On Approach to Optimize Manufacturing of P-N-heterojunctions in Tframework of a Multilevel Inverter with R-Load to Increase their Integration Rate. On Influence Mismatch-Induced Stress

International Journal of Microelectronics Engineering (IJME), Vol.11, No.1, January 2025
DOI: 10.5121/ijme.2024.11101 1
ON APPROACH TO OPTIMIZE MANUFACTURING OF
P-N-HETEROJUNCTIONS IN TFRAMEWORK OF A
MULTILEVEL INVERTER WITH R-LOAD TO
INCREASE THEIR INTEGRATION RATE.
ON INFLUENCE MISMATCH-INDUCED STRESS
Evgeny L. Pankratov
Department of Applied Mechanics, Physics and Higher Mathematics, Nizhny Novgorod
State Agrotechnical University, 97 Gagarin avenue, Nizhny Novgorod, 603950, Russia
ABSTRACT
In this paper we introduce an approach to increase density of p-n-heterojunctions in the framework of a
multilevel inverter with R-load. In the framework of 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 frame-
work 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.
KEYWORDS
P-n-heterojunctions; multilevel inverter with R-load; optimization of manufacturing; analytical approach
for prognosis.
1. INTRODUCTION
In the present time several actual problems of the solid state electronics (such as increasing of
performance, reliability and density of elements of integrated circuits: diodes, field-effect and
bipolar transistors) are intensively solving [1-6]. To increase the performance of these devices it
is attracted an interest determination of materials with higher values of charge carriers mobility
[7-10]. One way to decrease dimensions of elements of integrated circuits is manufacturing them
in thin film heterostructures [3-5,11]. In this case it is possible to use inhomogeneity of hetero-
structure and necessary optimization of doping of electronic materials [12,13] and development
of epitaxial technology to improve these materials (including analysis of mismatch induced
stress) [14-16]. An alternative approaches to increase dimensions of integrated circuits are using
of laser and microwave types of annealing [17-19].
Framework the paper we introduce an approach to manufacture p-n- heterojunctions. The ap-
proach gives a possibility to decrease their dimensions with increasing their density framework a
multilevel inverter with R-load. We also consider possibility to decrease mismatch-induced stress
to decrease quantity of defects, generated due to the stress. In this paper we consider a hetero-
structure, which consist of a substrate and an epitaxial layer (see Fig. 1). We also consider a buff-
er layer between the substrate and the epitaxial layer. The epitaxial layer includes into itself sev-
eral sections, which were manufactured by using another materials. These sections have been

2
doped by diffusion or ion implantation to manufacture the required types of conductivity (p or n).
These areas became sources, drains and gates (see Fig. 1). After this doping it is required anneal-
ing of dopant and/or radiation defects. Main aim of the present paper is analysis of redistribution
of dopant and radiation defects to determine conditions, which correspond to decreasing of ele-
ments of the considered filter and at the same time to increase their density. At the same time we
consider a possibility to decrease mismatch-induced stress.
Fig. 1a. Structure of the considered inverter [15]
2. METHOD OF SOLUTION
To solve our aim we determine and analyzed spatio-temporal distribution of concentration of do-
pant in the considered heterostructure. We determine the distribution by solving the second Fick's
law in the following form [1,20-24]
        



































z
t
z
y
x
C
D
z
y
t
z
y
x
C
D
y
x
t
z
y
x
C
D
x
t
t
z
y
x
C ,
,
,
,
,
,
,
,
,
,
,
,
       




























z
z L
S
S
L
S
S W
d
t
W
y
x
C
t
z
y
x
T
k
D
y
W
d
t
W
y
x
C
t
z
y
x
T
k
D
x 0
1
0
1 ,
,
,
,
,
,
,
,
,
,
,
, 
 (1)

3
Fig. 1b. Heterostructure with a substrate, epitaxial layers and buffer layer (view from side)
with boundary and initial conditions
  0
,
,
,
0




x
x
t
z
y
x
C
,
  0
,
,
,



 x
L
x
x
t
z
y
x
C
,   0
,
,
,
0




y
y
t
z
y
x
C
, C (x,y,z,0)=fC (x,y,z),
  0
,
,
,



 y
L
x
y
t
z
y
x
C
,
  0
,
,
,
0




z
z
t
z
y
x
C
,
  0
,
,
,



 z
L
x
z
t
z
y
x
C
.
Here C(x,y,z,t) is the spatio-temporal distribution of concentration of dopant;  is the atomic vol-
ume of dopant; s is the symbol of surficial gradient;  

z
L
z
d
t
z
y
x
C
0
,
,
, is the surficial concen-
tration of dopant on interface between layers of heterostructure (in this situation we assume, that
Z-axis is perpendicular to interface between layers of heterostructure); 1(x,y,z,t) is the chemical
potential due to the presence of mismatch-induced stress; D and DS are the coefficients of volu-
metric and surficial diffusions. Values of dopant diffusions coefficients depends on properties of
materials of heterostructure, speed of heating and cooling of materials during annealing and spa-
tio-temporal distribution of concentration of dopant. Dependences of dopant diffusions coeffi-
cients on parameters could be approximated by the following relations [22-24]
   
 
   
  





















2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
V
t
z
y
x
V
V
t
z
y
x
V
T
z
y
x
P
t
z
y
x
C
T
z
y
x
D
D L
C 




,
   
 
   
  





















2
*
2
2
*
1
,
,
,
,
,
,
1
,
,
,
,
,
,
1
,
,
,
V
t
z
y
x
V
V
t
z
y
x
V
T
z
y
x
P
t
z
y
x
C
T
z
y
x
D
D S
L
S
S 




. (2)
Here DL (x,y,z,T) and DLS (x,y,z,T) are the spatial (due to accounting all layers of heterostruicture)
and temperature (due to Arrhenius law) dependences of dopant diffusion coefficients; T is the
temperature of annealing; P (x,y,z,T) is the limit of solubility of dopant; parameter  depends on
properties of materials and could be integer in the following interval  [1,3] [22]; V (x,y,z,t) is
the spatio-temporal distribution of concentration of radiation vacancies; V*
is the equilibrium dis-
tribution of vacancies. Concentrational dependence of dopant diffusion coefficient has been de-
scribed in details in [22]. Spatio-temporal distributions of concentration of point radiation defects
have been determined by solving the following system of equations [20,23,24]

4
          














y
t
z
y
x
I
T
z
y
x
D
y
x
t
z
y
x
I
T
z
y
x
D
x
t
t
z
y
x
I
I
I









 ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
         








 T
z
y
x
k
t
z
y
x
I
T
z
y
x
k
z
t
z
y
x
I
T
z
y
x
D
z
V
I
I
I
I ,
,
,
,
,
,
,
,
,
,
,
,
,
,
, ,
2
,




        













z
L
S
IS
W
d
t
W
y
x
I
t
z
y
x
T
k
D
x
t
z
y
x
V
t
z
y
x
I
0
,
,
,
,
,
,
,
,
,
,
,
, 
    











z
L
S
IS
W
d
t
W
y
x
I
t
z
y
x
T
k
D
y 0
,
,
,
,
,
,
 (3)
          














y
t
z
y
x
V
T
z
y
x
D
y
x
t
z
y
x
V
T
z
y
x
D
x
t
t
z
y
x
V
V
V









 ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
         








 T
z
y
x
k
t
z
y
x
V
T
z
y
x
k
z
t
z
y
x
V
T
z
y
x
D
z
V
I
V
V
V ,
,
,
,
,
,
,
,
,
,
,
,
,
,
, ,
2
,




        













z
L
S
VS
W
d
t
W
y
x
V
t
z
y
x
T
k
D
x
t
z
y
x
V
t
z
y
x
I
0
,
,
,
,
,
,
,
,
,
,
,
, 
    











z
L
S
VS
W
d
t
W
y
x
V
t
z
y
x
T
k
D
y 0
,
,
,
,
,
,

  0
,
,
,
0


x
x
t
z
y
x
I


,
  0
,
,
,

 x
L
x
x
t
z
y
x
I


,
  0
,
,
,
0


y
y
t
z
y
x
I


,
  0
,
,
,

 y
L
y
y
t
z
y
x
I


,
  0
,
,
,
0


z
z
t
z
y
x
I


,
  0
,
,
,

 z
L
z
z
t
z
y
x
I


,
  0
,
,
,
0


x
x
t
z
y
x
V


,
  0
,
,
,

 x
L
x
x
t
z
y
x
V


,
  0
,
,
,
0


y
y
t
z
y
x
V


,
  0
,
,
,

 y
L
y
y
t
z
y
x
V


,
  0
,
,
,
0


z
z
t
z
y
x
V


,
  0
,
,
,

 z
L
z
z
t
z
y
x
V


,
I (x,y,z,0)=fI (x,y,z), V (x,y,z,0)=fV (x,y,z). (4)
Here I (x,y,z,t) is the spatio-temporal distribution of concentration of radiation interstitials; I*
is
the equilibrium distribution of interstitials; DI(x,y,z,T), DV(x,y,z,T), DIS(x,y, z,T), DVS(x,y,z,T) are
the coefficients of volumetric and surficial diffusions of interstitials and vacancies, respectively;
terms V2
(x,y,z,t) and I2
(x,y,z,t) correspond to generation of divacancies and diinterstitials, respec-
tively (see, for example, [24] and appropriate references in this book); 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 of
their complexes.
Spatio-temporal distributions of divacancies V (x,y,z,t) and diinterstitials I (x,y,z, t) could be
determined by solving the following system of equations [20,23,24]
          





 






 




y
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x I
I
I
I
I









 ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,

5
        

















 



z
I
I
L
I
S
S
I
W
d
t
W
y
x
t
z
y
x
T
k
D
x
z
t
z
y
x
T
z
y
x
D
z 0
1 ,
,
,
,
,
,
,
,
,
,
,
, 




       














t
z
y
x
I
T
z
y
x
k
W
d
t
W
y
x
t
z
y
x
T
k
D
y
I
I
L
I
S
S
z
I
,
,
,
,
,
,
,
,
,
,
,
, 2
,
0
1

   
t
z
y
x
I
T
z
y
x
kI ,
,
,
,
,
,
 (5)
          





 






 




y
t
z
y
x
T
z
y
x
D
y
x
t
z
y
x
T
z
y
x
D
x
t
t
z
y
x V
V
V
V
V









 ,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
        

















 



z
V
V
L
V
S
S
V
W
d
t
W
y
x
t
z
y
x
T
k
D
x
z
t
z
y
x
T
z
y
x
D
z 0
1 ,
,
,
,
,
,
,
,
,
,
,
, 




       














t
z
y
x
V
T
z
y
x
k
W
d
t
W
y
x
t
z
y
x
T
k
D
y
V
V
L
V
S
S
z
V
,
,
,
,
,
,
,
,
,
,
,
, 2
,
0
1

   
t
z
y
x
V
T
z
y
x
kV ,
,
,
,
,
,

  0
,
,
,
0



x
I
x
t
z
y
x


,
  0
,
,
,

 x
L
x
x
t
z
y
x
I


,
  0
,
,
,
0


y
y
t
z
y
x
I


,
  0
,
,
,

 y
L
y
y
t
z
y
x
I


,
  0
,
,
,
0



z
I
z
t
z
y
x


,
  0
,
,
,

 z
L
z
z
t
z
y
x
I


,
  0
,
,
,
0



x
V
x
t
z
y
x


,
  0
,
,
,

 x
L
x
x
t
z
y
x
V


,
  0
,
,
,
0


y
y
t
z
y
x
V


,
  0
,
,
,

 y
L
y
y
t
z
y
x
V


,
  0
,
,
,
0


z
z
t
z
y
x
V


,
  0
,
,
,


 z
L
z
V
z
t
z
y
x


,
I (x,y,z,0)=fI (x,y,z), V (x,y,z,0)=fV (x,y,z). (6)
Here DI(x,y,z,T), DV(x,y,z,T), DIS (x,y,z,T) and DVS(x,y,z,T) are the coefficients of volumetric
and surficial diffusions of complexes of radiation defects; kI(x,y,z,T) and kV(x,y,z,T) are the pa-
rameters of decay of complexes of radiation defects.
Chemical potential 1 in Eq.(1) could be determine by the following relation [20]
1=E(z)ij [uij(x,y,z,t)+uji(x,y,z,t)]/2, (7)
where E(z) is the Young modulus, ij is the stress tensor;














i
j
j
i
ij
x
u
x
u
u
2
1
is the deformation
tensor; ui, uj are the components ux(x,y,z,t), uy(x,y,z,t) and uz(x,y,z,t) of the displacement vector
 
t
z
y
x
u ,
,
,

; xi, xj are the coordinate x, y, z. The Eq. (3) could be transform to the following
form
         

































i
j
j
i
i
j
j
i
x
t
z
y
x
u
x
t
z
y
x
u
x
t
z
y
x
u
x
t
z
y
x
u
t
z
y
x
,
,
,
,
,
,
2
1
,
,
,
,
,
,
,
,
,


6
 
 
       
   
z
E
T
t
z
y
x
T
z
z
K
x
t
z
y
x
u
z
z
ij
k
k
ij
ij
2
,
,
,
3
,
,
,
2
1
0
0
0



















 






 ,
where  is Poisson coefficient; 0 = (as-aEL)/aEL is the mismatch parameter; as, aEL are lattice dis-
tances of the substrate and the epitaxial layer; K is the modulus of uniform compression;  is the
coefficient of thermal expansion; Tr is the equilibrium temperature, which coincide (for our case)
with room temperature. Components of displacement vector could be obtained by solution of the
following equations [25]
         
 
       
         












































z
t
z
y
x
y
t
z
y
x
x
t
z
y
x
t
t
z
y
x
u
z
z
t
z
y
x
y
t
z
y
x
x
t
z
y
x
t
t
z
y
x
u
z
z
t
z
y
x
y
t
z
y
x
x
t
z
y
x
t
t
z
y
x
u
z
zz
zy
zx
z
yz
yy
yx
y
xz
xy
xx
x
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
2
2
2
2
2
2












where
 
 
 
       






















k
k
k
k
ij
i
j
j
i
ij
x
t
z
y
x
u
x
t
z
y
x
u
x
t
z
y
x
u
x
t
z
y
x
u
z
z
E ,
,
,
,
,
,
3
,
,
,
,
,
,
1
2



       
 
r
ij T
t
z
y
x
T
z
K
z
z
K 

 ,
,
,

 ,  (z) is the density of materials of heterostructure, ij Is
the Kronecker symbol. With account the relation for ij last system of equation could be written
as
       
 
 
     
 
 























z
z
E
z
K
x
t
z
y
x
u
z
z
E
z
K
t
t
z
y
x
u
z x
x



1
3
,
,
,
1
6
5
,
,
,
2
2
2
2
   
 
 
       
 
 





























z
z
E
z
K
z
t
z
y
x
u
y
t
z
y
x
u
z
z
E
y
x
t
z
y
x
u z
y
y

 1
3
,
,
,
,
,
,
1
2
,
,
,
2
2
2
2
2
       
x
t
z
y
x
T
z
z
K
z
x
t
z
y
x
uz







,
,
,
,
,
,
2

 
   
 
 
     





















y
t
z
y
x
T
y
x
t
z
y
x
u
x
t
z
y
x
u
z
z
E
t
t
z
y
x
u
z x
y
y ,
,
,
,
,
,
,
,
,
1
2
,
,
, 2
2
2
2
2


     
 
 
     





























 2
2
,
,
,
,
,
,
,
,
,
1
2 y
t
z
y
x
u
y
t
z
y
x
u
z
t
z
y
x
u
z
z
E
z
z
z
K
y
z
y

 (8)
 
 
 
     
 
 
 
 
 
y
x
t
z
y
x
u
z
K
z
y
t
z
y
x
u
z
z
E
z
K
z
K
z
z
E y
y

























,
,
,
,
,
,
1
6
1
12
5
2
2


     
 
 
     

















z
x
t
z
y
x
u
y
t
z
y
x
u
x
t
z
y
x
u
z
z
E
t
t
z
y
x
u
z x
z
z
z ,
,
,
,
,
,
,
,
,
1
2
,
,
, 2
2
2
2
2
2
2


 
        



































z
t
z
y
x
u
y
t
z
y
x
u
x
t
z
y
x
u
z
K
z
z
y
t
z
y
x
u x
y
x
y ,
,
,
,
,
,
,
,
,
,
,
,
2
 
 
        































z
t
z
y
x
u
y
t
z
y
x
u
x
t
z
y
x
u
z
t
z
y
x
u
z
z
E
z
z
y
x
z ,
,
,
,
,
,
,
,
,
,
,
,
6
1
6
1


7
     
z
t
z
y
x
T
z
z
K



,
,
,
 .
Conditions for the system of Eq. (8) could be written in the form
  0
,
,
,
0



x
t
z
y
u

;
  0
,
,
,



x
t
z
y
L
u x

;
  0
,
,
0
,



y
t
z
x
u

;
  0
,
,
,



y
t
z
L
x
u y

;
  0
,
0
,
,



z
t
y
x
u

;
  0
,
,
,



z
t
L
y
x
u z

;   0
0
,
,
, u
z
y
x
u


 ;   0
,
,
, u
z
y
x
u



 .
We determine spatio-temporal distributions of concentrations of dopant and radiati-on defects by
solving the Eqs.(1), (3), (5) (8) in the framework of the standard method of averaging of function
corrections [26,29,31,32]. In the framework of this paper we determine concentration of dopant,
concentrations of radiation defects and components of displacement vector by using the second-
order approximation framework method of averaging of function corrections. This approximation
is usually enough good approximation to make qualitative analysis and to obtain some quantita-
tive results. All obtained results have been checked by comparison with results of numerical sim-
ulations.
3. DISCUSSION
In this section we analyzed dynamics of redistributions of dopant and radiation defects during
annealing and under influence of mismatch-induced stress. Typical distributions of concentra-
tions of dopant in heterostructures are presented on Figs. 2 and 3 for diffusion and ion types of
doping, respectively. These distributions have been calculated for the case, when value of dopant
diffusion coefficient in the epitaxial layer is larger, than in the substrate. The figures show, that
inhomogeneity of heterostructure gives us possibility to increase compactness of transistors. At
the same time one can find increasing homogeneity of dopant distribution in doped part of epitax-
ial layer. In-creasing of compactness of transistors gives us possibility to increase their density.
Fig.2. Distributions of concentration of infused dopant in heterostructure from Fig. 1 in direction, which is
perpendicular to interface between epitaxial layer substrate.

8
Increasing of number of curve corresponds to increasing of difference between values of dopant
diffusion coefficient in layers of heterostructure under condition, when value of dopant diffusion
coefficient in epitaxial layer is larger, than value of dopant diffusion coefficient in substrate
x
0.0
0.5
1.0
1.5
2.0
C(x,

)
2
3
4
1
0 L/4 L/2 3L/4 L
Epitaxial layer Substrate
Fig.3. Distributions of concentration of implanted dopant in heterostructure from Fig. 1 in direction, which
is perpendicular to interface between epitaxial layer substrate.
Curves 1 and 3 corresponds to annealing time  = 0.0048(Lx
2
+Ly
2
+Lz
2
)/D0. Curves 2 and 4 corre-
sponds to annealing time  = 0.0057(Lx
2
+Ly
2
+Lz
2
)/D0. Curves 1 and 2 corresponds to homoge-
nous sample. Curves 3 and 4 corresponds to heterostructure under condition, when value of do-
pant diffusion coefficient in epitaxial layer is larger, than value of dopant diffusion coefficient in
substrate
C(x,

)
0 Lx
2
1
3
4
Fig. 4. Spatial distributions of dopant in heterostructure after dopant infusion.
Curve 1 is idealized distribution of dopant. Curves 2-4 are real distributions of dopant for differ-
ent values of annealing time. Increasing of number of curve corresponds to increasing of anneal-
ing time

9
x
C(x,

)
1
2
3
4
0 L
Fig. 5. Spatial distributions of dopant in heterostructure after ion implantation.
Curve 1 is idealized distribution of dopant. Curves 2-4 are real distributions of dopant for differ-
ent values of annealing time. Increasing of number of curve corresponds to increasing of anneal-
ing time
The second effect leads to decreasing local heating of materials during functioning of transistors
or decreasing of their dimensions for fixed maximal value of local overheat. However framework
this approach of manufacturing of bipolar transistor it is necessary to optimize annealing of do-
pant and/or radiation defects. Reason of this optimization is following. If annealing time is small,
the dopant did not achieve any interfaces between materials of heterostructure. In this situation
one cannot find any modifications of distribution of concentration of dopant. If annealing time is
large, distribution of concentration of dopant is too homogenous. We optimize annealing time
framework recently introduces approach [15,25-32]. In the framework of this criterion we ap-
proximate real distribution of concentration of dopant by step-wise function (see Figs. 4 and 5).
Farther we determine optimal values of annealing time by minimization of the following mean-
squared error
   
 
   


x y z
L L L
z
y
x
x
d
y
d
z
d
z
y
x
z
y
x
C
L
L
L
U
0 0 0
,
,
,
,
,
1
 , (15)
where  (x,y,z) is the approximation function. Dependences of optimal values of annealing time
on parameters are presented on Figs. 6 and 7 for diffusion and ion types of doping, respectively.
It should be noted, that it is necessary to anneal radiation defects after ion implantation. One
could find spreading of concentration of distribution of dopant during this annealing. In the ideal
case distribution of dopant achieves appropriate interfaces between materials of heterostructure
during annealing of radiation defects. If dopant did not achieves any interfaces during annealing
of radiation defects, it is practicably to additionally anneal the dopant. In this situation optimal
value of additional annealing time of implanted dopant is smaller, than annealing time of infused
dopant.

10
0.0 0.1 0.2 0.3 0.4 0.5
a/L, , , 
0.0
0.1
0.2
0.3
0.4
0.5

D
0
L
-2
3
2
4
1
Fig.6. Dependences of dimensionless optimal annealing time for doping by diffusion, which have been
obtained by minimization of mean-squared error, on several parameters.
Curve 1 is the dependence of dimensionless optimal annealing time on the relation a/L and  = 
= 0 for equal to each other values of dopant diffusion coefficient in all parts of heterostructure.
Curve 2 is the dependence of dimensionless optimal annealing time on value of parameter  for
a/L=1/2 and  =  = 0. Curve 3 is the dependence of dimensionless optimal annealing time on
value of parameter  for a/L=1/2 and  =  = 0. Curve 4 is the dependence of dimensionless opti-
mal annealing time on value of parameter  for a/L=1/2 and  =  = 0
0.0 0.1 0.2 0.3 0.4 0.5
a/L, , , 
0.00
0.04
0.08
0.12

D
0
L
-2
3
2
4
1
Fig.7. Dependences of dimensionless optimal annealing time for doping by ion implantation, which have
been obtained by minimization of mean-squared error, on several parameters.
Curve 1 is the dependence of dimensionless optimal annealing time on the relation a/L and  = 
= 0 for equal to each other values of dopant diffusion coefficient in all parts of heterostructure.
Curve 2 is the dependence of dimensionless optimal annealing time on value of parameter  for
a/L=1/2 and  =  = 0. Curve 3 is the dependence of dimensionless optimal annealing time on
value of parameter  for a/L=1/2 and  =  = 0. Curve 4 is the dependence of dimensionless opti-
mal annealing time on value of parameter  for a/L=1/2 and  =  = 0

11
Fig. 8. Normalized dependences of component uz of displacement vector on coordinate z for nonporous
(curve 1) and porous (curve 2) epitaxial layers
Fig. 9. Normalized distributions of charge carrier mobility in the considered heterostructure.
Curve 1 corresponds to the heterostructure, which has been considered in Fig. 1. Curve 2 corre-
spond to a homogenous material with averaged parameters of heterostructure from Fig. 1
Next we analyzed influence of relaxation of mechanical stress on distribution of dopant in doped
areas of heterostructure. Under following condition 0< 0 one can find compression of distribu-
tion of concentration of dopant near interface between materials of heterostructure. Contrary (at
0>0) one can find spreading of distribution of concentration of dopant in this area. This changing
of distribution of concentration of dopant could be at least partially compensated by using laser
annealing [29]. This type of annealing gives us possibility to accelerate diffusion of dopant and
another processes in annealed area due to inhomogenous distribution of temperature and Arrhe-
nius law. Accounting relaxation of mismatch-induced stress in heterostructure could leads to
changing of optimal values of annealing time. Mismatch-induced stress could be used to increase
density of elements of integrated circuits. On the other hand could leads to generation disloca-
tions of the discrepancy. Fig. 8 shows distributions of component of displacement vector, which
is perpendicular to interface between layers of heterostructure.

12
4. CONCLUSION
In this paper we model redistribution of infused and implanted dopants with account relaxation
mismatch-induced stress during manufacturing p-n-heterojunctions framework a multilevel in-
verter with R-load. We formulate recommendations for optimization of annealing to decrease
dimensions of transistors and to increase their density. We formulate recommendations to de-
crease mismatch-induced stress. Analytical approach to model diffusion and ion types of doping
with account concurrent changing of parameters in space and time has been introduced. At the
same time the approach gives us possibility to take into account nonlinearity of considered pro-
cesses.
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On Approach to Optimize Manufacturing of P-N-heterojunctions in Tframework of a Multilevel Inverter with R-Load to Increase their Integration Rate. On Influence Mismatch-Induced Stress

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