Optimization of Dopant Diffusion and Ion Implantation to Increase Integration Rate of Field-Effect Heterotransistors. An Ap-Proach to Simplify Construction of the Heterotransistors
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION...ijrap
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach
based on manufacturing field-effect transistors in heterostructures and optimization of technological
processes. At the same time we consider possibility to simplify their constructions.
On Approach to Increase Integration rate of Elements of a Circuit Driver with...BRNSS Publication Hub
In this paper, we introduce an approach to increase the integration rate of elements of a driver with 2-tap de-emphasis and impendence matching. Framework the approach, we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized.
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 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.
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 Approach to Increase Integration Rate of Elements of a Current Source CircuitBRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a current source circuit.
Framework the approach, we consider a heterostructure with special configuration. Several specific
areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/
or radiation defects should be optimized.
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
of thickness of the heterotransistors and increasing of their density, which were comprised in integrated
circuits.
On Approach to Increase Integration Rate of Elements of a Switched-capacitor ...BRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a switched-
capacitor step-down DC–DC converter. Framework the approach, we consider a heterostructure with
special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion
implantation. Annealing of dopant and/or radiation defects should be optimized.
OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION...ijrap
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach
based on manufacturing field-effect transistors in heterostructures and optimization of technological
processes. At the same time we consider possibility to simplify their constructions.
On Approach to Increase Integration rate of Elements of a Circuit Driver with...BRNSS Publication Hub
In this paper, we introduce an approach to increase the integration rate of elements of a driver with 2-tap de-emphasis and impendence matching. Framework the approach, we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized.
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 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.
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 Approach to Increase Integration Rate of Elements of a Current Source CircuitBRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a current source circuit.
Framework the approach, we consider a heterostructure with special configuration. Several specific
areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/
or radiation defects should be optimized.
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
of thickness of the heterotransistors and increasing of their density, which were comprised in integrated
circuits.
On Approach to Increase Integration Rate of Elements of a Switched-capacitor ...BRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a switched-
capacitor step-down DC–DC converter. Framework the approach, we consider a heterostructure with
special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion
implantation. Annealing of dopant and/or radiation defects should be optimized.
OPTIMIZATION OF MANUFACTURE OF FIELDEFFECT HETEROTRANSISTORS WITHOUT P-NJUNCT...ijrap
It has been recently shown, that manufacturing p-n-junctions, field-effect and bipolar transistors, thyristors
in a multilayer structure by diffusion or ion implantation under condition of optimization of dopant and/or
radiation defects leads to increasing of sharpness of p-n-junctions (both single p-n-junctions and p-njunctions,
which include into their system). In this situation one can also obtain increasing of homogeneity
of dopant in doped area. In this paper we consider manufacturing a field-effect heterotransistor without pn-
junction. Optimization of technological process with using inhomogeneity of heterostructure give us
possibility to manufacture the transistors as more compact.
MODELING OF 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 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.
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.
On Optimization of Manufacturing of a Two-level Current-mode Logic Gates in a...BRNSS Publication Hub
In this paper, we introduce an approach to increase the density of field-effect transistors framework a two-level current-mode logic gates in a multiplexer. Framework the approach we consider manufacturing the inverter in heterostructure with the 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 the value of mismatch-induced stress in the considered heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures during the manufacturing of integrated circuits with account mismatch-induced stress.
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 Analytical Approach to Prognosis of Manufacturing of Voltage Divider Biasi...BRNSS Publication Hub
In this paper, we introduce an approach for prognosis of manufacturing of voltage divider biasing common emitter amplifier based on bipolar transistors with account mismatch-induced stress. Based on this prognosis, we formulate some recommendations for optimization of manufacturing of the amplifier. Main aims of the optimization are as follows: (1) Decreasing dimensions of elements of the considered operational amplifier and (2) increasing of performance and reliability of the considered bipolar transistors. Dimensions of considered bipolar 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 bipolar transistors could be increased by optimization of annealing of dopant and/or radiation defects and using inhomogeneity of the properties of heterostructure. Choosing of inhomogeneity 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.
Radix-3 Algorithm for Realization of Discrete Fourier TransformIJERA Editor
In this paper, a new radix-3 algorithm for realization of discrete Fourier transform (DFT) of length N = 3m (m =
1, 2, 3,...) is presented. The DFT of length N can be realized from three DFT sequences, each of length N/3. If
the input signal has length N, direct calculation of DFT requires O (N
2
) complex multiplications (4N
2
real
multiplications) and some additions. This radix-3 algorithm reduces the number of multiplications required for
realizing DFT. For example, the number of complex multiplications required for realizing 9-point DFT using the
proposed radix-3 algorithm is 60. Thus, saving in time can be achieved in the realization of proposed algorithm.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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.
Using Porosity of Epitaxial Layer to Decrease Quantity of Radiation Defects G...msejjournal
In this paper we consider redistribution of radiation defects, which were generated during radiation processing, in a multilayer structure with porous epitaxial layer. It has been shown, that porosity of epitaxial layer gives a possibility to decrease quantity of radiation defects.
OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION...ijrap
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
Optimization of 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 MANUFACTURE OF FIELDEFFECT HETEROTRANSISTORS WITHOUT P-NJUNCT...ijrap
It has been recently shown, that manufacturing p-n-junctions, field-effect and bipolar transistors, thyristors
in a multilayer structure by diffusion or ion implantation under condition of optimization of dopant and/or
radiation defects leads to increasing of sharpness of p-n-junctions (both single p-n-junctions and p-njunctions,
which include into their system). In this situation one can also obtain increasing of homogeneity
of dopant in doped area. In this paper we consider manufacturing a field-effect heterotransistor without pn-
junction. Optimization of technological process with using inhomogeneity of heterostructure give us
possibility to manufacture the transistors as more compact.
MODELING OF 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 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.
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.
On Optimization of Manufacturing of a Two-level Current-mode Logic Gates in a...BRNSS Publication Hub
In this paper, we introduce an approach to increase the density of field-effect transistors framework a two-level current-mode logic gates in a multiplexer. Framework the approach we consider manufacturing the inverter in heterostructure with the 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 the value of mismatch-induced stress in the considered heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures during the manufacturing of integrated circuits with account mismatch-induced stress.
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 Analytical Approach to Prognosis of Manufacturing of Voltage Divider Biasi...BRNSS Publication Hub
In this paper, we introduce an approach for prognosis of manufacturing of voltage divider biasing common emitter amplifier based on bipolar transistors with account mismatch-induced stress. Based on this prognosis, we formulate some recommendations for optimization of manufacturing of the amplifier. Main aims of the optimization are as follows: (1) Decreasing dimensions of elements of the considered operational amplifier and (2) increasing of performance and reliability of the considered bipolar transistors. Dimensions of considered bipolar 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 bipolar transistors could be increased by optimization of annealing of dopant and/or radiation defects and using inhomogeneity of the properties of heterostructure. Choosing of inhomogeneity 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.
Radix-3 Algorithm for Realization of Discrete Fourier TransformIJERA Editor
In this paper, a new radix-3 algorithm for realization of discrete Fourier transform (DFT) of length N = 3m (m =
1, 2, 3,...) is presented. The DFT of length N can be realized from three DFT sequences, each of length N/3. If
the input signal has length N, direct calculation of DFT requires O (N
2
) complex multiplications (4N
2
real
multiplications) and some additions. This radix-3 algorithm reduces the number of multiplications required for
realizing DFT. For example, the number of complex multiplications required for realizing 9-point DFT using the
proposed radix-3 algorithm is 60. Thus, saving in time can be achieved in the realization of proposed algorithm.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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.
Using Porosity of Epitaxial Layer to Decrease Quantity of Radiation Defects G...msejjournal
In this paper we consider redistribution of radiation defects, which were generated during radiation processing, in a multilayer structure with porous epitaxial layer. It has been shown, that porosity of epitaxial layer gives a possibility to decrease quantity of radiation defects.
The International Journal of Engineering and Science
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OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION...ijrap
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
Optimization of 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.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect heterotransistor. Based on analytical solution of the considered boundary problems some recommendations have been formulated to optimize technological processes.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect
heterotransistor. Based on analytical solution of the considered boundary problems some recommendations
have been formulated to optimize technological processes.
On optimization ofON OPTIMIZATION OF DOPING OF A HETEROSTRUCTURE DURING MANUF...ijcsitcejournal
We introduce an approach of manufacturing of a p-i-n-heterodiodes. The approach based on using a δ-
doped heterostructure, doping by diffusion or ion implantation of several areas of the heterostructure. After
the doping the dopant and/or radiation defects have been annealed. We introduce an approach to optimize
annealing of the dopant and/or radiation defects. We determine several conditions to manufacture more
compact p-i-n-heterodiodes
An Approach to Analyze Non-linear Dynamics of Mass Transport during Manufactu...BRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a hybrid comparator with the first dynamic amplifying stage and the second quasi-dynamic latching stage. Framework the approach, we consider a heterostructure with special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/or radiation defects should be optimized
On Decreasing of Dimensions of Field-Effect Heterotransistors in Logical CMOP...BRNSS Publication Hub
In this paper, we introduce an approach to decrease the dimensions of CMOP voltage differencing inverting buffered amplifier based on field-effect heterotransistors by increasing density of elements. Dimensions of the elements will be decreased due to manufacture heterostructure with a specific structure, doping of required areas of the heterostructure by diffusion or ion implantation, and optimization of annealing of dopant and/or radiation defects.
ON APPROACH TO INCREASE INTEGRATION RATE OF FIELD-EFFECT HETEROTRANSISTORS IN...IJMEJournal1
In this paper we introduce an approach to increase integration rate of field-effect heterotransistors in
the framework of a bootstrap switch. In the framework of the approach we consider a heterostructure
with special configuration. Several specific areas of the heterostructure should be doped by diffusion
or ion implantation. Annealing of dopant and/or radiation defects should be optimized.
ON APPROACH TO INCREASE INTEGRATION RATE OF FIELD-EFFECT HETEROTRANSISTORS IN...ijmejournal
In this paper we introduce an approach to increase integration rate of field-effect heterotransistors in
the framework of a bootstrap switch. In the framework of the approach we consider a heterostructure
with special configuration. Several specific areas of the heterostructure should be doped by diffusion
or ion implantation. Annealing of dopant and/or radiation defects should be optimized.
ON APPROACH TO INCREASE INTEGRATION RATE OF FIELD-EFFECT HETEROTRANSISTORS IN...IJMEJournal1
In this paper we introduce an approach to increase integration rate of field-effect heterotransistors in
the framework of a bootstrap switch. In the framework of 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.
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On the Unification of Physic and the Elimination of Unbound Quantitiesijrap
This paper supports Descartes' idea of a constant quantity of motion, modernized by Leibniz. Unlike Leibniz, the paper emphasizes that the idea is not realized by forms of energy, but by energy itself. It remains constant regardless of the form, type, or speed of motion, even that of light. Through force, energy is only transformed. Here it is proved that force is its derivative. It exists even at rest, representing the object's minimal energy state. With speed, we achieve its multiplication up to the maximum energy state, from which a maximum force is derived from the object. From this point, corresponding to Planck's Length, we find the value of the force wherever we want. Achieving this removes the differences between various natural forces. The new idea eliminates infinite magnitudes. The process allows the laws to transition from simple to complex forms and vice versa, through differentiation-integration. For this paper, this means achieving the Unification Theory.
Gravity Also Redshifts Light – the Missing Phenomenon That Could Resolve Most...ijrap
In this paper I discover that gravity also redshifts light like the velocity of its source does. When light travels towards a supermassive object, its waves (or photons) undergo continuous stretching, thereby shifting towards lower frequencies. Gravity redshifts light irrespective of whether its source is in motion or static with respect to its observer. An equation is derived for gravitational redshift, and a formula for combined redshift is presented by considering both the velocity, and gravity redshifts. Also explained is how frequencies of electromagnetic spectrum continuously downgrade as a light beam of mix frequencies passes towards a black hole. Further, a clear methodology is provided to figure out whether expansion of the universe is accelerating or decelerating, or alternatively, the universe is contracting.
In this paper I present a new theory that explains as to when and how dark energy is created as mass is destroyed. The theory extends Einstein’s mass energy equation to a more generic form in order to make it work even in high gravity conditions. It also explains why dark energy is created. Further, it is proved Einstein’s mass energy equation holds good only when the destroyed mass has no supermassive object in its close vicinity. The relationship between dark energy and dark matter is unveiled. An extended mathematical form of Einstein’s mass energy equation is derived, based on which the conditions leading to dark energy creation are explained. Three new physical parameters called dark energy discriminant, dark energy radius and dark energy boundary are introduced to facilitate easy understanding of the theory. It is explained in detail that an extremely superdense object has two dark energy boundaries, outer and inner. Mass destroyed only between these two boundaries creates dark energy. Dark energy space, the space between the two aforementioned boundaries, shrouds visible matter in obscurity from optical and electromagnetic telescopes. This theory identifies Gargantuan as a superdense black hole currently creating fresh dark energy, which could be the subject of interest for the astronomical research community having access to sophisticated telescopes, and working on dark energy. It also upholds dark energy and denies the existence of dark matter. Dark matter is nothing but the well-known visible matter positioned in dark energy space. An important relationship is derived between a photon’s frequency and its distance from a black hole to demonstrate the effect of gravity on light. Another important fact revealed by this theory is gravity stretches out light, thereby causing redshift, which is unaccounted in the computation of velocities of outer galaxies. Whether the universe is undergoing accelerated or decelerated expansion, or accelerated contraction can precisely be determined only after accounting for the redshift caused by gravity
International Journal on Soft Computing, Artificial Intelligence and Applicat...ijrap
International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI)
is an open access peer-reviewed journal that provides an excellent international forum for sharing
knowledge and results in theory, methodology and applications of Artificial Intelligence, Soft
Computing. The Journal looks for significant contributions to all major fields of the Artificial
Intelligence, Soft Computing in theoretical and practical aspects. The aim of the Journal is to
provide a platform to the researchers and practitioners from both academia as well as industry to
meet and share cutting-edge development in the field.
Authors are solicited to contribute to the journal by submitting articles that illustrate research
results, projects, surveying works and industrial experiences that describe significant advances in
the areas of Database management systems.
SOME THEORETICAL ASPECTS OF HYDROGEN DIFFUSION IN BCC METALS AT LOW TEMPERATURESijrap
Purpose of the work is to discuss some theoretical aspects of the diffusion of hydrogen atoms in the crystal
lattice of BCC metals at low temperatures using the methods of statistical thermodynamics. The values of
the statistical model calculations of H diffusion coefficients in α-Fe, V, Ta, Nb, K are in good agreement
with the experimental data. The statistical model can also explain deviations from the Arrhenius equation
at temperatures 300-100 K in α-Fe, V, Nb and K. It was suggested that thermally activated fast tunnelling
transition of hydrogen atoms through the potential barrier at a temperature below 300 K provides an
almost free movement of H atoms in the α-Fe and V lattice at these temperatures. The results show that
quantum-statistical effects play a decisive role in the H diffusion in BCC metals at low temperatures. Using
the statistical model allows for the prediction of the diffusion coefficient for H in BCC metals at low
temperatures, where it’s necessary to consider quantum effects.
MASSIVE PHOTON HYPOTHESIS OPENS DOORS TO NEW FIELDS OF RESEARCHijrap
Mass, an inherent property of matter, is calculated directly for the photon particle from the very classical
principles of the kinetic theory of gases. It is not an end result with no perspective nor other outcome.
Quite the opposite, a single ponderable tiny photon frees the mind of old ways of thinking and opens up
new paths to a broad field of investigation where the very large can then be described and explained by the
very small. This reality of a non-zero mass suddenly shows up in the interpretation of many experiments
which become clear and simple to comprehend. Besides, that same key particle has the potential to unlock
and solve some long lasting major observational issues or enigmas. All this converges upon its
acknowledgement and acceptance.
PHENOMENOLOGICAL METHOD REGARDING A THIRD THEORY OF PHYSICS “THE EVENT:THE TH...ijrap
The quest for a third theory uniting macro-cosmos (relativity) and micro-cosmos (quantum mechanics) has coexisted with the denial of feminine/subjective polarity to masculine/objective. The dismissal of electromagnetism as the tension of opposites in quest of inner/outer unity is sourced in the denial of the feminine qualia -- the negative force field attributed to dark energy/dark matter. However, a conversion philosophy sourced in the hieros gamos and signified by the Mobius strip has formulated an integral consciousness methodology producing quantum objects by means of embracing the shadow haunting contemporary physics. This Self-reflecting process integrating subject/object comprises an ontology of kairos as the “quantum leap.” An interdisciplinary quest to create a phenomenological narrative is disclosed via a holistic apparatus of hermeneutics manifesting image/text of a contemporary grail journey. Reflected in this Third space is the sacred reality of autonomous number unifying polarities of feminine/subjective (quality) and objective/masculine (quantity) as new measurement apparatus for the quantum wave collapse.
3rd International Conference on Integrating Technology in Education (ITE 2022)ijrap
3rd International Conference on Integrating Technology in Education (ITE 2022) This forum also aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals.
A SPECIAL RELATIONSHIP BETWEEN MATTER, ENERGY, INFORMATION, AND CONSCIOUSNESSijrap
This paper discusses the advantages of describing the universe, or nature, in terms of information and consciousness. Some problems encountered by theoretical physicists in the quest for the theory of everything stem from the limitations of trying to understand everything in terms of matter and energy only. However, if everything, including matter, energy, life, and mental processes, is described in terms of information and consciousness, much progress can be made in the search for the ultimate theory of the universe. As brilliant and successful as physics and chemistry have been over the last two centuries, it is important that nature is not viewed solely in terms of matter and energy. Two additional components are needed to unlock her secrets. While extensive writing exists that describes the connection between matter and energy and their physical basis, little work has been done to learn the special relationship between matter, energy, information, and consciousness.
This paper discusses the advantages of describing the universe, or nature, in terms of information and consciousness. Some problems encountered by theoretical physicists in the quest for the theory of everything stem from the limitations of trying to understand everything in terms of matter and energy only. However, if everything, including matter, energy, life, and mental processes, is described in terms of information and consciousness, much progress can be made in the search for the ultimate theory of the universe. As brilliant and successful as physics and chemistry have been over the last two centuries, it is important that nature is not viewed solely in terms of matter and energy. Two additional components are needed to unlock her secrets. While extensive writing exists that describes the connection between matter and energy and their physical basis, little work has been done to learn the special relationship between matter, energy, information, and
consciousness.
THE CONCEPT OF SPACE AND TIME: AN AFRICAN PERSPECTIVEijrap
Understanding the concept of space and time is critical, essential, and fundamental in searching for theall-encompassing theory or the theory of everything (ToE). Some physicists argue that time exists, whileothers posit that time is only a social or mental construct. The author presents an African thought systemon space and time conception, focusing on the African (Bantu) view of space and time. The author arguesthat before the advent of the Western linear view of space and time, Africans had their own visionregarding these two concepts. Their conception of time appears to be holistic, highly philosophical, non-linear, and thought-provoking. The author hopes that exploring these two concepts from an African perspective will provide a new and more in-depth insight into reality's nature. A scientific investigation of space and time from an African-centered perspective is a worthy and necessary endeavor in the quest forthe ToE
Learning to Pronounce as Measuring Cross Lingual Joint Orthography Phonology ...ijrap
Machine learning models allow us to compare languages by showing how hard a task in each language might be to learn and perform well on. Following this line of investigation, we explore what makes a language “hard to pronounce” by modelling the task of grapheme-to-phoneme (g2p) transliteration. By training a character-level transformer model on this task across 22 languages and measuring the model’s proficiency against its grapheme and phoneme inventories, we show that certain characteristics emerge that separate easier and harder languages with respect to learning to pronounce. Namely the complexity of a language's pronunciation from its orthography is due to the expressive or simplicity of its grapheme-to phoneme mapping. Further discussion illustrates how future studies should consider relative data sparsity per language to design fairer cross-lingual comparison tasks.
THE CONCEPT OF SPACE AND TIME: AN AFRICAN PERSPECTIVEijrap
Understanding the concept of space and time is critical, essential, and fundamental in searching for the all-encompassing theory or the theory of everything (ToE). Some physicists argue that time exists, while others posit that time is only a social or mental construct. The author presents an African thought system on space and time conception, focusing on the African (Bantu) view of space and time. The author argues
that before the advent of the Western linear view of space and time, Africans had their own vision
regarding these two concepts. Their conception of time appears to be holistic, highly philosophical, nonlinear, and thought-provoking. The author hopes that exploring these two concepts from an African
perspective will provide a new and more in-depth insight into reality's nature. A scientific investigation of space and time from an African-centered perspective is a worthy and necessary endeavor in the quest for the ToE.
International Journal of Recent advances in Physics (IJRAP)ijrap
International Journal of Recent advances in Physics (IJRAP) is a peer-reviewed, open access journal, addresses the impacts and challenges of Physics. The journal documents practical and theoretical results which make a fundamental contribution for the development of Physics.
The Concept of Space and Time: An African Perspectiveijrap
Understanding the concept of space and time is critical, essential, and fundamental in searching for the all-encompassing theory or the theory of everything (ToE). Some physicists argue that time exists, while others posit that time is only a social or mental construct. The author presents an African thought system on space and time conception, focusing on the African (Bantu) view of space and time. The author argues that before the advent of the Western linear view of space and time, Africans had their own vision regarding these two concepts. Their conception of time appears to be holistic, highly philosophical, nonlinear, and thought-provoking. The author hopes that exploring these two concepts from an African perspective will provide a new and more in-depth insight into reality's nature. A scientific investigation of space and time from an African-centered perspective is a worthy and necessary endeavor in the quest for the ToE.
The majority of physicists take it for granted that the universe is made up of matter. In turn, matter is composed of atoms; atoms are made up of particles such as electrons, protons, neutrons, etc. Also, protons
and neutrons are composed of quarks, etc. Furthermore, that everything in nature is governed by the known laws of physics and chemistry. The author only partially shares this view. He argues that many phenomena in the universe may depend on rules or factors as yet incorporated by the physical sciences.
The last few years have led him to reflect on the many unsolved physics problems, such as the quest for the theory of everything (ToE), the arrow of time, the interpretation of quantum mechanics, the fine-tuned
universe, etc. to mention just a few. The author posits that a field carries information, performs various mathematical and computational operations, and behaves as an intelligent entity embedded with consciousness.
Call For Papers - International Journal of Recent advances in Physics (IJRAP)ijrap
International Journal of Recent advances in Physics (IJRAP) is a peer-reviewed, open access journal, addresses the impacts and challenges of Physics. The journal documents practical and theoretical results which make a fundamental contribution for the development of Physics.
Call For Papers - International Journal of Recent advances in Physics (IJRAP)ijrap
International Journal of Recent advances in Physics (IJRAP) is a peer-reviewed, open access journal, addresses the impacts and challenges of Physics. The journal documents practical and theoretical results which make a fundamental contribution for the development of Physics.
Call For Papers - International Journal of Recent advances in Physics (IJRAP)ijrap
International Journal of Recent advances in Physics (IJRAP) is a peer-reviewed, open access journal, addresses the impacts and challenges of Physics. The journal documents practical and theoretical results which make a fundamental contribution for the development of Physics.
Call For Papers - International Journal of Recent advances in Physics (IJRAP)ijrap
International Journal of Recent advances in Physics (IJRAP) is a peer-reviewed, open access journal, addresses the impacts and challenges of Physics. The journal documents practical and theoretical results which make a fundamental contribution for the development of Physics
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
The increased availability of biomedical data, particularly in the public domain, offers the opportunity to better understand human health and to develop effective therapeutics for a wide range of unmet medical needs. However, data scientists remain stymied by the fact that data remain hard to find and to productively reuse because data and their metadata i) are wholly inaccessible, ii) are in non-standard or incompatible representations, iii) do not conform to community standards, and iv) have unclear or highly restricted terms and conditions that preclude legitimate reuse. These limitations require a rethink on data can be made machine and AI-ready - the key motivation behind the FAIR Guiding Principles. Concurrently, while recent efforts have explored the use of deep learning to fuse disparate data into predictive models for a wide range of biomedical applications, these models often fail even when the correct answer is already known, and fail to explain individual predictions in terms that data scientists can appreciate. These limitations suggest that new methods to produce practical artificial intelligence are still needed.
In this talk, I will discuss our work in (1) building an integrative knowledge infrastructure to prepare FAIR and "AI-ready" data and services along with (2) neurosymbolic AI methods to improve the quality of predictions and to generate plausible explanations. Attention is given to standards, platforms, and methods to wrangle knowledge into simple, but effective semantic and latent representations, and to make these available into standards-compliant and discoverable interfaces that can be used in model building, validation, and explanation. Our work, and those of others in the field, creates a baseline for building trustworthy and easy to deploy AI models in biomedicine.
Bio
Dr. Michel Dumontier is the Distinguished Professor of Data Science at Maastricht University, founder and executive director of the Institute of Data Science, and co-founder of the FAIR (Findable, Accessible, Interoperable and Reusable) data principles. His research explores socio-technological approaches for responsible discovery science, which includes collaborative multi-modal knowledge graphs, privacy-preserving distributed data mining, and AI methods for drug discovery and personalized medicine. His work is supported through the Dutch National Research Agenda, the Netherlands Organisation for Scientific Research, Horizon Europe, the European Open Science Cloud, the US National Institutes of Health, and a Marie-Curie Innovative Training Network. He is the editor-in-chief for the journal Data Science and is internationally recognized for his contributions in bioinformatics, biomedical informatics, and semantic technologies including ontologies and linked data.
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.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
In silico drugs analogue design: novobiocin analogues.pptx
Optimization of Dopant Diffusion and Ion Implantation to Increase Integration Rate of Field-Effect Heterotransistors. An Ap-Proach to Simplify Construction of the Heterotransistors
1. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
DOI : 10.14810/ijrap.2015.4103 43
OPTIMIZATION OF DOPANT DIFFUSION AND ION
IMPLANTATION TO INCREASE INTEGRATION RATE
OF FIELD-EFFECT HETEROTRANSISTORS. AN AP-
PROACH TO SIMPLIFY CONSTRUCTION OF THE HET-
EROTRANSISTORS
E.L. Pankratov1,3
, E.A. Bulaeva1,2
1
Nizhny Novgorod State University, 23 Gagarin avenue, Nizhny Novgorod, 603950,
Russia
2
Nizhny Novgorod State University of Architecture and Civil Engineering, 65 Il'insky
street, Nizhny Novgorod, 603950, Russia
3
Nizhny Novgorod Academy of the Ministry of Internal Affairs of Russia, 3 Ankudi-
novskoe Shosse, Nizhny Novgorod, 603950, Russia
ABSTRACT
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The ap-
proach based on manufacturing field-effect transistors in heterostructures and optimization of technologi-
cal processes. At the same time we consider possibility to simplify their constructions.
KEYWORDS
Field-effect heterotransistors; simplification of construction of heterotransistors; increasing integration
rate of transistors; optimization of manufacturing of heterotransistors; analytical modelling of technologi-
cal process
1. INTRODUCTION
One of the actual questions of the solid state electronics is increasing of integration rate of ele-
ments of integrated circuits [1-14]. At the same time with decreasing of integration rate of ele-
ments of integrated circuits one can find decreasing of dimensions of the elements. In the present
time it is known several approaches to decrease dimensions of elements of integrated circuits and
their discrete analogs. Two of them are laser and microwave types of annealing of dopants and
radiation defects [15-17]. Using this approaches leads to generation inhomogenous distribution of
temperature in annealed materials. Just this inhomogeneity leads to decreasing dimensions of
elements of integrated circuits and their discrete analogs. Another approach to decrease the above
dimensions is doping required areas of epitaxial layers of heterostructures by dopant diffusion or
ion implantation. However optimization of annealing of dopant and/or radiation defects is re-
quired in this case [18,19]. It is also attracted an interest radiation processing of doped materials.
The processing leads to changing distribution of concentration of dopants [20]. The changing
could also leads to decrease dimensions of elements of integrated circuits and their discrete ana-
logs [21-23].
2. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
44
Source Source
Gate Gate
Drain
Substrate
Fig. 1. Heterostructure, which consist of a substrate and epitaxial layer with several sections. Structure in
deep of heterostructure
In this paper we analysed redistribution of concentration of dopant with account redistribution of
radiation defects in the considered heterostructure, which is presented in Fig. 1. Some sections
have been manufactured in epitaxial layer so, as it is shown in the Fig. 1. Dopants have been in-
fused or implanted in the sections to produce required types of conductivity (n or p). Farther an-
nealing of dopant and/or radiation defects should be annealed. Main aim of our paper is analysis
of dynamic of redistribution of dopant and radiation defects in considered heterostructure during
annealing.
2. METHOD OF SOLUTION
To solve our aims we determine spatio-temporal distribution of concentration of dopant. To de-
termine the distribution one shall solve the following equation [1,3-5]
( ) ( ) ( ) ( )
+
+
=
z
t
z
y
x
C
D
z
y
t
z
y
x
C
D
y
x
t
z
y
x
C
D
x
t
t
z
y
x
C
C
C
C
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂ ,
,
,
,
,
,
,
,
,
,
,
,
. (1)
Boundary and initial conditions for the equation are
( ) 0
,
,
,
0
=
∂
∂
=
x
x
t
z
y
x
C
,
( ) 0
,
,
,
=
∂
∂
= x
L
x
x
t
z
y
x
C
,
( ) 0
,
,
,
0
=
∂
∂
=
y
y
t
z
y
x
C
,
( ) 0
,
,
,
=
∂
∂
= y
L
x
y
t
z
y
x
C
, (2)
( ) 0
,
,
,
0
=
∂
∂
=
z
z
t
z
y
x
C
,
( ) 0
,
,
,
=
∂
∂
= z
L
x
z
t
z
y
x
C
, C(x,y,z,0)=f (x,y,z).
The function C(x,y,z,t) describes the spatio-temporal distribution of concentration of dopant; T is
the temperature of annealing; DС is the dopant diffusion coefficient. Dopant diffusion coeffi-
cient is different in different materials. The diffusion coefficient is also depends on tem-
perature of annealing with account Arrhenius law. Dependences of dopant diffusion coef-
ficients could be approximated by the following function [3,24-26]
( ) ( )
( )
( ) ( )
( )
+
+
+
= 2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
V
t
z
y
x
V
V
t
z
y
x
V
T
z
y
x
P
t
z
y
x
C
T
z
y
x
D
D L
C ς
ς
ξ γ
γ
. (3)
The multiplier DL (x,y,z,T) depends on coordinate and temperature (due to Arrhenius law); P
(x,y,z,T) is the limit of solubility of dopant; the parameter γ is different in different materials and
should be integer in the following interval γ ∈[1,3] [3]; the function V(x,y,z,t) describes the spa-
3. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
45
tio-temporal distribution of concentration of radiation vacancies; parameter V*
describes the equi-
librium concentration of vacancies. Dependence of dopant diffusion coefficient on concentration
has been described in details in [3]. It should be noted, that diffusive type of doping did not leads
to radiation damage of materials and ζ1=ζ2=0. We determine spatio-temporal distributions of con-
centrations point radiation defects by solving the following system of equations [25,26]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
−
∂
∂
∂
∂
+
×
×
−
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
−
∂
∂
∂
∂
+
×
×
−
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
t
z
y
x
V
T
z
y
x
k
z
t
z
y
x
V
T
z
y
x
D
z
t
z
y
x
V
T
z
y
x
k
t
z
y
x
I
y
t
z
y
x
V
T
z
y
x
D
y
x
t
z
y
x
V
T
z
y
x
D
x
t
t
z
y
x
V
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
I
T
z
y
x
D
z
t
z
y
x
V
T
z
y
x
k
t
z
y
x
I
y
t
z
y
x
I
T
z
y
x
D
y
x
t
z
y
x
I
T
z
y
x
D
x
t
t
z
y
x
I
V
V
V
V
I
V
V
I
I
I
V
I
I
I
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
2
,
,
2
,
,
(4)
with boundary and boundary conditions
( ) 0
,
,
,
0
=
∂
∂
=
x
x
t
z
y
x
ρ
,
( ) 0
,
,
,
=
∂
∂
= x
L
x
x
t
z
y
x
ρ
,
( ) 0
,
,
,
0
=
∂
∂
=
y
y
t
z
y
x
ρ
,
( ) 0
,
,
,
=
∂
∂
= y
L
y
y
t
z
y
x
ρ
, (5)
( ) 0
,
,
,
0
=
∂
∂
=
z
z
t
z
y
x
ρ
,
( ) 0
,
,
,
=
∂
∂
= z
L
z
z
t
z
y
x
ρ
, ρ(x,y,z,0)=fρ(x,y,z).
Here ρ =I,V; the function I (x,y,z,t) describes the spatio-temporal distribution of concentration of
interstitials; Dρ(x,y,z,T) are the diffusion coefficients of vacancies and interstitials; terms
V2
(x,y,z,t) and I2
(x,y,z,t) corresponds to generation of divacancies and diinterstitials, respectively;
kI,V(x,y,z,T), kI,I(x,y,z, T) and kV,V(x,y,z,T) are the parameters of recombination of point radiation
defects and generation their complexes, respectively.
Spatio-temporal distributions of concentrations of simplest complexes of radiation defects (diva-
cancies ΦV (x,y,z,t) and diinterstitials ΦI (x,y,z,t)) have been determine by solving by solving the
following system of equations [25,26]
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
−
+
Φ
+
+
Φ
+
Φ
=
Φ
−
+
Φ
+
+
Φ
+
Φ
=
Φ
Φ
Φ
Φ
Φ
Φ
Φ
t
z
y
x
V
T
z
y
x
k
t
z
y
x
V
T
z
y
x
k
z
t
z
y
x
T
z
y
x
D
z
y
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x
t
z
y
x
I
T
z
y
x
k
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
T
z
y
x
D
z
y
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x
V
V
V
V
V
V
V
V
V
V
I
I
I
I
I
I
I
I
I
I
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
2
,
2
,
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
(6)
4. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
46
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
−
+
Φ
+
+
Φ
+
Φ
=
Φ
−
+
Φ
+
+
Φ
+
Φ
=
Φ
Φ
Φ
Φ
Φ
Φ
Φ
t
z
y
x
V
T
z
y
x
k
t
z
y
x
V
T
z
y
x
k
z
t
z
y
x
T
z
y
x
D
z
y
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x
t
z
y
x
I
T
z
y
x
k
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
T
z
y
x
D
z
y
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x
V
V
V
V
V
V
V
V
V
V
I
I
I
I
I
I
I
I
I
I
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
2
,
2
,
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
with boundary and initial conditions
( )
0
,
,
,
0
=
∂
Φ
∂
=
x
x
t
z
y
x
ρ
,
( )
0
,
,
,
=
∂
Φ
∂
= x
L
x
x
t
z
y
x
ρ
,
( )
0
,
,
,
0
=
∂
Φ
∂
=
y
y
t
z
y
x
ρ
,
( )
0
,
,
,
=
∂
Φ
∂
= y
L
y
y
t
z
y
x
ρ
,
( )
0
,
,
,
0
=
∂
Φ
∂
=
z
z
t
z
y
x
ρ
,
( )
0
,
,
,
=
∂
Φ
∂
= z
L
z
z
t
z
y
x
ρ
, ΦI(x,y,z,0)=fΦI(x,y,z), ΦV(x,y,z,0)=fΦV(x,y,z). (7)
Here DΦI(x,y,z,T) and DΦV(x,y,z,T) are diffusion coefficients of diinterstitials and divacancies; kI
(x,y,z,T) and kV (x,y,z,T) are parameters of decay of complexes.
It should be noted, that nonlinear equations with space and time varying coefficients are usually
used to describe physical processes. Although the equations are usually solved in different limit-
ing cases [27-30]. Spatio-temporal distribution of concentration of dopant have been calculated
by using method of averaging of function corrections [21,31] with decreased quantity of iteration
steps [32]. Framework this approach we used solutions of the above differential equations without
any nonlinearity and with averaged values of diffusion coefficients and thermal diffusivity D0L,
D0I, D0V, D0ΦI, D0ΦV, α0. The solutions could be written as
( ) ( ) ( ) ( ) ( )
∑
+
=
∞
=1
1
2
1
,
,
,
n
nC
n
n
n
nC
z
y
x
z
y
x
t
e
z
c
y
c
x
c
F
L
L
L
L
L
L
t
z
y
x
C ,
( ) ( ) ( ) ( ) ( )
∑
+
=
∞
=1
1
2
1
,
,
,
n
nI
n
n
n
nI
z
y
x
z
y
x
t
e
z
c
y
c
x
c
F
L
L
L
L
L
L
t
z
y
x
I ,
( ) ( ) ( ) ( ) ( )
∑
+
=
∞
=1
1
2
1
,
,
,
n
nV
n
n
n
nC
z
y
x
z
y
x
t
e
z
c
y
c
x
c
F
L
L
L
L
L
L
t
z
y
x
V ,
( ) ( ) ( ) ( ) ( )
∑
+
=
Φ
∞
=
Φ
Φ
1
1
2
1
,
,
,
n
n
n
n
n
n
z
y
x
z
y
x
I t
e
z
c
y
c
x
c
F
L
L
L
L
L
L
t
z
y
x I
I
,
( ) ( ) ( ) ( ) ( )
∑
+
=
Φ
∞
=
Φ
Φ
1
1
2
1
,
,
,
n
n
n
n
n
n
z
y
x
z
y
x
V t
e
z
c
y
c
x
c
F
L
L
L
L
L
L
t
z
y
x V
V
,
where ( )
+
+
−
= 2
2
2
0
2
2 1
1
1
exp
z
y
x
n
L
L
L
t
D
n
t
e ρ
ρ π , ( ) ( ) ( ) ( )
∫ ∫ ∫
=
x y z
L L L
n
n
n
n u
d
v
d
w
d
w
v
u
f
w
c
v
c
u
c
F
0 0 0
,
,
ρ
ρ , cn(χ)
=cos(πnχ/Lχ).
The second-order approximations and approximations with higher orders of concentration of do-
pant, concentrations of radiation defects and temperature have been calculated framework stan-
dard iteration procedure of method of averaging of function corrections [21,31,32]. Framework
the approach to calculate n-th-order approximations of the above concentrations and temperature
5. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
47
we replace the required functions C (x,y,z,t), I (x,y,z,t), V (x,y,z,t), ΦI (x,y,z,t) and ΦV (x,y,z,t) in the
right sides of Eqs. (1), (4), (6) on the following sums αnρ+ρn-1(x,y,z,t). The replacement gives us
possibility to obtain the following equations for the second-order approximation of above concen-
trations
( )
( )
( ) ( )
( )
( )
[ ]
( )
×
+
+
+
+
=
∗
∗
T
z
y
x
P
t
z
y
x
C
V
t
z
y
x
V
V
t
z
y
x
V
T
z
y
x
D
x
t
t
z
y
x
C C
L
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
,
,
, 1
2
2
2
2
1
2
γ
γ
α
ξ
ς
ς
∂
∂
∂
∂
( ) ( ) ( ) ( )
( )
( )
[ ]
( )
( )
+
+
+
+
+
+
×
∗
∗
y
t
z
y
x
C
T
z
y
x
P
t
z
y
x
C
V
t
z
y
x
V
V
t
z
y
x
V
T
z
y
x
D
y
x
t
z
y
x
C C
L
∂
∂
α
ξ
ς
ς
∂
∂
∂
∂
γ
γ
,
,
,
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
,
,
, 1
1
2
2
2
2
1
1
(8)
( )
( ) ( )
[ ]
( )
( )
( )
( )
+
+
+
+
+ ∗
∗ V
t
z
y
x
V
V
t
z
y
x
V
T
z
y
x
P
t
z
y
x
C
z
t
z
y
x
C
T
z
y
x
D
z
C
L
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
,
,
, 1
2
2
2
1
2
1
ς
ς
α
ξ
∂
∂
∂
∂
γ
γ
( )
( )
( )
( )
( )
( )
( )
( ) ( )
[ ] ( )
[ ]
( ) ( )
[ ]
( )
( )
( )
( )
( )
( )
( )
( ) ( )
[ ] ( )
[ ]
( ) ( )
[ ]
+
−
−
+
+
−
+
+
+
=
+
−
−
+
+
−
+
+
+
=
2
1
2
,
1
2
1
2
,
1
1
1
2
2
1
2
,
1
2
1
2
,
1
1
1
2
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
t
z
y
x
V
T
z
y
x
k
t
z
y
x
V
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
V
T
z
y
x
D
z
y
t
z
y
x
V
T
z
y
x
D
y
x
t
z
y
x
V
T
z
y
x
D
x
t
t
z
y
x
V
t
z
y
x
I
T
z
y
x
k
t
z
y
x
V
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
I
T
z
y
x
D
z
y
t
z
y
x
I
T
z
y
x
D
y
x
t
z
y
x
I
T
z
y
x
D
x
t
t
z
y
x
I
V
V
V
V
I
V
I
V
V
V
I
I
I
V
I
V
I
I
I
I
α
α
α
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
α
α
α
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
(9)
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( ) ( )
−
+
Φ
+
+
Φ
+
Φ
=
Φ
−
+
Φ
+
+
Φ
+
Φ
=
Φ
Φ
Φ
Φ
Φ
Φ
Φ
t
z
y
x
V
T
z
y
x
k
t
z
y
x
V
T
z
y
x
k
z
t
z
y
x
T
z
y
x
D
z
x
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x
t
z
y
x
I
T
z
y
x
k
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
T
z
y
x
D
z
x
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x
V
V
V
V
V
V
V
V
V
V
I
I
I
I
I
I
I
I
I
I
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
2
,
1
1
1
2
2
,
1
1
1
2
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
(10)
Farther we obtain the second-order approximations of concentrations of dopant and radiation de-
fects by integration of the left and right sides of the Eqs. (8)-(10)
( ) ( ) ( ) ( )
( )
( )
[ ]
( )
∫ ×
+
+
+
=
∗
∗
t
C
L
T
z
y
x
P
z
y
x
C
V
z
y
x
V
V
z
y
x
V
T
z
y
x
D
x
t
z
y
x
C
0
1
2
2
2
2
1
2
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
,
,
, γ
γ
τ
α
ξ
τ
ς
τ
ς
∂
∂
( ) ( ) ( )
( )
( )
[ ]
( )
∫ ×
+
+
+
+
×
∗
∗
t
C
T
z
y
x
P
z
y
x
C
V
z
y
x
V
V
z
y
x
V
y
d
x
z
y
x
C
0
1
2
2
2
2
1
1
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
γ
γ
τ
α
ξ
τ
ς
τ
ς
∂
∂
τ
∂
τ
∂
( ) ( ) ( ) ( )
( )
( )
∫ ×
+
+
×
∗
∗
t
L
y
z
y
x
C
V
z
y
x
V
V
z
y
x
V
z
y
z
y
x
C
T
z
y
x
D
0
1
2
2
2
1
1 ,
,
,
,
,
,
,
,
,
1
,
,
,
,
,
,
∂
τ
∂
τ
ς
τ
ς
∂
∂
∂
τ
∂
6. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
48
( )
( )
[ ]
( )
( )
z
y
x
f
T
z
y
x
P
z
y
x
C
T
z
y
x
D C
C
L ,
,
,
,
,
,
,
,
1
,
,
, 1
2
+
+
+
× γ
γ
τ
α
ξ (8a)
( ) ( )
( )
( )
( )
( )
( )
( ) ( )
[ ] ( )
( ) ( )
[ ] ( )
[ ]
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
[ ] ( )
( ) ( )
[ ] ( )
[ ]
∫ +
+
−
−
+
∫ +
−
∫
+
+
∫
+
∫
=
∫ +
+
−
−
+
∫ +
−
∫
+
+
∫
+
∫
=
t
V
I
V
I
V
t
V
V
V
t
V
t
V
t
V
t
V
I
V
I
I
t
I
I
I
t
I
t
I
t
I
d
z
y
x
V
z
y
x
I
T
z
y
x
k
z
y
x
f
d
z
y
x
V
T
z
y
x
k
d
z
z
y
x
V
T
z
y
x
D
z
d
y
z
y
x
V
T
z
y
x
D
y
d
x
z
y
x
V
T
z
y
x
D
x
t
z
y
x
V
d
z
y
x
V
z
y
x
I
T
z
y
x
k
z
y
x
f
d
z
y
x
I
T
z
y
x
k
d
z
z
y
x
I
T
z
y
x
D
z
d
y
z
y
x
I
T
z
y
x
D
y
d
x
z
y
x
I
T
z
y
x
D
x
t
z
y
x
I
0
1
2
1
2
,
0
2
1
2
,
0
1
0
1
0
1
2
0
1
2
1
2
,
0
2
1
2
,
0
1
0
1
0
1
2
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
τ
τ
α
τ
α
τ
τ
α
τ
∂
τ
∂
∂
∂
τ
∂
τ
∂
∂
∂
τ
∂
τ
∂
∂
∂
τ
τ
α
τ
α
τ
τ
α
τ
∂
τ
∂
∂
∂
τ
∂
τ
∂
∂
∂
τ
∂
τ
∂
∂
∂
(9a)
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( )
∫
−
−
∫
+
+
∫
Φ
+
+
∫
Φ
+
∫
Φ
=
Φ
∫
−
−
∫
+
+
∫
Φ
+
+
∫
Φ
+
∫
Φ
=
Φ
Φ
Φ
Φ
Φ
Φ
Φ
Φ
Φ
t
V
t
V
V
V
t
V
V
t
V
V
t
V
V
V
t
I
t
I
I
I
t
I
I
t
I
I
t
I
I
I
d
z
y
x
V
T
z
y
x
k
d
z
y
x
V
T
z
y
x
k
z
y
x
f
d
z
z
y
x
T
z
y
x
D
z
d
y
z
y
x
T
z
y
x
D
y
d
x
z
y
x
T
z
y
x
D
x
t
z
y
x
d
z
y
x
I
T
z
y
x
k
d
z
y
x
I
T
z
y
x
k
z
y
x
f
d
z
z
y
x
T
z
y
x
D
z
d
y
z
y
x
T
z
y
x
D
y
d
x
z
y
x
T
z
y
x
D
x
t
z
y
x
0
0
2
,
0
1
0
1
0
1
2
0
0
2
,
0
1
0
1
0
1
2
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
τ
τ
τ
τ
τ
∂
τ
∂
∂
∂
τ
∂
τ
∂
∂
∂
τ
∂
τ
∂
∂
∂
τ
τ
τ
τ
τ
∂
τ
∂
∂
∂
τ
∂
τ
∂
∂
∂
τ
∂
τ
∂
∂
∂
(10a)
We determine average values of the second-order approximations of the required functions by
using the following standard relations [21,31,32]
( ) ( )
[ ]
∫ ∫ ∫ ∫ −
Θ
=
Θ
0 0 0 0
1
2
2 ,
,
,
,
,
,
1 x y z
L L L
z
y
x
t
d
x
d
y
d
z
d
t
z
y
x
t
z
y
x
L
L
L
ρ
ρ
α ρ . (11)
Relations for the average values α2ρ could be obtain by substitution of the second-order approxi-
mations of the considered concentrations (8a)-(10a) and their the first-order approximations into
the relation (11)
( )
∫ ∫ ∫
=
x y z
L L L
C
z
y
x
С x
d
y
d
z
d
z
y
x
f
L
L
L 0 0 0
2 ,
,
1
α , (12)
7. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
49
( ) ( )
]}
( )
+
−
−
+
−
+
=
+
+
+
−
+
+
−
∫ ∫ ∫
−
−
+
+
+
=
,
4
4
4
2
1
2
1
,
,
1
4
1
2
1
4
3
1
3
4
2
3
4
2
00
00
2
10
01
2
1
11
20
0 0 0
10
2
00
2
00
2
10
01
00
2
B
A
B
A
B
y
B
y
B
A
B
B
A
A
A
A
A
A
x
d
y
d
z
d
z
y
x
f
L
L
L
A
A
A
A
A
A
V
II
IV
V
II
IV
IV
II
L L L
I
z
y
x
IV
V
II
IV
V
II
IV
II
I
x y z
α
α
α
α
α
(13)
where ( ) ( ) ( ) ( )
∫ ∫ ∫ ∫
−
Θ
Θ
=
Θ
0 0 0 0
1
1
, ,
,
,
,
,
,
,
,
,
1 x y z
L L L
j
i
b
a
z
y
x
abij t
d
x
d
y
d
z
d
t
z
y
x
V
t
z
y
x
I
T
z
y
x
k
t
L
L
L
A , ×
= 2
00
4 IV
A
B
( )2
00
00
2
00
2
00 2 VV
II
IV
IV A
A
A
A −
−
× , ( +
+
+
+
= 00
00
2
00
10
00
3
00
01
2
00
00
3 4 VV
II
IV
II
IV
IV
IV
IV
IV A
A
A
A
A
A
A
A
A
B
) ( ) ( )
[ ] +
−
+
+
−
+
+
+
+ 2
00
00
10
10
10
00
10
01
00
00
01
2
00 4
1
2
1
2
2 IV
II
IV
VV
IV
II
II
IV
IV
IV
IV
IV A
A
A
A
A
A
A
A
A
A
A
A
2
00
01
00
2 IV
IV
IV A
A
A
+ , ( )
×
∫ ∫ ∫
−
−
−
=
x y z
L L L
I
z
y
x
II
IV
IV
IV x
d
y
d
z
d
z
y
x
f
L
L
L
A
A
A
A
B
0 0 0
20
11
2
01
2
00
2 ,
,
1
4
( ) ( )} [
{ +
+
−
+
+
+
+
+
× 00
01
2
00
00
00
10
10
00
01
00
01
00
2
10
01
00 2
4
2
1
4 IV
IV
IV
IV
II
IV
II
IV
IV
IV
IV
IV
II
IV
II A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
( ) ( )] ( ) (
+
+
∫ ∫ ∫
+
+
+
−
+
+
+ 10
01
0 0 0
2
10
10
00
10
01
00 ,
,
2
2
1
2
1
2 II
IV
L L L
V
z
y
x
VV
IV
II
II
IV
IV A
A
x
d
y
d
z
d
z
y
x
f
L
L
L
A
A
A
A
A
A
x y z
] ( ) ( )] ( ) ( )
[ +
+
+
−
+
+
+
+
+
−
−
+
+ 1
2
1
2
1
2
1 10
10
00
10
01
00
10
01
01
11
20
00
01 VV
IV
II
II
IV
IV
II
IV
IV
IV
VV
II
IV A
A
A
A
A
A
A
A
A
A
A
A
A
]}
00
01
2 IV
IV A
A
+ , ( ) ( )
−
∫ ∫ ∫
−
−
+
+
=
x y z
L L L
I
z
y
x
IV
II
IV
IV
IV x
d
y
d
z
d
z
y
x
f
L
L
L
A
A
A
A
A
B
0 0 0
11
2
10
01
01
00
1 ,
,
1
8
1
2
] ( ) ( )
+
∫ ∫ ∫
−
−
+
+
+
−
x y z
L L L
I
z
y
x
II
II
IV
II
IV
IV
IV
IV
IV
II
IV
IV
II x
d
y
d
z
d
z
y
x
f
L
L
L
A
A
A
A
A
A
A
A
A
A
A
A
A
0 0 0
00
00
10
10
00
01
00
00
2
01
00
01
00
20 ,
,
2
2
4
( ) ( ) ( )] ( )
[ −
+
+
+
+
+
−
−
+
+
+ 10
01
00
10
01
01
11
20
00
10
01
01 1
2
1
2
1 II
IV
IV
II
IV
IV
IV
VV
II
II
IV
IV A
A
A
A
A
A
A
A
A
A
A
A
( ) ]
00
01
10
10
00 2
1
2 IV
IV
VV
IV
II A
A
A
A
A +
+
+
− , ( )
−
∫ ∫ ∫
=
x y z
L L L
I
z
y
x
II
IV x
d
y
d
z
d
z
y
x
f
L
L
L
A
A
B
0 0 0
00
2
01
0 ,
,
1
4
] ( ) ( ) ( )
×
+
+
+
∫ ∫ ∫
−
+
+
+
+
− 10
01
0 0 0
00
2
10
01
2
01
20
11 1
,
,
2
1 II
IV
L L L
V
z
y
x
II
II
IV
IV
II
IV A
A
x
d
y
d
z
d
z
y
x
f
L
L
L
A
A
A
A
A
A
x y z
( ) ( )]2
10
01
01
11
20
00
01 1
2 II
IV
IV
IV
VV
II
IV A
A
A
A
A
A
A +
+
+
−
−
× ,
6
2
3 3
2
3 3
2 B
q
p
q
q
p
q
y +
+
+
−
−
+
= ,
( ) ( )
48
8
2
8
4
216
2
0
3
1
2
1
2
3
2
0
3
2 B
B
B
B
B
B
B
B
B
q −
+
−
−
+
= ,
36
3
12
2
2
0
3
1 B
B
B
B
p −
−
= , 2
2
3 4
8 B
B
y
A −
+
= ,
( ) ( ) ( )
( )
( ) ( ) ( )
( )
∫ ∫ ∫
+
+
∫ ∫ ∫ ∫
−
Θ
Θ
−
=
∫ ∫ ∫
+
+
∫ ∫ ∫ ∫
−
Θ
Θ
−
=
Φ
Θ
Φ
Φ
Θ
Φ
x y z
x y z
V
x y z
x y z
I
L L L
V
z
y
x
L L L
V
z
y
x
VV
L L L
I
z
y
x
L L L
I
z
y
x
II
x
d
y
d
z
d
z
y
x
f
L
L
L
t
d
x
d
y
d
z
d
t
z
y
x
V
T
z
y
x
k
t
L
L
L
A
x
d
y
d
z
d
z
y
x
f
L
L
L
t
d
x
d
y
d
z
d
t
z
y
x
I
T
z
y
x
k
t
L
L
L
A
0 0 0
0 0 0 0
20
2
0 0 0
0 0 0 0
20
2
,
,
1
,
,
,
,
,
,
1
,
,
1
,
,
,
,
,
,
1
α
α
(14)
Value of the parameter α2C and final form of the appropriate equation depend on value of the pa-
rameter γ.
8. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
50
Farther we analyzed spatio-temporal distributions of concentrations of dopant and radiation de-
fects by using their the second-order approximations. Usually the second-order approximations of
calculated values gives us possibility to obtain main physical results.
3. DISCUSSION
In this section we analyzed dynamics of redistribution of dopant and radiation defects during an-
nealing. The Figs. 2 and 3 show distributions of concentrations of infused and implanted dopants
in heterostructure, which consist of two layers, respectively. In this case we consider doping of
sections of epitaxial layer in situation, when dopant diffusion coefficient in doped materials is
larger, than in nearest areas. The Figs. 2 and 3 show, that presents of interface between materials
of heterostructure gives us possibility to manufacture more compact field-effect transistor in
comparison with field-effect transistor in homogenous materials.
To increase compactness the considered field-effect transistor it is attracted an interest optimiza-
tion of annealing of dopant and/or radiation defects. Reason of this optimization is rather ho-
mogenous distribution of dopant and unnecessary doping of materials of heterostructure outside
the considered sections. During short-time annealing dopant can not achieves interface between
materials of heterostructure. We optimize annealing time framework recently introduced criterion
[18,19,21-23]. Framework the criterion we approximate real distributions of concentrations of
dopants by step-wise functions. We minimize the following mean-squared error to estimate opti-
mal values of annealing time
Fig.2. Typical distributions of concentration of dopant.
The dopant has been infused in the heterostructure from Fig. 1. The direction of the infusion is
perpendicular to interface between epitaxial layer substrate. The distributions have been calcu-
lated under condition, when value of dopant diffusion coefficient in epitaxial layer is larger, than
value of dopant diffusion coefficient in substrate. Increasing of number of curves corresponds to
increasing of difference between values of dopant diffusion coefficient in layers of heterostruc-
ture
9. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
51
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.3. Typical distributions of concentration of dopant.
The dopant has been implanted in the heterostructure from Fig. 1. The direction of the implanted
is perpendicular to interface between epitaxial layer substrate. The distributions have been calcu-
lated under condition, when value of dopant diffusion coefficient in epitaxial layer is larger, than
value of dopant diffusion coefficient in substrate. Increasing of number of curves corresponds to
increasing of difference between values of dopant diffusion coefficient in layers of heterostruc-
ture. Curves 1 and 3 corresponds to annealing time Θ = 0.0048(Lx
2
+Ly
2
+Lz
2
)/D0. Curves 2 and 4
corresponds to annealing time Θ=0.0057(Lx
2
+ Ly
2
+Lz
2
)/D0.
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
0
L
-2
3
2
4
1
Fig.4. Optimized annealing time of infused dopant as functions of parameters.
Curve 1 describes dependence of annealing time on the relation a/L for ξ=γ=0 for equal to each
other values of dopant diffusion coefficient in all parts of heterostructure. Curve 2 describes de-
pendence of annealing time on the parameter ε for a/L=1/2 and ξ = γ = 0. Curve 3 describes de-
pendence of annealing time on the parameter ξ for a/L=1/2 and ξ = γ = 0. Curve 4 describes de-
pendence of annealing time on the parameter γ for a/L=1/2 and ε =ξ=0
10. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
52
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
Θ
D
0
L
-2
3
2
4
1
Fig.5. Optimized annealing time of implanted dopant as functions of parameters.
Curve 1 describes dependence of annealing time on the relation a/L for ξ=γ=0 for equal to each
other values of dopant diffusion coefficient in all parts of heterostructure. Curve 2 describes de-
pendence of annealing time on the parameter ε for a/L=1/2 and ξ = γ = 0. Curve 3 describes de-
pendence of annealing time on the parameter ξ for a/L=1/2 and ξ = γ = 0. Curve 4 describes de-
pendence of annealing time on the parameter γ for a/L=1/2 and ε =ξ=0
( ) ( )
[ ]
∫ ∫ ∫ −
Θ
=
x y z
L L L
z
y
x
x
d
y
d
z
d
z
y
x
z
y
x
C
L
L
L
U
0 0 0
,
,
,
,
,
1
ψ . (15)
Here ψ (x,y,z) is the idealised step-wise distribution of concentration of dopant, which would like
to obtain for maximal decreasing of dimensions of transistors. Dependences of optimal values of
annealing time are presented on Figs. 4 and 5 for diffusion and ion types of doping, respectively.
It should be noted, that after finishing implantation of ions of dopant it is necessary to anneal of
radiation of defects. It could be find spreading of distribution of dopant during the annealing. In
the ideal case distribution of dopant achieves interface between materials of heterostructure dur-
ing annealing of radiation defects. It is necessary to anneal dopant after finishing of annealing of
radiation defects in the case, when the dopant did not achieves the interface between layers of
heterostructure during annealing of radiation defects. In this situation optimal value of continu-
ance of additional annealing is smaller, than continuance of annealing of infused dopant. It should
be noted, that introduced approach to increase integration rate of field-effect transistors gives us
possibility to simplify their common construction.
4. CONCLUSIONS
In this paper we introduce an approach to increase integration rate of field-effect heterotransis-
tors. Framework the approach one should manufacture a heterostructure with special construction.
After that appropriate areas of the heterostructure with account construction should be doped by
diffusion or ion implantation. After the doping dopant and/or radiation defects should be an-
nealed. It has been formulated a recommendation to optimize annealing to
The approach based on manufacture heterostructure with special construction, doping of required
areas of heterostructure by dopant diffusion or ion implantation and optimization of annealing of
dopant and/or radiation defects. The optimization of annealing gives us possibility to decrease
dimensions of transistors with increasing their integration rate. At the same time one can obtain
simplification of construction of integrated circuits.
11. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
53
ACKNOWLEDGMENTS
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 Nizhni Novgorod and educational fellowship for scientific research of Nizhny Nov-
gorod State University of Architecture and Civil Engineering.
REFERENCES
[1] I.P. Stepanenko. Basis of Microelectronics (Soviet Radio, Moscow, 1980).
[2] A.G. Alexenko, I.I. Shagurin. Microcircuitry. Moscow: Radio and communication, 1990.
[3] Z.Yu. Gotra, Technology of microelectronic devices (Radio and communication, Moscow, 1991).
[4] N.A. Avaev, Yu.E. Naumov, V.T. Frolkin. Basis of microelectronics (Radio and communication,
Mos-cow, 1991).
[5] V.I. Lachin, N.S. Savelov. Electronics. Rostov-on-Don: Phoenix, 2001.
[6] A. Polishscuk. "Ultrashallow p+−n junctions in silicon: electron-beam diagnostics of sub-surface re-
gion.". Modern Electronics. Issue 12. P. 8-11 (2004).
[7] G. Volovich. "Integration of on-chip field-effect transistor switches with dopantless Si/SiGe quantum
dots for high-throughput testing". Modern Electronics. Issue 2. P. 10-17 (2006).
[8] A. Kerentsev, V. Lanin. Design and technological features of MOSFETs, Power Electronics. Issue 1.
P. 34 (2008).
[9] A.O. Ageev, A.E. Belyaev, N.S. Boltovets, V.N. Ivanov, R.V. Konakova, Ya.Ya. Kudrik, P.M. Lit-
vin, V.V. Milenin, A.V. Sachenko. "Au–TiBx−n-6H-SiC Schottky barrier diodes: the features of cur-
rent flow in rectifying and nonrectifying contacts". Semiconductors. Vol. 43 (7). P. 897-903 (2009).
[10] Jung-Hui Tsai, Shao-Yen Chiu, Wen-Shiung Lour, Der-Feng Guo. "Au–TiBx−n-6H-SiC Schottky
barrier diodes: the features of current flow in rectifying and nonrectifying contacts.". Semiconduc-
tors. Vol. 43 (7). P. 971-974 (2009).
[11] E.I. Gol’dman, N.F. Kukharskaya, V.G. Naryshkina, G.V. Chuchueva. "The manifestation of exces-
sive centers of the electron-hole pair generation, appeared as a result to field and thermal stresses, and
their subsequent annihilation in the dynamic current-voltage characteristics of Si-MOS-structures with
the ultrathin oxide". Semiconductors. Vol. 45 (7). P. 974-979 (2011).
[12] T.Y. Peng, S.Y. Chen, L.C. Hsieh C.K. Lo, Y.W. Huang, W.C. Chien, Y.D. Yao. "Impedance behav-
ior of spin-valve transistor". J. Appl. Phys. Vol. 99 (8). P. 08H710-08H712 (2006).
[13] W. Ou-Yang, M. Weis, D. Taguchi, X. Chen, T. Manaka, M. Iwamoto. "Modeling of threshold volt-
age in pentacene organic field-effect transistors". J. Appl. Phys. Vol. 107 (12). P. 124506-124510
(2010).
[14] J. Wang, L. Wang, L. Wang, Z. Hao, Yi Luo, A. Dempewolf, M. M ller, F. Bertram, J rgen Christen.
"An improved carrier rate model to evaluate internal quantum efficiency and analyze efficiency droop
origin of InGaN based light-emitting diodes". J. Appl. Phys. Vol. 112 (2). P. 023107-023112 (2012).
[15] K.K. Ong, K.L. Pey, P.S. Lee, A.T.S. Wee, X.C. Wang, Y.F. Chong. "Dopant distribution in the re-
crystallization transient at the maximum melt depth induced by laser annealing". Appl. Phys. Lett. 89
(17), 172111-172114 (2006).
[16] H.T. Wang, L.S. Tan, E. F. Chor. "Pulsed laser annealing of Be-implanted GaN". J. Appl. Phys. 98
(9), 094901-094905 (2006).
[17] Yu.V. Bykov, A.G. Yeremeev, N.A. Zharova, I.V. Plotnikov, K.I. Rybakov, M.N. Drozdov, Yu.N.
Drozdov, V.D. Skupov. "Diffusion processes in semiconductor structures during microwave anneal-
ing". Radiophysics and Quantum Electronics. Vol. 43 (3). P. 836-843 (2003).
[18] E.L. Pankratov. "Dopant Diffusion dynamics and optimal diffusion time as influenced by diffusion-
coefficient nonuniformity". Russian Microelectronics. 2007. V.36 (1). P. 33-39.
[19] E.L. Pankratov. "Redistribution of a dopant during annealing of radiation defects in a multilayer struc-
ture by laser scans for production of an implanted-junction rectifier". Int. J. Nanoscience. Vol. 7 (4-5).
P. 187–197 (2008).
[20] V.V. Kozlivsky. Modification of semiconductors by proton beams (Nauka, Sant-Peterburg, 2003, in
Russian).
12. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
54
[21] E.L. Pankratov, E.A. Bulaeva. "Doping of materials during manufacture p–n-junctions and bipolar
transistors. analytical approaches to model technological approaches and ways of optimization of dis-
tributions of dopants". Reviews in Theoretical Science. Vol. 1 (1). P. 58-82 (2013).
[22] E.L. Pankratov, E.A. Bulaeva. "Optimization of manufacture of field-effect heterotransistors without
p-n-junctions to decrease their dimensions". International Journal of Recent Advances in Physics.
Vol. 3 (3). P. 1-16 (2014).
[23] E.L. Pankratov, E.A. Bulaeva. "Analytical approach to model mass transport in a heterostructure dur-
ing manufacturing an implanted-junction rectifiers". Quantum matter. Vol. 3 (5). P. 454-459 (2014).
[24] E.I. Zorin, P.V. Pavlov and D.I. Tetelbaum. Ion doping of semiconductors. Moscow: Energy, 1975.
[25] P.M. Fahey, P.B. Griffin, J.D. Plummer. "Point defects and dopant diffusion in silicon". Rev. Mod.
Phys. 1989. V. 61. № 2. P. 289-388.
[26] V.L. Vinetskiy, G.A. Kholodar'. Radiative physics of semiconductors. ("Naukova Dumka", Kiev,
1979, in Russian).
[27] W.-X. Ni, G.V. Hansson, J.-E. Sundgren, L. Hultman, L.R. Wallenberg, J.-Y. Yao, L.C. Markert, J.E.
Greene, Phys. Rev. B. Vol. 46 (12). P. 7551-7558 (1992)
[28] B.A. Zon, S.B. Ledovsky, A.N. Likholet. Tech. Phys. Vol. 45 (4). P. 419-424 (2000).
[29] F. Faupel, W. Frank, M.-P. Macht, H. Mehrer, V. Naundorf, K. Ratzke, H. R. Schober, S.K. Sharma,
H. Teichler. Reviews of modern physics. Vol. 75 (1). P. 237-280 (2003).
[30] S.A. Bahrani, Y. Jannot, A. Degiovanni. J. Appl. Phys. Vol. 114 (14). P. 143509-143516 (2014).
[31] Yu.D. Sokolov. "On the determination of the dynamic forces in mine hoist ropes". Applied Mechan-
ics. Vol.1 (1). P. 23-35 (1955).
[32] E.L. Pankratov. "Dynamics of delta-dopant redistribution during heterostructure growth". The
Europe-an Physical Journal B. 2007. V. 57, №3. P. 251-256.
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 110 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 63 published papers in area of her researches.