In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions (single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
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.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect heterotransistor. Based on analytical solution of the considered boundary problems some recommendations have been formulated to optimize technological processes.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect
heterotransistor. Based on analytical solution of the considered boundary problems some recommendations
have been formulated to optimize technological processes.
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.
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.
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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.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
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.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect heterotransistor. Based on analytical solution of the considered boundary problems some recommendations have been formulated to optimize technological processes.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect
heterotransistor. Based on analytical solution of the considered boundary problems some recommendations
have been formulated to optimize technological processes.
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.
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 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.
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Modeling of manufacturing of a field effect transistor to determine condition...ijcsa
In this paper we introduce an approach to model technological process of manufacture of a field-effect
heterotransistor. The modeling gives us possibility to optimize the technological process to decrease length
of channel by using mechanical stress. As accompanying results of the decreasing one can find decreasing
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circuits.
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
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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
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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
ON OPTIMIZATION OF MANUFACTURING OF AN AMPLIFIER TO INCREASE DENSITY OF BIPOL...ijoejournal
In this paper we consider a possibility to increase density of bipolar heterotransistor framework an amplifier
due to decreasing of their dimensions. The considered approach based on doping of required areas of
heterostructure with specific configuration by diffusion or ion implantation. The doping finished by optimized
annealing of dopant and/or radiation defects. Analysis of redistribution of dopant with account redistribution
of radiation defects (after implantation of ions of dopant) for optimization of the above annealing
have been done by using recently introduced analytical approach. The approach gives a possibility
to analyze mass and heat transports in a heterostructure without crosslinking of solutions on interfaces
between layers of the heterostructure with account nonlinearity of these transports and variation in time of
their parameters.
ON OPTIMIZATION 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.
AN APPROACH TO OPTIMIZE MANUFACTURE OF AN ACTIVE QUADRATURE SIGNAL GENERATOR ...antjjournal
In this paper we introduce an approach to increase density of field-effect transistors framework an active
quadrature signal generator. Framework the approach we consider manufacturing the generator 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.
MODELING OF MANUFACTURING OF A FIELDEFFECT TRANSISTOR TO DETERMINE CONDITIONS...antjjournal
In this paper we introduce an approach to model technological process of manufacture of a field-effect
heterotransistor. The modeling gives us possibility to optimize the technological process to decrease length
of channel by using mechanical stress. As accompanying results of the decreasing one can find decreasing
of thickness of the heterotransistors and increasing of their density, which were comprised in integrated
circuits.
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We introduce an approach of manufacturing of a p-i-n-heterodiodes. The approach based on using a δ-
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the doping the dopant and/or radiation defects have been annealed. We introduce an approach to optimize
annealing of the dopant and/or radiation defects. We determine several conditions to manufacture more
compact p-i-n-heterodiodes
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In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
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In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
ON 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.
MODIFICATION OF DOPANT CONCENTRATION PROFILE IN A FIELD-EFFECT HETEROTRANSIST...msejjournal
In this paper we consider an approach of manufacturing more compact field-effect heterotransistors. The
approach based on manufacturing a heterostructure, which consist of a substrate and an epitaxial layer
with specific configuration. After that several areas of the epitaxial layer have been doped by diffusion or
ion implantation with optimized annealing of dopant and /or radiation defects. At the same time we introduce
an approach of modification of energy band diagram by additional doping of channel of the transistors.
We also consider an analytical approach to model and optimize technological process.
MODIFICATION OF DOPANT CONCENTRATION PROFILE IN A FIELD-EFFECT HETEROTRANSIST...msejjournal
In this paper we consider an approach of manufacturing more compact field-effect heterotransistors. The
approach based on manufacturing a heterostructure, which consist of a substrate and an epitaxial layer
with specific configuration. After that several areas of the epitaxial layer have been doped by diffusion or
ion implantation with optimized annealing of dopant and /or radiation defects. At the same time we introduce an approach of modification of energy band diagram by additional doping of channel of the transistors. We also consider an analytical approach to model and optimize technological process.
ON MODIFICATION OF PROPERTIES OF P-N-JUNCTIONS DURING OVERGROWTHZac Darcy
In this paper we consider influence of overgrowth of doped by diffusion and ion implantation areas of heterostructures
on distributions of concentrations of dopants. Several conditions to increase sharpness of p-njunctions
(single and framework bipolar transistors), which were manufactured during considered technological
process, have been determined. At the same time we analyzed influence of speed of overgrowth of
doped areas and mechanical stress in the considered heterostructure on distribution of concentrations of
dopants in the structure.
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
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 to Increase Integration Rate of Elements of an Operational Amplif...BRNSS Publication Hub
In this paper, we introduce an approach to optimize manufacturing of an operational amplifier circuit based on field-effect transistors. Main aims of the optimization are (i) decreasing dimensions of elements of the considered operational amplifier and (ii) increasing of performance and reliability of the considered field-effect transistors. Dimensions of considered field-effect transistors will be decreased due to manufacture of these transistors framework heterostructure with specific structure, doping of required areas of the heterostructure by diffusion or ion implantation, and optimization of annealing of dopant and/or radiation defects. Performance and reliability of the above field-effect transistors could be increased by optimization of annealing of dopant and/or radiation defects and using inhomogeneity of properties of heterostructure. Choosing of inhomogeneity of properties of heterostructure leads to increasing of compactness of distribution of concentration of dopant. At the same time, one can obtain increasing of homogeneity of the above concentration. In this paper, we also introduce an analytical approach for prognosis of technological process of manufacturing of the considered operational amplifier. The approach gives a possibility to take into account variation of parameters of processes in space and at the same time in space. At the same time, one can take into account nonlinearity of the considered processes.
ON DECREASING OF DIMENSIONS OF FIELDEFFECT 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
ON DECREASING OF DIMENSIONS OF FIELDEFFECT 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
OPTIMIZING SIMILARITY THRESHOLD FOR ABSTRACT SIMILARITY METRIC IN SPEECH DIAR...mathsjournal
Speaker diarization is a critical task in speech processing that aims to identify "who spoke when?" in an
audio or video recording that contains unknown amounts of speech from unknown speakers and unknown
number of speakers. Diarization has numerous applications in speech recognition, speaker identification,
and automatic captioning. Supervised and unsupervised algorithms are used to address speaker diarization
problems, but providing exhaustive labeling for the training dataset can become costly in supervised
learning, while accuracy can be compromised when using unsupervised approaches. This paper presents a
novel approach to speaker diarization, which defines loosely labeled data and employs x-vector embedding
and a formalized approach for threshold searching with a given abstract similarity metric to cluster
temporal segments into unique user segments. The proposed algorithm uses concepts of graph theory,
matrix algebra, and genetic algorithm to formulate and solve the optimization problem. Additionally, the
algorithm is applied to English, Spanish, and Chinese audios, and the performance is evaluated using wellknown similarity metrics. The results demonstrate that the robustness of the proposed approach. The
findings of this research have significant implications for speech processing, speaker identification
including those with tonal differences. The proposed method offers a practical and efficient solution for
speaker diarization in real-world scenarios where there are labeling time and cost constraints.
A POSSIBLE RESOLUTION TO HILBERT’S FIRST PROBLEM BY APPLYING CANTOR’S DIAGONA...mathsjournal
We present herein a new approach to the Continuum hypothesis CH. We will employ a string conditioning,
a technique that limits the range of a string over some of its sub-domains for forming subsets K of R. We
will prove that these are well defined and in fact proper subsets of R by making use of Cantor’s Diagonal
argument in its original form to establish the cardinality of K between that of (N,R) respectively
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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 MODIFICATION OF PROPERTIES OF P-N-JUNCTIONS DURING OVERGROWTHZac Darcy
In this paper we consider influence of overgrowth of doped by diffusion and ion implantation areas of heterostructures
on distributions of concentrations of dopants. Several conditions to increase sharpness of p-njunctions
(single and framework bipolar transistors), which were manufactured during considered technological
process, have been determined. At the same time we analyzed influence of speed of overgrowth of
doped areas and mechanical stress in the considered heterostructure on distribution of concentrations of
dopants in the structure.
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
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 to Increase Integration Rate of Elements of an Operational Amplif...BRNSS Publication Hub
In this paper, we introduce an approach to optimize manufacturing of an operational amplifier circuit based on field-effect transistors. Main aims of the optimization are (i) decreasing dimensions of elements of the considered operational amplifier and (ii) increasing of performance and reliability of the considered field-effect transistors. Dimensions of considered field-effect transistors will be decreased due to manufacture of these transistors framework heterostructure with specific structure, doping of required areas of the heterostructure by diffusion or ion implantation, and optimization of annealing of dopant and/or radiation defects. Performance and reliability of the above field-effect transistors could be increased by optimization of annealing of dopant and/or radiation defects and using inhomogeneity of properties of heterostructure. Choosing of inhomogeneity of properties of heterostructure leads to increasing of compactness of distribution of concentration of dopant. At the same time, one can obtain increasing of homogeneity of the above concentration. In this paper, we also introduce an analytical approach for prognosis of technological process of manufacturing of the considered operational amplifier. The approach gives a possibility to take into account variation of parameters of processes in space and at the same time in space. At the same time, one can take into account nonlinearity of the considered processes.
ON DECREASING OF DIMENSIONS OF FIELDEFFECT 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
ON DECREASING OF DIMENSIONS OF FIELDEFFECT 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
Similar to Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant Under Influence of Variation of Pressure of Vapor of the Dopant (20)
OPTIMIZING SIMILARITY THRESHOLD FOR ABSTRACT SIMILARITY METRIC IN SPEECH DIAR...mathsjournal
Speaker diarization is a critical task in speech processing that aims to identify "who spoke when?" in an
audio or video recording that contains unknown amounts of speech from unknown speakers and unknown
number of speakers. Diarization has numerous applications in speech recognition, speaker identification,
and automatic captioning. Supervised and unsupervised algorithms are used to address speaker diarization
problems, but providing exhaustive labeling for the training dataset can become costly in supervised
learning, while accuracy can be compromised when using unsupervised approaches. This paper presents a
novel approach to speaker diarization, which defines loosely labeled data and employs x-vector embedding
and a formalized approach for threshold searching with a given abstract similarity metric to cluster
temporal segments into unique user segments. The proposed algorithm uses concepts of graph theory,
matrix algebra, and genetic algorithm to formulate and solve the optimization problem. Additionally, the
algorithm is applied to English, Spanish, and Chinese audios, and the performance is evaluated using wellknown similarity metrics. The results demonstrate that the robustness of the proposed approach. The
findings of this research have significant implications for speech processing, speaker identification
including those with tonal differences. The proposed method offers a practical and efficient solution for
speaker diarization in real-world scenarios where there are labeling time and cost constraints.
A POSSIBLE RESOLUTION TO HILBERT’S FIRST PROBLEM BY APPLYING CANTOR’S DIAGONA...mathsjournal
We present herein a new approach to the Continuum hypothesis CH. We will employ a string conditioning,
a technique that limits the range of a string over some of its sub-domains for forming subsets K of R. We
will prove that these are well defined and in fact proper subsets of R by making use of Cantor’s Diagonal
argument in its original form to establish the cardinality of K between that of (N,R) respectively
A Positive Integer 𝑵 Such That 𝒑𝒏 + 𝒑𝒏+𝟑 ~ 𝒑𝒏+𝟏 + 𝒑𝒏+𝟐 For All 𝒏 ≥ 𝑵mathsjournal
According to Bertrand's postulate, we have 𝑝𝑛 + 𝑝𝑛 ≥ 𝑝𝑛+1. Is it true that for all 𝑛 > 1 then 𝑝𝑛−1 + 𝑝𝑛 ≥𝑝𝑛+1? Then 𝑝𝑛 + 𝑝𝑛+3 > 𝑝𝑛+1 + 𝑝𝑛+2where 𝑛 ≥ 𝑁, 𝑁 is a large enough value?
A POSSIBLE RESOLUTION TO HILBERT’S FIRST PROBLEM BY APPLYING CANTOR’S DIAGONA...mathsjournal
We present herein a new approach to the Continuum hypothesis CH. We will employ a string conditioning,
a technique that limits the range of a string over some of its sub-domains for forming subsets K of R. We
will prove that these are well defined and in fact proper subsets of R by making use of Cantor’s Diagonal
argument in its original form to establish the cardinality of K between that of (N,R) respectively.
Moving Target Detection Using CA, SO and GO-CFAR detectors in Nonhomogeneous ...mathsjournal
systems in complex situations. A fundamental problem in radar systems is to automatically detect targets while maintaining a
desired constant false alarm probability. This work studies two detection approaches, the first with a fixed threshold and the
other with an adaptive one. In the latter, we have learned the three types of detectors CA, SO, and GO-CFAR. This research
aims to apply intelligent techniques to improve detection performance in a nonhomogeneous environment using standard
CFAR detectors. The objective is to maintain the false alarm probability and enhance target detection by combining
intelligent techniques. With these objectives in mind, implementing standard CFAR detectors is applied to nonhomogeneous
environment data. The primary focus is understanding the reason for the false detection when applying standard CFAR
detectors in a nonhomogeneous environment and how to avoid it using intelligent approaches.
OPTIMIZING SIMILARITY THRESHOLD FOR ABSTRACT SIMILARITY METRIC IN SPEECH DIAR...mathsjournal
Speaker diarization is a critical task in speech processing that aims to identify "who spoke when?" in an
audio or video recording that contains unknown amounts of speech from unknown speakers and unknown
number of speakers. Diarization has numerous applications in speech recognition, speaker identification,
and automatic captioning. Supervised and unsupervised algorithms are used to address speaker diarization
problems, but providing exhaustive labeling for the training dataset can become costly in supervised
learning, while accuracy can be compromised when using unsupervised approaches. This paper presents a
novel approach to speaker diarization, which defines loosely labeled data and employs x-vector embedding
and a formalized approach for threshold searching with a given abstract similarity metric to cluster
temporal segments into unique user segments. The proposed algorithm uses concepts of graph theory,
matrix algebra, and genetic algorithm to formulate and solve the optimization problem. Additionally, the
algorithm is applied to English, Spanish, and Chinese audios, and the performance is evaluated using wellknown similarity metrics. The results demonstrate that the robustness of the proposed approach. The
findings of this research have significant implications for speech processing, speaker identification
including those with tonal differences. The proposed method offers a practical and efficient solution for
speaker diarization in real-world scenarios where there are labeling time and cost constraints.
The Impact of Allee Effect on a Predator-Prey Model with Holling Type II Func...mathsjournal
There is currently much interest in predator–prey models across a variety of bioscientific disciplines. The focus is on quantifying predator–prey interactions, and this quantification is being formulated especially as regards climate change. In this article, a stability analysis is used to analyse the behaviour of a general two-species model with respect to the Allee effect (on the growth rate and nutrient limitation level of the prey population). We present a description of the local and non-local interaction stability of the model and detail the types of bifurcation which arise, proving that there is a Hopf bifurcation in the Allee effect module. A stable periodic oscillation was encountered which was due to the Allee effect on the
prey species. As a result of this, the positive equilibrium of the model could change from stable to unstable and then back to stable, as the strength of the Allee effect (or the ‘handling’ time taken by predators when predating) increased continuously from zero. Hopf bifurcation has arose yield some complex patterns that have not been observed previously in predator-prey models, and these, at the same time, reflect long term behaviours. These findings have significant implications for ecological studies, not least with respect to examining the mobility of the two species involved in the non-local domain using Turing instability. A spiral generated by local interaction (reflecting the instability that forms even when an infinitely large
carrying capacity is assumed) is used in the model.
A POSSIBLE RESOLUTION TO HILBERT’S FIRST PROBLEM BY APPLYING CANTOR’S DIAGONA...mathsjournal
We present herein a new approach to the Continuum hypothesis CH. We will employ a string conditioning,a technique that limits the range of a string over some of its sub-domains for forming subsets K of R. We will prove that these are well defined and in fact proper subsets of R by making use of Cantor’s Diagonal argument in its original form to establish the cardinality of K between that of (N,R) respectively.
Moving Target Detection Using CA, SO and GO-CFAR detectors in Nonhomogeneous ...mathsjournal
Modernization of radar technology and improved signal processing techniques are necessary to improve detection systems in complex situations. A fundamental problem in radar systems is to automatically detect targets while maintaining a
desired constant false alarm probability. This work studies two detection approaches, the first with a fixed threshold and the
other with an adaptive one. In the latter, we have learned the three types of detectors CA, SO, and GO-CFAR. This research
aims to apply intelligent techniques to improve detection performance in a nonhomogeneous environment using standard
CFAR detectors. The objective is to maintain the false alarm probability and enhance target detection by combining
intelligent techniques. With these objectives in mind, implementing standard CFAR detectors is applied to nonhomogeneous
environment data. The primary focus is understanding the reason for the false detection when applying standard CFAR
detectors in a nonhomogeneous environment and how to avoid it using intelligent approaches
OPTIMIZING SIMILARITY THRESHOLD FOR ABSTRACT SIMILARITY METRIC IN SPEECH DIAR...mathsjournal
Speaker diarization is a critical task in speech processing that aims to identify "who spoke when?" in an
audio or video recording that contains unknown amounts of speech from unknown speakers and unknown
number of speakers. Diarization has numerous applications in speech recognition, speaker identification,
and automatic captioning. Supervised and unsupervised algorithms are used to address speaker diarization
problems, but providing exhaustive labeling for the training dataset can become costly in supervised
learning, while accuracy can be compromised when using unsupervised approaches. This paper presents a
novel approach to speaker diarization, which defines loosely labeled data and employs x-vector embedding
and a formalized approach for threshold searching with a given abstract similarity metric to cluster
temporal segments into unique user segments. The proposed algorithm uses concepts of graph theory,
matrix algebra, and genetic algorithm to formulate and solve the optimization problem. Additionally, the
algorithm is applied to English, Spanish, and Chinese audios, and the performance is evaluated using wellknown similarity metrics. The results demonstrate that the robustness of the proposed approach. The
findings of this research have significant implications for speech processing, speaker identification
including those with tonal differences. The proposed method offers a practical and efficient solution for
speaker diarization in real-world scenarios where there are labeling time and cost constraints
Modified Alpha-Rooting Color Image Enhancement Method on the Two Side 2-D Qua...mathsjournal
Color in an image is resolved to 3 or 4 color components and 2-Dimages of these components are stored in separate channels. Most of the color image enhancement algorithms are applied channel-by-channel on each image. But such a system of color image processing is not processing the original color. When a color image is represented as a quaternion image, processing is done in original colors. This paper proposes an implementation of the quaternion approach of enhancement algorithm for enhancing color images and is referred as the modified alpha-rooting by the two-dimensional quaternion discrete Fourier transform (2-D QDFT). Enhancement results of this proposed method are compared with the channel-by-channel image enhancement by the 2-D DFT. Enhancements in color images are quantitatively measured by the color enhancement measure estimation (CEME), which allows for selecting optimum parameters for processing by thegenetic algorithm. Enhancement of color images by the quaternion based method allows for obtaining images which are closer to the genuine representation of the real original color.
An Application of Assignment Problem in Laptop Selection Problem Using MATLABmathsjournal
The assignment – selection problem used to find one-to- one match of given “Users” to “Laptops”, the main objective is to minimize the cost as per user requirement. This paper presents satisfactory solution for real assignment – Laptop selection problem using MATLAB coding.
The aim of this paper is to study the class of β-normal spaces. The relationships among s-normal spaces, pnormal spaces and β-normal spaces are investigated. Moreover, we study the forms of generalized β-closed
functions. We obtain characterizations of β-normal spaces, properties of the forms of generalized β-closed
functions and preservation theorems.
Cubic Response Surface Designs Using Bibd in Four Dimensionsmathsjournal
Response Surface Methodology (RSM) has applications in Chemical, Physical, Meteorological, Industrial and Biological fields. The estimation of slope response surface occurs frequently in practical situations for the experimenter. The rates of change of the response surface, like rates of change in the yield of crop to various fertilizers, to estimate the rates of change in chemical experiments etc. are of
interest. If the fit of second order response is inadequate for the design points, we continue the
experiment so as to fit a third order response surface. Higher order response surface designs are sometimes needed in Industrial and Meteorological applications. Gardiner et al (1959) introduced third order rotatable designs for exploring response surface. Anjaneyulu et al (1994-1995) constructed third order slope rotatable designs using doubly balanced incomplete block designs. Anjaneyulu et al (2001)
introduced third order slope rotatable designs using central composite type design points. Seshu babu et al (2011) studied modified construction of third order slope rotatable designs using central composite
designs. Seshu babu et al (2014) constructed TOSRD using BIBD. In view of wide applicability of third
order models in RSM and importance of slope rotatability, we introduce A Cubic Slope Rotatable Designs Using BIBD in four dimensions.
The caustic that occur in geodesics in space-times which are solutions to the gravitational field equations with the energy-momentum tensor satisfying the dominant energy condition can be circumvented if quantum variations are allowed. An action is developed such that the variation yields the field equations
and the geodesic condition, and its quantization provides a method for determining the extent of the wave packet around the classical path.
Approximate Analytical Solution of Non-Linear Boussinesq Equation for the Uns...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy perturbation transform method(HPTM). The solution is compared with the exact solution. The comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer
parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height of water table. The results resemble well with the physical phenomena.
Common Fixed Point Theorems in Compatible Mappings of Type (P*) of Generalize...mathsjournal
In this paper, we give some new definition of Compatible mappings of type (P), type (P-1) and type (P-2) in intuitionistic generalized fuzzy metric spaces and prove Common fixed point theorems for six mappings
under the conditions of compatible mappings of type (P-1) and type (P-2) in complete intuitionistic fuzzy
metric spaces. Our results intuitionistically fuzzify the result of Muthuraj and Pandiselvi [15]
Mathematics subject classifications: 45H10, 54H25
A Probabilistic Algorithm for Computation of Polynomial Greatest Common with ...mathsjournal
In the earlier work, Knuth present an algorithm to decrease the coefficient growth in the Euclidean algorithm of polynomials called subresultant algorithm. However, the output polynomials may have a small factor which can be removed. Then later, Brown of Bell Telephone Laboratories showed the subresultant in another way by adding a variant called 𝜏 and gave a way to compute the variant. Nevertheless, the way failed to determine every 𝜏 correctly.
In this paper, we will give a probabilistic algorithm to determine the variant 𝜏 correctly in most cases by adding a few steps instead of computing 𝑡(𝑥) when given 𝑓(𝑥) and𝑔(𝑥) ∈ ℤ[𝑥], where 𝑡(𝑥) satisfies that 𝑠(𝑥)𝑓(𝑥) + 𝑡(𝑥)𝑔(𝑥) = 𝑟(𝑥), here 𝑡(𝑥), 𝑠(𝑥) ∈ ℤ[𝑥]
Table of Contents - September 2022, Volume 9, Number 2/3mathsjournal
Applied Mathematics and Sciences: An International Journal (MathSJ ) aims to publish original research papers and survey articles on all areas of pure mathematics, theoretical applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant Under Influence of Variation of Pressure of Vapor of the Dopant
1. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
53
MODELING OF REDISTRIBUTION OF INFUSED DOPANT
IN A MULTILAYER STRUCTURE DOPANT UNDER
INFLUENCE OF VARIATION OF PRESSURE OF VAPOR OF
THE DOPANT
E.L. Pankratov1
, E.A. Bulaeva2
1
Nizhny Novgorod State University, 23 Gagarin avenue, Nizhny Novgorod, 603950,
Russia
2
Nizhny Novgorod State University of Architecture and Civil Engineering, 65 Il'insky
street, Nizhny Novgorod, 603950, Russia
ABSTRACT
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer struc-
ture with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technol-
ogical process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribu-
tion in doped area.
KEYWORDS
Dopant diffusion; multilayer structure; p-n-heterojunctions; optimization of technological process; influ-
ence of pressure of vapor
1. INTRODUCTION
One of actual problems of solid state electronics is increasing of degree of integration of elements
of integrated circuits (p-n- junctions, field and bipolar transistors, thyristors, …) [1-9]. At the
same time one can find decreasing dimensions of the elements. To decrease the dimensions dif-
ferent approaches are used. One group of the approaches including into itself laser and microwave
types of annealing [10-12]. One can found that during laser and microwave types of annealing
inhomogenous distribution of temperature is generated. In this situation dimensions of elements
of integrated circuits decreases due to Arrhenius law. To decrease dimensions elements of inte-
grated circuits it could be also used of inhomogeneity of heterostructures [13-15]. However it is
necessary to optimize technological process in this case [16,17]. It is known, that radiation dam-
age of semiconductor materials leads to changing of distribution of dopant concentration in p-n-
junctions and transistors [9,13,15,18]. In this situation radiation damage of semiconductor mate-
rials attracted an interest [19].
This paper is about doping by diffusion of a heterostructure, which consist of a substrate with
known type of conductivity (p or n) and epitaxial layer (see Fig. 1). A dopant has been infused in
2. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
54
the epitaxial layer from gaseous source to produce required type of conductivity (n or p). It is
known, that under special conditions sharpness of p-n- junctions increases [16,17]. Main our aim
framework the present paper is analysis of influence of pressure of vapor in source of dopant on
distribution of concentration of dopant in p-n- junction.
D0
D1
D2
0 a L
x
D(x)
Fig. 1. Heterostructure, which consist of a substrate and an epitaxial layer
2. Method of solution
We solve our aim by analysis of spatio-temporal distribution of concentration of dopant. To de-
termine the spatio-temporal distribution we solve the second Fick’s law [8,9,13]
( ) ( )
=
x
t
x
C
D
x
t
t
x
C
C
∂
∂
∂
∂
∂
∂ ,
,
(1)
with boundary and initial conditions
C(0,t)=N,
( ) 0
,
=
=L
x
x
t
x
C
∂
∂
, C(x >0,0)=0. (2)
We assume, that dopant infusing from infinite source with near-boundary concentration N, which
is essentially larger, than limit of solubility of dopant P. In the Eq.(1) and conditions (2) we used
the following notations: C (x,t) is the spatio-temporal distribution of concentration of dopant; T is
the temperature of annealing; DC is the dopant diffusion coefficient. Value of dopant diffusion
coefficient depends on temperature through the Arrhenius law (during heating and cooling of he-
terostructure) and properties of materials of layers of heterostructure. Properties of materials de-
pends on level of doping of materials. Approximation of dependences of dopant diffusion coeffi-
cient on parameters could be written as [8]
3. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
55
( ) ( )
( )
+
=
T
x
P
t
x
C
T
x
D
D L
C
,
,
1
, γ
γ
ξ . (3)
Here DL(x,T) taking into account the spatial (i.e. accounting several layers in heterostructure) and
temperature (due to Arrhenius law) dependences of dopant diffusion coefficient; P(x,T) is the de-
pendence of limit of solubility of dopant on coordinate and temperature; parameter γ depends on
properties of materials and could be integer in the following interval γ ∈[1,3] [8]. Concentrational
dependence of dopant diffusion coefficient has been described in details in [8].
To solve our aim let us determine solution of Eq.(1) and make analysis of dynamics of dopant. To
calculate analytical solution of Eq.(1) we used recently elaborated approach [16,17,19]. Frame-
work the approach we transform approximation of dopant diffusion coefficient to the following
form: DC=D0L[1+ε η(x,T)][1+ξ Cγ
(x,t)/Pγ
(x,T)], where 0≤ε <1, |η(x,T)|≤1, D0L is the average value
of dopant diffusion coefficient. Farther we solve Eq.(1) in the following form
( ) ( )
∑ ∑
=
∞
=
∞
=
0 0
,
,
k m
km
m
k
t
x
C
t
x
C ξ
ε . (4)
Functions Ckm(x,t) could be determine by solution of the following system of equation
( ) ( )
2
00
2
0
00 ,
,
x
t
x
C
D
t
t
x
C
L
∂
∂
=
∂
∂
( ) ( ) ( ) ( )
∂
∂
∂
∂
+
∂
∂
=
∂
∂ −
2
10
0
2
0
2
0
0 ,
,
,
,
x
t
x
C
T
x
x
D
x
t
x
C
D
t
t
x
C k
L
k
L
k
η , k ≥1
( ) ( ) ( )
( )
( )
∂
∂
∂
∂
+
∂
∂
=
∂
∂ −
2
1
0
00
0
2
0
2
0
0 ,
,
,
,
,
x
t
x
C
T
x
P
t
x
C
x
D
x
t
x
C
D
t
t
x
C m
L
m
L
m
γ
, m ≥1 (5)
( ) ( ) ( )
( )
( )
+
∂
∂
+
∂
∂
=
∂
∂
T
x
P
t
x
C
t
x
C
x
D
x
t
x
C
D
t
t
x
C
L
L
,
,
,
,
, 00
10
2
2
0
2
11
2
0
11
γ
γ
( ) ( ) ( ) ( )
( )
( )
∂
∂
∂
∂
+
∂
∂
∂
∂
+
x
t
x
C
T
x
P
t
x
C
T
x
x
D
x
t
x
C
T
x
x
D L
L
,
,
,
,
,
, 00
00
0
2
01
0
γ
η
η
with boundary and initial conditions
C00(0,t)=N,
( ) 0
,
0
=
∂
∂
=
x
km
x
t
x
C
,k≥1,m≥1; Ckm(0,t)=0, Ckm(x>0,0)=0, k≥1, m≥1;
C00(x,0)=0, C00(0,0)=N; Ckm(x,0)=0, k≥1,m≥1. (6)
4. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
56
Solutions of the system of equations (5) with account conditions (6) could be obtain by standard
approaches [20,21] and could be written as
C00(0,t)=N, ( ) ( ) ( )
∑
+
+
=
>
∞
=
+
+
0
5
.
0
5
.
0
0
00
5
.
0
sin
2
1
,
0
n
n
n
n
t
e
x
v
P
t
x
C
π
,
where vn=πnL-1
, ( ) ( )
∫
=
L
n
n u
d
u
v
u
f
F
0
cos , en(t)=exp(-vn
2
D0Lt), P0 is the average value of limit
solubility of dopant
( ) ( ) ( ) ( )×
∑ +
=
∞
=
+
+
0
5
.
0
5
.
0
3
0
10 sin
5
.
0
2
,
n
n
n t
e
x
v
n
L
D
t
x
C
π
( ) ( ) ( ) ( )
[ ]
∑ ∫ +
−
×
∞
=
−
+
+
+
+
0 0
1
5
.
0
5
.
0
m
t
m
n
m
n
n
n u
d
u
H
u
H
u
e
u
e ,
( ) ( ) ( ) ( ) ( ) ( ) ( )
∑ ∑∫ ×
−
+
∑ +
−
=
∞
=
∞
=
+
+
∞
=
+
+
0 10
5
.
0
5
.
0
2
0
5
.
0
5
.
0
6
20
5
.
0
sin
5
.
0
2
,
n m
t
n
k
k
k
k
u
e
u
e
n
t
e
x
v
k
L
t
x
C
( ) ( )
[ ] ( ) ( ) ( ) ( )
[ ] 2
0
3
0
1
5
.
0
5
.
0
1 D
u
d
d
H
H
e
e
u
H
u
H
u
m
n
m
n
m
n
k
n
k
n π
τ
τ
τ
τ
τ
∫ +
−
+
× +
+
−
+
+
+
+
− ,
where ( ) ( ) ( ) ( )
∫
=
L
n
n
u
d
u
v
T
u
P
T
u
t
H
0
sin
,
,
η .
( ) 2
1
01 α
γα −
−
=
t
,
x
C ,
where ( ) ( )
( ) ( ) ( )
[ ]
( ) ( ) ( )
∑ ∑ ∑ ×
+
−
+
−
+
−
+
=
∞
=
∞
=
∞
=
+
+
+
0 0 0
2
2
2
5
.
0
5
.
0
5
.
0
2
3
1
5
.
0
5
.
0
5
.
0
sin
5
.
0
2
n k m
n
km
n
n
k
m
n
t
e
t
e
t
e
x
v
n
π
α
( ) ( )
[ ] ( ) ( )
[ ]
{ }
1
2
2
1
2
2
1
5
.
0
5
.
0
5
.
0
1 −
−
+
+
−
+
−
−
−
+
+
× k
n
m
k
n
m
k
, ekm(t)=ek+0.5
(t)em+0.5(t),
( ) ( ) ( ) ( )
[ ]
{
∑ ∑ ∑ ∑ ∑ +
−
+
−
−
+
+
<
= ∞
=
∞
=
∞
=
∞
=
∞
=
−
+
+
0 0 0 0 0
1
2
5
.
0
5
.
0
3
5
2
5
.
0
1
sin
5
.
0
1
3
,
0
n k l i j
n
n
j
i
l
k
nn
k
t
e
x
v
n
π
γ
α
( ) ( )
[ ] ( ) ( )
[ ] ( )
[ −
+
−
+
+
+
−
−
+
−
+
−
−
−
+
+
−
− 2
1
2
2
1
2
2
5
.
0
1
5
.
0
5
.
0 n
j
i
l
k
n
j
i
l
k
n
( ) ] ( ) ( )
[ ] −
+
−
+
+
−
+
−
+
−
−
−
−
−
− 1
2
2
1
2
1
5
.
0
1 j
i
l
k
n
j
i
l
k
( ) ( )
[ ] +
+
−
−
−
−
+
−
−1
2
2
1
5
.
0 l
k
j
i
n
( ) ( )
[ ] ( ) ( )
[ ] }×
−
+
+
+
−
+
+
−
−
+
−
+
+
−
− 1
2
2
1
2
2
2
5
.
0
5
.
0 l
k
j
i
n
l
k
j
i
n
( ) ( ) ( ) ( ) ( )
[ ]
( ) ( ) ( ) ( ) ( )2
2
2
2
2
5
,
0
1
1
1
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
+
−
+
−
+
−
+
−
+
−
+
+
+
×
+
−
−
−
j
i
l
k
n
t
e
t
e
j
i
l n
klij
, γ =3,
C (x,t)=-γ2
α3-α4,
5. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
57
where
( ) ( ) ( ) ( ) ( )
[ ]
∑ ∑ ∑ ×
+
+
−
−
+
+
=
∞
=
∞
=
∞
=
+
+
0 1 0
2
2
5
.
0
5
.
0
2
5
3 1
5
.
0
1
sin
5
.
0
4
n k l
n
n k
n
k
n
k
t
e
x
v
n
π
α
( ) ( )
[ ] ( ) ( )
[ ] ( ) ( )
[ ]×
∑∑ ∑ −
−
+
+
+
+
+
−
+
−
−
+
×
∞
=
∞
=
∞
=
−
−
1 0 0
2
2
1
2
2
1
2
2
1
5
.
0
1
1
5
.
0
5
.
0
m i j
i
l
i
l
i
k
n
l
k
n
l
( ) ( ) ( )
[ ] ( ) ( )
[ ] ( ) ( )
[ ] ×
−
−
+
+
+
−
+
+
−
+
−
+
×
−
−
− 1
2
2
1
2
2
1
2
2
2
5
.
0
1
5
.
0
5
.
0
5
.
0
5
.
0 i
l
j
i
l
j
j
i
l
( ) ( ) ( )
( ) ( ) ( )
[ ] ( )
[ ] ( )
[ ]
∑ ∑ ×
−
−
+
+
−
+
−
+
−
+
−
−
+
+
+
+
×
∞
=
∞
=
0 0
2
2
2
2
2
2
2
3
1
5
.
0
5
.
0
5
.
0
1
5
.
0
1
5
.
0
i j i
l
jj
i
l
jj
j
i
l
i
l
i
l
i
l
( ) ( )
( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( )
+
−
+
−
+
−
−
+
−
+
−
+
−
+
−
× +
+
2
2
2
5
.
0
2
2
2
2
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0 l
k
n
t
e
t
e
j
i
k
n
t
e
t
e n
kl
n
klj
,
( ) ( ) ( ) ( ) ( ) ( )
[ ]
{
∑ ∑∑ −
−
−
+
+
+
+
=
=
= ∞
=
∞
=
∞
=
−
+
+
0 0 0
1
2
2
2
5
.
0
5
.
0
4
7
4
5
.
0
5
.
0
5
.
0
sin
5
.
0
3
2
,
1
,
0
n i j
n
n j
i
n
i
j
t
e
x
v
n
π
γ
γ
α
( ) ( )
[ ] ] ( )
[
{
∑ ∑ ∑ ∑ −
+
+
+
+
+
+
−
+
∞
=
∞
=
∞
=
∞
=
−
0 0 0 0
2
1
1
2
2
1 2
5
.
0
5
.
0
1
5
.
0
1
5
.
0
1
1
5
.
0
k l m m
j
m
l
k
j
i
n
( ) ] ( ) ( )
[ ] ( )
[ −
+
−
+
−
−
−
+
+
−
+
−
−
−
− 2
1
2
2
1
2
1
2
2
1 5
.
0
5
.
0 j
m
m
l
k
j
m
m
l
k
( ) ] ( ) ( )
[ ] ( )
[ −
+
−
−
−
−
−
−
+
−
+
+
−
−
−
− 2
1
2
2
1
2
1
2
2
1 5
.
0
1
5
.
0 j
m
m
l
k
j
m
m
l
k
( ) ] ( ) ( )
[ ] ( )
[ −
+
+
−
+
−
+
−
+
−
−
−
+
+
−
−
− 2
1
2
2
1
2
1
2
2
1 5
.
0
1
5
.
0
1 j
m
m
l
k
j
m
m
l
k
( ) ] ( ) ( )
[ ] }×
+
+
+
+
−
+
+
−
−
+
−
−
− 1
2
2
1
2
1
2
2
1 2
5
.
0 m
m
l
k
j
m
m
l
k
( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( )
−
+
−
+
−
+
−
+
−
+
−
+
−
+
−
× 2
2
2
1
2
2
2
2
2
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
2
1
m
m
l
k
j
i
n
t
e
t
e n
m
iklm
( ) ( )
( ) ( ) ( )
( ) ( )×
∑ +
+
+
+
−
+
−
+
−
−
∞
=
+
0
5
.
0
3
1
7
2
2
2
2
1
1
sin
5
.
0
4
5
.
0
1
5
.
0
5
.
0
5
.
0 n
n
n
ij
x
v
n
m
j
i
n
t
e
t
e
π
6. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
58
( ) ( )
[ ]
{
∑ ∑ ∑ ∑ +
+
−
−
−
+
+
+
+
×
∞
=
∞
=
∞
=
∞
=
−
0 0 0 0
1
2
5
4
3
2
2
1
4
3
2
2 3 4 5
5
.
0
5
.
0
1
5
.
0
1
5
.
0
1
n n n n
n
n
n
n
n
n
n
n
( ) ( )
[ ] ( ) ( )
[ ] −
+
−
+
+
−
+
−
−
+
−
−
+
+
−
− 1
2
5
4
3
2
2
1
1
2
5
4
3
2
2
1 1
5
.
0
5
.
0 n
n
n
n
n
n
n
n
n
n
( ) ( )
[ ] ( ) ( )
[ ] −
−
+
−
−
+
+
+
+
−
+
−
+
−
−
− 1
2
5
4
3
2
2
1
1
2
5
4
3
2
2
1 5
.
0
1
5
.
0 n
n
n
n
n
n
n
n
n
n
( ) ( )
[ ] ( ) ( )
[ ] −
+
+
−
+
−
+
−
+
−
+
+
−
+
−
−
− 1
2
5
4
3
2
2
1
1
2
5
4
3
2
2
1 1
5
.
0
1
5
.
0 n
n
n
n
n
n
n
n
n
n
( ) ( )
[ ] ( ) ( )
[ ] +
−
−
−
−
−
+
−
+
+
+
−
−
+
−
−
− 1
2
5
4
3
2
2
1
1
2
5
4
3
2
2
1 1
5
.
0
1
5
.
0 n
n
n
n
n
n
n
n
n
n
( ) ( )
[ ] ( ) ( )
[ ] }×
+
+
+
+
−
+
+
−
−
+
−
+
+
−
− 1
2
5
4
3
2
2
1
1
2
5
4
3
2
2
1 2
5
.
0
5
.
0 n
n
n
n
n
n
n
n
n
n
( )
( ) ( ) ( ) ( )
∑ ×
+
+
−
+
−
−
−
+
∑
+
+
×
∞
=
∞
= 0
2
5
2
2
5
2
0
2
5
1
5
.
0
1
5
.
0
1
5
.
0
5
.
0
m
k k
n
m
k
n
m
k
n
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
−
+
−
+
−
+
−
+
−
+
−
+
−
× 2
2
2
4
2
3
2
2
2
1 5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
1
4
3
2
m
k
n
n
n
n
t
e
t
e n
km
n
n
n
( ) ( )
( ) ( ) ( ) ( ) ( )2
2
2
5
2
5
2
1 5
.
0
5
.
0
5
.
0
1
5
.
0
5
.
0
1
5
+
−
+
−
+
+
−
+
−
−
m
k
n
n
n
t
e
t
e n
n
.
C11(x,t)=α5+2α6+2α7-2α8+2α9+α10+4α11,
where
( ) ( ) ( ) ( ) ( )
[
{
∑ ∑ ∑ ∑ −
+
+
+
+
=
∞
=
∞
=
∞
=
∞
=
+
+
0 0 0 0
2
3
5
.
0
5
.
0
3
0
5 5
.
0
5
.
0
1
5
.
0
sin
5
.
0
2
l n k m
l
l
L
m
k
n
t
e
x
v
l
L
D
π
γ
α
( ) ] ( ) ( )
[ ] }( ) ( ) ( )
[ ] ×
+
−
+
−
+
+
+
−
+
−
−
−
−
−
− 1
2
2
2
1
2
2
1
2
5
.
0
5
.
0
5
.
0
1
5
.
0 n
k
n
k
n
m
k
n
( ) ( )
[ ] ( ) ( ) ( ) ( ) ( )
[ ]
∫ −
−
−
+
× +
+
+
+
+
+
+
−
t
n
l
m
k
l
n
l
n
l u
d
u
e
u
e
u
e
u
e
u
e
u
H
u
H
0
5
.
0
5
.
0
5
.
0
5
.
0
5
.
0
1 ,
( ) ( ) ( ) ( ) ( ) ( )
[ ]
{
∑ ∑ ∑ −
−
−
+
+
+
=
∞
=
∞
=
∞
=
−
+
+
0 0 0
1
2
2
3
5
.
0
5
.
0
2
5
2
0
6 5
.
0
5
.
0
sin
5
.
0
n k l
n
n
L
k
n
l
k
t
e
x
v
n
L
D
γ
α
7. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
59
( ) ( )
[ ] } ( ) ( ) ( ) ( ) ( )
[ ]×
∑ ∫ +
∫ −
+
+
−
+
−
∞
=
+
+
−
+
+
+
−
0 0
1
0
5
.
0
5
.
0
5
.
0
1
2
2
1
5
.
0
m
u
m
l
m
l
t
l
k
n H
H
u
e
u
e
u
e
k
n
l τ
τ
( ) ( ) ( )2
5
.
0
5
.
0
5
.
0
+
−
× +
+
l
u
d
d
e
e m
l
τ
τ
τ ,
( ) ( ) ( )×
∑ +
=
∞
=
+
+
0
5
.
0
5
.
0
3
0
7 sin
5
.
0
n
n
n
L x
v
t
e
n
L
D
π
α
( ) ( ) ( ) ( )
[ ]
∑∫ +
−
×
∞
=
+
+
−
+
+
00
1
5
.
0
5
.
0
m
t
n
m
n
m
m
n u
d
u
H
u
H
u
e
u
e ,
( ) ( ) ( ) ( ) ( )
∑ ∑ ∑ ∫ ×
−
+
+
=
∞
=
∞
=
∞
=
+
+
+
0 0 0 0
5
,
0
5
,
0
5
,
0
3
0
8
5
,
0
1
sin
5
,
0
n m k
t
km
n
n
n
L
u
e
u
e
k
t
e
x
v
n
L
D
π
γ
α
×[Hn+k-m-0,5(u)+Hn-k+m+0,5(u)-Hn-k-m-0,5(u)-Hn+k+m+1,5(u)]d u,
( ) ( ) ( ) ( )
∑ ∑ ∑ ∑∫ ×
−
+
+
+
=
= ∞
=
∞
=
∞
=
∞
=
+
+
0 0 0 00
5
.
0
5
.
0
3
0
9
5
.
0
1
5
.
0
1
sin
5
.
0
1
,
0
n k l m
t
m
n
n
L
e
l
k
x
v
t
e
n
L
D
τ
π
γ
γ
α
×eklm(τ)[Ik-l-n+m(T)+Ik-l+n-m(T)+Ik-l-n-m-1(T)+Ik-l+n+m+1(T)-Ik-l-n-m-1(T)-
-Ik+l+n-m+1(T)-Im-k-l+n-(T)-Im+k+l+n+2-(T)]d τ, γ >2,
where ( ) ( ) ( )
∫
=
L
n
n u
d
u
v
T
u
T
I
0
cos
,
η ,
( ) ( ) ( ) ( ) ( ) ( )
[ ]
∑ ∑ ∫ ×
+
+
+
<
= ∞
=
∞
=
+
+
−
+
+
0 0 0
1
2
5
.
0
5
.
0
3
3
0
10
5
.
0
sin
5
.
0
2
3
,
0
i n
t
n
i
n
i
i
i
L
T
I
T
I
n
x
v
t
e
i
L
D
π
γ
α
( ) ( )
[ ]
{
∑ ∑ ∑ ∑ +
−
+
−
−
+
+
+
+
+
×
∞
=
∞
=
∞
=
∞
=
−
0 0 0 0
1
2
2
1
2
2
1
1 2
5
.
0
5
.
0
1
5
.
0
1
5
.
0
1
5
.
0
1
k l m m
m
m
l
k
n
m
m
l
k
+[(n+0.5)2
-(k-l-m1+m2)2
]-1
-[(n+0.5)2
-(k-l+m1+m2+1)]-1
-[(n+0.5)2
-(k-l-m1-m2-1)]-1
-
-[(n+0.5)2
-(k+l+m1--m2+1)]-1
-[(n+0.5)2
-(k+l-m1+m2++1)]-1
+[(n+0.5)2
-(k+l-m1-
-m2)]-1
+[(n+0.5)2
-(k+l+m1+m2+2)]-1
}[(n+0.5)2
-(k+0.5)2
-(l+0.5)2
-(m1+0.5)2
-
( ) ] ( ) ( ) ( ) ( )
[ ] u
d
u
e
u
e
u
e
u
e
m n
i
m
klm
i
−
−
−
+
−
−
2
1
1
2
5
.
0 , γ >3,
8. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
60
( ) ( ) ( ) ( )
∑ ∑ ∑ ∑ ∑ ×
+
+
+
+
+
<
= ∞
=
∞
=
∞
=
∞
=
∞
=
+
+
0 0 0 0 0
5
.
0
5
.
0
3
5
3
2
0
11
5
.
0
5
.
0
1
5
.
0
1
5
.
0
1
sin
5
.
0
3
,
0
i j k l n
i
i
L
n
l
k
j
x
v
t
e
i
L
D
π
γ
α
×{(i+0.5)2
-(j-k+l-n)2
]-1
+[(i+0.5)2
-(j-k-l+n)2
]-1
-[(i+0.5)2
-(j+k-l+n+1)2
]-1
-
-[(i+0.5)2
-(j+k-l-n+1)2
]-1
-[(i+0.5)2
-(j+k-l+n+1)2
]-1
+[(i+0.5)2
-(j+k-l-n)2
]-1
-
( ) ( )
[ ] } ( ) ( ) ( ) ( )
[ ] ×
∑∫ ∫ +
−
+
+
+
+
−
+
∞
=
+
+
−
+
−
00 0
1
5
,
0
1
2
1
5
.
0
m
t u
m
n
m
n
m
n d
T
I
T
I
e
e
n
l
k
j
i τ
τ
τ
( ) ( ) u
d
u
e
u
e jk
i ln
5
.
0 −
× +
, γ =3
( ) ( ) ( )
×
∑ ∑ ∑ ∑
+
+
+
+
<
= ∞
=
∞
=
∞
=
∞
=
+
+
0 0 0 0
5
.
0
5
.
0
3
2
2
0
11
5
.
0
1
5
.
0
1
5
.
0
1
sin
5
.
0
3
,
0
n k l m
n
n
L
m
l
k
x
v
t
e
n
L
D
π
γ
α
( ) ( ) ( ) ( ) ( )
{
∑∫ +
+
+
−
×
∞
=
+
−
+
+
−
+
−
+
−
−
+
+
−
+
−
+
0 0
5
.
0
5
.
0
5
.
0
5
.
0
i
t
m
l
i
n
k
m
l
i
n
k
m
l
i
n
k
klmi
n
u
H
u
H
u
H
u
e
u
e
+Hk+n-i-l+m+0.5(u)-Hk+n-i-l+m-0.5(u)-Hk-n+I+l-m+1.5(u)-Hk-n+i-l+m-0.5(u)-
-Hk+n-i+l-m+1.5(u)+Hk+n+i-l+m+1.5(u)+Hk-n-i+l-m-0.5(u)++Hk-n-i-l+m-0.5(u)+
+Hk+n+i+l-m+1.5(u)-Hk+n+i-l-m+0.5(u)-Hk-n-i+l+m+0.5(u)-Hk-n-i-l-m-1.5(u)-
-Hk+n+I+l+m+2.5(u)}d u.
Analysis of spatiotemporal distributions of dopant concentrations has been done analytically by
using the second-order approximation of dopant concentration on parameters ε and ξ.. Farther the
distribution has been amended numerically.
3. DISCUSSION
In this section we analyzed dynamics of redistribution of dopant in heterostructure from Fig. 1
based on calculated in previous section relations. Spatial distributions of concentration of dopant
in the considered heterostructure are presented on Fig. 2 for fixed value of annealing time. The
Fig. 2 shows, that increasing of difference between values of dopant diffusion coefficient in the
substrate and in the epitaxial layer gives us possibility to increase sharpness of p-n-junction and at
the same time to increase homogeneity of dopant distribution in doped area. However using this
type of doping leads to necessity in optimization of annealing time. Reason of this optimization is
following. If annealing time is small, dopant cannot achieves interface between layers of hetero-
structure. In this situation homogeneity of distribution of concentration of dopant became less,
than in heterostructure. If annealing time is large, distribution of concentration of dopant became
overly homogenous. We determine optimal annealing time by using recently introduced criterion
[16,17,19,22]. Framework the approach we approximate real distribution of concentration of do-
9. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
61
pant by step-wise function (see Fig. 3). Farther we determine optimal value of annealing time by
minimization of the following mean-squared error
( ) ( )
[ ]
∫ −
Θ
=
L
x
d
x
x
C
L
U
0
,
1
ψ . (7)
Here ψ (x) is the approximation time. Θ is the optimal value of annealing time. Dependences of
optimal value of annealing time on parameters are presented in Fig. 4.
Fig. 2. Distributions of concentration of dopant in heterostructure from Fig. 1 in direction x. The
direction x is perpendicular to interface between layers. Increasing of number of curves corres-
ponds to increasing of value of parameter ε. This curves correspond to situation, when value of
dopant diffusion coefficient in the epitaxial layer is larger, than in the substrate
x
C(x,
Θ
)
0 L
2
1
3
4
C0
l0
Fig.3. Spatial distributions of concentration of dopant. Curve 1 is required idealized distribution of concen-
tration of dopant. Curves 2-4 are real distributions of concentration of dopant.
Increasing of number of curves corresponds to increasing of annealing time
Farther we analyzed influence of value of pressure of vapor of dopant from infinite source on dis-
tribution of concentration of the dopant in the considered heterostructure. We assume, that ga-
10. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
62
seous source of dopant is ideal gas. In this case pressure of gas and surficial concentration of do-
pant are correlated with each other by linear law: p M = R TN, where M is the molar mass, R =
8.31 J/(mole⋅K) is the gas constant, p is the pressure of gas. In this situation increasing of pressure
of gas in source of dopant leads to proportional increasing of surficial concentration of dopant.
However dependence of optimal value of annealing time on pressure is not so simple due to non-
linearity of criterion of estimation of the time [16,17,19,22,23]. Analysis of dynamics of redistri-
bution of dopant shows, that variation of value of dynamics of vapor leads to quantitative varia-
tion of distribution of concentration of dopant inside of the considered heterostructure, but not to
quantitative variation.
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
Θ
D
0L
L
-2
3
2
4
1
Fig.4. Dependences of dimensionless optimal annealing time, which have been obtained by mi-
nimization of mean-squared error (7), on several parameters. Curve 1 is the dependence of dimen-
sionless optimal annealing time on the relation a/L and ξ=γ=0 for equal to each other values of
dopant diffusion coefficient in all parts of heterostructure. Curve 2 is the dependence of dimen-
sionless optimal annealing time on value of parameter ε for a/L=1/2 and ξ= γ= 0. Curve 3 is the
dependence of dimensionless optimal annealing time on value of parameter ξ for a/L=1/2 and ε=γ
= 0. Curve 4 is the dependence of dimensionless optimal annealing time on value of parameter γ
for a/L=1/2 and ε =ξ=0
4. CONCLUSION
In this paper we analyzed influence of changing of pressure of vapor of dopant from infinite
source on distribution of concentration of the dopant in the p-n- heterojunction. It has been
shown, that the changing of pressure leads to some quantitative variation of distribution of con-
centration of dopant, but not to quantitative variation.
Acknowledgements
This work is supported by the contract 11.G34.31.0066 of the Russian Federation Government,
grant of Scientific School of Russia, the agreement of August 27, 2013 № 02.В.49.21.0003 be-
tween The Ministry of education and science of the Russian Federation and Lobachevsky State
University of Nizhny Novgorod and educational fellowship for scientific research of Nizhny
Novgorod State University of Architecture and Civil Engineering.
11. Applied Mathematics and Sciences: An International Journal (MathSJ ), Vol. 1, No. 2, August 2014
63
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Authors
Pankratov Evgeny Leonidovich was born at 1977. From 1985 to 1995 he was educated in a secondary
school in Nizhny Novgorod. From 1995 to 2004 he was educated in Nizhny Novgorod State University:
from 1995 to 1999 it was bachelor course in Radiophysics, from 1999 to 2001 it was master course in Ra-
diophysics with specialization in Statistical Radiophysics, from 2001 to 2004 it was PhD course in Radio-
physics. From 2004 to 2008 E.L. Pankratov was a leading technologist in Institute for Physics of Micro-
structures. From 2008 to 2012 E.L. Pankratov was a senior lecture/Associate Professor of Nizhny Novgo-
rod State University of Architecture and Civil Engineering. Now E.L. Pankratov is in his Full Doctor
course in Radiophysical Department of Nizhny Novgorod State University. He has 96 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. E.A. Bulaeva was a contributor of grant of President of Russia (grant № MK-548.2010.2).
She has 35 published papers in area of her researches.