u-v is removed from the network and the node u is connected to a randomly
chosen node w (other than nodes u and v). Our objective in this paper is to analyze the distribution of the
maximal clique size per node by varying the probability of link rewiring and the degree per node (number
of links incident on a node) in the initial regular network. For a given probability of rewiring and initial
number of links per node, we observe the distribution of the maximal clique per node to follow a Poisson
distribution. We also observe the maximal clique size per node in the small-world network to be very close
to that of the average value and close to that of the maximal clique size in a regular network. There is no
appreciable decrease in the maximal clique size per node when the network transforms from a regular
network to a small-world network. On the other hand, when the network transforms from a small-world
network to a random network, the average maximal clique size value decreases significantly
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Optimization of Technological Process to Decrease Dimensions of Circuits XOR, Manufectured Based on Field-Effect Heterotransistors
1. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
DOI:10.5121/ijfcst.2016.6101 1
OPTIMIZATION OF TECHNOLOGICAL PROCESS TO
DECREASE DIMENSIONS OF CIRCUITS XOR, MANU-
FECTURED BASED ON FIELD-EFFECT HETEROTRAN-
SISTORS
E.L. Pankratov1
, E.A. Bulaeva1,2
1
Nizhny Novgorod State University, 23 Gagarin Avenue, Nizhny Novgorod, 603950,
Russia
2
Nizhny Novgorod State University of Architecture and Civil Engineering, 65 Il'insky
Street, Nizhny Novgorod, 603950, Russia
ABSTRACT
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of do-
pant and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
KEYWORDS
Circuits XOR; increasing of density of elements; optimization of technological process.
1. INTRODUCTION
One of intensively solving problems of solid state electronics is improvement of frequency cha-
racteristics of electronic devices and their reliability. Another intensively solving problem is in-
creasing of integration rate of integrated circuits with decreasing of their dimensions [1-9]. To
solve these problems they were used searching materials with higher values of charge carriers
motilities, development new and elaboration existing technological approaches [1-14]. In the
present paper we consider circuit XOR from [15]. Based on recently considered approaches [16-
23] we consider an approach to decrease dimensions of the circuit. The approach based on manu-
facturing a heterostructure, which consist of a substrate and an epitaxial layer. The epitaxial layer
manufactured with several sections. To manufacture these sections another materials have been
used. These sections have been doped by diffusion or ion implantation. The doping gives a possi-
bility to generate another type of conductivity (p or n). After finishing of manufacturing of the
circuit XOR these sections will be used by sources, drains and gates (see Fig. 1). Dopant and rad-
iation defects should be annealed after finishing the dopant diffusion and the ion implantation.
Our aim framework the paper is analysis of redistribution of dopant and redistribution of radiation
defects to prognosis technological process. The accompanying aim of the present paper is devel-
opment of analytical approach for prognosis technological processes with account all required
influenced factors.
2. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
2
2. METHOD OF SOLUTION
We solve our aim by calculation and analysis distribution of concentrations of dopants in space
and time. The required distribution has been determined by solving the second Fick's law in the
following form [24,25]
( ) ( ) ( ) ( )
+
+
=
z
t
z
y
x
C
D
z
y
t
z
y
x
C
D
y
x
t
z
y
x
C
D
x
t
t
z
y
x
C
C
C
C
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂ ,
,
,
,
,
,
,
,
,
,
,
,
. (1)
Boundary and initial conditions for the equations are
Fig. 1. Structure of epitaxial layer. View from top
3. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
3
( ) 0
,
,
,
0
=
∂
∂
=
x
x
t
z
y
x
C
,
( ) 0
,
,
,
=
∂
∂
= x
L
x
x
t
z
y
x
C
,
( ) 0
,
,
,
0
=
∂
∂
=
y
y
t
z
y
x
C
,
( ) 0
,
,
,
=
∂
∂
= y
L
x
y
t
z
y
x
C
,
( ) 0
,
,
,
0
=
∂
∂
=
z
z
t
z
y
x
C
,
( ) 0
,
,
,
=
∂
∂
= z
L
x
z
t
z
y
x
C
, C(x,y,z,0)=f (x,y,z). (2)
Here the function C(x,y,z,t) describes the distribution of concentration of dopant in space and
time. DС describes distribution the dopant diffusion coefficient in space and as a function of tem-
perature of annealing. Dopant diffusion coefficient will be changed with changing of materials of
heterostructure, heating and cooling of heterostructure during annealing of dopant or radiation
defects (with account Arrhenius law). Dependences of dopant diffusion coefficient on coordinate
in heterostructure, temperature of annealing and concentrations of dopant and radiation defects
could be written as [26-28]
( ) ( )
( )
( ) ( )
( )
+
+
+
= 2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
V
t
z
y
x
V
V
t
z
y
x
V
T
z
y
x
P
t
z
y
x
C
T
z
y
x
D
D L
C ς
ς
ξ γ
γ
. (3)
Here function DL (x,y,z,T) describes dependences of dopant diffusion coefficient on coordinate
and temperature of annealing T. Function P (x,y,z,T) describes the same dependences of the limit
of solubility of dopant. The parameter γ is integer and usually could be varying in the following
interval γ ∈[1,3]. The parameter describes quantity of charged defects, which interacting (in aver-
age) with each atom of dopant. Ref.[26] describes more detailed information about dependence of
dopant diffusion coefficient on concentration of dopant. Spatio-temporal distribution of concen-
tration of radiation vacancies described by the function V (x,y,z,t). The equilibrium distribution of
concentration of vacancies has been denoted as V*
. It is known, that doping of materials by diffu-
sion did not leads to radiation damage of materials. In this situation ζ1=ζ2=0. We determine spa-
tio-temporal distributions of concentrations of radiation defects by solving the following system
of equations [27,28]
( ) ( ) ( ) ( ) ( ) ( ) ×
−
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
T
z
y
x
k
y
t
z
y
x
I
T
z
y
x
D
y
x
t
z
y
x
I
T
z
y
x
D
x
t
t
z
y
x
I
I
I
I
I ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
( ) ( ) ( ) ( ) ( ) ( )
t
z
y
x
V
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
I
T
z
y
x
D
z
t
z
y
x
I V
I
I ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
, ,
2
−
∂
∂
∂
∂
+
× (4)
( ) ( ) ( ) ( ) ( ) ( )×
−
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
T
z
y
x
k
y
t
z
y
x
V
T
z
y
x
D
y
x
t
z
y
x
V
T
z
y
x
D
x
t
t
z
y
x
V
V
V
V
V ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
( ) ( ) ( ) ( ) ( ) ( )
t
z
y
x
V
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
V
T
z
y
x
D
z
t
z
y
x
V V
I
V ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
, ,
2
−
∂
∂
∂
∂
+
× .
Boundary and initial conditions for these equations are
( ) 0
,
,
,
0
=
∂
∂
=
x
x
t
z
y
x
ρ
,
( ) 0
,
,
,
=
∂
∂
= x
L
x
x
t
z
y
x
ρ
,
( ) 0
,
,
,
0
=
∂
∂
=
y
y
t
z
y
x
ρ
,
( ) 0
,
,
,
=
∂
∂
= y
L
y
y
t
z
y
x
ρ
,
4. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
4
( ) 0
,
,
,
0
=
∂
∂
=
z
z
t
z
y
x
ρ
,
( ) 0
,
,
,
=
∂
∂
= z
L
z
z
t
z
y
x
ρ
, ρ (x,y,z,0)=fρ (x,y,z). (5)
Here ρ =I,V. We denote spatio-temporal distribution of concentration of radiation interstitials as I
(x,y,z,t). Dependences of the diffusion coefficients of point radiation defects on coordinate and
temperature have been denoted as Dρ(x,y,z,T). The quadric on concentrations terms of Eqs. (4)
describes generation divacancies and diinterstitials. Parameter of recombination of point radiation
defects and parameters of generation of simplest complexes of point radiation defects have been
denoted as the following functions kI,V(x,y,z,T), kI,I(x,y,z,T) and kV,V(x,y,z,T), respectively.
Now let us calculate distributions of concentrations of divacancies ΦV(x,y,z,t) and diinterstitials
ΦI(x,y,z,t) in space and time by solving the following system of equations [27,28]
( ) ( ) ( ) ( ) ( ) +
Φ
+
Φ
=
Φ
Φ
Φ
y
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x I
I
I
I
I
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂ ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
( ) ( ) ( ) ( ) ( ) ( )
t
z
y
x
I
T
z
y
x
k
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
T
z
y
x
D
z
I
I
I
I
I ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
, 2
, −
+
Φ
+ Φ
∂
∂
∂
∂
(6)
( ) ( ) ( ) ( ) ( ) +
Φ
+
Φ
=
Φ
Φ
Φ
y
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x V
V
V
V
V
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂ ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
( ) ( ) ( ) ( ) ( ) ( )
t
z
y
x
V
T
z
y
x
k
t
z
y
x
V
T
z
y
x
k
z
t
z
y
x
T
z
y
x
D
z
V
V
V
V
V ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
, 2
, −
+
Φ
+ Φ
∂
∂
∂
∂
.
Boundary and initial conditions for these equations are
( )
0
,
,
,
0
=
∂
Φ
∂
=
x
x
t
z
y
x
ρ
,
( )
0
,
,
,
=
∂
Φ
∂
= x
L
x
x
t
z
y
x
ρ
,
( )
0
,
,
,
0
=
∂
Φ
∂
=
y
y
t
z
y
x
ρ
,
( )
0
,
,
,
=
∂
Φ
∂
= y
L
y
y
t
z
y
x
ρ
,
( )
0
,
,
,
0
=
∂
Φ
∂
=
z
z
t
z
y
x
ρ
,
( )
0
,
,
,
=
∂
Φ
∂
= z
L
z
z
t
z
y
x
ρ
, ΦI (x,y,z,0)=fΦI (x,y,z), ΦV (x,y,z,0)=fΦV (x,y,z). (7)
The functions DΦρ(x,y,z,T) describe dependences of the diffusion coefficients of the above com-
plexes of radiation defects on coordinate and temperature. The functions kI(x,y,z,T) and kV(x,y,z,
T) describe the parameters of decay of these complexes on coordinate and temperature.
To describe physical processes they are usually solving nonlinear equations with space and time
varying coefficients. In this situation only several limiting cases have been analyzed [29-32]. One
way to solve the problem is solving the Eqs. (1), (4), (6) by the Bubnov-Galerkin approach [33]
after appropriate transformation of these transformation. To determine the spatio-temporal distri-
bution of concentration of dopant we transform the Eq.(1) to the following integro- differential
form
( ) ( )
( ) ( )
( )
×
∫ ∫ ∫
+
+
=
∫ ∫ ∫
t y
L
z
L
L
x
L
y
L
z
L
z
y
x y z
x y z V
w
v
x
V
V
w
v
x
V
T
w
v
x
D
u
d
v
d
w
d
t
w
v
u
C
L
L
L
z
y
x
0
2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
,
,
,
τ
ς
τ
ς
5. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
5
( )
( )
( ) ( ) ( )
( )
×
∫ ∫ ∫
+
+
+
×
t x
L
z
L
L
z
y x z T
z
y
x
P
w
y
u
C
T
w
y
u
D
L
L
z
y
d
x
w
v
x
C
T
w
v
x
P
w
v
x
C
0 ,
,
,
,
,
,
1
,
,
,
,
,
,
,
,
,
,
,
,
1 γ
γ
γ
γ
τ
ξ
τ
∂
τ
∂
τ
ξ
( ) ( )
( )
( ) ( ) ×
∫ ∫ ∫
+
+
+
×
t x
L
y
L
L
z
x x y
T
z
v
u
D
L
L
z
x
d
y
w
y
u
C
V
w
y
u
V
V
w
y
u
V
0
2
*
2
2
*
1 ,
,
,
,
,
,
,
,
,
,
,
,
1 τ
∂
τ
∂
τ
ς
τ
ς
( ) ( )
( )
( )
( )
( ) +
+
+
+
×
y
x
L
L
y
x
d
z
z
v
u
C
T
z
y
x
P
z
v
u
C
V
z
v
u
V
V
z
v
u
V
τ
∂
τ
∂
τ
ξ
τ
ς
τ
ς γ
γ
,
,
,
,
,
,
,
,
,
1
,
,
,
,
,
,
1 2
*
2
2
*
1
( )
∫ ∫ ∫
+
x
L
y
L
z
L
z
y
x x y z
u
d
v
d
w
d
w
v
u
f
L
L
L
z
y
x
,
, . (1a)
Now let us determine solution of Eq.(1a) by Bubnov-Galerkin approach [33]. To use the ap-
proach we consider solution of the Eq.(1a) as the following series
( ) ( ) ( ) ( ) ( )
∑
=
=
N
n
nC
n
n
n
nC t
e
z
c
y
c
x
c
a
t
z
y
x
C
0
0 ,
,
, .
Here ( ) ( )
[ ]
2
2
2
0
2
2
exp −
−
−
+
+
−
= z
y
x
C
nC L
L
L
t
D
n
t
e π , cn(χ) =cos(π nχ/Lχ). Number of terms N in the
series is finite. The above series is almost the same with solution of linear Eq.(1) (i.e. for ξ=0)
and averaged dopant diffusion coefficient D0. Substitution of the series into Eq.(1a) leads to the
following result
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
∫ ∫ ∫
×
∑
+
−
=
∑
=
=
t y
L
z
L
N
n
nC
n
n
n
nC
z
y
N
n
nC
n
n
n
C
y z
e
w
c
v
c
x
c
a
L
L
z
y
t
e
z
s
y
s
x
s
n
a
z
y
x
0 1
1
3
2
1
γ
τ
π
( )
( ) ( )
( )
( ) ( ) ( )×
∑
+
+
×
=
N
n
n
n
nC
L v
c
x
s
a
T
w
v
x
D
V
w
v
x
V
V
w
v
x
V
T
w
v
x
P 1
2
*
2
2
*
1 ,
,
,
,
,
,
,
,
,
1
,
,
,
τ
ς
τ
ς
ξ
γ
( ) ( ) ( ) ( ) ( ) ( )
( )
∫ ∫ ∫ ×
∑
+
−
×
=
t x
L
z
L
N
m
mC
m
m
m
mC
z
x
nC
n
x z T
w
y
u
P
e
w
c
y
c
u
c
a
L
L
z
x
d
e
w
c
n
0 1 ,
,
,
1 γ
γ
ξ
τ
τ
τ
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ×
∑
+
+
×
=
τ
τ
τ
ς
τ
ς d
e
w
c
y
s
u
c
n
V
w
y
u
V
V
w
y
u
V
T
w
y
u
D
N
n
nC
n
n
n
L
1
2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
( )
( )
( ) ( ) ( ) ( ) ×
∫ ∫ ∫
∑
+
−
×
=
t x
L
y
L
N
n
nC
n
n
n
nC
L
y
x
nC
x y
e
z
c
v
c
u
c
a
T
z
v
u
P
T
z
v
u
D
L
L
y
x
a
0 1
,
,
,
1
,
,
,
γ
γ
τ
ξ
( ) ( )
( )
( ) ( ) ( ) ( ) ×
+
∑
+
+
×
=
z
y
x
N
n
nC
n
n
n
nC
L
L
L
z
y
x
d
e
z
s
v
c
u
c
a
n
V
z
v
u
V
V
z
v
u
V
τ
τ
τ
ς
τ
ς
1
2
*
2
2
*
1
,
,
,
,
,
,
1
( )
∫ ∫ ∫
×
x
L
y
L
z
L
x y z
u
d
v
d
w
d
w
v
u
f ,
, ,
6. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
6
where sn(χ)=sin(πnχ/Lχ). We used condition of orthogonality to determine coefficients an in the
considered series. The coefficients an could be calculated for any quantity of terms N. In the
common case the relations could be written as
( ) ( ) ( ) ( ) ( ) ( )
∫ ∫ ∫ ∫
×
∑
+
−
=
∑
−
=
=
t L L L N
n
nC
n
n
n
nC
L
z
y
N
n
nC
nC
z
y
x
x y z
e
z
c
y
c
x
c
a
T
z
y
x
D
L
L
t
e
n
a
L
L
L
0 0 0 0 1
2
1
6
5
2
2
2
1
,
,
,
2
γ
τ
π
π
( )
( ) ( )
( )
( ) ( ) ( ) ( )×
∑
+
+
×
=
N
n
nC
n
n
n
nC
e
z
c
y
c
x
s
n
a
V
z
y
x
V
V
z
y
x
V
T
z
y
x
P 1
2
*
2
2
*
1 2
,
,
,
,
,
,
1
,
,
,
τ
τ
ς
τ
ς
ξ
γ
( ) ( )
[ ] ( ) ( )
[ ] ( )×
∫ ∫ ∫ ∫
−
−
+
−
+
×
t L L L
L
n
z
n
n
y
n
x y z
T
z
y
x
D
d
x
d
y
d
z
d
z
c
n
L
z
s
z
y
c
n
L
y
s
y
0 0 0 0
,
,
,
1
1 τ
π
π
( ) ( ) ( ) ( ) ( )
( )
( )
+
+
∑
+
×
=
*
1
1
,
,
,
1
,
,
,
1
,
,
,
V
z
y
x
V
T
z
y
x
P
e
z
c
y
c
x
c
a
T
z
y
x
D
N
n
nC
n
n
n
nC
L
τ
ς
ξ
τ γ
γ
( )
( )
( ) ( )
( )
( ) ( )
[ ]
∑ ×
−
+
+
+
+
=
N
n
nC
n
x
n
n
a
x
c
n
L
x
s
x
V
z
y
x
V
V
z
y
x
V
V
z
y
x
V
1
2
*
2
2
*
1
2
*
2
2
1
,
,
,
,
,
,
1
,
,
,
π
τ
ς
τ
ς
τ
ς
( ) ( ) ( ) ( ) ( ) ( )
[ ] ×
−
−
+
× 2
2
2
1
2
2 π
τ
π
τ
π
y
x
n
z
n
nC
n
n
n
z
x
L
L
d
x
d
y
d
z
d
z
c
n
L
z
s
z
e
z
c
y
s
x
c
L
L
( ) ( ) ( ) ( )
( )
( )
( )
∫ ∫ ∫ ∫
+
+
∑
+
×
=
t L L L N
n
nC
n
n
n
nC
x y z
V
z
y
x
V
T
z
y
x
P
e
z
c
y
c
x
c
a
0 0 0 0
2
*
2
2
1
,
,
,
1
,
,
,
1
τ
ς
ξ
τ γ
γ
( ) ( ) ( ) ( ) ( ) ( ) ( )
[ ] ×
∑
−
+
+
=
N
n
n
x
n
n
n
n
nC
L x
c
n
L
x
s
x
z
s
y
c
x
c
n
a
T
z
y
x
D
V
z
y
x
V
1
*
1 1
,
,
,
,
,
,
π
τ
ς
( ) ( )
[ ] ( ) ( ) ( )
[ ]
∑ ∫ ×
−
+
+
−
+
×
=
N
n
L
n
x
n
nC
n
y
n
x
x
c
n
L
x
s
x
d
x
d
y
d
z
d
e
y
c
n
L
y
s
y
1 0
1
1
π
τ
τ
π
( ) ( )
[ ] ( ) ( )
[ ] ( )
∫ ∫
−
+
−
+
×
y z
L L
n
z
n
n
y
n x
d
y
d
z
d
z
y
x
f
z
c
n
L
z
s
z
y
c
n
L
y
s
y
0 0
,
,
1
1
π
π
.
As an example for γ=0 we obtain
( ) ( )
[ ] ( ) ( )
[ ] ( ) ( )
{
∫ ∫ ∫ +
−
+
−
+
=
x y z
L L L
n
n
y
n
n
y
n
nC x
s
x
y
d
z
d
z
y
x
f
z
c
n
L
z
s
z
y
c
n
L
y
s
y
a
0 0 0
,
,
1
1
π
π
( )
[ ] ( ) ( ) ( ) ( )
[ ] ( )
∫ ∫ ∫ ∫ ×
−
+
−
×
t L L L
L
n
y
n
n
n
x
n
x y z
T
z
y
x
D
y
c
n
L
y
s
y
y
c
x
s
n
x
d
n
L
x
c
0 0 0 0
,
,
,
1
2
2
1
π
π
7. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
7
( ) ( )
[ ] ( ) ( )
( ) ( )
×
+
+
+
−
+
×
T
z
y
x
P
V
z
y
x
V
V
z
y
x
V
z
c
n
L
z
s
z n
y
n
,
,
,
1
,
,
,
,
,
,
1
1 2
*
2
2
*
1 γ
ξ
τ
ς
τ
ς
π
( ) ( ) ( ) ( ) ( ) ( )
[ ] ( ) ( )×
∫ ∫ ∫ ∫
−
+
+
×
t L L L
n
n
n
y
n
n
nC
nC
n
x y z
z
c
y
s
x
c
n
L
x
s
x
x
c
e
d
e
x
d
y
d
z
d
z
c
0 0 0 0
2
1
π
τ
τ
τ
( ) ( )
[ ]
( )
( ) ( )
( )
×
+
+
+
−
+
× 2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
1
1
V
z
y
x
V
V
z
y
x
V
T
z
y
x
P
z
c
n
L
z
s
z n
y
n
τ
ς
τ
ς
ξ
π γ
( ) ( ) ( ) ( ) ( )
[ ] ( ) ( )
{
∫ ∫ ∫ ×
−
+
+
×
t L L
n
n
n
x
n
n
nC
L
x y
y
s
y
c
x
c
n
L
x
s
x
x
c
e
d
x
d
y
d
z
d
T
z
y
x
D
0 0 0
1
,
,
,
π
τ
τ
( )
[ ] ( ) ( )
( )
( )
( )
∫
+
+
+
−
+
×
z
L
L
n
n
y
V
z
y
x
V
T
z
y
x
P
T
z
y
x
D
z
s
y
c
n
L
y
0
2
*
2
2
,
,
,
1
,
,
,
1
,
,
,
2
1
τ
ς
ξ
π γ
( ) ( )
1
6
5
2
2
2
*
1
,
,
,
−
−
+ t
e
n
L
L
L
d
x
d
y
d
z
d
V
z
y
x
V
nC
z
z
z
π
τ
τ
ς .
For γ = 1 one can obtain the following relation to determine required parameters
( ) ( ) ( ) ( )
∫ ∫ ∫
+
±
−
=
x y z
L L L
n
n
n
n
n
n
n
nC
x
d
y
d
z
d
z
y
x
f
z
c
y
c
x
c
a
0 0 0
2
,
,
4
2
α
β
α
β
,
where ( ) ( ) ( ) ( ) ( ) ( )
( )
∫ ∫ ∫ ∫ ×
+
+
=
t L L L
n
n
n
nC
z
y
n
x y z
V
z
y
x
V
V
z
y
x
V
z
c
y
c
x
s
e
n
L
L
0 0 0 0
2
*
2
2
*
1
2
,
,
,
,
,
,
1
2
2
τ
ς
τ
ς
τ
π
ξ
α
( )
( )
( ) ( )
[ ] ( ) ( )
[ ] ×
+
−
+
−
+
×
n
L
L
d
x
d
y
d
z
d
z
c
n
L
z
s
z
y
c
n
L
y
s
y
T
z
y
x
P
T
z
y
x
D z
x
n
z
n
n
y
n
L
2
2
1
1
,
,
,
,
,
,
π
ξ
τ
π
π
( ) ( ) ( ) ( )
[ ] ( ) ( )
( )
( ) ( )
[ ] ×
∫ ∫ ∫ ∫
−
−
−
+
×
t L L L
n
z
n
L
n
n
x
n
n
nC
x y z
z
c
n
L
z
s
z
T
z
y
x
P
T
z
y
x
D
z
c
x
c
n
L
x
s
x
x
c
e
0 0 0 0
1
,
,
,
,
,
,
1
π
π
τ
( )
( )
( ) ( )
( )
( ) ×
+
+
+
×
n
L
L
d
x
d
y
d
y
s
z
d
V
z
y
x
V
V
z
y
x
V
T
z
y
x
P
T
z
y
x
D y
x
n
L
2
2
*
2
2
*
1
2
2
,
,
,
,
,
,
1
,
,
,
,
,
,
π
ξ
τ
τ
ς
τ
ς
( ) ( ) ( ) ( ) ( )
( )
( ) ( )
( )
×
∫ ∫ ∫ ∫
+
+
×
t L L L
L
n
n
n
nC
x y z
V
z
y
x
V
V
z
y
x
V
T
z
y
x
P
T
z
y
x
D
z
s
y
c
x
c
e
0 0 0 0
2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
,
,
,
2
τ
ς
τ
ς
τ
( ) ( )
[ ] ( ) ( )
[ ] τ
π
π
d
x
d
y
d
z
d
y
c
n
L
y
s
y
x
c
n
L
x
s
x n
y
n
n
x
n
−
+
−
+
× 1
1 , ( )×
∫
=
t
nC
z
y
n e
n
L
L
0
2
2
τ
π
β
( ) ( ) ( ) ( )
[ ] ( ) ( ) ( )
( )
∫ ∫ ∫ ×
+
+
−
+
×
x y z
L L L
n
n
y
n
n
n
V
z
y
x
V
V
z
y
x
V
z
c
y
c
n
L
y
s
y
y
c
x
s
0 0 0
2
*
2
2
*
1
,
,
,
,
,
,
1
1
2
τ
ς
τ
ς
π
8. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
8
( ) ( ) ( )
[ ] ( ) ( ) ( )×
∫ ∫ ∫
+
−
+
×
t L L
n
n
nC
z
x
n
z
n
L
x y
y
s
x
c
e
n
L
L
d
x
d
y
d
z
d
z
c
n
L
z
s
z
T
z
y
x
D
0 0 0
2
2
2
1
,
,
, τ
π
τ
π
( ) ( )
[ ] ( ) ( ) ( ) ( )
( )
×
∫
+
+
−
+
×
z
L
n
L
n
x
n
V
z
y
x
V
V
z
y
x
V
z
c
T
z
y
x
D
x
c
n
L
x
s
x
0
2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
1
τ
ς
τ
ς
π
( ) ( )
[ ] ( ) ( ) ( )
[ ] ×
∫ ∫
−
+
+
−
+
×
t L
n
x
n
nC
y
x
n
z
n
x
x
c
n
L
x
s
x
e
n
L
L
d
x
d
y
d
z
d
z
c
n
L
z
s
z
0 0
2
1
2
1
π
τ
π
τ
π
( ) ( ) ( )
[ ] ( ) ( ) ( )
( )
∫ ∫ ×
+
+
−
+
×
y z
L L
L
n
y
n
n
V
z
y
x
V
V
z
y
x
V
T
z
y
x
D
y
c
n
L
y
s
y
x
c
0 0
2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
1
τ
ς
τ
ς
π
( ) ( ) ( ) 6
5
2
2
2
2 n
t
e
L
L
L
d
x
d
y
d
y
c
z
d
z
s nC
z
y
x
n
n π
τ −
× .
The same approach could be used for calculation parameters an for different values of parameterγ.
However the relations are bulky and will not be presented in the paper. Advantage of the ap-
proach is absent of necessity to join dopant concentration on interfaces of heterostructure.
The same Bubnov-Galerkin approach has been used for solution the Eqs.(4). Previously we trans-
form the differential equations to the following integro- differential form
( ) ( ) ( ) +
∫ ∫ ∫
∂
∂
=
∫ ∫ ∫
t y
L
z
L
I
z
y
x
L
y
L
z
L
z
y
x y z
x y z
d
v
d
w
d
x
w
v
x
I
T
w
v
x
D
L
L
z
y
u
d
v
d
w
d
t
w
v
u
I
L
L
L
z
y
x
0
,
,
,
,
,
,
,
,
, τ
τ
( ) ( ) ( ) ( )×
∫ ∫ ∫
−
∫ ∫ ∫
∂
∂
+
x
L
y
L
z
L
V
I
z
y
x
t x
L
z
L
I
z
x x y z
x z
t
w
v
u
I
T
w
v
u
k
L
L
L
z
y
x
d
u
d
w
d
x
w
y
u
I
T
w
y
u
D
L
L
z
x
,
,
,
,
,
,
,
,
,
,
,
, ,
0
τ
τ
( ) ( ) ( ) ×
−
∫ ∫ ∫
∂
∂
+
×
z
y
x
t x
L
y
L
I
y
x
L
L
L
z
y
x
d
u
d
v
d
T
z
v
u
D
z
z
v
u
I
L
L
y
x
u
d
v
d
w
d
t
w
v
u
V
x y
0
,
,
,
,
,
,
,
,
, τ
τ
( ) ( ) ( )
∫ ∫ ∫
+
∫ ∫ ∫
×
x
L
y
L
z
L
I
z
y
x
x
L
y
L
z
L
I
I
x y z
x y z
u
d
v
d
w
d
w
v
u
f
L
L
L
z
y
x
u
d
v
d
w
d
t
w
v
u
I
T
w
v
u
k ,
,
,
,
,
,
,
, 2
, (4a)
( ) ( ) ( ) +
∫ ∫ ∫
∂
∂
=
∫ ∫ ∫
t y
L
z
L
V
z
y
x
L
y
L
z
L
z
y
x y z
x y z
d
v
d
w
d
x
w
v
x
V
T
w
v
x
D
L
L
z
y
u
d
v
d
w
d
t
w
v
u
V
L
L
L
z
y
x
0
,
,
,
,
,
,
,
,
, τ
τ
( ) ( ) ( ) ×
∫ ∫ ∫
∂
∂
+
∫ ∫ ∫
∂
∂
+
t x
L
y
L
y
x
t x
L
z
L
V
z
x x y
x z z
z
v
u
V
L
L
y
x
d
u
d
w
d
x
w
y
u
V
T
w
y
u
D
L
L
z
x
0
0
,
,
,
,
,
,
,
,
,
τ
τ
τ
( ) ( ) ( ) ( ) −
∫ ∫ ∫
−
×
x
L
y
L
z
L
V
I
z
y
x
V
x y z
u
d
v
d
w
d
t
w
v
u
V
t
w
v
u
I
T
w
v
u
k
L
L
L
z
y
x
d
u
d
v
d
T
z
v
u
D ,
,
,
,
,
,
,
,
,
,
,
, ,
τ
( ) ( ) ( )
∫ ∫ ∫
+
∫ ∫ ∫
−
x
L
y
L
z
L
V
z
y
x
x
L
y
L
z
L
V
V
z
y
x x y z
x y z
u
d
v
d
w
d
w
v
u
f
L
L
L
z
y
x
u
d
v
d
w
d
t
w
v
u
V
T
w
v
u
k
L
L
L
z
y
x
,
,
,
,
,
,
,
, 2
, .
9. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
9
We determine spatio-temporal distributions of concentrations of point defects as the same series
( ) ( ) ( ) ( ) ( )
∑
=
=
N
n
n
n
n
n
n t
e
z
c
y
c
x
c
a
t
z
y
x
1
0 ,
,
, ρ
ρ
ρ .
Parameters anρ should be determined in future. Substitution of the series into Eqs.(4a) leads to the
following results
( ) ( ) ( ) ( ) ( ) ( ) ( ) ×
∑ ∫ ∫ ∫
−
=
∑
=
=
N
n
t y
L
z
L
I
n
n
nI
z
y
x
N
n
nI
n
n
n
nI
y z
v
d
w
d
T
w
v
x
D
z
c
y
c
a
L
L
L
z
y
t
e
z
s
y
s
x
s
n
a
z
y
x
1 0
1
3
3
,
,
,
π
π
( ) ( ) ( ) ( ) ( ) ( ) ( ) −
∑ ∫ ∫ ∫
−
×
=
N
n
t x
L
z
L
I
n
n
nI
n
nI
z
y
x
n
nI
x z
d
u
d
w
d
T
w
y
u
D
z
c
x
c
e
y
s
a
L
L
L
z
x
x
s
d
e
1 0
,
,
, τ
τ
π
τ
τ
( ) ( ) ( ) ( ) ( ) ( )×
∫ ∫ ∫
−
∑ ∫ ∫ ∫
−
=
x
L
y
L
z
L
I
I
N
n
t x
L
y
L
I
n
n
nI
n
nI
z
y
x x y z
x y
T
v
v
u
k
d
u
d
v
d
T
z
v
u
D
y
c
x
c
e
z
s
a
L
L
L
y
x
,
,
,
,
,
, ,
1 0
τ
τ
π
( ) ( ) ( ) ( ) ( ) ( ) ( )×
∫ ∫ ∫ ∑
−
∑
×
=
=
x
L
y
L
z
L
N
n
n
n
n
nI
z
y
x
z
y
x
N
n
nI
n
n
n
nI
x y z
w
c
v
c
u
c
a
L
L
L
z
y
x
L
L
L
z
y
x
u
d
v
d
w
d
t
e
w
c
v
c
u
c
a
1
2
1
( ) ( ) ( ) ( ) ( ) ( ) ( ) ×
∫ ∫ ∫
+
∑
×
=
x
L
y
L
z
L
I
N
n
V
I
nV
n
n
n
nV
nI
x y z
u
d
v
d
w
d
w
v
u
f
u
d
v
d
w
d
T
v
v
u
k
t
e
w
c
v
c
u
c
a
t
e ,
,
,
,
,
1
,
z
y
x
L
L
L
z
y
x
×
( ) ( ) ( ) ( ) ( ) ( ) ( ) ×
∑ ∫ ∫ ∫
−
=
∑
=
=
N
n
t y
L
z
L
V
n
n
nV
z
y
x
N
n
nV
n
n
n
nV
y z
v
d
w
d
T
w
v
x
D
z
c
y
c
a
L
L
L
z
y
t
e
z
s
y
s
x
s
n
a
z
y
x
1 0
1
3
3
,
,
,
π
π
( ) ( ) ( ) ( ) ( ) ( ) ( ) −
∑ ∫ ∫ ∫
−
×
=
N
n
t x
L
z
L
V
n
n
nV
n
nV
z
y
x
n
nV
x z
d
u
d
w
d
T
w
y
u
D
z
c
x
c
e
y
s
a
L
L
L
z
x
x
s
d
e
1 0
,
,
, τ
τ
π
τ
τ
( ) ( ) ( ) ( ) ( ) ( )×
∫ ∫ ∫
−
∑ ∫ ∫ ∫
−
=
x
L
y
L
z
L
V
V
N
n
t x
L
y
L
V
n
n
nV
n
nV
z
y
x x y z
x y
T
v
v
u
k
d
u
d
v
d
T
z
v
u
D
y
c
x
c
e
z
s
a
L
L
L
y
x
,
,
,
,
,
, ,
1 0
τ
τ
π
( ) ( ) ( ) ( ) ( ) ( ) ( )×
∫ ∫ ∫ ∑
−
∑
×
=
=
x
L
y
L
z
L
N
n
n
n
n
nI
z
y
x
z
y
x
N
n
nI
n
n
n
nV
x y z
w
c
v
c
u
c
a
L
L
L
z
y
x
L
L
L
z
y
x
u
d
v
d
w
d
t
e
w
c
v
c
u
c
a
1
2
1
( ) ( ) ( ) ( ) ( ) ( ) ( ) ×
∫ ∫ ∫
+
∑
×
=
x
L
y
L
z
L
V
N
n
V
I
nV
n
n
n
nV
nI
x y z
u
d
v
d
w
d
w
v
u
f
u
d
v
d
w
d
T
v
v
u
k
t
e
w
c
v
c
u
c
a
t
e ,
,
,
,
,
1
,
z
y
x
L
L
L
z
y
x
× .
We used orthogonality condition of functions of the considered series framework the heterostruc-
ture to calculate coefficients anρ. The coefficients an could be calculated for any quantity of terms
N. In the common case equations for the required coefficients could be written as
( ) ( )
[ ] ( ) ( )
[ ] ×
∑ ∫ ∫ ∫
−
+
+
−
−
=
∑
−
=
=
N
n
t L L
n
y
n
y
n
nI
x
N
n
nI
nI
z
y
x
x y
y
c
n
L
y
s
y
L
x
c
n
a
L
t
e
n
a
L
L
L
1 0 0 0
2
1
6
5
2
2
2
1
2
2
2
2
1
2
1
π
π
π
10. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
10
( ) ( ) ( )
[ ] ( ) ( )
{
∑ ∫ ∫ +
−
∫
−
+
×
=
N
n
t L
n
nI
y
L
nI
n
z
n
I
x
z
x
s
x
n
a
L
d
e
x
d
y
d
z
d
z
c
n
L
z
s
z
T
z
y
x
D
1 0 0
2
0
2
2
1
1
2
,
,
,
π
τ
τ
π
( )
[ ] ( ) ( ) ( )
[ ] ( )
[ ]×
∫ ∫ −
−
+
+
−
+
+
y z
L L
n
n
z
n
z
I
n
x
x
y
c
z
d
z
c
n
L
z
s
z
L
T
z
y
x
D
x
c
n
L
L
0 0
2
1
1
2
2
2
,
,
,
1
2
π
π
( ) ( ) ( ) ( )
[ ] ( ) −
∫
−
+
+
×
z
L
nI
n
z
n
z
I
nI d
e
x
d
y
d
z
d
z
c
n
L
z
s
z
L
T
z
y
x
D
d
e
x
d
y
d
0
1
2
2
2
,
,
, τ
τ
π
τ
τ
( ) ( )
[ ] ( ) ( )
[ ] ×
∑ ∫ ∫ ∫
−
+
+
−
+
+
−
=
N
n
t L L
n
y
n
y
n
x
n
x
nI
z
x y
y
c
n
L
y
s
y
L
x
c
n
L
x
s
x
L
n
a
L 1 0 0 0
2
1
2
2
2
1
2
2
2
2
1
π
π
π
( )
[ ] ( ) ( ) ( ) ( )
[ ]
∑ ∫
+
−
+
−
∫ −
×
=
N
n
L
n
x
x
nI
nI
L
nI
I
n
x
z
x
c
n
L
L
t
e
a
d
e
x
d
y
d
z
d
T
z
y
x
D
z
c
1 0
2
0
1
2
2
2
,
,
,
2
1
π
τ
τ
( )} ( ) ( )
[ ] ( ) ( )
[ ]
∫ ∫
+
−
+
−
+
+
+
y z
L L
n
z
z
I
I
n
y
n
y
n z
c
n
L
L
T
z
y
x
k
y
c
n
L
y
s
y
L
x
s
x
0 0
, 1
2
2
,
,
,
1
2
2
2
2
π
π
( )} ( ) ( ) ( ) ( )
[ ] {
∑ ∫ ∫ +
−
+
+
−
+
=
N
n
L L
y
n
x
n
x
nV
nI
nV
nI
n
x y
L
x
c
n
L
x
s
x
L
t
e
t
e
a
a
x
d
y
d
z
d
z
s
z
1 0 0
1
2
2
2
2
π
( ) ( )
[ ] ( ) ( ) ( )
[ ]
∫ ×
−
+
+
−
+
+
z
L
n
z
n
z
V
I
n
y
n z
d
z
c
n
L
z
s
z
L
T
z
y
x
k
y
c
n
L
y
s
y
0
, 1
2
2
2
,
,
,
1
2
2
2
π
π
( ) ( )
[ ] ( ) ( )
[ ] ( )×
∑ ∫ ∫ ∫
−
+
−
+
+
×
=
N
n
L L L
I
n
y
n
n
x
n
x y z
T
z
y
x
f
y
c
n
L
y
s
y
x
c
n
L
x
s
x
x
d
y
d
1 0 0 0
,
,
,
1
1
π
π
( ) ( )
[ ] x
d
y
d
z
d
z
c
n
L
z
s
z
L n
z
n
z
−
+
+
× 1
2
2
2
π
( ) ( )
[ ] ( ) ( )
[ ] ×
∑ ∫ ∫ ∫
−
+
+
−
−
=
∑
−
=
=
N
n
t L L
n
y
n
y
n
nV
x
N
n
nV
nV
z
y
x
x y
y
c
n
L
y
s
y
L
x
c
n
a
L
t
e
n
a
L
L
L
1 0 0 0
2
1
6
5
2
2
2
1
2
2
2
2
1
2
1
π
π
π
( ) ( ) ( )
[ ] ( ) ( )
{
∑ ∫ ∫ +
−
∫
−
+
×
=
N
n
t L
n
nV
y
L
nV
n
z
n
V
x
z
x
s
x
n
a
L
d
e
x
d
y
d
z
d
z
c
n
L
z
s
z
T
z
y
x
D
1 0 0
2
0
2
2
1
1
2
,
,
,
π
τ
τ
π
( )
[ ] ( ) ( ) ( )
[ ] ( )
[ ]×
∫ ∫ −
−
+
+
−
+
+
y z
L L
n
n
z
n
z
V
n
x
x
y
c
z
d
z
c
n
L
z
s
z
L
T
z
y
x
D
x
c
n
L
L
0 0
2
1
1
2
2
2
,
,
,
1
2
π
π
( ) ( ) ( ) ( )
[ ] ( ) −
∫
−
+
+
×
z
L
nV
n
z
n
z
V
nV
d
e
x
d
y
d
z
d
z
c
n
L
z
s
z
L
T
z
y
x
D
d
e
x
d
y
d
0
1
2
2
2
,
,
, τ
τ
π
τ
τ
11. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
11
( ) ( )
[ ] ( ) ( )
[ ] ×
∑ ∫ ∫ ∫
−
+
+
−
+
+
−
=
N
n
t L L
n
y
n
y
n
x
n
x
nV
z
x y
y
c
n
L
y
s
y
L
x
c
n
L
x
s
x
L
n
a
L 1 0 0 0
2
1
2
2
2
1
2
2
2
2
1
π
π
π
( )
[ ] ( ) ( ) ( ) ( )
[ ]
∑ ∫
+
−
+
−
∫ −
×
=
N
n
L
n
x
x
nV
nV
L
nV
V
n
x
z
x
c
n
L
L
t
e
a
d
e
x
d
y
d
z
d
T
z
y
x
D
z
c
1 0
2
0
1
2
2
2
,
,
,
2
1
π
τ
τ
( )} ( ) ( )
[ ] ( ) ( )
[ ]
∫ ∫
+
−
+
−
+
+
+
y z
L L
n
z
z
V
V
n
y
n
y
n z
c
n
L
L
T
z
y
x
k
y
c
n
L
y
s
y
L
x
s
x
0 0
, 1
2
2
,
,
,
1
2
2
2
2
π
π
( )} ( ) ( ) ( ) ( )
[ ] {
∑ ∫ ∫ +
−
+
+
−
+
=
N
n
L L
y
n
x
n
x
nV
nI
nV
nI
n
x y
L
x
c
n
L
x
s
x
L
t
e
t
e
a
a
x
d
y
d
z
d
z
s
z
1 0 0
1
2
2
2
2
π
( ) ( )
[ ] ( ) ( ) ( )
[ ]
∫ ×
−
+
+
−
+
+
z
L
n
z
n
z
V
I
n
y
n z
d
z
c
n
L
z
s
z
L
T
z
y
x
k
y
c
n
L
y
s
y
0
, 1
2
2
2
,
,
,
1
2
2
2
π
π
( ) ( )
[ ] ( ) ( )
[ ] ( )×
∑ ∫ ∫ ∫
−
+
−
+
+
×
=
N
n
L L L
V
n
y
n
n
x
n
x y z
T
z
y
x
f
y
c
n
L
y
s
y
x
c
n
L
x
s
x
x
d
y
d
1 0 0 0
,
,
,
1
1
π
π
( ) ( )
[ ] x
d
y
d
z
d
z
c
n
L
z
s
z
L n
z
n
z
−
+
+
× 1
2
2
2
π
.
In the final form relations for required parameters could be written as
( )
−
+
−
+
±
+
−
=
A
y
b
y
b
A
b
b
A
b
a nI
nV
nI
2
3
4
2
3
4
3
4
4
4
λ
γ
,
nI
nI
nI
nI
nI
nI
nI
nV
a
a
a
a
χ
λ
δ
γ +
+
−
=
2
,
where ( ) ( ) ( ) ( )
[ ] ( )
{
∫ ∫ ∫ +
+
−
+
+
=
x y z
L L L
y
n
n
x
n
x
n
n L
y
s
y
x
c
n
L
x
s
x
L
T
z
y
x
k
t
e
0 0 0
, 2
1
2
2
2
,
,
,
2
π
γ ρ
ρ
ρ
ρ
( )
[ ] ( ) ( )
[ ] x
d
y
d
z
d
z
c
n
L
z
s
z
L
y
c
n
L
n
z
n
z
n
y
−
+
+
−
+ 1
2
2
2
1
2
2 π
π
, ( )×
∫
=
t
n
x
n e
n
L 0
2
2
1
τ
π
δ ρ
ρ
( ) ( )
[ ] ( ) ( )
[ ] ( ) [
∫ ∫ ∫ −
−
+
−
+
×
x y z
L L L
n
z
n
n
y
n y
d
z
d
T
z
y
x
D
z
c
n
L
z
s
z
y
c
n
L
y
s
y
0 0 0
1
,
,
,
1
2
1
2
ρ
π
π
( )] ( ) ( ) ( )
[ ] ( )
[ ] {
∫ ∫ ∫ ∫ +
−
−
+
+
+
−
t L L L
z
n
n
x
n
x
n
y
n
x y z
L
y
c
x
c
n
L
x
s
x
L
e
n
L
d
x
d
x
c
0 0 0 0
2
2
1
1
2
2
2
1
2
π
τ
π
τ ρ
( ) ( )
[ ] ( ) ( ) ( )
{
∫ ∫ +
+
−
+
+
t L
n
n
z
n
z
n
x
x
s
x
e
n
L
d
x
d
y
d
z
d
T
z
y
x
D
z
c
n
L
z
s
z
0 0
2
2
2
1
,
,
,
1
2
2
2 τ
π
τ
π
ρ
ρ
12. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
12
( )
[ ] ( ) ( )
[ ] ( )
[ ] ( ) ×
∫ ∫ −
−
+
+
−
+
+
y z
L L
n
n
y
n
y
n
x
x z
d
T
z
y
x
D
z
c
y
c
n
L
y
s
y
L
x
c
n
L
L
0 0
,
,
,
2
1
1
2
1
2 ρ
π
π
( )
t
e
n
L
L
L
d
x
d
y
d n
z
y
x
ρ
π
τ 6
5
2
2
2
−
× , ( ) ( )
[ ] ( )
[ ]
∫ ∫
+
−
+
−
+
=
x y
L L
n
y
y
n
x
n
nIV y
c
n
L
L
x
c
n
L
x
s
x
0 0
1
2
2
1
π
π
χ
( )} ( ) ( ) ( )
[ ] ( ) ( )
t
e
t
e
x
d
y
d
z
d
z
c
n
L
z
s
z
L
T
z
y
x
k
y
s
y nV
nI
L
n
z
n
z
V
I
n
z
∫
−
+
+
+
0
, 1
2
2
2
,
,
,
2
π
,
( ) ( )
[ ] ( ) ( )
[ ] ( ) ( )
[ ]
∫ ∫ ∫ ×
−
+
−
+
−
+
=
x y z
L L L
n
z
n
n
y
n
n
x
n
n z
c
n
L
z
s
z
y
c
n
L
y
s
y
x
c
n
L
x
s
x
0 0 0
1
1
1
π
π
π
λ ρ
( ) x
d
y
d
z
d
T
z
y
x
f ,
,
,
ρ
× , 2
2
4 nI
nI
nI
nV
b χ
γ
γ
γ −
= , nI
nI
nV
nI
nI
nI
nI
nV
b γ
χ
δ
χ
δ
δ
γ
γ −
−
= 2
3
2 ,
2
2
3
4
8 b
b
y
A −
+
= , ( ) 2
2
2
2 nI
nI
nV
nI
nI
nV
nI
nV
nI
nI
nV
b χ
λ
λ
δ
χ
δ
γ
γ
λ
δ
γ −
+
−
+
= , ×
= nI
b λ
2
1
nI
nI
nV
nI
nV
λ
χ
δ
δ
γ −
× ,
4
3
3 3
2
3 3
2
3b
b
q
p
q
q
p
q
y −
+
+
−
−
+
= , 2
4
2
3
4
2
9
3
b
b
b
b
p
−
= ,
( ) 3
4
2
4
1
3
2
3
3
54
27
9
2 b
b
b
b
b
b
q +
−
= .
We determine distributions of concentrations of simplest complexes of radiation defects in space
and time as the following functional series
( ) ( ) ( ) ( ) ( )
∑
=
Φ
=
Φ
N
n
n
n
n
n
n t
e
z
c
y
c
x
c
a
t
z
y
x
1
0 ,
,
, ρ
ρ
ρ .
Here anΦρ are the coefficients, which should be determined. Let us previously transform the Eqs.
(6) to the following integro-differential form
( ) ( ) ( ) ×
∫ ∫ ∫
Φ
=
∫ ∫ ∫Φ Φ
t y
L
z
L
I
I
x
L
y
L
z
L
I
z
y
x y z
x y z
d
v
d
w
d
x
w
v
x
T
w
v
x
D
u
d
v
d
w
d
t
w
v
u
L
L
L
z
y
x
0
,
,
,
,
,
,
,
,
, τ
∂
τ
∂
( ) ( ) ( )
∫ ∫ ∫ ×
+
∫ ∫ ∫
Φ
+
× Φ
Φ
t x
L
y
L
I
y
x
t x
L
z
L
I
I
z
x
z
y x y
x z
T
z
v
u
D
L
L
y
x
d
u
d
w
d
y
w
y
u
T
w
y
u
D
L
L
z
x
L
L
z
y
0
0
,
,
,
,
,
,
,
,
, τ
∂
τ
∂
( ) ( ) ( ) −
∫ ∫ ∫
+
Φ
×
x
L
y
L
z
L
I
I
z
y
x
I
x y z
u
d
v
d
w
d
w
v
u
I
T
w
v
u
k
L
L
L
z
y
x
d
u
d
v
d
z
z
v
u
τ
τ
∂
τ
∂
,
,
,
,
,
,
,
,
, 2
, (6a)
( ) ( ) ( )
∫ ∫ ∫
+
∫ ∫ ∫
− Φ
x
L
y
L
z
L
I
z
y
x
x
L
y
L
z
L
I
z
y
x x y z
x y z
u
d
v
d
w
d
w
v
u
f
L
L
L
z
y
x
u
d
v
d
w
d
w
v
u
I
T
w
v
u
k
L
L
L
z
y
x
,
,
,
,
,
,
,
, τ
( ) ( ) ( ) ×
∫ ∫ ∫
Φ
=
∫ ∫ ∫Φ Φ
t y
L
z
L
V
V
x
L
y
L
z
L
V
z
y
x y z
x y z
d
v
d
w
d
x
w
v
x
T
w
v
x
D
u
d
v
d
w
d
t
w
v
u
L
L
L
z
y
x
0
,
,
,
,
,
,
,
,
, τ
∂
τ
∂
( ) ( ) ( )
∫ ∫ ∫ ×
+
∫ ∫ ∫
Φ
+
× Φ
Φ
t x
L
y
L
V
y
x
t x
L
z
L
V
V
z
x
z
y x y
x z
T
z
v
u
D
L
L
y
x
d
u
d
w
d
y
w
y
u
T
w
y
u
D
L
L
z
x
L
L
z
y
0
0
,
,
,
,
,
,
,
,
, τ
∂
τ
∂
13. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
13
( ) ( ) ( ) −
∫ ∫ ∫
+
Φ
×
x
L
y
L
z
L
V
V
z
y
x
V
x y z
u
d
v
d
w
d
w
v
u
V
T
w
v
u
k
L
L
L
z
y
x
d
u
d
v
d
z
z
v
u
τ
τ
∂
τ
∂
,
,
,
,
,
,
,
,
, 2
,
( ) ( ) ( )
∫ ∫ ∫
+
∫ ∫ ∫
− Φ
x
L
y
L
z
L
V
z
y
x
x
L
y
L
z
L
V
z
y
x x y z
x y z
u
d
v
d
w
d
w
v
u
f
L
L
L
z
y
x
u
d
v
d
w
d
w
v
u
V
T
w
v
u
k
L
L
L
z
y
x
,
,
,
,
,
,
,
, τ .
Substitution of the previously considered series in the Eqs.(6a) leads to the following form
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )×
∑ ∫ ∫ ∫
−
=
∑
−
=
Φ
=
Φ
N
n
t y
L
z
L
n
n
nI
n
I
n
z
y
x
N
n
nI
n
n
n
I
n
y z
w
c
v
c
t
e
x
s
a
n
L
L
L
z
y
t
e
z
s
y
s
x
s
n
a
z
y
x
1 0
1
3
3
π
π
( ) ( ) ( ) ( ) ×
∑ ∫ ∫ ∫
−
×
=
Φ
Φ
Φ
N
n
t x
L
z
L
I
n
n
I
n
z
y
x
I
x z
d
u
d
w
d
T
w
v
u
D
w
c
u
c
a
L
L
L
z
x
d
v
d
w
d
T
w
v
x
D
1 0
,
,
,
,
,
, τ
π
τ
( ) ( ) ( ) ( ) ( ) ( ) ( ) +
∑ ∫ ∫ ∫
−
×
=
Φ
Φ
Φ
Φ
N
n
t x
L
y
L
I
n
n
I
n
n
I
n
z
y
x
I
n
n
x y
d
u
d
v
d
T
z
v
u
D
v
c
u
c
t
e
z
s
a
n
L
L
L
y
x
t
e
y
s
n
1 0
,
,
, τ
π
( ) ( ) ( ) ×
∫ ∫ ∫
+
∫ ∫ ∫
+ Φ
x
L
y
L
z
L
I
x
L
y
L
z
L
I
I
z
y
x x y z
x y z
u
d
v
d
w
d
w
v
u
f
u
d
v
d
w
d
w
v
u
I
T
w
v
u
k
L
L
L
z
y
x
,
,
,
,
,
,
,
, 2
, τ
( ) ( )
∫ ∫ ∫
−
×
x
L
y
L
z
L
I
z
y
x
z
y
x x y z
u
d
v
d
w
d
w
v
u
I
T
w
v
u
k
L
L
L
z
y
x
L
L
L
z
y
x
τ
,
,
,
,
,
,
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )×
∑ ∫ ∫ ∫
−
=
∑
−
=
Φ
=
Φ
N
n
t y
L
z
L
n
n
nV
n
V
n
z
y
x
N
n
nV
n
n
n
V
n
y z
w
c
v
c
t
e
x
s
a
n
L
L
L
z
y
t
e
z
s
y
s
x
s
n
a
z
y
x
1 0
1
3
3
π
π
( ) ( ) ( ) ( ) ×
∑ ∫ ∫ ∫
−
×
=
Φ
Φ
N
n
t x
L
z
L
V
n
n
z
y
x
V
x z
d
u
d
w
d
T
w
v
u
D
w
c
u
c
n
L
L
L
z
x
d
v
d
w
d
T
w
v
x
D
1 0
,
,
,
,
,
, τ
π
τ
( ) ( ) ( ) ( ) ( ) ( ) ( ) ×
∑ ∫ ∫ ∫
−
×
=
Φ
Φ
Φ
Φ
N
n
t x
L
y
L
V
n
n
V
n
n
z
y
x
V
n
n
V
n
x y
d
u
d
v
d
T
z
v
u
D
v
c
u
c
t
e
z
s
n
L
L
L
y
x
t
e
y
s
a
1 0
,
,
, τ
π
( ) ( ) ( ) ×
∫ ∫ ∫
+
∫ ∫ ∫
+
× Φ
Φ
x
L
y
L
z
L
V
x
L
y
L
z
L
V
V
z
y
x
V
n
x y z
x y z
u
d
v
d
w
d
w
v
u
f
u
d
v
d
w
d
w
v
u
V
T
w
v
u
k
L
L
L
z
y
x
a ,
,
,
,
,
,
,
, 2
,
τ
( ) ( )
∫ ∫ ∫
−
×
x
L
y
L
z
L
V
z
y
x
z
y
x x y z
u
d
v
d
w
d
w
v
u
V
T
w
v
u
k
L
L
L
z
y
x
L
L
L
z
y
x
τ
,
,
,
,
,
, .
We used orthogonality condition of functions of the considered series framework the heterostruc-
ture to calculate coefficients anΦρ. The coefficients anΦρ could be calculated for any quantity of
terms N. In the common case equations for the required coefficients could be written as
( ) ( )
[ ] ( ) ( )
[ ] ×
∑∫ ∫ ∫
−
+
+
−
−
=
∑
−
=
=
Φ
Φ
N
n
t L L
n
y
n
y
n
x
N
n
I
n
I
n
z
y
x
x y
y
c
n
L
y
s
y
L
x
c
L
t
e
n
a
L
L
L
1 0 0 0
1
6
5
2
2
2
1
2
2
2
2
1
2
1
π
π
π
14. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
14
( ) ( ) ( )
[ ] ( ) ( )
{
∑∫ ∫ +
−
∫
−
+
×
=
Φ
Φ
Φ
N
n
t L
n
L
I
n
n
z
n
I
I
n
x
z
x
s
x
d
e
x
d
y
d
z
d
z
c
n
L
z
s
z
T
z
y
x
D
n
a
1 0 0
0
2
2
2
1
1
2
,
,
,
π
τ
τ
π
( )
[ ] ( )
[ ] ( ) ( ) ( )
[ ] ×
∫ ∫
−
+
−
−
+
+ Φ
y z
L L
n
z
n
I
n
n
x
x x
d
y
d
z
d
z
c
n
L
z
s
z
T
z
y
x
D
y
c
x
c
n
L
L
0 0
1
2
,
,
,
2
1
1
2
2 π
π
( ) ( ) ( )
[ ] ( ) ( )
[ ]
∑ ∫ ∫ ∫
+
−
+
−
+
−
×
=
Φ
Φ
Φ
N
n
t L L
n
y
n
n
x
n
I
n
x
y
I
n
I
n
x y
y
c
n
L
y
s
y
x
c
n
L
x
s
x
n
a
L
d
L
n
e
a
1 0 0 0
2
2
1
2
2
2
1
2
2
1
π
π
π
τ
τ
} ( )
[ ] ( ) ( ) ( ) ( )
[ ]
∑ ∫ ∫
+
−
+
∫ −
+
=
Φ
Φ
Φ
Φ
N
n
t L
n
x
I
n
I
n
L
I
n
I
n
y
x
z
x
c
n
L
e
n
a
d
e
x
d
y
d
z
d
T
z
y
x
D
y
c
L
1 0 0
3
3
0
1
2
1
,
,
,
2
1
π
τ
π
τ
τ
( )} ( ) ( )
[ ] ( ) ( ) ( )
[ ]
∫
+
−
∫
−
+
+
z
y L
n
z
I
I
L
n
y
n
n z
c
n
L
T
z
y
x
k
t
z
y
x
I
y
c
n
L
y
s
y
x
s
x
0
,
2
0
1
2
,
,
,
,
,
,
1
2 π
π
( )} ( ) ( ) ( )
[ ] ( )
[ ]
∑ ∫ ∫ ∫
+
−
−
+
−
+
=
Φ
Φ
N
n
t L L
n
y
n
x
n
I
n
I
n
n
x y
y
c
n
L
x
c
n
L
x
s
x
e
n
a
x
d
y
d
z
d
z
s
z
1 0 0 0
3
3
1
2
1
2
1
π
π
τ
π
( )} ( ) ( )
[ ] ( ) ( ) ×
∑
+
∫
−
+
+
=
Φ
N
n
I
n
L
I
n
z
n
n
n
a
x
d
y
d
z
d
t
z
y
x
I
T
z
y
x
k
z
c
n
L
z
s
z
y
s
y
z
1
3
3
0
1
,
,
,
,
,
,
1
2 π
π
( ) ( ) ( )
[ ] ( ) ( )
[ ] ( )
[ ]
∫ ∫ ∫ ∫
+
−
−
+
−
+
× Φ
t L L L
n
z
n
y
n
n
x
n
I
n
x y z
z
c
n
L
y
c
n
L
y
s
y
x
c
n
L
x
s
x
e
0 0 0 0
1
2
1
2
1
2 π
π
π
τ
( )} ( ) x
d
y
d
z
d
z
y
x
f
z
s
z I
n
,
,
Φ
+
( ) ( )
[ ] ( ) ( )
[ ] ×
∑∫ ∫ ∫
−
+
+
−
−
=
∑
−
=
=
Φ
Φ
N
n
t L L
n
y
n
y
n
x
N
n
V
n
V
n
z
y
x
x y
y
c
n
L
y
s
y
L
x
c
L
t
e
n
a
L
L
L
1 0 0 0
1
6
5
2
2
2
1
2
2
2
2
1
2
1
π
π
π
( ) ( ) ( )
[ ] ( ) ( )
{
∑∫ ∫ +
−
∫
−
+
×
=
Φ
Φ
Φ
N
n
t L
n
L
V
n
n
z
n
V
V
n
x
z
x
s
x
d
e
x
d
y
d
z
d
z
c
n
L
z
s
z
T
z
y
x
D
n
a
1 0 0
0
2
2
2
1
1
2
,
,
,
π
τ
τ
π
( )
[ ] ( )
[ ] ( ) ( ) ( )
[ ] ×
∫ ∫
−
+
−
−
+
+ Φ
y z
L L
n
z
n
V
n
n
x
x x
d
y
d
z
d
z
c
n
L
z
s
z
T
z
y
x
D
y
c
x
c
n
L
L
0 0
1
2
,
,
,
2
1
1
2
2 π
π
( ) ( ) ( )
[ ] ( ) ( )
[ ]
∑ ∫ ∫ ∫
+
−
+
−
+
−
×
=
Φ
Φ
Φ
N
n
t L L
n
y
n
n
x
n
V
n
x
y
V
n
V
n
x y
y
c
n
L
y
s
y
x
c
n
L
x
s
x
n
a
L
d
L
n
e
a
1 0 0 0
2
2
1
2
2
2
1
2
2
1
π
π
π
τ
τ
} ( )
[ ] ( ) ( ) ( ) ( )
[ ]
∑ ∫ ∫
+
−
+
∫ −
+
=
Φ
Φ
Φ
Φ
N
n
t L
n
x
V
n
V
n
L
V
n
V
n
y
x
z
x
c
n
L
e
n
a
d
e
x
d
y
d
z
d
T
z
y
x
D
y
c
L
1 0 0
3
3
0
1
2
1
,
,
,
2
1
π
τ
π
τ
τ
15. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
15
( )} ( ) ( )
[ ] ( ) ( ) ( )
[ ]
∫
+
−
∫
−
+
+
z
y L
n
z
V
V
L
n
y
n
n z
c
n
L
T
z
y
x
k
t
z
y
x
V
y
c
n
L
y
s
y
x
s
x
0
,
2
0
1
2
,
,
,
,
,
,
1
2 π
π
( )} ( ) ( ) ( )
[ ] ( )
[ ]
∑ ∫ ∫ ∫
+
−
−
+
−
+
=
Φ
Φ
N
n
t L L
n
y
n
x
n
V
n
V
n
n
x y
y
c
n
L
x
c
n
L
x
s
x
e
n
a
x
d
y
d
z
d
z
s
z
1 0 0 0
3
3
1
2
1
2
1
π
π
τ
π
( )} ( ) ( )
[ ] ( ) ( ) ×
∑
+
∫
−
+
+
=
Φ
N
n
V
n
L
V
n
z
n
n
n
a
x
d
y
d
z
d
t
z
y
x
V
T
z
y
x
k
z
c
n
L
z
s
z
y
s
y
z
1
3
3
0
1
,
,
,
,
,
,
1
2 π
π
( ) ( ) ( )
[ ] ( ) ( )
[ ] ( )
[ ]
∫ ∫ ∫ ∫
+
−
−
+
−
+
× Φ
t L L L
n
z
n
y
n
n
x
n
V
n
x y z
z
c
n
L
y
c
n
L
y
s
y
x
c
n
L
x
s
x
e
0 0 0 0
1
2
1
2
1
2 π
π
π
τ
( )} ( ) x
d
y
d
z
d
z
y
x
f
z
s
z V
n
,
,
Φ
+ .
3. DISCUSSION
In this section we analyzed redistribution of dopant with account redistribution of radiation de-
fects. The analysis shown, that presents of interface between materials of heterostructure gives a
possibility to increase absolute value of gradient of concentration of dopant outside of enriched
are by the dopant (see Figs. 2 and 3). At the same time homogeneity of concentration of dopant in
enriched area increases (see Figs. 2 and 3). The effects could be find, when dopant diffusion coef-
ficient in the doped area is larger, than in the nearest areas. Otherwise absolute value of gradient
of concentration of dopant decreases outside enriched by the dopant area (see Fig. 4). However
the decreasing could be partially or fully compensated by using high doping of materials. The
high doping leads to significant nonlinearity of diffusion of dopant. To increase compactness of
the considered circuits XOR it is attracted an interest the first relation between values of dopant
diffusion coefficient.
Fig.2a. Spatial distributions of infused dopant concentration in the considered heterostructure. The consi-
dered direction perpendicular to the interface between epitaxial layer substrate. Difference between values
of dopant diffusion coefficient in layers of heterostructure increases with increasing of number of curves
16. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
16
x
0.0
0.5
1.0
1.5
2.0
C(x,
Θ
)
2
3
4
1
0 L/4 L/2 3L/4 L
Epitaxial layer Substrate
Fig.2b. Spatial distributions of infused dopant concentration in the considered heterostructure. Curves 1 and
3 corresponds to annealing time Θ=0.0048(Lx
2
+Ly
2
+Lz
2
)/D0. Curves 2 and 4 corresponds to annealing time
Θ=0.0057(Lx
2
+Ly
2
+Lz
2
)/D0. Curves 1 and 2 corresponds to homogenous sample. Curves 3 and 4 corres-
ponds to the considered heterostructure. Difference between values of dopant diffusion coefficient in layers
of heterostructure increases with increasing of number of curves
x
0.00000
0.00001
0.00010
0.00100
0.01000
0.10000
1.00000
C(x,
Θ
)
fC(x)
L/4
0 L/2 3L/4 L
x0
1
2
Substrate
Epitaxial
layer 1
Epitaxial
layer 2
Fig.3. Implanted dopant distributions in heterostructure in heterostructure with two epitaxial layers (solid
lines) and with one epitaxial layer (dushed lines) for different values of annealing time. Difference between
values of dopant diffusion coefficient in layers of heterostructure increases with increasing of number of
curves
Increasing of annealing time leads to acceleration of diffusion. In this situation one can find in-
creasing quantity of dopant in materials near doped sections. If annealing time is small, the do-
pant can not achieves nearest interface between layers of heterostructure. These effects are shown
by Figs. 5 and 6. We used recently introduced criterion [16-23] to estimate compromise value of
annealing time. Framework the criterion we approximate real distribution of concentration of do-
pant by idealized step-wise distribution ψ (x,y,z), which would be better to use for minimization
dimensions of elements of the considered circuit XOR [19-26]. Farther the required compromise
annealing time has been calculated by minimization the following mean-squared error
17. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
17
( ) ( )
[ ]
∫ ∫ ∫ −
Θ
=
x y z
L L L
z
y
x
x
d
y
d
z
d
z
y
x
z
y
x
C
L
L
L
U
0 0 0
,
,
,
,
,
1
ψ . (8)
C(x,
Θ
)
0 Lx
2
1
3
4
Fig. 4. Distributions of concentrations of infused dopant in the considered heterostructure. Curve 1 is the
idealized distribution of dopant. Curves 2-4 are the real distributions of concentrations of dopant for differ-
ent values of annealing time for increasing of annealing time with increasing of number of curve
x
C(x,
Θ
)
1
2
3
4
0 L
Fig. 5. Distributions of concentrations of implanted dopant in the considered heterostructure. Curve 1 is the
idealized distribution of dopant. Curves 2-4 are the real distributions of concentrations of dopant for differ-
ent values of annealing time for increasing of annealing time with increasing of number of curve
We analyzed optimal value of annealing time. The analysis shows, that optimal value of anneal-
ing time for ion type of doping is smaller, than optimal value of annealing time for diffusion type
of doping. It is known, that ion doping of materials leads to radiation damage of doped materials.
In this situation radiation defects should be annealed. The annealing leads to the above difference
between optimal values of annealing time of dopant. The annealing of implanted dopant is neces-
sary in the case, when the dopant did not achieved nearest interface between layers of heterostruc-
ture during annealing of radiation defects.
18. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
18
It should be noted, that using diffusion type of doping did not leads to radiation damage of mate-
rials. However radiation damage of materials during ion doping gives a possibility to decrease
mismatch-induced stress in heterostructure [34].
4. CONCLUSIONS
In this paper we introduced an approach to decrease dimensions of a circuit XOR. The approach
based on optimization of manufacturing field-effect heterotransistors, which includes into itself
the considered circuit.
ACKNOWLEDGEMENTS
This work is supported by the agreement of August 27, 2013 № 02.В.49.21.0003 between The
Ministry of education and science of the Russian Federation and Lobachevsky State University of
Nizhni Novgorod, educational fellowship for scientific research of Government of Russian, edu-
cational fellowship for scientific research of Government of Nizhny Novgorod region of Russia
and of Nizhny Novgorod State University of Architecture and Civil Engineering.
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AUTHORS
Pankratov Evgeny Leonidovich was born at 1977. From 1985 to 1995 he was educated in a secondary
school in Nizhny Novgorod. From 1995 to 2004 he was educated in Nizhny Novgorod State University:
from 1995 to 1999 it was bachelor course in Radiophysics, from 1999 to 2001 it was master course in Ra-
diophysics with specialization in Statistical Radiophysics, from 2001 to 2004 it was PhD course in Radio-
physics. From 2004 to 2008 E.L. Pankratov was a leading technologist in Institute for Physics of Micro-
structures. From 2008 to 2012 E.L. Pankratov was a senior lecture/Associate Professor of Nizhny Novgo-
rod State University of Architecture and Civil Engineering. 2012-2015 Full Doctor course in Radi-
ophysical Department of Nizhny Novgorod State University. Since 2015 E.L. Pankratov is an Associate
Professor of Nizhny Novgorod State University. He has 135 published papers in area of his researches.
Bulaeva Elena Alexeevna was born at 1991. From 1997 to 2007 she was educated in secondary school of
village Kochunovo of Nizhny Novgorod region. From 2007 to 2009 she was educated in boarding school
“Center for gifted children”. From 2009 she is a student of Nizhny Novgorod State University of Architec-
20. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.6, No.1, January 2016
20
ture and Civil Engineering (spatiality “Assessment and management of real estate”). At the same time she
is a student of courses “Translator in the field of professional communication” and “Design (interior art)” in
the University. Since 2014 E.A. Bulaeva is in a PhD program in Radiophysical Department of Nizhny
Novgorod State University. She has 90 published papers in area of her researches.