an approach for optimization of
DESCRIPTION
ENHANCED ACTIVITY OF ANTIBIOTICS BYLIPOSOMAL DRUG DELIVERYTRANSCRIPT
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1
AN APPROACH FOR OPTIMIZATION OF
MANUFACTURE MULTIEMITTER
HETEROTRANSISTORS
E.L. Pankratov1 and E.A. Bulaeva2
1 Nizhny Novgorod State University, 23 Gagarin avenue, Nizhny Novgorod, 603950,
Russia 2 Nizhny Novgorod State University of Architecture and Civil Engineering, 65 Il'insky
street, Nizhny Novgorod, 603950, Russia
ABSTRACT
In this paper we introduced an approach to model manufacture process of a multiemitter heterotransistor. The approach gives us also possibility to optimize manufacture process. p-n-junctions, which include into the multiemitter heterotransistor, have higher sharpness and higher homogeneity of dopants distributions in enriched by the dopant area.
KEYWORDS
Multiemitter heterotransistor, Approach to optimize technological processes.
1. INTRODUCTION
Logical elements often include into itself multiemitter transistors [1-4]. To manufacture bipolar transistors it could be used dopant diffusion, ion doping or epitaxial layer [1-8]. It is attracted an interest increasing of sharpness of p-n-junctions, which include into bipolar transistors and decreasing of dimensions of the transistors, which include into integrated circuits [1-4]. Dimensions of transistors will be decreased by using inhomogenous distribution of temperature during laser or microwave types of annealing [9,10], using defects of materials (for example, defects could be generated during radiation processing of materials) [11-14], native inhomogeneity (multilayer property) of heterostructure [12-14].
Framework this paper we consider a heterostructure, which consist of a substrate and three epitaxial layers (see Fig. 1). Some dopants are infused in the epitaxial layers to manufacture p and n types of conductivities during manufacture a multiemitter transistor. Let us consider two cases: infusion of dopant by diffusion or ion implantation. Farther in the first case we consider annealing of dopant so long, that after the annealing the dopants should achieve interfaces between epitaxial layers. In this case one can obtain increasing of sharpness of p-n-junctions [12-14]. The increasing of sharpness could be obtained under conditions, when values of dopant diffusion coefficients in last epitaxial layers is larger, than values of dopant diffusion coefficient in average epitaxial layer. At the same time homogeneity of dopant distributions in doped areas increases. It is attracted an interest higher doping of last epitaxial layers, than doping of average epitaxial layer, because the higher doping gives us possibility to increase sharpness of p-n-junctions. It is
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also practicably to choose materials of epitaxial layers and substrate so; those values of dopant diffusion coefficients in the substrate should be smaller, than in the epitaxial layer. In this situation one can obtain thinner transistor. In the case of ion doping of heterostructure it should be done annealing of radiation defects. It is practicably to choose so regimes of annealing of radiation defects, that dopant should achieves interface between epitaxial layers. At the same time the dopant could not diffuse into another epitaxial layer. If dopant did not achieves interface between epitaxial layers during annealing of radiation defects, additional annealing of dopant required.
Main aims of the present paper are analysis of dynamics of redistribution of dopants in considered heterostructure (Figs. 1) and optimization of annealing times of dopants. In some recent papers analogous analysis have been done [4,10,12-14]. However we can not find in literature any similar heterostructures as we consider in the paper.
Substrate
Epitaxial layer 1
Epitaxial layer 2
Epitaxial layer 3
n-type dopant p-type dopant n-type dopant
Fig. 1a. Heterostructure, which consist of a substrate and three epitaxial layers. View from above
Epitaxial layer 1 Epitaxial layer 2 Epitaxial layer 3
n-type dopantp-type dopant
n-type dopant 1
n-type dopant 2
n-type dopant 3
n-type dopant 4
Fig. 1b. Heterostructure, which consist of a substrate and three epitaxial layers. View from one side
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2. Method of Analysis
Redistribution of dopant in the considered heterostructure has been described by the second Ficks low [1-4]
( ) ( ) ( ) ( )
+
+
=
z
tzyxCDzy
tzyxCDyx
tzyxCDxt
tzyxCCCC
,,,,,,,,,,,,
(1)
with boundary and initial conditions
( ) 0,,,0
=
=xx
tzyxC,
( ) 0,,, =
= xLx
x
tzyxC,
( ) 0,,,0
=
=yy
tzyxC,
( ) 0,,, =
= yLy
ytzyxC
,
( ) 0,,,0
=
=zz
tzyxC,
( ) 0,,, =
= zLz
z
tzyxC, C (x,y,z,0)=fC (x,y,z). (2)
Here C(x,y,z,t) is the spatio-temporal distribution of concentration of dopant; x, y, z and t are current coordinates and times; D is the dopant diffusion coefficient. Value of dopant diffusion coefficient depends on properties of materials in layers of heterostructure, speed of heating and cooling of heterostructure (with account Arrhenius low), spatio-temporal distributions of concentrations of dopants and radiation defects. Two last dependences of dopant diffusion coefficient could be approximated by the following relation [15,16]
( ) ( )( )( ) ( )
( )
++
+= 2*
2
2*1
,,,,,,1,,,
,,,1,,,V
tzyxVV
tzyxVTzyxPtzyxCTzyxDD LC
. (3)
Here DL (x,y,z,T) is the spatial (due to inhomogeneity () of heterostructure) and temperature (due to Arrhenius low) dependences of dopant diffusion coefficient; P
(x,y,z,T) is the limit of solubility of dopant; parameter depends of properties of materials and could be integer in the interval
[1,3] [15]; V
(x,y,z,t) is the spatio-temporal distribution of concentration of radiation vacancies; V* is the equilibrium distribution of vacancies. Concentrational dependence of dopant diffusion coefficient has been discussed in details in [15]. It should be noted, that radiation damage absents in the case of diffusion doping of haterostructure. In this situation 1= 2= 0. Spatio-temporal distributions of concentrations of point radiation defects could be determine by solution of the following system of equations [17-19]
( ) ( ) ( ) ( ) ( ) ( )
+
=
tzyxIy
tzyxITzyxDyx
tzyxITzyxDxt
tzyxIII ,,,
,,,
,,,
,,,
,,,
,,, 2
( ) ( ) ( ) ( ) ( ) ( )tzyxVtzyxITzyxkz
tzyxITzyxDz
Tzyxk VIIII ,,,,,,,,,,,,
,,,,,,,,
+ (4)
( ) ( ) ( ) ( ) ( ) ( )
+
=
tzyxVy
tzyxVTzyxDyx
tzyxVTzyxDxt
tzyxVVV ,,,
,,,
,,,
,,,
,,,
,,, 2
( ) ( ) ( ) ( ) ( ) ( )tzyxVtzyxITzyxkz
tzyxVTzyxD
zTzyxk VIVVV ,,,,,,,,,
,,,
,,,,,,,,
+
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with initial (x,y,z,0)=f (x,y,z) (5a)
and boundary conditions ( ) 0,,, =
= yLy
ytzyx
,
( ) 0,,,0
=
=zz
tzyx,
( ) 0,,, =
= zLz
z
tzyx. (5b)
Here =I,V; I (x,y,z,t) is the spatio-temporal distribution of concentration of interstitials; D(x,y, z,T) are diffusion coefficients of interstitials and vacancies; terms V2(x,y, z,t) and I2(x,y,z,t) correspond to generation of divacancies and analogous complexes of interstitials; kI,V(x,y,z,T), kI,I(x,y,z,T) and kV,V(x,y,z,T) parameters of recombination of point radiation defects and generation of complexes.
Spatio-temporal distributions of concentrations of divacancies V(x,y,z,t) and analogous complexes of interstitials I(x,y,z,t) will be determined by solving the following systems of equations [17-19]
( ) ( ) ( ) ( ) ( ) +
+
=
y
tzyxTzyxD
yxtzyx
TzyxDxt
tzyx II
II
I
,,,
,,,
,,,
,,,
,,,
( ) ( ) ( ) ( ) ( ) ( )tzyxITzyxktzyxITzyxkz
tzyxTzyxD
zIII
II ,,,,,,,,,,,,
,,,
,,,2
,+
+
(6)
( ) ( ) ( ) ( ) ( ) +
+
=
y
tzyxTzyxD
yxtzyx
TzyxDxt
tzyx VV
VV
V
,,,
,,,
,,,
,,,
,,,
( ) ( ) ( ) ( ) ( ) ( )tzyxVTzyxktzyxVTzyxkz
tzyxTzyxD
zVVV
VV ,,,,,,,,,,,,
,,,
,,,2
,+
+
with boundary and initial conditions ( )
0,,,
0
=
=xx
tzyx,
( )0
,,,
=
= xLxx
tzyx,
( )0
,,,
0
=
=yy
tzyx,
( )0
,,,
=
= yLyy
tzyx,
( )0
,,,
0
=
=zz
tzyx,
( )0
,,,
=
= zLzz
tzyx, I(x,y,z,0)=fI (x,y,z), V(x,y,z,0)=fV (x,y,z). (7)
Here DI(x,y,z,T) and DV(x,y,z,T) are diffusion coefficients of complexes of point radiation defects; kI(x,y,z,T) and kV(x,y,z,T) are parameters of decay of the complexes.
To determine spatio-temporal distributions of concentrations of complexes of radiation defects we used considered in Refs. [14,19] approach. Framework the approach we transform approxi-mations of diffusion coefficients of complexes of point radiation defects to the following form: D (x,y,z,T) = D0 [1+ g (x,y,z,T)] and kI,V (x,y,z,T)=k0I,V[1+ h(x,y,z,T)], where D0 and k0I,V are the average values of appropriate parameters, 0V
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2
2
2
2
1z
y
x
y
y LL
LL
b ++= , 2
2
2
2
1y
z
x
z
z LL
LLb ++= . Using the above variables leads to transformation Eqs. (4) to
the following form
( ) ( )[ ] ( ) +
+=V
I
y
II
V
I
xDD
bITg
DD
bI
0
0
0
0 1,,,~
,,,11,,,~
( )[ ] ( ) ( )[ ] ( )
++
+
,,,~,,,11,,,
~
,,,1 ITgb
ITg II
z
II
( )[ ] ( ) ( ) ,,,~,,,~,,,1*
*
0
0 VIThIV
DD
V
I + (8)
( ) ( )[ ] ( ) +
+=I
V
y
VV
I
V
xDD
bV
TgDD
bV
0
0
0
0 1,,,~
,,,11,,,~
( )[ ] ( ) ( )[ ] ( )
++
+
,,,~,,,1,,,
~
,,,1 VTgVTg VVVV
( )[ ] ( ) ( ) ,,,~,,,~,,,11*
*
0
0 VIThVI
DD
b IV
z
+ .
We will determine solution of Eqs. (8) as the following power series
( ) ( ) = =
=
=0 0 0~ ,,,
~
,,,~
i j k ijkkji . (9)
Substitution of the series into Eqs. (8) gives us possibility to obtain system of equations for initial-order approximations of concentrations of defects ( ) ,,,~000 and corrections for them
( ) ,,,~ijk (i1, j1, k1). The equations are presented in Appendix.
Substitution of the series (9) into appropriate boundary and initial conditions gives us possibility to obtain boundary and initial conditions for the functions ( ) ,,,~ijk . The conditions dard approaches [21,22], are presented in Appendix. and solutions for the functions ( ) ,,,~ijk (i0, j0, k0), which have been obtained by stan
Farther we determine spatio-temporal distributions of concentrations of point radiation defects. To calculate the distributions we transform approximations of diffusion coefficients to the following form: DI(x,y,z,T)=D0I[1+IgI(x,y,z,T)], DV(x,y,z,T)= D0V[1+VgV (x,y,z,T)]. In this situation Eqs. (6) will be transform to the following form
( ) ( )[ ] ( ) ( )[ ]
++
+=
Tzyxgyxtzyx
Tzyxgxt
tzyxII
III
I,,,1,,,,,,1,,,
( ) ( ) ( ) ( ) ( )tzyxITzyxktzyxITzyxkDy
tzyxIIII
I,,,,,,,,,,,,
,,, 2,0 +
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( ) ( )[ ] ( ) ( )[ ]
++
+=
Tzyxgyxtzyx
Tzyxgxt
tzyxVV
VVV
V,,,1
,,,
,,,1,,,
( ) ( ) ( ) ( ) ( )tzyxVTzyxktzyxVTzyxkDy
tzyxVVVV
V,,,,,,,,,,,,
,,, 2,0 +
.
We determine solutions of these equations as the following power series
( ) ( ) = =
0
,,,,,,
ii
i tzyxtzyx , (10)
where =I,V. Substitution of the series (10) into Eqs. (6) and appropriate boundary and initial conditions gives us possibility to obtain equations for initial-order approximations of concentrations of complexes of point radiation defects, corrections for them, boundary and initial conditions for all above functions. The equations, conditions and solutions, which have been obtained by standard approaches [21,22], are presented in the Appendix.
Analysis of spatio-temporal distributions of concentrations of radiation defects has been done by using the second-order approximations on parameters, which used in appropriate series, and have been defined more precisely by using numerical simulation.
Farther we determine solution of the Eq.(1). To calculate the solution we used the approach, which has been considered in [13,18]. Framework the approach we transform approximation of dopant diffusion coefficient DL(x,y,z,T) into following form: DL(x,y,z,T) =D0L[1+ L gL(x,y,z,T)]. We determine solution of the Eq.(1) as the following power series
( ) ( ) = =
=0 0,,
i j ijji
L txCtxC . (11)
Substitution of the series into Eq. (1) gives us possibility to obtain system of equations for initial-order approximation of dopant concentration C00(x,y,z,t) and corrections for them Cij(x,y,z,t) (i1, j1). Substitution of the series (11) into appropriate boundary and initial conditions for the functions Cij(x,y,z,t) (i0, j0)
( )0
,,,
0
=
=x
ij
x
tzyxC
;
( )0
,,,
=
= xLx
ij
x
tzyxC
;
( )0
,,,
0
=
=y
ij
ytzyxC
; ( )
0,,,
=
= yLy
ij
ytzyxC
;
( )0
,,,
0
=
=z
ij
z
tzyxC
;
( )0
,,,
=
= zLz
ij
z
tzyxC
; C00(x,y,z,0)=fC (x,y,z); Cij(x,y,z,0)=0, i0, j0.
Solutions of equations for the functions Cij(x,y,z,t) (i0, j0), which has been calculated by standard approaches [21,22], are presented in the Appendix.
Analysis of spatio-temporal distribution of dopant concentration has been done analytically by using the second-order approximation on parameters, which has been used in appropriate series and have been defined more precisely by using numerical simulation.
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3. Discussion
In this section we analyzed dynamics of redistribution of dopant with account relaxation of distributions of concentrations of radiation defects (in the case of ion doping of heterostructure). The Figs. 2 show distributions of concentrations of infused and implanted dopants in one of last epitaxial layers in direction, which is perpendicular to interfaces between epitaxial layers, after annealing of dopant and/or radiation defects, respectively. In this case values of dopant diffusion coefficient in last epitaxial layers is larger, than value of dopant diffusion coefficient in average epitaxial layer. The figures show, that interfaces between epitaxial layers under the above conditions give us possibility to increase sharpness of p-n-junctions and at the same time to increase homogeneity of distributions of concentrations of dopants in enriched by the dopants areas.
The Figs. 3 show distributions of concentrations of infused and implanted dopants in one of last epitaxial layers in direction, which is perpendicular to interfaces between epitaxial layers, after annealing of dopant and/or radiation defects, respectively. In this case values of dopant diffusion coefficient in last epitaxial layers is smaller, than value of dopant diffusion coefficient in average epitaxial layer. The figures show, that presents of last epitaxial layers leads to increasing of homogeneity of dopant in the average epitaxial layers. However sharpness of p-n-junctions decreases in comparison with p-n-junctions for Figs. 2. In this case one can obtain accelerated diffusion in last epitaxial layers. The decreasing of sharpness of p-n-junctions is a reason to use higher level of doping of last epitaxial layer to use nonlinearity of dopant diffusion. In this case one obtain n+-p-n+ and/or p+-n-p+ structures.
x
0.0
0.5
1.0
1.5
C(x,
)
12
34
56
0 L/4 L/2 3L/4 L
Interface
Epitaxial layer2
Epitaxial layer1
Fig. 2a. Distributions of concentrations of infused dopant in heterostructure from Fig. 1. Increasing of number of curves corresponds to increasing of difference between values of dopant diffusion coefficient
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x
0.0
0.5
1.0
1.5
2.0
C(x,
)
12
34
0 L/4 L/2 3L/4 L
Interface
Epitaxial layer2
Epitaxial layer1
Fig. 2b. Distributions of concentrations of implanted dopant in heterostructure from Fig. 1. Increasing of number of curves corresponds to increasing of difference between values of dopant diffusion coefficient
x
0.0
0.5
1.0
1.5
C(x,
)
0 a=2L/3 L-a1 =-L/3
1
3
2
Fig. 3a. Distributions of concentration of infused in average epitaxial layer dopant in the heterostructure in Fig. 1 without another epitaxial layers (curve 1) and with them for the case, when dopant diffusion
coefficient in the average epitaxial layer is smaller in comparison with dopant diffusion coefficients in another layers (curves 2 and 3). Increasing of number of curves corresponds to increasing of difference
between values of dopant diffusion coefficients epitaxial layers of heterostructure
x
0.00001
0.00010
0.00100
0.01000
0.10000
1.00000
C(x,
)
fC(x)
L/40 L/2 3L/4 Lx0
1
2
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Fig. 3b. Distributions of concentration of implanted in average epitaxial layer dopant in the heterostructure in Fig. 1 without another epitaxial layers (curve 1) and with them for the case, when dopant diffusion coefficient in the average epitaxial layer is smaller in comparison with dopant diffusion coefficients in another layers (curves 2 and 3). Increasing of number of curves corresponds to increasing of difference
between values of dopant diffusion coefficients epitaxial layers of heterostructure
Optimal value of annealing time we determine framework recently introduced criterion [12-14]. Framework the criterion we approximate real distributions of dopant by step-wise function and minimize the following mean-squared error
( ) ( )[ ] = L xdxxCLU 02
,
1 (12)
at annealing time . Dependences of the optimal value of annealing time from different parameters are presented on Figs. 4.
0.0 0.1 0.2 0.3 0.4 0.5a/L, , ,
0.0
0.1
0.2
0.3
0.4
0.5
D
0 L-
2
3
2
4
1
Fig. 4a. Dependences of dimensionless optimal value of annealing time of infused dopant, which has been calculated by minimization the mean-squared error (12), on different parameters of heterostructure. Curve 1
is the dependence of annealing time on relation a/L, = = 0 and equal to each other values of dopant diffusion coefficient in epitaxial layers. Curve 2 is the dependence of annealing time on parameter for
a/L=1/2 and = = 0. Curve 3 is the dependence of annealing time on parameter for a/L=1/2 and = = 0. Curve 4 is the dependence of annealing time on parameter for a/L=1/2 and = = 0
0.0 0.1 0.2 0.3 0.4 0.5a/L, , ,
0.00
0.04
0.08
0.12
D
0 L-
2
3
2
4
1
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Fig. 4b. Dependences of dimensionless optimal value time of additional annealing of implanted dopant, which has been calculated by minimization the mean-squared error (12), on different parameters of
heterostructure. Curve 1 is the dependence of annealing time on relation a/L, = = 0 and equal to each other values of dopant diffusion coefficient in epitaxial layers. Curve 2 is the dependence of annealing time
on parameter for a/L=1/2 and = = 0. Curve 3 is the dependence of annealing time on parameter for a/L=1/2 and = = 0. Curve 4 is the dependence of annealing time on parameter for a/L=1/2 and = = 0
The figures show, that optimal values of annealing time after ion implantation are smaller, than optimal values of annealing time after infusion of dopant. Reason of the difference is necessity to use annealing of radiation defects after ion implantation. After that (if necessary) it could be used additional annealing of dopant. One can obtain spreading of distribution of concentration during annealing of radiation defects. Increasing of annealing time with increasing of thickness of epitaxial layer is the consequence of necessity of higher time for dopant to achieve interfaces between epitaxial layers of heterostructure. Decreasing of annealing time with increasing of values of parameters and is the consequence of increasing of values of dopant diffusion coefficient in the area, where main part of dopant has been diffused. Increasing of annealing time with increasing of the parameter is the consequence of decreasing of the term [C (x,y,z,t)/ P (x,y,z,T)] in approximation of dopant diffusion coefficient (3) with increasing of the parameter , because dopant concentration did not usually achieved value of limit of solubility of dopant and parameter is not smaller, than 1.
4. Conclusion
In this paper we introduce an approach of manufacturing multiemitter heterotransistors. Framework the approach the considered transistors became more compact and will include into itself p-n-junctions with higher sharpness.
ACKNOWLEDGEMENTS
This work is supported by the contract 11.G34.31.0066 of the Russian Federation Government, grant of Scientific School of Russia and educational fellowship for scientific research.
APPENDIX
Equations and conditions for functions ( ) ,,,~ijk (i0, j0, k0) could be written as
( ) ( ) ( ) ( )
++=
2000
2
2000
2
2000
2
0
0000 ,,,~1,,,~1,,,~1,,,~
I
bI
bI
bDDI
zyxV
I ;
( ) ( ) ( ) ( )
++=
2000
2
2000
2
2000
2
0
0000 ,,,~1,,,~1,,,~1,,,~
V
bV
bV
bDDV
zyxI
V ;
( ) ( ) ( ) ( )+
++=
200
2
200
2
200
2
0
000 ,,,~1,,,~1,,,~1,,,~
i
z
i
y
i
xV
Ii Ib
Ib
IbD
DI
( ) ( ) ( ) ( )
+
+
+
,,,~
,,,
1,,,~,,,
1 1001000
0 iI
y
iI
xV
I ITgb
ITg
bDD
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( ) ( )
+
,,,~
,,,
1 100iI
z
ITg
b, i 1;
( ) ( ) ( ) ( )+
++=
200
2
200
2
200
2
0
000 ,,,~1,,,~1,,,~1,,,~
i
z
i
y
i
xI
Vi Vb
Vb
VbD
DV
( ) ( ) ( ) ( )
+
+
+
,,,~
,,,
1,,,~,,,
1 1001000
0 iV
y
iV
xI
V VTgb
VTg
bDD
( ) ( )
+
,,,~
,,,
1 100iV
z
VTgb
, i 1;
( ) ( ) ( ) ( )
++=
2010
2
2010
2
2010
2
0
0010 ,,,~1,,,~1,,,~1,,,~
I
bI
bI
bDDI
zyxV
I
( ) ( ) ,,,~,,,~ 000000**
VIIV
;
( ) ( ) ( ) ( )
++=
2010
2
2010
2
2010
2
0
0010 ,,,~1,,,~1,,,~1,,,~
V
bV
bV
bDDV
zyxI
V
( ) ( ) ,,,~,,,~ 000000**
VIIV
;
( ) ( ) ( ) ( )
++=
2020
2
2020
2
2020
2
0
0020 ,,,~1,,,~1,,,~1,,,~
I
bI
bI
bDDI
zyxV
I
( ) ( ) ( ) ( ) ,,,~,,,~,,,~,,,~ 010000**
000010*
*
VIIVVI
IV
( ) ( ) ( ) ( )
++=
2020
2
2020
2
2020
2
0
0020 ,,,~1,,,~1,,,~1,,,~
V
bV
bV
bDDV
zyxI
V
( ) ( ) ( ) ( ) ,,,~,,,~,,,~,,,~ 010000**
000010*
*
VIVIVI
VI
;
( ) ( ) ( ) ( )+
++=
2110
2
2110
2
2110
2
0
0110 ,,,~1,,,~1,,,~1,,,~
I
bI
bI
bDDI
zyxV
I
( ) ( ) ( ) ( )
+
+
+
,,,~
,,,
1,,,~,,,
1 0100100
0 ITgb
ITg
bDD
I
y
I
xV
I
( ) ( ) ( ) ( )
+
*
*
000100*
*
010,,,
~
,,,
~,,,
~
,,,
1IVVI
IVITg
b Iz
( ) ( ) ,,,~,,,~ 100000 VI ; ( ) ( ) ( ) ( )
+
++=
2110
2
2110
2
2110
2
0
0110 ,,,~1,,,~1,,,~1,,,~
V
bV
bV
bDDV
zyxI
V
( ) ( ) ( ) ( )
+
+
+
,,,~
,,,
1,,,~,,,
1 0100100
0 VTgb
VTg
bDD
V
y
V
xI
V
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( ) ( ) ( ) ( )
+
*
*
000100*
*
010,,,
~
,,,
~,,,
~
,,,
1IIVI
IIVTg
b Vz
( ) ( ) ,,,~,,,~ 100000 VI ; ( ) ( ) ( ) ( )
++=
200
2
200
2
200
2
0
000 ,,,~1,,,~1,,,~1,,,~
k
z
k
y
k
xV
Ik Ib
Ib
IbD
DI
( ) ( ) ( ) ( )
++=
200
2
200
2
200
2
0
000 ,,,~1,,,~1,,,~1,,,~
k
z
k
y
k
xI
Vk Ib
Ib
IbD
DV;
( ) ( ) ( ) ( )+
++=
2101
2
2101
2
2101
2
0
0101 ,,,~1,,,~1,,,~1,,,~
I
bI
bI
bDDI
zyxV
I
( ) ( ) ( ) ( )
+
+
+
,,,~
,,,
1,,,~,,,
1 0010010
0 ITgb
ITg
bDD
I
y
I
xV
I
( ) ( )
+
,,,~
,,,
1 001ITgb I
z
;
( ) ( ) ( ) ( )+
++=
2101
2
2101
2
2101
2
0
0101 ,,,~1,,,~1,,,~1,~
V
bV
bV
bDDV
zyxI
V
( ) ( ) ( ) ( )
+
+
+
,,,~
,,,
1,,,~,,,
1 0010010
0 ITgb
ITg
bDD
V
y
V
xI
V
( ) ( )
+
,,,~
,,,
1 001ITgb V
z
;
( ) ( ) ( ) ( )+
++=
2
0112
2
0112
2
0112
0
0011 ,,,~1,,,~1,,,~1,,,~
I
bI
bI
bDDI
zyxV
I
( ) ( ) ( ) ( ) ( )[ ,,,~,,,~,,,,,,~,,,~ 000000000001** VIThVIIV ( ) ( )] ,,,~,,,~ 001000 VI
( ) ( ) ( ) ( )
++=
2011
2
2011
2
2011
2
0
0011 ,,,~1,,,~1,,,~1,,,~
V
bV
bV
bDDV
zyxI
V
( ) ( ) ( ) ( ) ( )[ ,,,~,,,~,,,,,,~,,,~ 000000000001** VIThVIIV ( ) ( )] ,,,~,,,~ 001000 VI .
( )0
,,,~
0
=
= ijk ; ( ) 0,,,~
1
=
= ijk ; ( ) 0,,,~
0
=
= ijk ; ( ) 0,,,~
1
=
= ijk ;
( )0
,,,~
0
=
= ijk ; ( ) 0,,,
~
1
=
= ijk
, i 1, j 1, k 1; ( ) ( )*
,,
0,,,~000 f= ;
( ) 00,,,~ = ijk , i 1, j 1, k 1. Solutions of equations for the functions ( ) ,,,~ijk (i0, j0, k0) could be written as
-
Advanced Nanoscience and Technology: An International Journal (ANTJ), Vol. 1, No. 1, June 2015
13
( ) ( ) ( ) ( ) ( )+= =1
000
21,,,
~
nnn
ecccFLL
,
where ( ) ( ) ( ) ( ) = 10
1
0
1
0*
,,
1udvdwdwvufwcvcucF
nn , cn() = cos (pi n ), ( ) ( )IVnI DDne 0022exp pi = , ( ) ( )VInV DDne 0022exp pi = ;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = =1 0
1
0
1
0
1
02
000 ,,,
*
2,,,
~
nVnnnnnnn
zyxx
i TwvugvcuseecccnLLLbD
pi
( ) ( ) ( ) ( ) ( ) ( ) ( )
=
1 02
0100
*
2,,,~n
nnnnn
zyxy
in
eecccnLLLb
Ddudvdwd
u
wvuwc
pi
( ) ( ) ( ) ( ) ( ) ( )
=
12
01
0
1
0
1
0
100
*
2,,,~,,,
nn
zyxz
iVnnn cnLLLb
Ddudvdwd
v
wvuTwvugwcvsuc
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
0
1
0
1
0
1
0
100,,,
,,,~
dudvdwdTwvugw
wvuwsvcuceecc V
innnnnnn
, i 1;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = =1 0
1
0
1
0
1
0*
*
0010
*
2,,,
~
nnnnInInnnn
zyx
I wcvcuceecccIV
LLLIDI
( ) ( ) dudvdwdwvuVwvuI ,,,~,,,~ 000000 ; ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =
=1 0
1
0
1
0
1
0*
*
0010
*
2,,,
~
nnnnVnVnnnn
zyx
I wcvcuceecccVI
LLLVD
V
( ) ( ) dudvdwdwvuVwvuI ,,,~,,,~ 000000 ; ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =
=1 0
1
0
1
0
1
0*
*
0020
*
2,,,
~
nnnnInInnnn
zyx
I wcvcuceecccIV
LLLID
I
( ) ( ) ( ) ( ) ( ) ( ) =1*
*
0000010
*
2,,,
~
,,,
~
nInnnn
zyx
I ecccIV
LLLIDdudvdwdwvuVwvuI
( ) ( ) ( ) ( ) ( ) ( ) 0
1
0
1
0
1
0010000 ,,,
~
,,,
~ dudvdwdwvuVwvuIwcvcucennnIn ;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = =1 0
1
0
1
0
1
0*
*
0020
*
2,,,
~
nnnnVnVnnnn
zyx
I wcvcuceecccVI
LLLVDV
( ) ( ) ( ) ( ) ( ) ( ) =1*
*
0000010
*
2,,,
~
,,,
~
nVnnnn
zyx
I ecccVI
LLLVDdudvdwdwvuVwvuI
( ) ( ) ( ) ( ) ( ) ( ) 0
1
0
1
0
1
0010000 ,,,
~
,,,
~ dudvdwdwvuVwvuIwcvcucennnVn ;
( ) ( ) ( ) ( ) 0,,,~,,,~,,,~,,,~ 002001002001 ==== VVII ; ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =
=1 0
1
0
1
0
1
0*
*
20
110*
2,,,
~
nnnnInInnnn
zyxx
I wcvcuseecccnIV
LLLIbDI
pi
( ) ( ) ( ) ( ) ( ) ( ) + =1*
*
20010
*
2,,,~,,,
nInnnn
zyxy
II ecccI
VLLLIb
Ddudvdwdu
wvuITwvug pi
( ) ( ) ( ) ( ) ( ) ( ) + 200
1
0
1
0
1
0
010
*
2,,,~,,,
zyxz
IInnnIn LLLIb
Ddudvdwdv
wvuITwvugwcvsucen pi
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Advanced Nanoscience and Technology: An International Journal (ANTJ), Vol. 1, No. 1, June 2015
14
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =1 0
1
0
1
0
1
0
010*
*,,,
~
,,,
nInnnInnn dudvdwd
w
wvuITwvugwsvcuceccnIV
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =1 0
1
0
1
0
1
0100*
*
0,,,
~
*
2n
nnInInnnn
zyx
IInn wvuIvcuceecccI
VLLLI
Dec
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =1 0
1
0
1
0
1
0*
*
0000
*
2,,,
~
nnnnInInn
In
wcvcuceecIV
LIDdudvdwdwvuVwc
( ) ( ) ( ) ( )nn
ccdudvdwdwvuVwvuI ,,,~,,,~ 100000 ;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = =1 0
1
0
1
0
1
0*
*
20
110*
2,,,
~
nnnnVnVnnnn
zyxx
V wcvcuseecccnVI
LLLIbD
V
pi
( ) ( ) ( ) ( ) ( ) ( ) + =1*
*
2
0010
*
2,,,~,,,
nVnnnn
zyxy
V
V ecccnVI
LLLVbD
dudvdwdu
wvuVTwvug
pi
( ) ( ) ( ) ( ) ( ) ( ) + **
20
0
1
0
1
0
1
0
010
*
2,,,~,,,
VI
LLLVbDdudvdwd
v
wvuVTwvugwcvsuce
zyxz
VVnnnVn
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =1 0
1
0
1
0
1
0
010 ,,,~
,,,
nVnnnVnnnn dudvdwd
w
wvuVTwvugwsvcucecccn
( ) ( ) ( ) ( ) ( ) ( ) ( ) =1 0
1
0000100
0,,,
~
,,,
~
*
2n
nVnVnn
zyx
VVn dudvdwdwvuVwvuIvceecLLLV
De
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =1 0
1
0
1
0
1
0000*
*
0*
*
,,,
~
*
2n
nnnVnnnnV
nnwvuIwcvcuceccc
VI
LVD
VI
cc
( ) ( ) VnedudvdwdwvuV ,,,~100 ; ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =
=1 0
1
0
1
0
1
02101
,,,
*
2,,,
~
nInnInInnnn
zyxx
TwvugvcuseecccnLLLIb
I
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + =1 0
1
02
001
*
2,,,~
nnInInnnn
zyxy
nuceeccc
LLLIbdudvdwd
u
wvuIwc
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )+ =1
1
0
1
0
001
*
2,,,~,,,
nInnnn
z
Inn ecccnIbdudvdwd
v
wvuITwvugwcvsn pi
( ) ( ) ( ) ( ) ( ) ( )2
0
1
0
1
0
1
0
001 1,,,~
,,,
zyx
InnnIn LLLdudvdwd
w
wvuITwvugwsvcuce
;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = =1 0
1
0
1
0
1
02101
,,,
*
2,,,
~
nVnnVnVnnnn
zyxx
TwvugvcuseecccLLLVb
V
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) + =1 0
2001 2,,,
~
nVnVnnnn
yzyx
neecccn
bLLLdudvdwd
u
wvuVwcn
pi
( ) ( ) ( ) ( ) ( ) ( ) + =12
1
0
1
0
1
0
001
*
2,,,~
*
,,,
nn
zyxz
Vnnn
cnLLLVb
dudvdwdv
wvuVV
Twvugwcvsuc pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
0
1
0
1
0
1
0
001 ,,,~
,,, dudvdwdw
wvuVTwvugwsvcuceecc VnnnVnVnnn ;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = =1 0
1
0
1
0
1
0001011 ,,,
~
*
2,,,
~
nnnInInnnn
zyx
wvuIvcuceecccLLLI
I
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Advanced Nanoscience and Technology: An International Journal (ANTJ), Vol. 1, No. 1, June 2015
15
( ) ( ) ( ) ( ) ( ) ( ) ( ) =1 0
*
*
*
*
000*
2,,,
~
nInInnnn
zyx
neeccc
IV
LLLIIVdudvdwdwvuVwc
( ) ( ) ( ) ( ) ( ) ( ) ( ) =1*
*1
0
1
0
1
0001000
*
2,,,
~
,,,
~
nnn
zyx
nnncc
IV
ILLLdudvdwdwvuVwvuIwcvcuc
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0
1
0
1
0
1
0001000 ,,,
~
,,,
~
,,, dudvdwdwvuVwvuIwcTwvuhvcuceecnnnInInn ;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = =1 0
1
0
1
0
1
0*
*
011*
2,,,
~
nnnnVnVnnnn
zyx
wcvcuceecccVI
LLLVV
( ) ( ) ( ) ( ) ( ) ( ) ( ) =1 0
000001*
2,,,
~
,,,
~
nVnVnnnn
zyx
eecccLLLV
dudvdwdwvuVwvuI
( ) ( ) ( ) ( ) ( ) ( ) =1
1
0
1
0
1
0001000*
*
*
2,,,
~
,,,
~
nn
zyx
nnnc
LLLVdudvdwdwvuVwvuIwcvcuc
VI
( ) ( ) ( ) ( ) ( ) ( ) ( ) 0
1
0
1
0
1
0001000*
*
,,,
~
,,,
~
,,, dudvdwdwvuVwvuIwcTwvuhvcuceVI
nnnVn
( ) ( ) ( ) Vnnn ecc . Equations for the functions i(x,y,z,t) are
( ) ( ) ( ) ( )+
+
+
=
2
02
20
2
20
2
00 ,,,,,,,,,,,,
z
tzyxy
tzyxx
tzyxDt
tzyx IIII
I
( ) ( ) ( ) ( )tzyxITzyxktzyxITzyxk III ,,,,,,,,,,,, 2, + ; ( ) ( ) ( ) ( )
+
+
+
=
2
02
20
2
20
2
00 ,,,,,,,,,,,,
z
tzyxy
tzyxx
tzyxDt
tzyx VVVV
V
( ) ( ) ( ) ( )tzyxVTzyxktzyxVTzyxk VVV ,,,,,,,,,,,, 2, + ; ( ) ( ) ( ) ( )
+
+
+
=
2
2
02
2
02
2
0
,,,,,,,,,,,,
z
tzyxD
ytzyx
Dx
tzyxD
t
tzyx iII
iII
iII
iI
( ) ( ) ( ) ( ) +
+
+
ytzyx
Tzyxgy
Dx
tzyxTzyxg
xD iIII
iIII
,,,
,,,
,,,
,,,1
01
0
( ) ( )
+
z
tzyxTzyxg
zD iIII
,,,
,,,1
0 , i1;
( ) ( ) ( ) ( )+
+
+
=
2
2
02
2
02
2
0
,,,,,,,,,,,,
z
tzyxD
ytzyx
Dx
tzyxD
t
tzyx iVV
iVV
iVV
iV
( ) ( ) ( ) ( ) +
+
+
ytzyx
Tzyxgy
Dx
tzyxTzyxg
xD iVVV
iV
VV
,,,
,,,
,,,
,,,1
01
0
( ) ( )
+
z
tzyxTzyxg
zD iVVV
,,,
,,,1
0 , i1;
( )0
,,,
0
=
=x
i
x
tzyx,
( )0
,,,
=
= xLx
i
x
tzyx,
( )0
,,,
0
=
=y
i
ytzyx
,
( )0
,,,
=
= yLy
i
ytzyx
,
( )0
,,,
0
=
=z
i
z
tzyx,
( )0
,,,
=
= zLz
i
z
tzyx, i0; I0(x,y,z,0)=fI (x,y,z), Ii(x,y,z,0)=0,
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Advanced Nanoscience and Technology: An International Journal (ANTJ), Vol. 1, No. 1, June 2015
16
V0(x,y,z,0)=fV (x,y,z), Vi(x,y,z,0)=0, i1. Solutions of the equations could be written as
( ) ( ) ( ) ( ) ( )+= =
1
0
21,,,
nnn
zyxzyx
tezcycxcFLLLLLL
tzyx
,
where ( )
++= 2220
22 111expzyx
n LLLtDnte
pi , ( ) ( ) ( ) ( ) = x
L yL zL
nnnnxdydzdzyxfzcycxcF
0 0 0,,
,
cn() = cos (pi n /L); ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =
=
1 0 0 0 0
2.,,
2,,,
n
t xL yL zL
nnnnnnnn
zyx
i TwvugwcvcusetezcycxcnLLLtzyx
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =
1 0 0 02
1 2,,,n
t xL yL
nnnnnnn
zyx
iIvsucetezcycxcn
LLLdudvdwd
u
wvu
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) =
120
1 2,,,.,,
nnnnn
zyx
zL iI
ntezcycxcn
LLLdudvdwd
v
wvuTwvugwc
pi
( ) ( ) ( ) ( ) ( ) ( ) t xL yL zL iI
nnnndudvdwd
w
wvuTwvugwsvcuce
0 0 0 0
1 ,,,
.,,
, i1,
where sn() = sin (pi n/L).
System of equations for functions Cijk(x,y,z,t) (i0, j0, k0) could be written as
( ) ( ) ( ) ( )
+
+
=
200
2
200
2
200
2
000 ,,,,,,,,,,,,
z
tzyxCy
tzyxCx
tzyxCDt
tzyxCL ;
( ) ( ) ( ) ( )+
+
+
=
20
2
020
2
020
2
00 ,,,,,,,,,,,,
z
tzyxCD
ytzyxC
Dx
tzyxCD
t
tzyxC iL
iL
iL
i
( ) ( ) ( ) ( ) +
+
+ y
tzyxCTzyxg
yD
x
tzyxCTzyxg
xD iLL
iLL
,,,
,,,
,,,
,,,10
010
0
( ) ( )
+ z
tzyxCTzyxg
zD iLL
,,,
,,,10
0 , i 1;
( ) ( ) ( ) ( )+
+
+
=
201
2
0201
2
0201
2
001 ,,,,,,,,,,,,
z
tzyxCD
ytzyxC
Dx
tzyxCD
t
tzyxCLLL
( )( )
( ) ( )( )
( )+
+
+y
tzyxCTzyxPtzyxC
yD
x
tzyxCTzyxPtzyxC
xD LL
,,,
,,,
,,,,,,
,,,
,,, 00000
00000
( )( )
( )
+z
tzyxCTzyxPtzyxC
zD L
,,,
,,,
,,, 00000
;
( ) ( ) ( ) ( )+
+
+
=
LLLL Dz
tzyxCD
ytzyxC
Dx
tzyxCD
t
tzyxC02
022
0202
2
0202
2
002 ,,,,,,,,,,,,
( ) ( )( )( ) ( ) ( )( )
( )
+
+
ytzyxC
TzyxPtzyxC
tzyxCyx
tzyxCTzyxPtzyxC
tzyxCx
,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,00
100
0100
100
01
-
Advanced Nanoscience and Technology: An International Journal (ANTJ), Vol. 1, No. 1, June 2015
17
( ) ( )( )( ) ( )
( )( )
+
+
+
x
tzyxCTzyxPtzyxC
xD
z
tzyxCTzyxPtzyxC
tzyxCz
L
,,,
,,,
,,,,,,
,,,
,,,
,,,0100
000
100
01
( )( )
( ) ( )( )
( )
+
+z
tzyxCTzyxPtzyxC
zytzyxC
TzyxPtzyxC
y,,,
,,,
,,,,,,
,,,
,,, 01000100
;
( ) ( ) ( ) ( )+
+
+
=
LLLL Dz
tzyxCD
ytzyxC
Dx
tzyxCD
t
tzyxC02
112
0211
2
0211
2
011 ,,,,,,,,,,,,
( ) ( )( )( ) ( ) ( )( )
( )+
+
ytzyxC
TzyxPtzyxC
tzyxCyx
tzyxCTzyxPtzyxC
tzyxCx
,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,00
100
1000
100
10
( ) ( )( )( ) ( )
( )( )
+
+
+
x
tzyxCtzyxPtzyxC
xD
z
tzyxCTzyxPtzyxC
tzyxCz
L
,,,
,,,
,,,,,,
,,,
,,,
,,,1000
000
100
10
( )( )
( ) ( )( )
( ) ( )
+
+
+ Tzyxgxz
tzyxCtzyxPtzyxC
zytzyxC
tzyxPtzyxC
y L,,,
,,,
,,,
,,,,,,
,,,
,,, 10001000
( ) ( ) ( ) ( ) ( ) LLL Dz
tzyxCTzyxg
zytzyxC
Tzyxgyx
tzyxC0
010101 ,,,,,,
,,,
,,,
,,,
+
+
.
Solutions of equations for functions Cij(x,y,z,t) (i0, j0) with account appropriate conditions takes the form
( ) ( ) ( ) ( ) ( )+= =1
00
21,,,
nnCnC
zyxzyx
tezcycxcFLLLLLL
tzyxC ,
where ( )
++=
222022 111exp
zyx
CnC LLLtDnte pi , ( ) ( ) ( ) ( ) = xL y
L zL
CnnnCn xdydzdzyxfzcycxcF0 0 0
,, ;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = =1 0 0 0 0
20,,,
2,,,
n
t xL yL zL
LnnnnCnCnnnnC
zyx
i TwvugwcvcusetezcycxcFLLLtzyxC pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
=
1 0 0 02
10 2,,,n
t xL yL
nnnCnCnnnnC
zyx
i vsucetezcycxcFnLLL
ndudvdwdu
wvuC
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
=
1 02
0
10 2,,,,,,
n
t
nCnCnnn
zyx
zLi
Ln etezcycxcLLLdudvdwd
v
wvuCTwvugwc pi
( ) ( ) ( ) ( ) ( )
xL yL zL
iLnnnnC dudvdwd
w
wvuCTwvugwsvcucFn
0 0 0
10 ,,,,,,
, i 1;
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) =
=1 0 0 0 0
00201
,,,
,,,2,,,
n
t xL yL zL
nnnCnCnnnnC
zyx TwvuPwvuC
vcusetezcycxcFnLLL
tzyxC
pi
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
=1 0 02
00 2,,,n
t xL
nnCnCnnnnC
zyx
nucetezcycxcFn
LLLdudvdwd
u
wvuCwc
pi
( ) ( ) ( )( )( ) ( ) ( ) ( )
=120 0
0000 2,,,,,,
,,,
nnnnnC
zyx
yL zL
nnzcycxcFn
LLLdudvdwd
v
wvuCTwvuP
wvuCwcvs
pi
( ) ( ) ( ) ( ) ( ) ( )( )( )
t xL yL zL
nnnnCnC dudvdwdw
wvuCTwvuP
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Advanced Nanoscience and Technology: An International Journal (ANTJ), Vol. 1, No. 1, June 2015
18
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Advanced Nanoscience and Technology: An International Journal (ANTJ), Vol. 1, No. 1, June 2015
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pnp delta-doped heterojunction bipolar transistor, Semiconductors. Vol. 43 (7). P. 971-974 (2009). [6] T. Y. Peng, S. Y. Chen, L. C. Hsieh, C. K. Lo, Y. W. Huang, W. C. Chien, Y. D. Yao. Impedance
behavior of spin-valve transistor, J. Appl. Phys. Vol. 99 (8). P. 08H710-08H712 (2006). [7] S. Maximenko, S. Soloviev, D. Cherednichenko, T. Sudarshan. Observation of dislocations in
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[8] I.E. Tyschenko, V.A. Volodin. Quantum confinement effect in silicon-on-insulator films implanted with high dose hydrogen ions, Semiconductors. Vol.46 (10). P.1309-1313 (2012).
[9] K.K. Ong, K.L. Pey, P.S. Lee, A.T.S. Wee, X.C. Wang, Y.F. Chong. Dopant distribution in the recrystallization transient at the maximum melt depth induced by laser annealing, Appl. Phys. Lett. Vol. 89 (17). P. 172111 (2006).
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[11] V.V. Kozlivsky. Modification of semiconductors by proton beams, Sant-Peterburg, Nauka, 2003, in Russian.
[12] E.L. Pankratov. Application of porous layers and optimization of annealing of dopant and radiation defects to increase sharpness of p-n-junctions in a bipolar heterotransistors, J. Optoel. Nanoel. Vol. 6 (2). P. 188 (2011).
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[14] E.L. Pankratov, E.A. Bulaeva. Increasing of sharpness of diffusion-junction heterorectifier by using radiation pro-cessing, Int. J. Nanoscience. Vol. 11 (5). P. 1250028 (2012).
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Author
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 Radiophysics with specialization in Statistical Radiophysics, from 2001 to 2004 it was PhD course in Radiophysics. From 2004 to 2008 E.L. Pankratov was a leading technologist in Institute for Physics of Microstructures. From 2008 to 2012 E.L. Pankratov was a senior lecture/Associate Professor of Nizhny Novgorod State University of Architecture and Civil Engineering. Now E.L. Pankratov is in his Full Doctor course in Radiophysical Department of Nizhny Novgorod State University. He has 96 published papers in area of his researches.
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Advanced Nanoscience and Technology: An International Journal (ANTJ), Vol. 1, No. 1, June 2015
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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 Architecture 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 29 published papers in area of her researches.