OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION RATE OF FIELD-EFFECT HETEROTRANSISTORS. AN APPROACH 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.
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
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.
On prognozisys of manufacturing doublebaseijaceeejournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this
heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects.
The approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher
compactness of the considered bipolar transistor.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect heterotransistor. Based on analytical solution of the considered boundary problems some recommendations have been formulated to optimize technological processes.
ON OPTIMIZATION OF MANUFACTURING PLANAR DOUBLE-BASE HETEROTRANSISTORS TO DECR...ijaceeejournal
In this paper we consider an approach of manufacturing of double-base hetero transistors to decrease their
dimensions. Framework the approach it should be manufactured a heterostructure with specific configuration.
Farther it is necessary to dope certain areas of the hetero structure by diffusion or by ion implantation.
After finishing of the doping process the dopant and/or radiation defects should be annealed. We consider
an approach of optimization of dopant and/or radiation defects for manufacturing more compact double base
heterotransistors.
On prognozisys of manufacturing double basemsejjournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this heterostructure
by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects. The
approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher compactness
of the considered bipolar transistor.
AN APPROACH TO OPTIMIZE MANUFACTURE OF AN ACTIVE QUADRATURE SIGNAL GENERATOR ...antjjournal
In this paper we introduce an approach to increase density of field-effect transistors framework an active
quadrature signal generator. Framework the approach we consider manufacturing the generator in heterostructure
with specific configuration. Several required areas of the heterostructure should be doped by diffusion
or ion implantation. After that dopant and radiation defects should by annealed framework optimized
scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered
heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures
during manufacturing of integrated circuits with account mismatch-induced stress.
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 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
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.
On prognozisys of manufacturing doublebaseijaceeejournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this
heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects.
The approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher
compactness of the considered bipolar transistor.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect heterotransistor. Based on analytical solution of the considered boundary problems some recommendations have been formulated to optimize technological processes.
ON OPTIMIZATION OF MANUFACTURING PLANAR DOUBLE-BASE HETEROTRANSISTORS TO DECR...ijaceeejournal
In this paper we consider an approach of manufacturing of double-base hetero transistors to decrease their
dimensions. Framework the approach it should be manufactured a heterostructure with specific configuration.
Farther it is necessary to dope certain areas of the hetero structure by diffusion or by ion implantation.
After finishing of the doping process the dopant and/or radiation defects should be annealed. We consider
an approach of optimization of dopant and/or radiation defects for manufacturing more compact double base
heterotransistors.
On prognozisys of manufacturing double basemsejjournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this heterostructure
by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects. The
approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher compactness
of the considered bipolar transistor.
AN APPROACH TO OPTIMIZE MANUFACTURE OF AN ACTIVE QUADRATURE SIGNAL GENERATOR ...antjjournal
In this paper we introduce an approach to increase density of field-effect transistors framework an active
quadrature signal generator. Framework the approach we consider manufacturing the generator in heterostructure
with specific configuration. Several required areas of the heterostructure should be doped by diffusion
or ion implantation. After that dopant and radiation defects should by annealed framework optimized
scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered
heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures
during manufacturing of integrated circuits with account mismatch-induced stress.
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.
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.
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.
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.
In this paper based on recently introduced approach we formulated some recommendations to optimize
manufacture drift bipolar transistor to decrease their dimensions and to decrease local overheats during
functioning. The approach based on manufacture a heterostructure, doping required parts of the heterostructure
by dopant diffusion or by ion implantation and optimization of annealing of dopant and/or radiation
defects. The optimization gives us possibility to increase homogeneity of distributions of concentrations
of dopants in emitter and collector and specific inhomogenous of concentration of dopant in base and at the
same time to increase sharpness of p-n-junctions, which have been manufactured framework the transistor.
We obtain dependences of optimal annealing time on several parameters. We also introduced an analytical
approach to model nonlinear physical processes (such as mass- and heat transport) in inhomogenous media
with time-varying parameters.
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.
AN APPROACH TO OPTIMIZE OF MANUFACTURING OF A VOLTAGE REFERENCE BASED ON HETE...JaresJournal
In this paper we introduce an approach to increase density of field-effect transistors framework a voltage
reference. Framework the approach we consider manufacturing the inverter in heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or ion implantation. After that dopant and radiation defects should by annealed framework optimized scheme. We also
consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We
introduce an analytical approach to analyze mass and heat transport in heterostructures during manufacturing of integrated circuits with account mismatch-induced stress.
On 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.
Optimization of technological process to decrease dimensions of circuits xor ...ijfcstjournal
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of dopant
and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
ON OPTIMIZATION OF MANUFACTURING OF FIELD-EFFECT HETERO TRANSISTORS A THREE S...jedt_journal
In this paper we introduce an approach to increase density of field-effect hetero transistors framework a three-stage
amplifier circuit. At the same time one can obtain decreasing of dimensions of the above transistors. Dimensions of the elements will be decreased due to manufacture heterostructure with specific structure, doping of required areas of the hetero structure by diffusion or ion implantation and optimization of annealing of dopant and/or radiation defects.
ON OPTIMIZATION OF MANUFACTURING OF AN AMPLIFIER TO INCREASE DENSITY OF BIPOL...ijoejournal
In this paper we consider a possibility to increase density of bipolar heterotransistor framework an amplifier
due to decreasing of their dimensions. The considered approach based on doping of required areas of
heterostructure with specific configuration by diffusion or ion implantation. The doping finished by optimized
annealing of dopant and/or radiation defects. Analysis of redistribution of dopant with account redistribution
of radiation defects (after implantation of ions of dopant) for optimization of the above annealing
have been done by using recently introduced analytical approach. The approach gives a possibility
to analyze mass and heat transports in a heterostructure without crosslinking of solutions on interfaces
between layers of the heterostructure with account nonlinearity of these transports and variation in time of
their parameters.
On 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.
Nov 12 Webcast: Eliminate Pitfalls of DDR Memory Testing
Join Teledyne LeCroy's, Mike Hertz, for this free webinar on using an oscilloscope for validation and debug of DDR2/3/4 physical layer measurements.
Topics covered will include: probing, connectivity, recommended device patterns, de-embedding, examples of good and bad waveforms, and debugging steps and techniques.
Mike Hertz has been a Field Applications Engineer with Teledyne LeCroy in Michigan for 14 years.
A brief overview of the processes involved in nanolithography & nanopatterning. It mainly discusses the steps, mechanism & instrumentation of the electron beam lithography in detail. It also gives a small view on other technologies as well.
This presentation includes basis of lithography i.e. (photo-lithography e-beam lithography) in nano-lithography includes (AFM, Soft, NIL and DPN lithography)
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.
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.
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.
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.
In this paper based on recently introduced approach we formulated some recommendations to optimize
manufacture drift bipolar transistor to decrease their dimensions and to decrease local overheats during
functioning. The approach based on manufacture a heterostructure, doping required parts of the heterostructure
by dopant diffusion or by ion implantation and optimization of annealing of dopant and/or radiation
defects. The optimization gives us possibility to increase homogeneity of distributions of concentrations
of dopants in emitter and collector and specific inhomogenous of concentration of dopant in base and at the
same time to increase sharpness of p-n-junctions, which have been manufactured framework the transistor.
We obtain dependences of optimal annealing time on several parameters. We also introduced an analytical
approach to model nonlinear physical processes (such as mass- and heat transport) in inhomogenous media
with time-varying parameters.
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.
AN APPROACH TO OPTIMIZE OF MANUFACTURING OF A VOLTAGE REFERENCE BASED ON HETE...JaresJournal
In this paper we introduce an approach to increase density of field-effect transistors framework a voltage
reference. Framework the approach we consider manufacturing the inverter in heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or ion implantation. After that dopant and radiation defects should by annealed framework optimized scheme. We also
consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We
introduce an analytical approach to analyze mass and heat transport in heterostructures during manufacturing of integrated circuits with account mismatch-induced stress.
On 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.
Optimization of technological process to decrease dimensions of circuits xor ...ijfcstjournal
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of dopant
and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
ON OPTIMIZATION OF MANUFACTURING OF FIELD-EFFECT HETERO TRANSISTORS A THREE S...jedt_journal
In this paper we introduce an approach to increase density of field-effect hetero transistors framework a three-stage
amplifier circuit. At the same time one can obtain decreasing of dimensions of the above transistors. Dimensions of the elements will be decreased due to manufacture heterostructure with specific structure, doping of required areas of the hetero structure by diffusion or ion implantation and optimization of annealing of dopant and/or radiation defects.
ON OPTIMIZATION OF MANUFACTURING OF AN AMPLIFIER TO INCREASE DENSITY OF BIPOL...ijoejournal
In this paper we consider a possibility to increase density of bipolar heterotransistor framework an amplifier
due to decreasing of their dimensions. The considered approach based on doping of required areas of
heterostructure with specific configuration by diffusion or ion implantation. The doping finished by optimized
annealing of dopant and/or radiation defects. Analysis of redistribution of dopant with account redistribution
of radiation defects (after implantation of ions of dopant) for optimization of the above annealing
have been done by using recently introduced analytical approach. The approach gives a possibility
to analyze mass and heat transports in a heterostructure without crosslinking of solutions on interfaces
between layers of the heterostructure with account nonlinearity of these transports and variation in time of
their parameters.
On 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.
Nov 12 Webcast: Eliminate Pitfalls of DDR Memory Testing
Join Teledyne LeCroy's, Mike Hertz, for this free webinar on using an oscilloscope for validation and debug of DDR2/3/4 physical layer measurements.
Topics covered will include: probing, connectivity, recommended device patterns, de-embedding, examples of good and bad waveforms, and debugging steps and techniques.
Mike Hertz has been a Field Applications Engineer with Teledyne LeCroy in Michigan for 14 years.
A brief overview of the processes involved in nanolithography & nanopatterning. It mainly discusses the steps, mechanism & instrumentation of the electron beam lithography in detail. It also gives a small view on other technologies as well.
This presentation includes basis of lithography i.e. (photo-lithography e-beam lithography) in nano-lithography includes (AFM, Soft, NIL and DPN lithography)
Similar to OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION RATE OF FIELD-EFFECT HETEROTRANSISTORS. AN APPROACH TO SIMPLIFY CONSTRUCTION OF THE HETEROTRANSISTORS
Optimization of Dopant Diffusion and Ion Implantation to Increase Integration...ijrap
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION...ijrap
In this work we introduce an approach to decrease dimensions of a field-effect heterotransistors. The approach based on manufacturing field-effect transistors in heterostructures and optimization of technological processes. At the same time we consider possibility to simplify their constructions.
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.
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.
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect
heterotransistor. Based on analytical solution of the considered boundary problems some recommendations
have been formulated to optimize technological processes.
On Approach to 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.
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 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 a Switched-capacitor ...BRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a switched-
capacitor step-down DC–DC converter. Framework the approach, we consider a heterostructure with
special configuration. Several specific areas of the heterostructure should be doped by diffusion or ion
implantation. Annealing of dopant and/or radiation defects should be optimized.
ON PROGNOZISYS OF MANUFACTURING DOUBLE-BASE HETEROTRANSISTOR AND OPTIMIZATION...msejjournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects. The
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OPTIMIZATION OF DOPANT DIFFUSION AND ION IMPLANTATION TO INCREASE INTEGRATION RATE OF FIELD-EFFECT HETEROTRANSISTORS. AN APPROACH 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 SourceGate GateDrain
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
tzyxC
D
zy
tzyxC
D
yx
tzyxC
D
xt
tzyxC
CCC
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂ ,,,,,,,,,,,,
. (1)
Boundary and initial conditions for the equation are
( ) 0
,,,
0
=
∂
∂
=x
x
tzyxC
,
( ) 0
,,,
=
∂
∂
= xLx
x
tzyxC
,
( ) 0
,,,
0
=
∂
∂
=y
y
tzyxC
,
( ) 0
,,,
=
∂
∂
= yLx
y
tzyxC
, (2)
( ) 0
,,,
0
=
∂
∂
=z
z
tzyxC
,
( ) 0
,,,
=
∂
∂
= zLx
z
tzyxC
, 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
tzyxV
V
tzyxV
TzyxP
tzyxC
TzyxDD LC ςςξ 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]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
−
∂
∂
∂
∂
+×
×−
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
−
∂
∂
∂
∂
+×
×−
∂
∂
∂
∂
+
∂
∂
∂
∂
=
∂
∂
tzyxVTzyxk
z
tzyxV
TzyxD
z
tzyxVTzyxk
tzyxI
y
tzyxV
TzyxD
yx
tzyxV
TzyxD
xt
tzyxV
tzyxITzyxk
z
tzyxI
TzyxD
z
tzyxVTzyxk
tzyxI
y
tzyxI
TzyxD
yx
tzyxI
TzyxD
xt
tzyxI
VVVVI
VV
IIIVI
II
,,,,,,
,,,
,,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,,,,
,,,
,,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,
2
,,
2
,,
(4)
with boundary and boundary conditions
( ) 0
,,,
0
=
∂
∂
=x
x
tzyxρ
,
( ) 0
,,,
=
∂
∂
= xLx
x
tzyxρ
,
( ) 0
,,,
0
=
∂
∂
=y
y
tzyxρ
,
( ) 0
,,,
=
∂
∂
= yLy
y
tzyxρ
, (5)
( ) 0
,,,
0
=
∂
∂
=z
z
tzyxρ
,
( ) 0
,,,
=
∂
∂
= zLz
z
tzyxρ
, 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
ΦΦ
Φ
ΦΦ
tzyxVTzyxktzyxVTzyxk
z
tzyx
TzyxD
z
y
tzyx
TzyxD
yx
tzyx
TzyxD
xt
tzyx
tzyxITzyxktzyxITzyxk
z
tzyx
TzyxD
z
y
tzyx
TzyxD
yx
tzyx
TzyxD
xt
tzyx
VVV
V
V
V
V
V
V
V
III
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
ΦΦ
Φ
ΦΦ
tzyxVTzyxktzyxVTzyxk
z
tzyx
TzyxD
z
y
tzyx
TzyxD
yx
tzyx
TzyxD
xt
tzyx
tzyxITzyxktzyxITzyxk
z
tzyx
TzyxD
z
y
tzyx
TzyxD
yx
tzyx
TzyxD
xt
tzyx
VVV
V
V
V
V
V
V
V
III
I
I
I
I
I
I
I
,,,,,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,,,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,
2
,
2
,
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
with boundary and initial conditions
( )
0
,,,
0
=
∂
Φ∂
=x
x
tzyxρ
,
( )
0
,,,
=
∂
Φ∂
= xLx
x
tzyxρ
,
( )
0
,,,
0
=
∂
Φ∂
=y
y
tzyxρ
,
( )
0
,,,
=
∂
Φ∂
= yLy
y
tzyxρ
,
( )
0
,,,
0
=
∂
Φ∂
=z
z
tzyxρ
,
( )
0
,,,
=
∂
Φ∂
= zLz
z
tzyxρ
, ΦI(x,y,z,0)=fΦI(x,y,z), ΦV(x,y,z,0)=fΦV(x,y,z). (7)
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
21
,,,
n
nCnnnnC
zyxzyx
tezcycxcF
LLLLLL
tzyxC ,
( ) ( ) ( ) ( ) ( )∑+=
∞
=1
1
21
,,,
n
nInnnnI
zyxzyx
tezcycxcF
LLLLLL
tzyxI ,
( ) ( ) ( ) ( ) ( )∑+=
∞
=1
1
21
,,,
n
nVnnnnC
zyxzyx
tezcycxcF
LLLLLL
tzyxV ,
( ) ( ) ( ) ( ) ( )∑+=Φ
∞
=
ΦΦ
1
1
21
,,,
n
nnnnn
zyxzyx
I tezcycxcF
LLLLLL
tzyx II
,
( ) ( ) ( ) ( ) ( )∑+=Φ
∞
=
ΦΦ
1
1
21
,,,
n
nnnnn
zyxzyx
V tezcycxcF
LLLLLL
tzyx VV
,
where ( )
++−= 2220
22 111
exp
zyx
n
LLL
tDnte ρρ π , ( ) ( ) ( ) ( )∫ ∫ ∫=
x y zL L L
nnnn udvdwdwvufwcvcucF
0 0 0
,,ρρ , 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
( )
( )
( ) ( )
( )
( )[ ]
( )
×
+
+
++=
∗∗
TzyxP
tzyxC
V
tzyxV
V
tzyxV
TzyxD
xt
tzyxC C
L
,,,
,,,
1
,,,,,,
1,,,
,,, 12
2
2
21
2
γ
γ
α
ξςς
∂
∂
∂
∂
( ) ( ) ( ) ( )
( )
( )[ ]
( )
( )
+
+
+
+++
×
∗∗
y
tzyxC
TzyxP
tzyxC
V
tzyxV
V
tzyxV
TzyxD
yx
tzyxC C
L
∂
∂α
ξςς
∂
∂
∂
∂
γ
γ
,,,
,,,
,,,
1
,,,,,,
1,,,
,,, 112
2
2
21
1
(8)
( )
( ) ( )[ ]
( )
( )
( )
( )
++
+
++ ∗∗ V
tzyxV
V
tzyxV
TzyxP
tzyxC
z
tzyxC
TzyxD
z
C
L
,,,,,,
1
,,,
,,,
1
,,,
,,, 12
2
2
121
ςς
α
ξ
∂
∂
∂
∂
γ
γ
( )
( )
( )
( )
( )
( )
( )
( ) ( )[ ] ( )[ ]
( ) ( )[ ]
( )
( )
( )
( )
( )
( )
( )
( ) ( )[ ] ( )[ ]
( ) ( )[ ]
+−
−++−
+
+
+
=
+−
−++−
+
+
+
=
2
12,
1212,
1
112
2
12,
1212,
1
112
,,,,,,
,,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,,,,
,,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,
tzyxVTzyxk
tzyxVtzyxITzyxk
z
tzyxV
TzyxD
z
y
tzyxV
TzyxD
yx
tzyxV
TzyxD
xt
tzyxV
tzyxITzyxk
tzyxVtzyxITzyxk
z
tzyxI
TzyxD
z
y
tzyxI
TzyxD
yx
tzyxI
TzyxD
xt
tzyxI
VVV
VIVIV
VV
III
VIVII
II
α
αα
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
α
αα
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
(9)
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( ) ( )
−+
Φ
+
+
Φ
+
Φ
=
Φ
−+
Φ
+
+
Φ
+
Φ
=
Φ
Φ
ΦΦ
Φ
ΦΦ
tzyxVTzyxktzyxVTzyxk
z
tzyx
TzyxD
z
x
tzyx
TzyxD
yx
tzyx
TzyxD
xt
tzyx
tzyxITzyxktzyxITzyxk
z
tzyx
TzyxD
z
x
tzyx
TzyxD
yx
tzyx
TzyxD
xt
tzyx
VVV
V
V
V
V
V
V
V
III
I
I
I
I
I
I
I
,,,,,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,,,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,
2
,
1
112
2
,
1
112
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
(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
TzyxP
zyxC
V
zyxV
V
zyxV
TzyxD
x
tzyxC
0
12
2
2
212
,,,
,,,
1
,,,,,,
1,,,,,, γ
γ
τα
ξ
τ
ς
τ
ς
∂
∂
( ) ( ) ( )
( )
( )[ ]
( )
∫ ×
+
+
++
×
∗∗
t
C
TzyxP
zyxC
V
zyxV
V
zyxV
y
d
x
zyxC
0
12
2
2
21
1
,,,
,,,
1
,,,,,,
1
,,,
γ
γ
τα
ξ
τ
ς
τ
ς
∂
∂
τ
∂
τ∂
( ) ( ) ( ) ( )
( )
( )
∫ ×
++
×
∗∗
t
L
y
zyxC
V
zyxV
V
zyxV
zy
zyxC
TzyxD
0
1
2
2
21
1 ,,,,,,,,,
1
,,,
,,,
∂
τ∂τ
ς
τ
ς
∂
∂
∂
τ∂
6. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
48
( )
( )[ ]
( )
( )zyxf
TzyxP
zyxC
TzyxD C
C
L ,,
,,,
,,,
1,,, 12
+
+
+× γ
γ
τα
ξ (8a)
( ) ( )
( )
( )
( )
( )
( )
( ) ( )[ ] ( )
( ) ( )[ ] ( )[ ]
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )[ ] ( )
( ) ( )[ ] ( )[ ]
∫ ++−
−+∫ +−
∫+
+
∫+
∫=
∫ ++−
−+∫ +−
∫+
+
∫+
∫=
t
VIVI
V
t
VVV
t
V
t
V
t
V
t
VIVI
I
t
III
t
I
t
I
t
I
dzyxVzyxITzyxk
zyxfdzyxVTzyxkd
z
zyxV
TzyxD
z
d
y
zyxV
TzyxD
y
d
x
zyxV
TzyxD
x
tzyxV
dzyxVzyxITzyxk
zyxfdzyxITzyxkd
z
zyxI
TzyxD
z
d
y
zyxI
TzyxD
y
d
x
zyxI
TzyxD
x
tzyxI
0
1212,
0
2
12,
0
1
0
1
0
1
2
0
1212,
0
2
12,
0
1
0
1
0
1
2
,,,,,,,,,
,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,,,,
,,,,,,,,,
,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,,,,
ττατα
ττατ
∂
τ∂
∂
∂
τ
∂
τ∂
∂
∂
τ
∂
τ∂
∂
∂
ττατα
ττατ
∂
τ∂
∂
∂
τ
∂
τ∂
∂
∂
τ
∂
τ∂
∂
∂
(9a)
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( )
∫−
−∫++
∫
Φ
+
+
∫
Φ
+
∫
Φ
=Φ
∫−
−∫++
∫
Φ
+
+
∫
Φ
+
∫
Φ
=Φ
ΦΦ
ΦΦ
ΦΦ
ΦΦ
t
V
t
VVV
t
V
V
t
V
V
t
V
VV
t
I
t
III
t
I
I
t
I
I
t
I
II
dzyxVTzyxk
dzyxVTzyxkzyxfd
z
zyx
TzyxD
z
d
y
zyx
TzyxD
y
d
x
zyx
TzyxD
x
tzyx
dzyxITzyxk
dzyxITzyxkzyxfd
z
zyx
TzyxD
z
d
y
zyx
TzyxD
y
d
x
zyx
TzyxD
x
tzyx
0
0
2
,
0
1
0
1
0
1
2
0
0
2
,
0
1
0
1
0
1
2
,,,,,,
,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,,,,
,,,,,,
,,,,,,,,
,,,
,,,
,,,
,,,
,,,
,,,,,,
ττ
τττ
∂
τ∂
∂
∂
τ
∂
τ∂
∂
∂
τ
∂
τ∂
∂
∂
ττ
τττ
∂
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
122 ,,,,,,
1 x y zL L L
zyx
tdxdydzdtzyxtzyx
LLL
ρρα 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 zL L L
C
zyx
С xdydzdzyxf
LLL 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
42
1
2
1
,,
1
41
2
1
4
313
4
2
3
4
2
00
0021001
2
1
11
20
0 0 0
10200
2
0021001
00
2
B
AB
A
ByB
yB
AB
B
A
AAA
A
Axdydzdzyxf
LLL
AAAAA
A
V
II
IVVIIIV
IV
II
L L L
I
zyx
IVVIIIVVIIIV
II
I
x y z
α
α
ααα
(13)
where ( ) ( ) ( ) ( )∫ ∫ ∫ ∫−Θ
Θ
=
Θ
0 0 0 0
11, ,,,,,,,,,
1 x y zL L L
ji
ba
zyx
abij tdxdydzdtzyxVtzyxITzyxkt
LLL
A , ×= 2
004 IVAB
( )2
0000
2
00
2
00 2 VVIIIVIV AAAA −−× , ( ++++= 0000
2
001000
3
0001
2
00003 4 VVIIIVIIIVIVIVIVIV AAAAAAAAAB
) ( ) ( )[ ] +−++−++++ 2
0000101010001001000001
2
00 412122 IVIIIVVVIVIIIIIVIVIVIVIV AAAAAAAAAAAA
2
0001002 IVIVIV AAA+ , ( )
×
∫ ∫ ∫−−−=
x y zL L L
I
zyx
IIIVIVIV xdydzdzyxf
LLL
AAAAB
0 0 0
2011
2
01
2
002 ,,
1
4
( ) ( )} [{ ++−+++++× 0001
2
00000010100001000100
2
100100 24214 IVIVIVIVIIIVIIIVIVIVIVIVIIIVII AAAAAAAAAAAAAAA
( ) ( )] ( ) (
++∫ ∫ ∫+++−+++ 1001
0 0 0
2
101000100100 ,,
2
21212 IIIV
L L L
V
zyx
VVIVIIIIIVIV AAxdydzdzyxf
LLL
AAAAAA
x y z
] ( ) ( )] ( ) ( )[ +++−+++++−−++ 1212121 10100010010010010111200001 VVIVIIIIIVIVIIIVIVIVVVIIIV AAAAAAAAAAAAA
]}00012 IVIV AA+ , ( ) ( )
−∫ ∫ ∫−−++=
x y zL L L
I
zyx
IVIIIVIVIV xdydzdzyxf
LLL
AAAAAB
0 0 0
11
2
100101001 ,,
1
812
] ( ) ( )
+∫ ∫ ∫−−+++−
x y zL L L
I
zyx
II
IIIVIIIVIVIVIVIVIIIVIVII xdydzdzyxf
LLL
A
AAAAAAAAAAAA
0 0 0
00
00101000010000
2
0100010020 ,,
2
24
( ) ( ) ( )] ( )[ −+++++−−+++ 100100100101112000100101 12121 IIIVIVIIIVIVIVVVIIIIIVIV AAAAAAAAAAAA
( ) ]0001101000 212 IVIVVVIVII AAAAA +++− , ( )
−∫ ∫ ∫=
x y zL L L
I
zyx
IIIV xdydzdzyxf
LLL
AAB
0 0 0
00
2
010 ,,
1
4
] ( ) ( ) ( )
×+++∫ ∫ ∫−++++− 1001
0 0 0
002
1001
2
012011 1,,
2
1 IIIV
L L L
V
zyx
II
IIIVIVIIIV AAxdydzdzyxf
LLL
A
AAAAA
x y z
( ) ( )]2
10010111200001 12 IIIVIVIVVVIIIV AAAAAAA +++−−× ,
6
23 323 32 B
qpqqpqy +++−−+= ,
( ) ( )
48
82
8
4
216
2
031
2
1
2
320
3
2 B
BBB
BBBBB
q −+
−−
+= ,
36312
2
2031 BBBB
p −−= , 2
2
3 48 BByA −+= ,
( ) ( ) ( )
( )
( ) ( ) ( )
( )
∫ ∫ ∫+
+∫ ∫ ∫ ∫−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
zyx
L L L
V
zyx
VV
L L L
I
zyx
L L L
I
zyx
II
xdydzdzyxf
LLL
tdxdydzdtzyxVTzyxkt
LLL
A
xdydzdzyxf
LLL
tdxdydzdtzyxITzyxkt
LLL
A
0 0 0
0 0 0 0
202
0 0 0
0 0 0 0
202
,,
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
ΘD0L
-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
ΘD0L
-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 zL L L
zyx
xdydzdzyxzyxC
LLL
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.
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Authors:
Pankratov Evgeny Leonidovich was born at 1977. From 1985 to 1995 he was educated in a secondary
school in Nizhny Novgorod. From 1995 to 2004 he was educated in Nizhny Novgorod State University:
from 1995 to 1999 it was bachelor course in Radiophysics, from 1999 to 2001 it was master course in Ra-
diophysics with specialization in Statistical Radiophysics, from 2001 to 2004 it was PhD course in Radio-
physics. From 2004 to 2008 E.L. Pankratov was a leading technologist in Institute for Physics of Micro-
structures. From 2008 to 2012 E.L. Pankratov was a senior lecture/Associate Professor of Nizhny Novgo-
rod State University of Architecture and Civil Engineering. Now E.L. Pankratov is in his Full Doctor
course in Radiophysical Department of Nizhny Novgorod State University. He has 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.
![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].](https://image.slidesharecdn.com/optimizationofdopantdiffusionandion-150313022111-conversion-gate01/85/OPTIMIZATION-OF-DOPANT-DIFFUSION-AND-ION-IMPLANTATION-TO-INCREASE-INTEGRATION-RATE-OF-FIELD-EFFECT-HETEROTRANSISTORS-AN-APPROACH-TO-SIMPLIFY-CONSTRUCTION-OF-THE-HETEROTRANSISTORS-1-320.jpg)
![International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
44
Source SourceGate GateDrain
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
tzyxC
D
zy
tzyxC
D
yx
tzyxC
D
xt
tzyxC
CCC
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂ ,,,,,,,,,,,,
. (1)
Boundary and initial conditions for the equation are
( ) 0
,,,
0
=
∂
∂
=x
x
tzyxC
,
( ) 0
,,,
=
∂
∂
= xLx
x
tzyxC
,
( ) 0
,,,
0
=
∂
∂
=y
y
tzyxC
,
( ) 0
,,,
=
∂
∂
= yLx
y
tzyxC
, (2)
( ) 0
,,,
0
=
∂
∂
=z
z
tzyxC
,
( ) 0
,,,
=
∂
∂
= zLx
z
tzyxC
, 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
tzyxV
V
tzyxV
TzyxP
tzyxC
TzyxDD LC ςςξ 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-](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)