We analyzed mass and heat transport during manufacturing field-effect heterotransistors with several
sources to decrease their dimensions. Framework the result of manufacturing it is necessary to manufacture
heterostructure with specific configuration. After that it is necessary to dope required areas of the heterostructure by diffusion or ion implantation to manufacture the required type of conductivity (p or n). After
the doping it is necessary to do optimize annealing. We introduce an analytical approach to prognosis mass
and heat transport during technological processes. Using the approach leads to take into account nonlinearity of mass and heat transport and variation in space and time (at one time) physical parameters of these
processes
ON OPTIMIZATION OF MANUFACTURING OF MULTICHANNEL HETEROTRANSISTORS TO INCREAS...ijrap
In this paper we consider an approach to increase integration rate of field-effect heterotransistors. Framework
the approach we consider a heterostructure with specific configuration. After manufacturing the
heterostructure we consider doping of required areas of the heterostructure by diffusion or ion implantation.
The doping finished by optimized annealing of dopant and/or radiation defects. Framework this paper
we consider a possibility to manufacture with several channels. Manufacturing multi-channel transistors
gives us a possibility the to increase integration rate of transistors and to increase electrical current
through the transistor.
ON INCREASING OF DENSITY OF ELEMENTS IN A MULTIVIBRATOR ON BIPOLAR TRANSISTORSijcsitcejournal
In this paper we consider an approach to increase density of elements of a multivibrator on bipolar transistors.
The considered approach based on manufacturing a heterostructure with necessity configuration,
doping by diffusion or ion implantation of required areas to manufacture the required type of conductivity
(p or n) in the areas and optimization of annealing of dopant and/or radiation defects to manufacture more
compact distributions of concentrations of dopants. We also introduce an analytical approach to prognosis
technological process.
ON OPTIMIZATION OF MANUFACTURING OF FIELD EFFECT HETEROTRANSISTORS FRAMEWORK ...antjjournal
We consider an approach for increasing density of field-effect heterotransistors in a single-stage multi-path
operational amplifier. At the same time one can obtain decreasing of dimensions of the above transistors.
Dimensions of the elements could be decreased by manufacturing of these elements in a heterostructure
with specific structure. The manufacturing is doing by doping of required areas of the heterostructure by
diffusion or ion implantation with future optimization of annealing of dopant and/or radiation defects.
ON OPTIMIZATION OF MANUFACTURING OF FIELD-EFFECT HETEROTRANSISTORS FRAMEWORK ...ijoejournal
In this paper we introduce an approach to increase density of field-effect transistors framework a voltage reference. Framework the approach we consider manufacturing the inverter in heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or ion implantation. After that dopant and radiation defects should by annealed framework optimized scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures during manufacturing of integrated circuits with account mismatch-induced stress.
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.
ON APPROACH OF OPTIMIZATION OF FORMATION OF INHOMOGENOUS DISTRIBUTIONS OF DOP...ijcsa
We introduce an approach of manufacturing of a field-effect heterotransistor with inhomogenous doping of channel. The inhomogenous distribution of concentration of dopant gives a possibility to change speed of transport of charge carriers and to decrease length of channel.
Dependence of Charge Carriers Mobility in the P-N-Heterojunctions on Composit...msejjournal
In this paper we consider manufacturing a p-n-junctions by dopant diffusion or ion implantation into a multilayer structure. We introduce an approach to increase sharpness of these p-n-junctions and at the same time to increase homogeneity of distributions of dopants in enriched by these dopants areas. We consider influence of the above changing of distribution of dopant on charge carrier mobility. We also consider an approach to decrease value of mismatch-induced stress in the considered multilayer structure by using a buffer layer. The decreasing gives a possibility to increase value of charge carrier mobility.
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 OF MULTICHANNEL HETEROTRANSISTORS TO INCREAS...ijrap
In this paper we consider an approach to increase integration rate of field-effect heterotransistors. Framework
the approach we consider a heterostructure with specific configuration. After manufacturing the
heterostructure we consider doping of required areas of the heterostructure by diffusion or ion implantation.
The doping finished by optimized annealing of dopant and/or radiation defects. Framework this paper
we consider a possibility to manufacture with several channels. Manufacturing multi-channel transistors
gives us a possibility the to increase integration rate of transistors and to increase electrical current
through the transistor.
ON INCREASING OF DENSITY OF ELEMENTS IN A MULTIVIBRATOR ON BIPOLAR TRANSISTORSijcsitcejournal
In this paper we consider an approach to increase density of elements of a multivibrator on bipolar transistors.
The considered approach based on manufacturing a heterostructure with necessity configuration,
doping by diffusion or ion implantation of required areas to manufacture the required type of conductivity
(p or n) in the areas and optimization of annealing of dopant and/or radiation defects to manufacture more
compact distributions of concentrations of dopants. We also introduce an analytical approach to prognosis
technological process.
ON OPTIMIZATION OF MANUFACTURING OF FIELD EFFECT HETEROTRANSISTORS FRAMEWORK ...antjjournal
We consider an approach for increasing density of field-effect heterotransistors in a single-stage multi-path
operational amplifier. At the same time one can obtain decreasing of dimensions of the above transistors.
Dimensions of the elements could be decreased by manufacturing of these elements in a heterostructure
with specific structure. The manufacturing is doing by doping of required areas of the heterostructure by
diffusion or ion implantation with future optimization of annealing of dopant and/or radiation defects.
ON OPTIMIZATION OF MANUFACTURING OF FIELD-EFFECT HETEROTRANSISTORS FRAMEWORK ...ijoejournal
In this paper we introduce an approach to increase density of field-effect transistors framework a voltage reference. Framework the approach we consider manufacturing the inverter in heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or ion implantation. After that dopant and radiation defects should by annealed framework optimized scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures during manufacturing of integrated circuits with account mismatch-induced stress.
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.
ON APPROACH OF OPTIMIZATION OF FORMATION OF INHOMOGENOUS DISTRIBUTIONS OF DOP...ijcsa
We introduce an approach of manufacturing of a field-effect heterotransistor with inhomogenous doping of channel. The inhomogenous distribution of concentration of dopant gives a possibility to change speed of transport of charge carriers and to decrease length of channel.
Dependence of Charge Carriers Mobility in the P-N-Heterojunctions on Composit...msejjournal
In this paper we consider manufacturing a p-n-junctions by dopant diffusion or ion implantation into a multilayer structure. We introduce an approach to increase sharpness of these p-n-junctions and at the same time to increase homogeneity of distributions of dopants in enriched by these dopants areas. We consider influence of the above changing of distribution of dopant on charge carrier mobility. We also consider an approach to decrease value of mismatch-induced stress in the considered multilayer structure by using a buffer layer. The decreasing gives a possibility to increase value of charge carrier mobility.
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 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.
AN APPROACH TO OPTIMIZE OF MANUFACTURING OF A VOLTAGE REFERENCE BASED ON HETE...JaresJournal
In this paper we introduce an approach to increase density of field-effect transistors framework a voltage
reference. Framework the approach we consider manufacturing the inverter in heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or ion implantation. After that dopant and radiation defects should by annealed framework optimized scheme. We also
consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We
introduce an analytical approach to analyze mass and heat transport in heterostructures during manufacturing of integrated circuits with account mismatch-induced stress.
ON APPROACH TO INCREASE DENSITY OF FIELD- EFFECT TRANSISTORS IN AN INVERTER C...antjjournal
In this paper we consider an approach to decrease dimensions of field-effect transistors framework invertors with increasing of their density. Framework the approach it is necessary to manufacture a
heterostructure, which consist of two layers. One of them includes into itself several sections. After manufacturing of the heterostructure these sections should be doped by diffusion or by ion implantation with future optimized annealing of dopant and/or radiation defects. To prognosis the technological process we consider an analytical approach, which gives a possibility to take into account variation of physical parameters in space and time. At the same time the approach gives a possibility to take into
account nonlinearity of mass and heat transport and to analyze the above transport without crosslinking solutions on interfaces between materials of heterostructure.
ON OPTIMIZATION OF MANUFACTURING OF FIELD-EFFECT HETERO TRANSISTORS A THREE S...jedt_journal
In this paper we introduce an approach to increase density of field-effect hetero transistors framework a three-stage
amplifier circuit. At the same time one can obtain decreasing of dimensions of the above transistors. Dimensions of the elements will be decreased due to manufacture heterostructure with specific structure, doping of required areas of the hetero structure by diffusion or ion implantation and optimization of annealing of dopant and/or radiation defects.
Decreasing of quantity of radiation de fects inijcsa
Recently we introduced an approach to increase sharpness of diffusion-junction and implanted-junction
heterorectifiers. The heterorectifiers could by single and as a part of heterobipolar transistors. However
manufacturing p-n-junctions by ion implantation leads to generation of radiation defects in materials of
heterostructure. In this paper we introduce an approach to use an overlayer and optimization of annealing
of radiation defects to decrease quantity of radiation defects.
OPTIMIZATION OF MANUFACTURING OF LOGICAL ELEMENTS "AND" MANUFACTURED BY USING...ijcsitcejournal
In this paper we introduce an approach to decrease dimensions of logical elements "AND" based on fieldeffect
heterotransistors. Framework the approach one shall consider a heterostructure with specific structure.
Several specific areas of the het
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.
ANALYSIS OF MANUFACTURING OF VOLTAGE RESTORE TO INCREASE DENSITY OF ELEMENTS ...ijoejournal
We introduce an approach for increasing density of voltage restore elements. The approach based on
manufacturing of a heterostructure, which consist of a substrate and an epitaxial layer with special configuration.
Several required sections of the layer should be doped by diffusion or ion implantation. After
that dopants and/or radiation defects should be annealed.
ON OPTIMIZATION OF MANUFACTURING OF ELEMENTS OF AN BINARY-ROM CIRCUIT TO INCR...JaresJournal
In this paper we introduce an approach to increase integration rate of elements of an binary-ROM 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.
On Decreasing of Dimensions of Field-Effect Transistors with Several Sourcesmsejjournal
We analyzed mass and heat transport during manufacturing field-effect heterotransistors with several
sources to decrease their dimensions. Framework the result of manufacturing it is necessary to manufacture
heterostructure with specific configuration. After that it is necessary to dope required areas of the heterostructure by diffusion or ion implantation to manufacture the required type of conductivity (p or n). After
the doping it is necessary to do optimize annealing. We introduce an analytical approach to prognosis mass
and heat transport during technological processes. Using the approach leads to take into account nonlinearity of mass and heat transport and variation in space and time (at one time) physical parameters of these
processes
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 Optimization of Manufacturing of Field-Effect Heterotransistors Frame-work...antjjournal
We consider an approach for increasing density of field-effect heterotransistors in a single-stage multi-path
operational amplifier. At the same time one can obtain decreasing of dimensions of the above transistors.
Dimensions of the elements could be decreased by manufacturing of these elements in a heterostructure
with specific structure. The manufacturing is doing by doping of required areas of the heterostructure by
diffusion or ion implantation with future optimization of annealing of dopant and/or radiation defects.
On Optimization of Manufacturing of Field-Effect Heterotransistors Frame-work...antjjournal
We consider an approach for increasing density of field-effect heterotransistors in a single-stage multi-path operational amplifier. At the same time one can obtain decreasing of dimensions of the above transistors.
Dimensions of the elements could be decreased by manufacturing of these elements in a heterostructure with specific structure. The manufacturing is doing by doping of required areas of the heterostructure by
diffusion or ion implantation with future optimization of annealing of dopant and/or radiation defects.
Influence of Overlayers on Depth of Implanted-Heterojunction RectifiersZac Darcy
In this paper we compare distributions of concentrations of dopants in an implanted-junction rectifiers in a
heterostructures with an overlayer and without the overlayer. Conditions for decreasing of depth of the
considered p-n-junction have been formulated.
INFLUENCE OF OVERLAYERS ON DEPTH OF IMPLANTED-HETEROJUNCTION RECTIFIERSZac Darcy
In this paper we compare distributions of concentrations of dopants in an implanted-junction rectifiers in a
heterostructures with an overlayer and without the overlayer. Conditions for decreasing of depth of the
considered p-n-junction have been formulated.
Optimization of Manufacture of Field-Effect Heterotransistors without P-N-Jun...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.
Optimization of Manufacture of Field-Effect Heterotransistors without P-N-Jun...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.
DEPENDENCE OF CHARGE CARRIERS MOBILITY IN THE P-N-HETEROJUNCTIONS ON COMPOSIT...msejjournal
In this paper we consider manufacturing a p-n-junctions by dopant diffusion or ion implantation into a
multilayer structure. We introduce an approach to increase sharpness of these p-n-junctions and at the
same time to increase homogeneity of distributions of dopants in enriched by these dopants areas. We consider influence of the above changing of distribution of dopant on charge carrier mobility. We also consider an approach to decrease value of mismatch-induced stress in the considered multilayer structure by using a buffer layer. The decreasing gives a possibility to increase value of charge carrier mobility.
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 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.
AN APPROACH TO OPTIMIZE OF MANUFACTURING OF A VOLTAGE REFERENCE BASED ON HETE...JaresJournal
In this paper we introduce an approach to increase density of field-effect transistors framework a voltage
reference. Framework the approach we consider manufacturing the inverter in heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or ion implantation. After that dopant and radiation defects should by annealed framework optimized scheme. We also
consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We
introduce an analytical approach to analyze mass and heat transport in heterostructures during manufacturing of integrated circuits with account mismatch-induced stress.
ON APPROACH TO INCREASE DENSITY OF FIELD- EFFECT TRANSISTORS IN AN INVERTER C...antjjournal
In this paper we consider an approach to decrease dimensions of field-effect transistors framework invertors with increasing of their density. Framework the approach it is necessary to manufacture a
heterostructure, which consist of two layers. One of them includes into itself several sections. After manufacturing of the heterostructure these sections should be doped by diffusion or by ion implantation with future optimized annealing of dopant and/or radiation defects. To prognosis the technological process we consider an analytical approach, which gives a possibility to take into account variation of physical parameters in space and time. At the same time the approach gives a possibility to take into
account nonlinearity of mass and heat transport and to analyze the above transport without crosslinking solutions on interfaces between materials of heterostructure.
ON OPTIMIZATION OF MANUFACTURING OF FIELD-EFFECT HETERO TRANSISTORS A THREE S...jedt_journal
In this paper we introduce an approach to increase density of field-effect hetero transistors framework a three-stage
amplifier circuit. At the same time one can obtain decreasing of dimensions of the above transistors. Dimensions of the elements will be decreased due to manufacture heterostructure with specific structure, doping of required areas of the hetero structure by diffusion or ion implantation and optimization of annealing of dopant and/or radiation defects.
Decreasing of quantity of radiation de fects inijcsa
Recently we introduced an approach to increase sharpness of diffusion-junction and implanted-junction
heterorectifiers. The heterorectifiers could by single and as a part of heterobipolar transistors. However
manufacturing p-n-junctions by ion implantation leads to generation of radiation defects in materials of
heterostructure. In this paper we introduce an approach to use an overlayer and optimization of annealing
of radiation defects to decrease quantity of radiation defects.
OPTIMIZATION OF MANUFACTURING OF LOGICAL ELEMENTS "AND" MANUFACTURED BY USING...ijcsitcejournal
In this paper we introduce an approach to decrease dimensions of logical elements "AND" based on fieldeffect
heterotransistors. Framework the approach one shall consider a heterostructure with specific structure.
Several specific areas of the het
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.
ANALYSIS OF MANUFACTURING OF VOLTAGE RESTORE TO INCREASE DENSITY OF ELEMENTS ...ijoejournal
We introduce an approach for increasing density of voltage restore elements. The approach based on
manufacturing of a heterostructure, which consist of a substrate and an epitaxial layer with special configuration.
Several required sections of the layer should be doped by diffusion or ion implantation. After
that dopants and/or radiation defects should be annealed.
ON OPTIMIZATION OF MANUFACTURING OF ELEMENTS OF AN BINARY-ROM CIRCUIT TO INCR...JaresJournal
In this paper we introduce an approach to increase integration rate of elements of an binary-ROM 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.
On Decreasing of Dimensions of Field-Effect Transistors with Several Sourcesmsejjournal
We analyzed mass and heat transport during manufacturing field-effect heterotransistors with several
sources to decrease their dimensions. Framework the result of manufacturing it is necessary to manufacture
heterostructure with specific configuration. After that it is necessary to dope required areas of the heterostructure by diffusion or ion implantation to manufacture the required type of conductivity (p or n). After
the doping it is necessary to do optimize annealing. We introduce an analytical approach to prognosis mass
and heat transport during technological processes. Using the approach leads to take into account nonlinearity of mass and heat transport and variation in space and time (at one time) physical parameters of these
processes
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 Optimization of Manufacturing of Field-Effect Heterotransistors Frame-work...antjjournal
We consider an approach for increasing density of field-effect heterotransistors in a single-stage multi-path
operational amplifier. At the same time one can obtain decreasing of dimensions of the above transistors.
Dimensions of the elements could be decreased by manufacturing of these elements in a heterostructure
with specific structure. The manufacturing is doing by doping of required areas of the heterostructure by
diffusion or ion implantation with future optimization of annealing of dopant and/or radiation defects.
On Optimization of Manufacturing of Field-Effect Heterotransistors Frame-work...antjjournal
We consider an approach for increasing density of field-effect heterotransistors in a single-stage multi-path operational amplifier. At the same time one can obtain decreasing of dimensions of the above transistors.
Dimensions of the elements could be decreased by manufacturing of these elements in a heterostructure with specific structure. The manufacturing is doing by doping of required areas of the heterostructure by
diffusion or ion implantation with future optimization of annealing of dopant and/or radiation defects.
Influence of Overlayers on Depth of Implanted-Heterojunction RectifiersZac Darcy
In this paper we compare distributions of concentrations of dopants in an implanted-junction rectifiers in a
heterostructures with an overlayer and without the overlayer. Conditions for decreasing of depth of the
considered p-n-junction have been formulated.
INFLUENCE OF OVERLAYERS ON DEPTH OF IMPLANTED-HETEROJUNCTION RECTIFIERSZac Darcy
In this paper we compare distributions of concentrations of dopants in an implanted-junction rectifiers in a
heterostructures with an overlayer and without the overlayer. Conditions for decreasing of depth of the
considered p-n-junction have been formulated.
Optimization of Manufacture of Field-Effect Heterotransistors without P-N-Jun...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.
Optimization of Manufacture of Field-Effect Heterotransistors without P-N-Jun...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.
DEPENDENCE OF CHARGE CARRIERS MOBILITY IN THE P-N-HETEROJUNCTIONS ON COMPOSIT...msejjournal
In this paper we consider manufacturing a p-n-junctions by dopant diffusion or ion implantation into a
multilayer structure. We introduce an approach to increase sharpness of these p-n-junctions and at the
same time to increase homogeneity of distributions of dopants in enriched by these dopants areas. We consider influence of the above changing of distribution of dopant on charge carrier mobility. We also consider an approach to decrease value of mismatch-induced stress in the considered multilayer structure by using a buffer layer. The decreasing gives a possibility to increase value of charge carrier mobility.
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.
INFLUENCE OF OVERLAYERS ON DEPTH OF IMPLANTED-HETEROJUNCTION RECTIFIERSZac Darcy
In this paper we compare distributions of concentrations of dopants in an implanted-junction rectifiers in a
heterostructures with an overlayer and without the overlayer. Conditions for decreasing of depth of the
considered p-n-junction have been formulated.
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.
An approach to decrease dimentions of logicalijcsa
In this paper we consider manufacturing logical elements with function AND-NOT based on bipolar transistors.Based on recently considered approach to decrease dimensions of solid state electronic devices with the same time increasing of their performance we introduce an approach to decrease dimensions of transistors and p-n-junctions, which became a part of the logical element. Framework the approach a heterostructure
with required configuration should be manufactured. After the manufacture required areas of the heterostructures should be doped by diffusion or ion implantation. The doping should be finished by optimized annealing of dopant and/or radiation defects.
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.
On prognozisys of manufacturing doublebaseijaceeejournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this
heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects.
The approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher
compactness of the considered bipolar transistor.
On prognozisys of manufacturing double basemsejjournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this heterostructure
by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects. The
approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher compactness
of the considered bipolar transistor.
ON PROGNOZISYS OF MANUFACTURING DOUBLE-BASE HETEROTRANSISTOR AND OPTIMIZATION...msejjournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects. The
approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher compactness of the considered bipolar transistor.
Modelling and Simulation of Composition and Mechanical Properties of High Ent...msejjournal
Magnesium alloys are high potential materials for application in the aerospace and automotive industries
due to their lightweight properties. They can help to lower dead weight and fuel consumption to contribute
to sustainability and efficiency. It is possible to achieve high specific strength and high stiffness of the
alloys by varying compositions of alloying elements. Applications of magnesium are limited due to its low
strength and relatively low stiffness. This research focuses on a recipe of multi component alloys of
magnesium with varied percentages of Mg, Al, Cu, Mn and Zn obtained from literature and optimizes the
percentage compositions to obtain for high specific strength and specific stiffness. Relationships among
percentage constituents of the alloy components are examined in Matlab R2022b using multiple linear
regression. Optimization is achieved using genetic algorithm to determine the specific strengths and
stiffness. The resulting optimal alloy component percentages by weight are used for microstructure
simulation of thermodynamic properties, diffusion and phase transformations of proposed alloy is done in
MatCalc software version 6.04. Results show potential for improved mechanical properties resulting from
disordered structure in the high entropy magnesium alloy. Future research should focus on production and
characterization of the proposed alloy.
Thermal and Metrological Studies on YTTRIA Stabilized Zirconia Thermal Barrie...msejjournal
Thermal Barrier Coatings (TBCs), routinely prepared from Ceramic based compositions (typically
8%Y2O3-ZrO2or 8YSZ) are being engineered to protect the metallic components from degradation in
applications like gas turbines, jet and automotive engines. With a goal of finding improved TBC materials
a wide variety of ceramics are being researched worldwide. Before physically preparing the TBCs of
uncommon compositions in the laboratory, their suitability to perform can be predicted. Limited
accessibility to detailed and realistic information on the influence of newer compositions (other than 8YSZ)
on TBCs warrants methods to obtain this information.
In this paper, 8YSZ TBCs coated onto aluminium substratesare studied for thermal fatigue, thermal barrier
and materials characteristics to determine the reliability of the coating configuration to withstand the
harshness of test conditions under the framework of experiments. Thereafter, the results have been used to
corroboratethe developed simulation model. Results obtained via thermal tests confirm the suitability of the
model and we can predict the thermal barrier effects of TBCs when prepared from materials other than
YSZ.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
New Experiment System for the Interaction Between Soft Rock and Water : A Cas...msejjournal
The strength of rock strongly depends on the water content especially when the rocks contain clay
materials. The interaction between soft rock and water always threaten the soft rock engineering projects.
For this problem, new sets of laboratory experiment systems are developed to simulate the interaction
between soft rock and water or vapor. In this paper, the principles of experiment systems are introduced
with particular reference to the application on soft rock in Mogao Grottoes, one of the world famous
ancient sites in China. Two kinds of rock samples, the sandstone and muddy sandstone, are obtained by insitu sampling system. Then the laboratory experiments are performed under different environment
conditions. By the specific boundary conditions design, the physical-chemical effect and mechanic effect on
water absorption of rock samples are separated for further mechanism study by the experiment system, and
the different hydrological actions of water and vapor under variable experiment environment are obtained.
The interaction mechanism is discussed with assistant methods, such as SEM (Scanning Electron
Microscope), mercury injection test, X-ray diffraction analysis and etc. With the relation between water
content and soft rock strength, the study may provide guidance and basis for the soft rock engineering in
the future.
International Conference on Embedded Systems and VLSI (EMVL 2023)msejjournal
International Conference on Embedded Systems and VLSI (EMVL 2023) will provide an excellent International forum for sharing knowledge and results in theory, methodology and applications of Embedded Systems.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
Modeling, Analyzing and Safety Aspects of Torsion and Noise Effects on Round ...msejjournal
Each material has its own effect and behavior on external impacts like heat, force, tension, compression,
torsion etc. It is important to study and analyze these behaviors before selecting a material for an
engineering application in the design aspects itself. If predicted values analyzed by both mathematical and
software are available it is easy to get the reliable details in the pre design itself. By this one can ensure the
safety of the component and the system also. In this investigation, the effects of torsional loads on mild steel
round shafts with various diameters and lengths have been analyzed. The additional effects like angle of
rotation, rpm and duration also considered to find the optimum predicted value. The data observed by
various experiments are analyzed by design of experiments especially by response surface methodology.
Minitab software is used for canalization. The data are tabulated and kept for future reference. Noise effect
due to the gradual torsional load performed in the gear box and other rotating components is also studied
for healthy working environment. The nature and characteristics of material also be explained by this noise
analysis.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Using Advanced Inspection Method (Three-Dimensional Ultrasonic) in Recognitio...msejjournal
In this study, using Harfang Code 32 device, the slag catcher pipelines in one of the South Pars phases
were tested. In radiography method of these lines, no clear defect was observed in radiographic films due
to the high thickness of 40 mm. However, marvelous results were obtained using advanced ultrasonic.
Review and analysis of the results will result in high potential of three-dimensional ultrasonic method in
identifying defects in pipelines with high thicknesses and preventing financial and life-threatening risks
during the use of these refineries in the future.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Flammability Characteristics of Chemical Treated Woven Hemp Fabricmsejjournal
Woven hemp fabric was treated with sodium hydroxide, commercial flame retardant chemical, and
combination of both to increase its fire-retardant properties. Treatments of fire-retardant changed the
properties of woven hemp fabric such as increased its fabric shrinkage and density of fibres which ranges
from 0.67 to 5% and 1.43 to 1.53 g/cm3
respectively. After the treatment, the fire retardancy of the fabric
increased tremendously which was observed by the burning, thermogravimetry and limiting oxygen index
tests. Some of the samples were not burnt when exposed to flame source and the burning rate needed to be
measured under exaggeration of flame at longer time. The limiting oxygen index value increased from 18.6
to 51 after the treatments which explained the scenario happened in the burning tests. Nevertheless, its
mechanical properties decreased slightly that ranges from 18 to 32% and 23 to 39% for warp and weft
respectively compared to untreated fibre.
Advances in Materials Science and Engineering: An International Journal (MSEJ) msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ) msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal (MSEJ)msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Advances in Materials Science and Engineering: An International Journal ...msejjournal
Advances in Materials Science and Engineering: An International Journal (MSEJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.
The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on Materials Science and Engineering advancements, and establishing new collaborations in these areas. Original research papers, state-of-the-art reviews are invited for publication in all areas of Materials Science and Engineering.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
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Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
ON DECREASING OF DIMENSIONS OF FIELDEFFECT TRANSISTORS WITH SEVERAL SOURCES
1. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
DOI:10.5121/msej.2016.3301 1
ON DECREASING OF DIMENSIONS OF FIELD-
EFFECT TRANSISTORS WITH SEVERAL
SOURCES
E.L. Pankratov, E.A. Bulaeva
Nizhny Novgorod State University, 2 Gagarin avenue, Nizhny Novgorod, 603950, Russia
ABSTRACT
We analyzed mass and heat transport during manufacturing field-effect heterotransistors with several
sources to decrease their dimensions. Framework the result of manufacturing it is necessary to manufacture
heterostructure with specific configuration. After that it is necessary to dope required areas of the hetero-
structure by diffusion or ion implantation to manufacture the required type of conductivity (p or n). After
the doping it is necessary to do optimize annealing. We introduce an analytical approach to prognosis mass
and heat transport during technological processes. Using the approach leads to take into account nonlineari-
ty of mass and heat transport and variation in space and time (at one time) physical parameters of these
processes
KEYWORDS
Field-effect transistor, transistor with several channels, increasing of compactness of transistors
1. INTRODUCTION
Now several problems of solid state electronic intensively solving. The problems are increasing
of density of elements of integrated circuits and at the same time decreasing of dimensions of
these elements [1-4], increasing performance [5-7] and increasing reliability [8,9]. Now one can
find intensive development of both power electronic devices and logical elements. In this paper
we consider an approach to manufacture more compact field-effect heterotransistor with several
sources. Framework the approach it is necessary to manufacture a heterostructure. The hetero-
structure consist of a substrate and an epitaxial layer (see Fig. 1). Several sections have been
manufactured into the epitaxial layer. These sections manufactured by using other materials (see
Fig. 1). The sections have been doped by diffusion or ion implantation to obtain required type of
conductivity (n or p). After the doping one can manufacture a field-effect transistor framework
the considered heterostructure so as it is shown on the Fig. 1. The doping should be finished by
annealing of dopant and/or radiation defects. The annealing should be optimized. The optimiza-
tion attracted an interest to manufacture more compact distributions of concentrations of dopant.
Framework the paper we formulate conditions to increase compactness and at the same time to
increase homogeneity of distribution of concentration of dopant in enriched by the dopant area.
Fig. 1. Structure of a field-effect heterotransistor. Top side of the structure
2. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
2
2. METHOD OF SOLUTION
To solve our aim we determine distribution of concentration of dopant C(x,y,z,t) in space and
time. To determine the distribution we solve the following boundary problem
( ) ( ) ( ) ( )
∂
∂
∂
∂
+
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
z
tzyxC
D
zy
tzyxC
D
yx
tzyxC
D
xt
tzyxC ,,,,,,,,,,,,
(1)
( ) 0
,,,
0
=
∂
∂
=x
x
tzyxC
,
( ) 0
,,,
=
∂
∂
= xLx
x
tzyxC
,
( )
0
,,,
0
=
∂
∂
=y
y
tzyxC
,
( ) 0
,,,
=
∂
∂
= yLx
y
tzyxC
,
( ) 0
,,,
0
=
∂
∂
=z
z
tzyxC
,
( ) 0
,,,
=
∂
∂
= zLx
z
tzyxC
, C(x,y,z,0)=fC(x,y,z). (2)
Here T is the temperature of annealing; DС is the dopant diffusion coefficient. Dopant diffusion
coefficient takes another value in other materials. Heating and cooling of heterostructure (see
Arrhenius law) also leads to changing of value of diffusion coefficient. We consider following
approximation of concentrational dependences of dopant diffusion coefficient [10-12]
( ) ( )
( )
( ) ( )
( )
++
+= 2*
2
2*1
,,,,,,
1
,,,
,,,
1,,,
V
tzyxV
V
tzyxV
TzyxP
tzyxC
TzyxDD LC ςςξ γ
γ
. (3)
Here function DL (x,y,z,T) describes dependences of dopant diffusion coefficient on coordinate
and temperature; function P (x,y,z,T) describes dependences of limit of solubility on coordinate
and temperature; parameter γ ∈[1,3] is integer and depends on properties of materials; function V
(x,y,z,t) describes distribution of concentration of radiation vacancies on space and time with
equilibrium distribution V*
. Dependence of dopant diffusion coefficient on concentration of do-
pant has been investigated and described in details in [10]. Diffusion of dopant gives a possibility
to dope materials without generation radiation defects. In this situation ζ1= ζ2= 0. Ion doping of
dopant leads to generation radiation defects. Distributions of concentrations of point radiation
defects have been determined by solving the following boundary problem [11,12]
( ) ( ) ( ) ( ) ( ) ( ) ×−
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
Tzyxk
y
tzyxI
TzyxD
yx
tzyxI
TzyxD
xt
tzyxI
IIII ,,,
,,,
,,,
,,,
,,,
,,,
,
( ) ( ) ( ) ( ) ( ) ( )tzyxVtzyxITzyxk
z
tzyxI
TzyxD
z
tzyxI VII ,,,,,,,,,
,,,
,,,,,, ,
2
−
∂
∂
∂
∂
+× (4)
( )
( )
( )
( )
( )
( ) ×−
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
Tzyxk
y
tzyxV
TzyxD
yx
tzyxV
TzyxD
xt
tzyxV
VVVV ,,,
,,,
,,,
,,,
,,,
,,,
,
( ) ( ) ( ) ( ) ( ) ( )tzyxVtzyxITzyxk
z
tzyxV
TzyxD
z
tzyxV VIV ,,,,,,,,,
,,,
,,,,,, ,
2
−
∂
∂
∂
∂
+×
( ) 0
,,,
0
=
∂
∂
=x
x
tzyxρ
,
( ) 0
,,,
=
∂
∂
= xLx
x
tzyxρ
,
( ) 0
,,,
0
=
∂
∂
=y
y
tzyxρ
,
( ) 0
,,,
=
∂
∂
= yLy
y
tzyxρ
,
( ) 0
,,,
0
=
∂
∂
=z
z
tzyxρ
,
( ) 0
,,,
=
∂
∂
= zLz
z
tzyxρ
, ρ(x,y,z,0)=fρ (x,y,z). (5)
3. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
3
Here ρ=I,V; distribution of concentration of radiation interstitials in space and time describes by
the function I (x,y,z,t); terms of Eqs.(4) with quadric concentrations of point radiation defects
(V2
(x,y,z,t) and I2
(x,y,z,t)) correspond to generation of simplest complexes of radiation defects
(divacancies and diinterstitials); temperature and spatial dependences of diffusion coefficients of
point radiation defects describe by functions Dρ(x,y,z,T); temperature and spatial dependences of
parameter of recombination of point radiation defects describe by function kI,V(x,y,z,T); functions
kI,I(x,y,z,T) and kV,V(x,y,z,T) describe spatial and temperature dependences of parameters of gener-
ation of simplest complexes of point radiation defects.
Concentrations of divacancies ΦV (x,y,z,t) and dinterstitials ΦI (x,y,z,t) have been calculated by
solution of the following boundary problem [11,12]
( ) ( ) ( ) ( ) ( ) +
Φ
+
Φ
=
Φ
ΦΦ
y
tzyx
TzyxD
yx
tzyx
TzyxD
xt
tzyx I
I
I
I
I
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂ ,,,
,,,
,,,
,,,
,,,
( ) ( ) ( ) ( ) ( ) ( )tzyxITzyxktzyxITzyxk
z
tzyx
TzyxD
z
III
I
I ,,,,,,,,,,,,
,,,
,,, 2
, −+
Φ
+ Φ
∂
∂
∂
∂
(6)
( ) ( ) ( ) ( ) ( ) +
Φ
+
Φ
=
Φ
ΦΦ
y
tzyx
TzyxD
yx
tzyx
TzyxD
xt
tzyx V
V
V
V
V
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂ ,,,
,,,
,,,
,,,
,,,
( ) ( ) ( ) ( ) ( ) ( )tzyxVTzyxktzyxVTzyxk
z
tzyx
TzyxD
z
VVV
V
V ,,,,,,,,,,,,
,,,
,,, 2
, −+
Φ
+ Φ
∂
∂
∂
∂
( )
0
,,,
0
=
∂
Φ∂
=x
x
tzyxρ
,
( )
0
,,,
=
∂
Φ∂
= xLx
x
tzyxρ
,
( )
0
,,,
0
=
∂
Φ∂
=y
y
tzyxρ
,
( )
0
,,,
=
∂
Φ∂
= yLy
y
tzyxρ
,
( )
0
,,,
0
=
∂
Φ∂
=z
z
tzyxρ
,
( )
0
,,,
=
∂
Φ∂
= zLz
z
tzyxρ
, ΦI(x,y,z,0)=fΦI (x,y,z), ΦV(x,y,z,0)=fΦV (x,y,z). (7)
Functions DΦρ(x,y,z,T) describe spatial and temperature dependences of diffusion coefficients of
simplest complexes of point radiation defects; functions kI(x,y,z,T) and kV (x,y,z,T) describe spatial
and temperature dependences of parameters of decay of the above complexes.
Now let us consider equivalent integro-differential form of Eq.(1)
( ) ( ) ( ) ( )
( )
×∫ ∫ ∫
++=∫ ∫ ∫
t y
L
z
L
L
x
L
y
L
z
Lzyx y zx y z V
wvxV
V
wvxV
TwvxDudvdwdtwvuC
LLL
zyx
0
2*
2
2*1
,,,,,,
1,,,,,,
τ
ς
τ
ς
( )
( )
( ) ( ) ( )
×∫ ∫ ∫+
+×
t x
L
z
L
L
zxzy x z y
wyuC
TwyuD
LL
zx
LL
zy
d
x
wvxC
TwvxP
wvxC
0
,,,
,,,
,,,
,,,
,,,
1
∂
τ∂
τ
∂
τ∂τ
ξ γ
γ
( ) ( )
( )
( )
( )
( )∫ ∫ ∫ ×+
+
++×
t x
L
y
L
L
yx x y
TzvuD
LL
yx
d
TzyxP
wyuC
V
wyuV
V
wyuV
0
2*
2
2*1 ,,,
,,,
,,,
1
,,,,,,
1 τ
τ
ξ
τ
ς
τ
ς γ
γ
( ) ( )
( )
( )
( )
( ) ×+
+
++×
zyx LLL
zyx
d
z
zvuC
TzyxP
zvuC
V
zvuV
V
zvuV
τ
∂
τ∂τ
ξ
τ
ς
τ
ς γ
γ
,,,
,,,
,,,
1
,,,,,,
1 2*
2
2*1
( )∫ ∫ ∫×
x
L
y
L
z
Lx y z
udvdwdwvuf ,, . (1a)
4. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
4
We used the Bubnov-Galerkin approach [13] to calculate solution of the above equation. To use
the approach we consider of the Eq.(1a) as the following series
( ) ( ) ( ) ( ) ( )∑=
=
N
n
nCnnnnC tezcycxcatzyxC
0
0 ,,, .
Here ( ) ( )[ ]222
0
22
exp −−−
++−= zyxCnC LLLtDnte π , cn(χ) = cos (π n χ/Lχ). Number of terms N of the
above series is finite. The series is almost coincides with solution of Eq.(1) in the linear case (i.e.
with ξ = 0) and average value of dopant diffusion coefficient D0. Framework the approach we
substitute the above series into Eq.(1a). After the substitution we obtain
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( )∫ ∫ ∫ ×
∑+−=∑
==
t y
L
z
L
N
n
nCnnnnC
N
n
nCnnn
C
y z TwvxP
ewcvcxcatezsysxs
n
azyx
0 11
32
,,,
1 γ
γ
ξ
τ
π
( ) ( )
( )
( ) ( ) ( ) ( ) ( ) −∑
++×
=
zy
N
n
nCnnnnCL
LL
zy
dewcvcxsanTwvxD
V
wvxV
V
wvxV
1
2*
2
2*1 ,,,
,,,,,,
1 ττ
τ
ς
τ
ς
( ) ( )
( )
( ) ( ) ( ) ( )∫ ∫ ∫
×
∑+
++−
=
t x
L
z
L
N
m
mCmmmmC
zx x z
ewcycuca
V
wyuV
V
wyuV
LL
zx
0 1
2*
2
2*1 1
,,,,,,
1
γ
τ
τ
ς
τ
ς
( )
( ) ( ) ( ) ( ) ( ) ( ) ×∫ ∫ ∫−∑
×
=
t x
L
y
L
L
yx
N
n
nCnnnnCL
x y
TzvuD
LL
yx
dewcysucanTwyuD
TwyuP 01
,,,,,,
,,,
ττ
ξ
γ
( )
( ) ( ) ( ) ( ) ( ) ( )
( )
×
++
∑+×
=
2*
2
2*1
1
,,,,,,
1
,,,
1
V
zvuV
V
zvuV
ezcvcuca
TzvuP
N
n
nCnnnnC
τ
ς
τ
ςτ
ξ γ
γ
( ) ( ) ( ) ( ) ( )∫ ∫ ∫+∑×
=
x
L
y
L
z
Lzyx
N
n
nCnnnnC
x y z
udvdwdwvuf
LLL
zyx
dezsvcucan ,,
1
ττ . (8)
Here sn(χ)=sin(πnχ/Lχ). To determine coefficients an it is necessary to use orthogonality condi-
tion of terms of the above series framework scale of heterostructure. Using the condition leads to
the following equations to calculate of coefficients an for any quantity of terms N
( ) ( ) ( ) ( ) ( ) ( )
( )∫ ∫ ∫ ∫ ×
∑+−=∑−
==
t L L L N
n
nCnnnnCL
N
n
nC
nCzyx
x y z
TzyxP
ezcycxcaTzyxDte
n
aLLL
0 0 0 0 11
65
222
,,,
1,,, γ
γ
ξ
τ
π
( ) ( )
( )
( ) ( ) ( ) ( )[ ] ×∑
−+
++×
=
N
n
n
y
nnn
nCzy
yc
n
L
ysyycxs
n
a
V
zyxV
V
zyxVLL
1
2*
2
2*12
12
,,,,,,
1
2 π
τ
ς
τ
ς
π
( ) ( ) ( ) ( )[ ] ( ) ( ) ( ) ( ) ×∫ ∫ ∫ ∫
∑−
−+×
=
t L L L N
n
nCnnnnCn
z
nnCn
x y z
ezcycxcadxdydzdzc
n
L
zszezc
0 0 0 0 1
1
γ
ττ
π
τ
( )
( ) ( ) ( )
( )
( )
++
++
+× *12*
2
2*1
,,,
1
,,,,,,
1,,,1
,,, V
zyxV
V
zyxV
V
zyxV
TzyxD
TzyxP
L
τ
ς
τ
ς
τ
ς
ξ
γ
( )
( )
( ) ( )[ ] ( ) ( )[ ] ( ) ( ) ( )∑ ×
−+
−+
+
=
N
n
nnnn
z
nn
x
n
znC
zcysxczc
n
L
zszxc
n
L
xsx
n
La
V
zyxV
1
22*
2
2 211
2
,,,
πππ
τ
ς
( ) ( ) ( ) ( ) ( )
( )∫ ∫ ∫ ∫ ×
∑+−×
=
t L L L N
n
nCnnnnC
yx
nC
x y z
TzyxP
ezcycxca
LL
dxdydzde
0 0 0 0 1
2
,,,
1
2 γ
γ
ξ
τ
π
ττ
5. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
5
( ) ( )
( )
( ) ( ) ( ) ( )[ ] ×∑
−+
++×
=
N
n
n
x
nn
nC
L xc
n
L
xsxxc
n
a
V
zyxV
V
zyxV
TzyxD
1
*12*
2
2 1
,,,,,,
1,,,
π
τ
ς
τ
ς
( ) ( ) ( ) ( )[ ] ( ) ( ) ( )[ ]∑ ∫ ×
−++
−+×
=
N
n
L
n
x
nnCn
y
nnn
x
xc
n
L
xsxdxdydzdeyc
n
L
ysyzsyc
1 0
11
π
ττ
π
( ) ( )[ ] ( ) ( )[ ] ( )∫ ∫
−+
−+×
y z
L L
n
z
nn
y
n xdydzdzyxfzc
n
L
zszyc
n
L
ysy
0 0
,,11
ππ
. (9)
Now we consider several examples. For γ=0 we obtain
( ) ( )[ ] ( ) ( )[ ] ( ) ( )∫ ∫ ∫
×+
−+
−+=
x y zL L L
x
nn
y
nn
y
nnC
n
L
xsxydzdzyxfzc
n
L
zszyc
n
L
ysya
0 0 0
,,11
πππ
( )[ ]} ( ) ( ) ( ) ( ) ( ) ( )[ ] ( ){
∫ ∫ ∫ ∫ +
−+−×
t L L L
nn
y
nLnnnn
x y z
ysyzc
n
L
zszTzyxDzcycxs
n
xdxc
0 0 0 0
1,,,2
2
1
π
( )[ ] ( ) ( )
( ) ( )
( ) ×
+
++
−+ xdydzdzc
TzyxPV
zyxV
V
zyxV
yc
n
L
nn
y
,,,
1
,,,,,,
11 2*
2
2*1 γ
ξτ
ς
τ
ς
π
( ) ( ) ( ) ( ) ( )[ ] ( ) ( ) ( ) ( )[ ] ×∫ ∫ ∫ ∫
−+
−++×
t L L L
n
y
nnnn
y
nnnCnC
x y z
zc
n
L
zszzcysxc
n
L
xsxxcede
0 0 0 0
121
ππ
τττ
( )
( )
( ) ( )
( )
+
++
+× τ
τ
ς
τ
ς
ξ
γ
dxdydzd
V
zyxV
V
zyxV
TzyxP
TzyxDL 2*
2
2*1
,,,,,,
1
,,,
1,,,
( ) ( ) ( ) ( )[ ] ( ) ( ) ( )[ ] ( ) ×∫ ∫ ∫ ∫
−+
−++
t L L L
Ln
y
nnn
x
nnnC
x y z
TzyxDyc
n
L
ysyycxc
n
L
xsxxce
0 0 0 0
,,,11
ππ
τ
( )
( )
( )
( )
( )
1
65
222
*12*
2
2
,,,,,,
1
,,,
12
−
−
++
+×
n
LLL
dxdydzd
V
zyxV
V
zyxV
TzyxP
zs zzz
n
π
τ
τ
ς
τ
ς
ξ
γ
.(10)
For γ=1 calculation of parameters an leads to the following results
( ) ( ) ( ) ( )∫ ∫ ∫+±−=
x y zL L L
nnnnn
n
n
nC xdydzdzyxfzcycxca
0 0 0
2
,,4
2
αβ
α
β
. (11)
Here ( ) ( )
( )
( )
( ) ( )
( )
∫ ∫ ∫ ∫ ×
++=
t L L L
L
nn
zy
n
x y z
V
zyxV
V
zyxV
TzyxP
TzyxD
ycxs
n
LL
0 0 0 0
2*
2
2*12
,,,,,,
1
,,,
,,,
2
2
τ
ς
τ
ς
π
ξ
α
( ) ( ) ( )[ ] ( ) ( )[ ] ( ) ×+
−+
−+×
n
LL
dexdydzdzc
n
L
zszyc
n
L
ysyzc zx
nCn
z
nn
y
nn 2
2
11
π
ξ
ττ
ππ
( ) ( ) ( ) ( )[ ] ( ) ( )
( )
( ) ( )[ ] ×∫ ∫ ∫ ∫
−−
−+×
t L L L
n
z
n
L
nn
x
nnnC
x y z
zc
n
L
zsz
TzyxP
TzyxD
ysxc
n
L
xsxxce
0 0 0 0
1
,,,
,,,
21
ππ
τ
( ) ( ) ( )
( )
( ) ( ) ( )×∫ ∫ ∫+
++×
t L L
nnnC
yx
n
x y
ycxce
n
LL
dxdydzd
V
zyxV
V
zyxV
zc
0 0 0
22*
2
2*1
2
,,,,,,
1 τ
π
ξ
τ
τ
ς
τ
ς
6. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
6
( )
( )
( )
( ) ( )
( )
( ) ( )[ ] ( ){∫ ×
−+
++×
zL
nn
x
n
L
n ysxc
n
L
xsx
V
zyxV
V
zyxV
TzyxP
TzyxD
zs
0
2*
2
2*1 1
,,,,,,
1
,,,
,,,
2
π
τ
ς
τ
ς
( )[ ] τ
π
dxdydzdyc
n
L
y n
y
−+× 1 , ( ) ( ) ( ) ( ) ( ) ×∫ ∫ ∫ ∫=
t L L L
LnnnnC
zy
n
x y z
TzyxDzcycxse
n
LL
0 0 0 0
2
,,,2
2
τ
π
β
( ) ( )
( )
( ) ( )[ ] ( )[ ] ( ) ×
+−
−+
++× ysyyc
n
L
zdzc
n
L
zsz
V
zyxV
V
zyxV
nn
y
n
z
n 11
,,,,,,
1 2*
2
2*1
ππ
τ
ς
τ
ς
( ) ( ) ( ) ( )[ ] ( ) ( ) ( )
∫ ∫ ∫ ∫
++
−++×
t L L L
nnn
x
nnnC
zx
x y z
V
zyxV
zcysxc
n
L
xsxxce
n
LL
dxdyd
0 0 0 0
*12
,,,
121
2
τ
ς
π
τ
π
τ
( )
( )
( ) ( ) ( )[ ] ( )∫ ×+
−+
+
t
nC
yx
n
z
nL e
n
LL
dxdydzdzc
n
L
zszTzyxD
V
zyxV
0
22*
2
2
2
1,,,
,,,
τ
π
τ
π
τ
ς
( ) ( )[ ] ( ) ( )[ ] ( ) ( )
( )
∫ ∫ ∫ ×
++
−+
−+×
x y zL L L
n
y
nn
x
n
V
zyxV
V
zyxV
yc
n
L
ysyxc
n
L
xsx
0 0 0
2*
2
2*1
,,,,,,
111
τ
ς
τ
ς
ππ
( ) ( ) ( ) ( ) ( ) 65222
,,,2 nteLLLdxdxcydyczdTzyxDzs nCzyxnnLn πτ −× .
It could be used the same approach to calculate values of parameters an for larger values of the
parameterγ. However the relations became more bulky and will not be present in the paper. The
considered approach gives a possibility to calculate distributions of concentrations of dopant and
radiation defects without joining of the above concentration on interfaces of the considered hete-
rostructure.
We solved equations of the system (4) by using Bubnov-Galerkin approach. To use the approach
we previously transform the differential equations to the following integro-differential form
( ) ( ) ( ) ×+∫ ∫ ∫
∂
∂
=∫ ∫ ∫
zx
t y
L
z
L
I
zy
x
L
y
L
z
Lzyx LL
zx
dvdwd
x
wvxI
TwvxD
LL
zy
udvdwdtwvuI
LLL
zyx
y zx y z 0
,,,
,,,,,, τ
τ
( ) ( ) ( ) ( ) −∫ ∫ ∫
∂
∂
+∫ ∫ ∫
∂
∂
×
t x
L
y
L
I
yx
t x
L
z
L
I
x yx z
dudvd
z
zvuI
TzvuD
LL
yx
dudwd
x
wyuI
TwyuD
00
,,,
,,,
,,,
,,, τ
τ
τ
τ
( ) ( ) ( ) ( ) ×∫ ∫ ∫−∫ ∫ ∫−
x
L
y
L
z
L
II
zyx
x
L
y
L
z
L
VI
zyx x y zx y z
Twvuk
LLL
zyx
udvdwdtwvuVtwvuITwvuk
LLL
zyx
,,,,,,,,,,,, ,,
( ) ( )∫ ∫ ∫+×
x
L
y
L
z
L
I
zyx x y z
udvdwdwvuf
LLL
zyx
udvdwdtwvuI ,,,,,2
(4a)
( ) ( ) ( ) ×+∫ ∫ ∫
∂
∂
=∫ ∫ ∫
zx
t y
L
z
L
V
zy
x
L
y
L
z
Lzyx LL
zx
dvdwd
x
wvxV
TwvxD
LL
zy
udvdwdtwvuV
LLL
zyx
y zx y z 0
,,,
,,,,,, τ
τ
( ) ( ) ( ) ( ) −∫ ∫ ∫
∂
∂
+∫ ∫ ∫
∂
∂
×
t x
L
y
L
V
yx
t x
L
z
L
V
x yx z
dudvd
z
zvuV
TzvuD
LL
yx
dudwd
x
wyuV
TwyuD
00
,,,
,,,
,,,
,,, τ
τ
τ
τ
( ) ( ) ( ) ( ) ×∫ ∫ ∫−∫ ∫ ∫−
x
L
y
L
z
L
VV
zyx
x
L
y
L
z
L
VI
zyx x y zx y z
Twvuk
LLL
zyx
udvdwdtwvuVtwvuITwvuk
LLL
zyx
,,,,,,,,,,,, ,,
( ) ( )∫ ∫ ∫+×
x
L
y
L
z
L
V
zyx x y z
udvdwdwvuf
LLL
zyx
udvdwdtwvuV ,,,,,2
.
Now we consider solutions of the above integro-differential equations as the following series
7. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
7
( ) ( ) ( ) ( ) ( )∑=
=
N
n
nnnnn tezcycxcatzyx
1
0 ,,, ρρρ .
Here anρ are coefficients, which should be determined. After substitution of the series into Eqs.
(4a) one can obtain
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ×∑ ∫ ∫ ∫−=∑
==
N
n
t y
L
z
L
InnnInI
zyx
N
n
nInnn
nI
y z
dvdwdTwvxDzcycea
LLL
zy
tezsysxs
n
azyx
1 01
33
,,, ττ
π
π
( ) ( ) ( ) ( ) ( ) ( ) ( )×∑−∑ ∫ ∫ ∫−×
==
N
n
nnI
zyx
N
n
t x
L
z
L
InnnInnI
zyx
n zsa
LLL
yx
dudwdTwyuDzcxceysa
LLL
zx
xs
x z 11 0
,,,
π
ττ
π
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ×∫ ∫ ∫
∑−∫ ∫ ∫×
=
x
L
y
L
z
L
N
n
nInnnnI
zyx
t x
L
y
L
InnnI
x y zx y
tewcvcuca
LLL
zyx
dudvdTzvuDycxce
2
10
,,, ττ
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ×∫ ∫ ∫ ∑ ∑−×
= =
x
L
y
L
z
L
N
n
N
n
nnnnVnInnnnI
zyx
II
x y z
wcvcucatewcvcuca
LLL
zyx
udvdwdTvvuk
1 1
, ,,,
( ) ( ) ( )∫ ∫ ∫+×
x
L
y
L
z
L
I
zyx
VInV
x y z
udvdwdwvuf
LLL
zyx
udvdwdTvvukte ,,,,,, (12)
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ×∑ ∫ ∫ ∫−=∑
==
N
n
t y
L
z
L
VnnnVnV
zyx
N
n
nVnnn
nV
y z
dvdwdTwvxDzcycea
LLL
zy
tezsysxs
n
azyx
1 01
33
,,, ττ
π
π
( ) ( ) ( ) ( ) ( ) ( ) ( ) ×∑−∑ ∫ ∫ ∫−×
==
N
n
nnV
zyx
N
n
t x
L
z
L
VnnnVnnV
zyx
n zsa
LLL
yx
dudwdTwyuDzcxceysa
LLL
zx
xs
x z 11 0
,,,
π
ττ
π
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ×∫ ∫ ∫
∑−∫ ∫ ∫×
=
x
L
y
L
z
L
N
n
nVnnnnV
zyx
t x
L
y
L
VnnnV
x y zx y
tewcvcuca
LLL
zyx
dudvdTzvuDycxce
2
10
,,, ττ
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ×∫ ∫ ∫ ∑ ∑−×
= =
x
L
y
L
z
L
N
n
N
n
nnnnVnInnnnI
zyx
VV
x y z
wcvcucatewcvcuca
LLL
zyx
udvdwdTvvuk
1 1
, ,,,
( ) ( ) ( )∫ ∫ ∫+×
x
L
y
L
z
L
V
zyx
VInV
x y z
udvdwdwvuf
LLL
zyx
udvdwdTvvukte ,,,,,, .
We use orthogonality condition of functions in the above series on scale of the heterostructure to
calculate coefficients anρ. Using the condition gives a possibility to obtain equations for calcula-
tion the above coefficients for any quantity N of terms of considered series
( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫ ∫
−++−−=∑−
==
N
n
t L L
n
y
nynnI
nI
x
N
n
nI
nIzyx
x y
yc
n
L
ysyLxce
n
a
L
te
n
aLLL
1 0 0 0
2
1
65
222
12
2
221
2
1
π
τ
ππ
( ) ( ) ( )[ ] ( )[ ]∑ ∫ ∫
++−−∫
−+×
=
N
n
t L
xn
xnI
y
L
n
z
nI
xz
Lxc
n
L
n
a
L
dxdydzdzc
n
L
zszTzyxD
1 0 0
2
0
12
2
1
1
2
,,,
ππ
τ
π
( )} ( ) ( ) ( )[ ] ( )[ ] ( ) −∫ ∫ −
−+++
y z
L L
nInn
z
nzIn dexdydyczdzc
n
L
zszLTzyxDxsx
0 0
2112
2
2,,,2 ττ
π
( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫ ∫
−++
−++−
=
N
n
t L L
n
y
nyn
x
nxnI
nI
z
x y
yc
n
L
ysyLxc
n
L
xsxLe
n
a
L 1 0 0 0
2
12
2
212
2
2
2
1
ππ
τ
π
8. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
8
( )[ ] ( ) ( ) ( )[ ] ( ) ×∑ ∫
+−+−∫ −×
=
N
n
L
nn
x
xnInI
L
In
xz
xsxxc
n
L
LteadxdydzdTzyxDzc
1 0
2
0
212
2
2,,,21
π
τ
( ) ( )[ ] ( ) ( )[ ] ( ) −∫ ∫
+−+
−++×
y z
L L
nn
z
zIIn
y
ny xdydzdzszzc
n
L
LTzyxkyc
n
L
ysyL
0 0
, 212
2
,,,12
2
2
ππ
( ) ( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫
−++
−++−
=
N
n
L L
n
y
nyn
x
nxnVnInVnI
x y
yc
n
L
ysyLxc
n
L
xsxLteteaa
1 0 0
12
2
212
2
2
ππ
( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫
−++∫
−++×
=
N
n
L
n
x
n
L
n
z
nzVI
xz
xc
n
L
xsxxdydzdzc
n
L
zszLTzyxk
1 00
, 112
2
2,,,
ππ
( ) ( )[ ] ( ) ( ) ( )[ ]∫ ∫
−++
−+×
y z
L L
n
z
nzIn
y
n xdydzdzc
n
L
zszLTzyxfyc
n
L
ysy
0 0
12
2
2,,,1
ππ
(13)
( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫ ∫
−++−−=∑−
==
N
n
t L L
n
y
nynnV
nV
x
N
n
nV
nVzyx
x y
yc
n
L
ysyLxce
n
a
L
te
n
aLLL
1 0 0 0
2
1
65
222
12
2
221
2
1
π
τ
ππ
( ) ( ) ( )[ ] ( )[ ]∑ ∫ ∫
++−−∫
−+×
=
N
n
t L
xn
xnV
y
L
n
z
nV
xz
Lxc
n
L
n
a
L
dxdydzdzc
n
L
zszTzyxD
1 0 0
2
0
12
2
1
1
2
,,,
ππ
τ
π
( )} ( ) ( ) ( )[ ] ( )[ ] ( ) −∫ ∫ −
−+++
y z
L L
nVnn
z
nzVn dexdydyczdzc
n
L
zszLTzyxDxsx
0 0
2112
2
2,,,2 ττ
π
( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫ ∫
−++
−++−
=
N
n
t L L
n
y
nyn
x
nxnV
nV
z
x y
yc
n
L
ysyLxc
n
L
xsxLe
n
a
L 1 0 0 0
2
12
2
212
2
2
2
1
ππ
τ
π
( )[ ] ( ) ( ) ( )[ ] ( ) ×∑ ∫
+−+−∫ −×
=
N
n
L
nn
x
xnVnV
L
Vn
xz
xsxxc
n
L
LteadxdydzdTzyxDzc
1 0
2
0
212
2
2,,,21
π
τ
( ) ( )[ ] ( ) ( )[ ] ( ) −∫ ∫
+−+
−++×
y z
L L
nn
z
zVVn
y
ny xdydzdzszzc
n
L
LTzyxkyc
n
L
ysyL
0 0
, 212
2
,,,12
2
2
ππ
( ) ( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫
−++
−++−
=
N
n
L L
n
y
nyn
x
nxnVnInVnI
x y
yc
n
L
ysyLxc
n
L
xsxLteteaa
1 0 0
12
2
212
2
2
ππ
( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫
−++∫
−++×
=
N
n
L
n
x
n
L
n
z
nzVI
xz
xc
n
L
xsxxdydzdzc
n
L
zszLTzyxk
1 00
, 112
2
2,,,
ππ
( ) ( )[ ] ( ) ( ) ( )[ ]∫ ∫
−++
−+×
y z
L L
n
z
nzVn
y
n xdydzdzc
n
L
zszLTzyxfyc
n
L
ysy
0 0
12
2
2,,,1
ππ
.
Final relations for the above parameters takes the form
( )
−
+−
+
±
+
−=
A
yb
yb
Ab
b
Ab
a nInV
nI
2
3
4
2
3
4
3
4
44
λγ
,
nInI
nInInInInI
nV
a
aa
a
χ
λδγ ++
−=
2
. (14)
Here ( ) ( ) ( ) ( )[ ] ( )∫ ∫ ∫
×++
−++=
x y zL L L
y
ynn
x
nxnn
n
L
Lysyxc
n
L
xsxLTzyxkte
0 0 0
,
2
212
2
2,,,2
ππ
γ ρρρρ
9. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
9
( )[ ]} ( ) ( )[ ] xdydzdzc
n
L
zszLyc n
z
nzn
−++−× 12
2
212
π
, ( ) ( ){∫ ∫ ∫ +=
t L L
nn
x
n
x y
ysye
nL 0 0 0
2
2
1
τ
π
δ ρρ
( )[ ] ( ) ( )[ ] ( ) ( )[ ] ×+∫ −
−+
−+
y
L
nn
z
nn
y
L
dxdxcydzdTzyxDzc
n
L
zszyc
n
L z
π
τ
ππ
ρ
2
1
21,,,1
2
1
2 0
( ) ( ) ( )[ ] ( )[ ] ( ) ( )[ ]∫ ∫ ∫ ∫
+−−
−++×
t L L L
n
z
nn
x
nxn
x y z
zc
n
L
TzyxDycxc
n
L
xsxLe
n 0 0 0 0
2
12
2
,,,21122
2
1
ππ
τ ρρ
( ) } ( ) ( ) ( )[ ] ( ){∫ ∫ ∫ +
−+++++
t L L
nn
x
xnn
z
zn
x y
ysyxc
n
L
Lxsxe
nL
dxdydzdLzsz
0 0 0
2
122
2
1
2
π
τ
π
τ ρ
( )[ ] ( )[ ] ( ) ( )te
n
LLL
dxdydzdTzyxDzcyc
n
L
L n
zyx
L
nn
y
y
z
ρρ
π
τ
π 65
222
0
,,,211
2
−∫ −
−++ , ( ) ×= tenInIVχ
( ) ( ) ( )[ ] ( )[ ] ( ) ( ) ( ){∫ ∫ ∫ ++
+−+
−+×
x y zL L L
nzVInn
y
yn
x
nnV zszLTzyxkysyyc
n
L
Lxc
n
L
xsxte
0 0 0
, 2,,,212
2
1
ππ
( )[ ] xdydzdzc
n
L
n
z
−+ 12
2π
, ( ) ( )[ ] ( ) ( )[ ] {∫ ∫ ∫ ×
−+
−+=
x y zL L L
n
y
nn
x
nn zyc
n
L
ysyxc
n
L
xsx
0 0 0
11
ππ
λ ρ
( ) ( )[ ] ( ) xdydzdTzyxfzc
n
L
zs n
z
n ,,,1 ρ
π
−+× , 22
4 nInInInVb χγγγ −= , −−= 2
3 2 nInInInInVb χδδγγ
nInInV γχδ− , ( ) 22
2 2 nInInVnInInVnInVnInInVb χλλδχδγγλδγ −+−+= , nInInVnInVnIb λχδδγλ −= 21 ,
2
2
3 48 bbyA −+= , 2
4
2
342
9
3
b
bbb
p
−
= , 3
4
2
4132
3
3
54
2792
b
bbbbb
q
+−
= , −++−−+= 3 323 32
qpqqpqy
43 3bb− .
Now we will calculate distributions of concentrations of simplest complexes of radiation defects
as the following functional series
( ) ( ) ( ) ( ) ( )∑=Φ
=
Φ
N
n
nnnnn tezcycxcatzyx
1
0 ,,, ρρρ (15)
with not yet known coefficients anΦρ. To calculate these coefficient we transform the Eqs.(6) to
the following integro-differential form
( ) ( )
( )
+∫ ∫ ∫
Φ
=∫ ∫ ∫ Φ Φ
t y
L
z
L
I
I
zy
x
L
y
L
z
L
I
zyx y zx y z
dvdwd
x
wvx
TwvxD
LL
zy
udvdwdtwvu
LLL
zyx
0
,,,
,,,,,, τ
∂
τ∂
( )
( )
( )
( )
∫ ∫ ∫ ×
Φ
+∫ ∫ ∫
Φ
+ ΦΦ
t x
L
y
L
I
I
t x
L
z
L
I
I
zx x yx z
dudvd
z
zvu
TzvuDdudwd
y
wyu
TwyuD
LL
zx
00
,,,
,,,
,,,
,,, τ
∂
τ∂
τ
∂
τ∂
( ) ( ) ( ) ×∫ ∫ ∫−∫ ∫ ∫+×
x
L
y
L
z
L
I
zyx
x
L
y
L
z
L
II
zyxyx x y zx y z
Twvuk
LLL
zyx
udvdwdwvuITwvuk
LLL
zyx
LL
yx
,,,,,,,,, 2
, τ
( ) ( )∫ ∫ ∫+× Φ
x
L
y
L
z
L
I
zyx x y z
udvdwdwvuf
LLL
zyx
udvdwdwvuI ,,,,, τ (6a)
( ) ( )
( )
+∫ ∫ ∫
Φ
=∫ ∫ ∫ Φ Φ
t y
L
z
L
V
V
zy
x
L
y
L
z
L
V
zyx y zx y z
dvdwd
x
wvx
TwvxD
LL
zy
udvdwdtwvu
LLL
zyx
0
,,,
,,,,,, τ
∂
τ∂
( )
( )
( )
( )
∫ ∫ ∫ ×
Φ
+∫ ∫ ∫
Φ
+ ΦΦ
t x
L
y
L
V
V
t x
L
z
L
V
V
zx x yx z
dudvd
z
zvu
TzvuDdudwd
y
wyu
TwyuD
LL
zx
00
,,,
,,,
,,,
,,, τ
∂
τ∂
τ
∂
τ∂
10. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
10
( ) ( ) ( ) ×∫ ∫ ∫−∫ ∫ ∫+×
x
L
y
L
z
L
V
zyx
x
L
y
L
z
L
VV
zyxyx x y zx y z
Twvuk
LLL
zyx
udvdwdwvuVTwvuk
LLL
zyx
LL
yx
,,,,,,,,, 2
, τ
( ) ( )∫ ∫ ∫+× Φ
x
L
y
L
z
L
V
zyx x y z
udvdwdwvuf
LLL
zyx
udvdwdwvuV ,,,,, τ .
Further we substitute the previously considered series in the Eqs.(6a). In this situation we obtain
the following equation
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )×∑ ∫ ∫ ∫−=∑−
=
ΦΦ
=
Φ
N
n
t y
L
z
L
InnInIn
zyx
N
n
nInnn
In
y z
TwvxDvctexsan
LLL
zy
tezsysxs
n
a
zyx
1 01
33
,,,
π
π
( ) ( ) ( ) ( ) ( ) ( ) −∑ ∫ ∫ ∫−×
=
ΦΦΦ
N
n
t x
L
z
L
InnInnIn
zyx
n
x z
dudwdTwvuDwcucteysna
LLL
zx
dvdwdwc
1 0
,,, τ
π
τ
( ) ( ) ( ) ( ) ( ) ( ) ×∫ ∫ ∫+∑ ∫ ∫ ∫−
=
ΦΦΦ
x
L
y
L
z
L
II
N
n
t x
L
y
L
InnInnIn
zyx x y zx y
TwvukdudvdTzvuDvcuctezsan
LLL
yx
,,,,,, ,
1 0
τ
π
( ) ( ) ( ) ×+∫ ∫ ∫−×
zyx
x
L
y
L
z
L
I
zyxzyx LLL
zyx
udvdwdwvuITwvuk
LLL
zyx
LLL
zyx
udvdwdwvuI
x y z
ττ ,,,,,,,,,2
( )∫ ∫ ∫× Φ
x
L
y
L
z
L
I
x y z
udvdwdwvuf ,, (16)
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ×∑ ∫ ∫ ∫−=∑−
=
ΦΦ
=
Φ
N
n
t y
L
z
L
VnnVnVn
zyx
N
n
nVnnn
Vn
y z
TwvxDvctexsan
LLL
zy
tezsysxs
n
a
zyx
1 01
33
,,,
π
π
( ) ( ) ( ) ( ) ( ) ( ) −∑ ∫ ∫ ∫−×
=
ΦΦΦ
N
n
t x
L
z
L
VnnVnnVn
zyx
n
x z
dudwdTwvuDwcucteysna
LLL
zx
dvdwdwc
1 0
,,, τ
π
τ
( ) ( ) ( ) ( ) ( ) ( ) ×∫ ∫ ∫+∑ ∫ ∫ ∫−
=
ΦΦΦ
x
L
y
L
z
L
VV
N
n
t x
L
y
L
VnnVnnVn
zyx x y zx y
TwvukdudvdTzvuDvcuctezsan
LLL
yx
,,,,,, ,
1 0
τ
π
( ) ( ) ( ) ×+∫ ∫ ∫−×
zyx
x
L
y
L
z
L
V
zyxzyx LLL
zyx
udvdwdwvuVTwvuk
LLL
zyx
LLL
zyx
udvdwdwvuV
x y z
ττ ,,,,,,,,,2
( )∫ ∫ ∫× Φ
x
L
y
L
z
L
V
x y z
udvdwdwvuf ,, .
We use orthogonality condition of functions in the above series on scale of the heterostructure to
calculate coefficients anΦρ. Using the condition gives a possibility to obtain equations for calcula-
tion the above coefficients for any quantity N of terms of considered series
( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫ ∫
−++−−=∑−
=
Φ
=
Φ
Φ
N
n
t L L
n
y
nyn
In
x
N
n
In
Inzyx
x y
yc
n
L
ysyLxc
n
a
L
te
n
aLLL
1 0 0 0
2
1
65
222
12
2
221
2
1
πππ
( ) ( ) ( )[ ] ( ) ( ){∑ ∫ ∫ ++−∫
−+×
=
Φ
ΦΦ
N
n
t L
xn
y
In
L
Inn
z
nI
xz
Lxsx
Ln
a
dexdydzdzc
n
L
zszTzyxD
1 0 0
2
0
2
2
1
1
2
,,,
π
ττ
π
( ) ( )[ ] ( ) ( ) ( )[ ] ( ) ×−∫ ∫
−+−
−
+ ΦΦ
x
L L
Inn
z
nIn
n
x
L
dexdydzdzc
n
L
zszTzyxDyc
n
xc
L
y z
π
ττ
ππ
1
1
2
,,,21
2
12
0 0
11. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
11
( ) ( ) ( )[ ] ( ) ( )[ ] ( ) ×∑ ∫ ∫ ∫ ∫
+−+
−+×
=
ΦΦ
Φ
N
n
t L L L
Iyn
y
nn
x
nIn
In
x y z
TzyxDLyc
n
L
ysyxc
n
L
xsxe
n
a
1 0 0 0 0
2
,,,12
2
21
22 ππ
τ
( )[ ] ( ) ( )[ ] ( ) ( ) ( )[ ] ×∑∫ ∫ ∫
−+
+−+−×
=
Φ
N
n
t L L
n
y
nnn
x
Inn
x y
yc
n
L
ysyxsxxc
n
L
edxdydzdyc
10 0 0
1
2
1
2
21
ππ
ττ
( ) ( ) ( )[ ] ( ) ( ) ( ){∑∫ ∫ +−∫
+−×
=
Φ
Φ
N
n
t L
nIn
L
nn
z
II
In
xz
xsxexdydzdzszzc
n
L
TzyxktzyxI
n
a
10 00
,
2
33
1
2
,,,,,, τ
ππ
( )[ ] ( )[ ] ( ) ( ) ( ) ( )[ ]∫ ∫
+−
+−
−+ Φ
y z
L L
n
z
Inn
yIn
n
x
zc
n
L
tzyxITzyxkysyyc
n
L
n
a
xc
n
L
0 0
33
1
2
,,,,,,1
2
1
2 ππππ
( )} ( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫ ∫
−+
−+++
=
Φ
Φ
N
n
t L L
n
y
nn
x
nIn
In
n
x y
yc
n
L
ysyxc
n
L
xsxe
n
a
xdydzdzsz
1 0 0 0
33
1
2
1
2 ππ
τ
π
( )[ ] ( ) ( )∫
+−× Φ
zL
Inn
z
xdydzdzyxfzszzc
n
L
0
,,1
2π
(17)
( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫ ∫
−++−−=∑−
=
Φ
=
Φ
Φ
N
n
t L L
n
y
nyn
Vn
x
N
n
Vn
Vnzyx
x y
yc
n
L
ysyLxc
n
a
L
te
n
aLLL
1 0 0 0
2
1
65
222
12
2
221
2
1
πππ
( ) ( ) ( )[ ] ( ) ( ){∑ ∫ ∫ ++−∫
−+×
=
Φ
ΦΦ
N
n
t L
xn
y
Vn
L
Vnn
z
nV
xz
Lxsx
Ln
a
dexdydzdzc
n
L
zszTzyxD
1 0 0
2
0
2
2
1
1
2
,,,
π
ττ
π
( )
( )[ ] ( ) ( ) ( )[ ] ( ) ×−∫ ∫
−+−
−
+ ΦΦ
x
L L
Vnn
z
nVn
n
x
L
dexdydzdzc
n
L
zszTzyxDyc
n
xc
L
y z
π
ττ
ππ
1
1
2
,,,21
2
12
0 0
( ) ( ) ( )[ ] ( ) ( )[ ] ( ) ×∑ ∫ ∫ ∫ ∫
+−+
−+×
=
ΦΦ
Φ
N
n
t L L L
Vyn
y
nn
x
nVn
Vn
x y z
TzyxDLyc
n
L
ysyxc
n
L
xsxe
n
a
1 0 0 0 0
2
,,,12
2
21
22 ππ
τ
( )[ ] ( ) ( )[ ] ( ) ( ) ( )[ ] ×∑∫ ∫ ∫
−+
+−+−×
=
Φ
N
n
t L L
n
y
nnn
x
Vnn
x y
yc
n
L
ysyxsxxc
n
L
edxdydzdyc
10 0 0
1
2
1
2
21
ππ
ττ
( ) ( ) ( )[ ] ( ) ( ) ( ){∑∫ ∫ +−∫
+−×
=
Φ
Φ
N
n
t L
nVn
L
nn
z
VV
Vn
xz
xsxexdydzdzszzc
n
L
TzyxktzyxV
n
a
10 00
,
2
33
1
2
,,,,,, τ
ππ
( )[ ] ( )[ ] ( ) ( ) ( ) ( )[ ]∫ ∫
+−
+−
−+ Φ
y z
L L
n
z
Vnn
yVn
n
x
zc
n
L
tzyxVTzyxkysyyc
n
L
n
a
xc
n
L
0 0
33
1
2
,,,,,,1
2
1
2 ππππ
( )} ( ) ( ) ( )[ ] ( ) ( )[ ] ×∑ ∫ ∫ ∫
−+
−+++
=
Φ
Φ
N
n
t L L
n
y
nn
x
nVn
Vn
n
x y
yc
n
L
ysyxc
n
L
xsxe
n
a
xdydzdzsz
1 0 0 0
33
1
2
1
2 ππ
τ
π
( )[ ] ( ) ( )∫
+−× Φ
zL
Vnn
z
xdydzdzyxfzszzc
n
L
0
,,1
2π
.
12. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
12
Fig.2a. Spatial distributions of concentration of dopant after infusion and annealing with the same anneal-
ing time before and after interface between layers of heterostructure. Curve 1 is the distribution of concen-
tration of dopant in homogenous sample with averaged dopant diffusion coefficient D0. Curves 2-6 are the
distribution of concentration of dopant in heterostructure with increasing difference between values of dif-
fusion coefficient. Value of dopant diffusion coefficient in the substrate is smaller, than in epitaxial the
layer
3. DISCUSSION
In this section analysis of distributions of concentration of dopant, infused (see Fig. 2a) or im-
planted (see Fig. 2b) into epitaxial layer have been done. Annealing time is the same for all
curves of these figures. One can find from these figures, that absolute value of gradient of con-
centration of dopant increases due to presents an interface between layers of heterostructure. In
this situation dimensions of the considered transistors decreases. At the same time homogeneity of
concentration of dopant in enriched area increases.
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 concentration of dopant after implantation and annealing with the same an-
nealing time before and after interface between layers of heterostructure. Annealing time for curves 1 and 3
is equal to Θ = 0.0048(Lx
2
+Ly
2
+Lz
2
)/D0. Annealing time for curves 2 and 4 is equal to Θ = 0.0057(Lx
2
+Ly
2
+Lz
2
)/D0. Curves 1 and 2 are the distributions of concentration of dopant in homogenous sample.
Curves 3 and 4 are distributions of concentration of dopant in heterostructure under condition, when value
of dopant diffusion coefficient in the substrate is smaller, than in epitaxial the layer
13. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
13
To estimate optimal annealing time we estimate decreasing of absolute value of gradient of con-
centration of dopant near interface between layers of the heterostructure with increasing of an-
nealing time. Decreasing of annealing time leads to increasing inhomogeneity of distribution of
concentration of dopant. Estimation of the compromise value of annealing time has been done by
using recently introduced criterion [14,15]. To use the criterion we approximate real spatial dis-
tribution of concentration of dopant by idealized step-wise function ψ(x,y,z). After that we esti-
mate the required optimal annealing time by minimization of mean-square error [16-20]
( ) ( )[ ]∫ ∫ ∫ −Θ=
x y zL L L
zyx
xdydzdzyxzyxC
LLL
U
0 0 0
,,,,,
1
ψ . (18)
Minimization of the above mean-squared error leads to dependences of optimal annealing time on
parameters, which are presented on Figs. 3. It should be noted, that radiation defects, generated
during ion implantation, should be annealed. After ideal optimization of annealing time the im-
planted dopant should achieve the interface between layers of heterostructure. If annealing time is
smaller, it is attracted an interest to make additional annealing to achieve the interface. The Fig.
3b shows dependences of additional annealing time.
The figures shows, that optimal annealing time of implanted dopant is smaller in comparison with
optimal annealing time of infused dopant. If the considered heterostructure have been doped by
diffusion, any radiation damage of materials of layers is absent. On the other hand radiation
processing of materials of heterostructure (including of ion implantation) leads to decreasing of
mismatch-induced stress in the processed heterostructure [20].
0.0 0.1 0.2 0.3 0.4 0.5
a/L, ξ, ε, γ
0.0
0.1
0.2
0.3
0.4
0.5
ΘD0L
-2
3
2
4
1
Fig. 3a. Dependences of optimal annealing time of infused dopant on several parameters. Dependence of
the optimal annealing time on normalized thickness of the epitaxial layer a/L describes by curve 1 for ξ=γ=
0 for equal to each other values of dopant diffusion coefficient in both parts of heterostructure. Curve 2
describes dependence of the optimal annealing time on the parameter ε for a/L=1/2 and ξ= γ = 0. Curve 3
describes dependence of the optimal annealing time on the parameter ξ for a/L=1/2 and ε= γ = 0. Curve 4
describes dependence of the optimal annealing time on parameter γ for a/L=1/2 and ε=ξ=0
14. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
14
0.0 0.1 0.2 0.3 0.4 0.5
a/L, ξ, ε, γ
0.00
0.04
0.08
0.12
ΘD0L
-2
3
2
4
1
Fig.3b. Dependences of optimal annealing time of implanted dopant on several parameters. Dependence of
the optimal annealing time on normalized thickness of the epitaxial layer a/L describes by curve 1 for ξ=γ=
0 for equal to each other values of dopant diffusion coefficient in both parts of heterostructure. Curve 2
describes dependence of the optimal annealing time on the parameter ε for a/L=1/2 and ξ= γ = 0. Curve 3
describes dependence of the optimal annealing time on the parameter ξ for a/L=1/2 and ε= γ = 0. Curve 4
describes dependence of the optimal annealing time on parameter γ for a/L=1/2 and ε=ξ=0
4. CONCLUSIONS
In this paper we formulate several recommendations to optimize manufacture heterotransistor
with several source based on prognosis of time varying of spatial distributions of concentrations
of infused and implanted dopants in specific heterostructure. We also introduce analytical ap-
proach to prognosis diffusion and ion types of doping with account variation in space and time
parameters of technological parameters and nonlinearity of mass and heat transport.
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 and
educational fellowship for scientific research of Government of Nizhny Novgorod region of Rus-
sia.
REFERENCES
[1] Z. Ramezani, A.A. Orouji. A silicon-on-insulator metal semiconductor field-effect transistor with an L-
shaped buried oxide for high output-power density. Mat. Sci. Sem. Proc. Vol. 19. P. 124-129 (2014).
[2] Ch. Dong, J. Shi, J. Wu, Y. Chen, D. Zhou, Z. Hu, H. Xie, R. Zhan, Zh. Zou. Improvements in passiva-
tion effect of amorphous InGaZnO thin film transistors. Mat. Sci. Sem. Proc. Vol. 20. P. 7-11 (2014).
[3] V. Papageorgiou, A. Khalid, C. Li, M.J. Steer, D.R.S. Cumming. Integration techniques of pHEMTs
and planar Gunn diodes on GaAs substrates. Solid-State Electronics. Vol. 102. P. 87-92 (2014).
[4] R. Grassi, A. Gnudi, V. Di Lecce, E. Gnani, S. Reggiani, G. Baccarani. Boosting the voltage gain of
graphene FETs through a differential amplifier scheme with positive feedback. Solid-State Electronics.
Vol. 100. P. 54-60 (2014).
[5] A.O. Ageev, A.E. Belyaev, N.S. Boltovets, V.N. Ivanov, R.V. Konakova, Ya.Ya. Kudrik, P.M. Litvin,
V.V. Milenin, A.V. Sachenko. Au-TiBx-n-6H-SiC Schottky barrier diodes: Specific features of charge
transport in rectifying and nonrectifying contacts. Semiconductors. Vol. 43 (7). P. 897-903 (2009).
[6] A.G. Alexenko, I.I. Shagurin. Microcircuitry (Radio and communication, Moscow, 1990).
15. Advances in Materials Science and Engineering: An International Journal (MSEJ), Vol. 3, No. 3, September 2016
15
[7] T.T.A. Tuan, D.-H. Kuo, C.-C. Li, G.-Z. Li. Effect of temperature dependence on electrical characteri-
zation of p-n GaN diode fabricated by RF magnetron sputtering. Mat. Sci. Appl. Vol. 6. P. 809-817
(2015).
[8] V.I. Lachin, N.S. Savelov. Electronics (Phoenix, Rostov-na-Donu, 2001).
[9] R. Pal, R. Pandey, N. Pandey, R.Ch. Tiwari. Single CDBA Based Voltage Mode Bistable Multivibrator
and Its Applications. Circuits and Systems. Vol. 6 (11). P. 237-251 (2015).
[10] Z.Yu. Gotra. Technology of microelectronic devices (Radio and communication, Moscow, 1991).
[11] V.L. Vinetskiy, G.A. Kholodar', Radiative physics of semiconductors. ("Naukova Dumka", Kiev,
1979, in Russian).
[12] P.M. Fahey, P.B. Griffin, J.D. Plummer. Point defects and dopant diffusion in silicon. Rev. Mod. Phys.
Vol. 61 (2). P. 289-388 (1989).
[13] M.L. Krasnov, A.I. Kiselev, G.I. Makarenko. Integral equations ("Science", Moscow, 1976).
[14] E.L. Pankratov. Dopant diffusion dynamics and optimal diffusion time as influenced by diffusion-
coefficient nonuniformity. Russian Microelectronics. Vol. 36 (1). P. 33-39 (2007).
[15] E.L. Pankratov. Redistribution of dopant during annealing of radiative defects in a multilayer structure
by laser scans for production an implanted-junction rectifiers. Int. J. Nanoscience. Vol. 7 (4-5). P. 187–
197 (2008).
[16] E.L. Pankratov. Decreasing of depth of implanted-junction rectifier in semiconductor heterostructure
by optimized laser annealing. J. Comp. Theor. Nanoscience. Vol. 7 (1). P. 289-295 (2010).
[17] E.L. Pankratov, E.A. Bulaeva. Optimization of manufacturing of emitter-coupled logic to decrease
surface of chip. International Journal of Modern Physics B. Vol. 29 (5). P. 1550023-1-1550023-12
(2015).
[18] E.L. Pankratov, E.A. Bulaeva. An approach to manufacture of bipolar transistors in thin film struc-
tures. On the method of optimization. Int. J. Micro-Nano Scale Transp. Vol. 4 (1). P. 17-31 (2014).
[19] E.L. Pankratov, E.A. Bulaeva. Increasing of sharpness of diffusion-junction heterorectifier by using
radiation processing. Int. J. Nanoscience. Vol. 11 (5). P. 1250028-1250035 (2012).
[20] E.L. Pankratov, E.A. Bulaeva. Decreasing of mechanical stress in a semiconductor heterostructure by
radiation processing. J. Comp. Theor. Nanoscience. Vol. 11 (1). P. 91-101 (2014).
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 Radiophysical
Department of Nizhny Novgorod State University. Since 2015 E.L. Pankratov is an Associate Professor of
Nizhny Novgorod State University. He has 155 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-
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 103 published papers in area of her researches.