Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures
The criteria for formation of an inhomogeneous structure based on vitreous Ge₂S₃ with modifiers Al, Bi, Pb, and Te that are identified due to changes in the condensed medium (evaporation temperature, condensation velocity, increasing or decreasing the intensity of the fluctuations of the active fiel...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2018
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| Cite this: | Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures / N.V. Yurkovych, M.I. Mar'yan, V. Seben // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 365-373. — Бібліогр.: 24 назв. — англ. |
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| author | Yurkovych, N.V. Mar'yan, M.I. Seben, V. |
| author_facet | Yurkovych, N.V. Mar'yan, M.I. Seben, V. |
| citation_txt | Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures / N.V. Yurkovych, M.I. Mar'yan, V. Seben // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 365-373. — Бібліогр.: 24 назв. — англ. |
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| description | The criteria for formation of an inhomogeneous structure based on vitreous Ge₂S₃ with modifiers Al, Bi, Pb, and Te that are identified due to changes in the condensed medium (evaporation temperature, condensation velocity, increasing or decreasing the intensity of the fluctuations of the active field) have been determined. The article analyzes the obtained equations describing the formation of inhomogeneous amorphous structures and taking into account the dynamics of the concentration of the modifier owing to the source of the atomic flow of a chemical element, structural heterogeneity (availability of vacancies, micropores), and particle diffusion. Computer simulation of the source of the atomic flow of the modifier has been carried out, which makes it possible to form gradient structures with the predicted distribution of the chemical element according to the film thickness. Morphology of gradient structure surfaces and the mechanism of condensation of modifiers Al, Bi, Pb, Te with the amorphous matrix of Ge₂S₃ have been ascertained.
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ISSN 1560-8034, 1605-6582 (On-line), SPQEO, 2018. V. 21, N 4. P. 365-373.
© 2018, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
365
Semiconductor physics
Synergetics of the instability and randomness in formation of gradient
modified semiconductor structures
N.V. Yurkovych
1, *
, M.I. Mar’yan
1
, V. Seben
2
1
Uzhhorod National University, 54, Voloshina str., 88000 Uzhhorod, Ukraine
*
E-mail:yurkovich@ukr.net
2
University of Presov, 1, 17 Novembra str., 08116 Presov, Slovakia
Abstract. The criteria for formation of an inhomogeneous structure based on vitreous
Ge2S3 with modifiers Al, Bi, Pb, Te that are identified due to changes in the condensed
medium (evaporation temperature, condensation velocity, increasing or decreasing the
intensity of the fluctuations of the active field) have been determined. The article analyzes
the obtained equations describing formation of inhomogeneous amorphous structures and
taking into account the dynamics of the concentration of modifier owing to the source of
the atomic flow of a chemical element, structural heterogeneity (availability of vacancies,
micropores) and particle diffusion. Computer simulation of the source of the atomic flow of
the modifier has been carried out, which makes it possible to form gradient structures with
the predicted distribution of the chemical element according to the film thickness.
Morphology of gradient structure surfaces and the mechanism of condensation of modifiers
Al, Bi, Pb, Te with the amorphous matrix of Ge2S3 have been ascertained.
Keywords: computer modeling, heterogeneous modified structures, morphology of
gradient structures surfaces, non-crystalline state, self-organizing processes, synergetics.
doi: https://doi.org/10.15407/spqeo21.04.365
PACS 78.66.Jg, 68.35.bj, 89.75.Fb
Manuscript received 18.10.18; revised version received 20.11.18; accepted for publication
29.11.18; published online 03.12.18.
1. Introduction
The current state of development of materials science and
information technology sets the research task to
purposefully create crystalline and non-crystalline
materials with structural-sensitive properties [1, 2].
Amorphous chalcogenides (S, Se, Te) and their
multicomponent alloys are very interesting objects with
wide practical applications. Due to the transparency in
the near, medium and far infrared regions, their
significant non-linearity, chalcogenide semiconductor
materials are used as active and passive elements in
optics and sensor devices [3, 4], telecommunications [1]
as a thermal image and generation of nonlinear light [3-
5]. Intensive and reverse crystallization observed in some
thin-film systems of chalcogenides is the basis for using
these materials in creation of non-volatile memory [3, 5-
6]. The mentioned applications of the chalcogenide
materials of As(Ge)-S(Se, Te) systems could not be
realized without the knowledge of the basic properties
and processes occurring in these unique materials [4, 6-
10]. In addition, the fundamental research into the
influence of random processes on formation of the
structure of modified semiconductor systems by using
synergetics and computer simulation is extremely
important [11-13]. From this perspective, the study of
formation processes in ordered structures in thin-film
systems continues to arouse lasting and constant interest
in the synergetic approach and their practical application
[13-15].
This paper presents the complex theoretical and
experimental research of thin-film semiconductor
structures made of As(Ge)-S(Se, Te) with using
computer modeling. The aim of the research is to
establish the possibility to form a controlled distribution
of the modifier concentration in the thin film gradient
structures Ge2S3:X (X = Al, Bi, Pb, Te) and the
corresponding implementation of anticipated structural-
sensitive properties.
SPQEO, 2018. V. 21, N 4. P. 365-373.
Yurkovych N.V., Mar’yan M.I., Seben V. Synergetics of the instability and randomness in formation of gradient …
366
2. The computer modeling: initial equations and
conditions
An example of using computer modeling to form thin-
film inhomogeneous modified structures is shown in
Fig. 1. Application of computer modeling implies the
iterativeness and “formation” of the model in the cycle: 1
– physical model, 2 – mathematical model, 3 –
calculation methods, 4 – algorithm and program for
model calculations, 5 – testing and model research, 6 –
comparison of calculation results with experimental data
and subsequent refinement of the model. This cycle is
repeated a required number of times approaching the real
object (phenomenon). Each step of computer modeling
(Fig. 1) will be considered.
The first stage is the physical model. A physical
model for inhomogeneous modified structures is a model
of an open system, for which the transition to a non-
crystalline state can be considered as a cooperative self-
organized process by using the principles of synergetics.
Indeed, the conditions necessary to form self-organized
structures in open systems are as follows [11, 12]:
– The system should be thermodynamically open, i.e.,
there should be the exchange of mass, energy, and
information with environment.
– The system is at a significant deviation from
equilibrium.
– The self-organization of structures has a threshold
character; the behavior of a significant number of
subsystems belonging to the system must be
consistent.
– Dynamic equations describing the behavior of the
system are nonlinear and stochastic.
The following part of the paper analyzes how these
conditions are fulfilled in formation of the investigated
structures:
– The technological process for obtaining
inhomogeneous modified structures (for example, in
the process of cooling the fusion, sedimentation of
layers) occurs in a thermodynamically open system
that exchanges mass and energy with the
surrounding medium.
– Such structure is formed at significant deviation of
the system from equilibrium (for example, fusion,
charged material), which corresponds to
homogeneous or quasi-homogeneous distribution of
physical quantities. The inhomogeneity can be given
by distribution of atoms in different phase states (for
example, soft (vacancies, pores, dislocations) and
rigid (matrix frame) configurations). The degree of
deviation is determined by the order parameter,
calculated as deviation of the part of atoms from the
homogeneous distribution of the thermodynamically
equilibrium state.
Fig. 1. Computer modeling of the gradient non-crystalline
structures.
– Formation of modified films has a threshold
character and is realized at certain values of the
external control parameter (e.g., cooling rate,
deposition rate). In the process of transition to the
vitreous condition, there is self-consistent interaction
of different subsystems, which determines the
nonlinear nature of the system behavior. The system
is characterized by stochasticity, i.e., the time
reliance of the system depends on the reasons that
cannot be predicted with absolute precision.
– The inhomogeneous modified structure has features
of a dissipative structure that is characterized by
much higher space-time correlation of the motion of
atoms and their groups than that of the initial
homogeneous system [15].
SPQEO, 2018. V. 21, N 4. P. 365-373.
Yurkovych N.V., Mar’yan M.I., Seben V. Synergetics of the instability and randomness in formation of gradient …
367
3. Modified non-crystalline structures based on the
systems As(Ge)-S(Se, Te) and self-organization
processes
A non-crystalline system that contains N particles (atoms,
molecules), a part Nmod of which is components of the
modifier (the atoms of the chemical elements Al, Te, Bi,
etc.), and a part Nmat includes components of the matrix
(elements of the vitreous Ge2S3), which is considered in
[2, 8, 14]. The process of modified non-crystalline
structure formation can be described by the following
physical-chemical reaction:
( )
( )
( )Lk
CBLA
Lk
−
+
→←+ . (1)
Here the symbol A(L) identifies the components of
the modifier in the spatial domain that consists of L
particles (hereinafter the size of the domain will be
understood as the number of particles), B identifies the
components of the matrix (Fig. 2). Reactions (1) suggest
that the domain is growing or decreasing (in relation to
velocity ( )Lk
+ , ( )Lk
− by joining or separating
individual modifier particles in the matrix. Behavior of
the domain set with the size L in time will be described
by means of the size distribution function ( )trLg ,,
r
,
where ( )zyxrr ,,
rr
= is the radius vector, which spatial
coordinate z is perpendicular to the plane (x, y).
The dynamics of the change in the distribution
function ( )trLg ,,
r
is given by the Fokker–Planck
equation [16]:
( ) ( )
L
tLI
t
trLg
∂
∂
−=
∂
∂ ,,,
r
, (2)
where ( ) ( ) ( )( )trLgLD
L
trLgLVtLI ,,)(,,)(,
rr
∂
∂
−= is a
flux, the density of which is set by the velocity of
component evaporation, )()()( LkLkLV
−+ −= ,
( ) 2)()()( LkLkLD
−+ += – growth velocity and
diffusion coefficient in the space of sizes. The initial and
boundary conditions are as follows:
( ) ,0,, 0 =∂∂ =zLtrLg
r
strLg ρ=== )0,,1(
r
,
( ) 10,, ==∑
L
trLg
r
(ρs – the density of dislocations,
micropores). Thus, the equation (2) can be rewritten in
the form:
( ) ( ) ( )[ ] ( ) ( )trLgLDtrLgLV
Lt
trLg
,,,,
,, 2 rr
r
∇+
∂
∂
−=
∂
∂
Here,
2
2
2
2
22
2
2
2
2
2
2 11
zzyx ∂
∂
+
ϕ∂
∂
ρ
+
ρ∂
∂
ρ
ρ∂
∂
ρ
=
∂
∂
+
∂
∂
+
∂
∂
=∇ is
Fig. 2. An example of forming an amorphous layer (a matrix
consisting of n = 15 elements links between modifier atoms
visually single out the domain L = 8); ○ – matrix’s components,
● – modifier’s components.
Laplacian in the cylindrical coordinate system ),,( zϕρ .
The growth velocity of domains will be approximated by
the following expression: ( ) mod)( NLDLV a ⋅= ,
2
aDDa = , where a is the interatomic distance, D –
diffusion coefficient of particles, and diffusion in the
space of sizes ( ) 2
0 LLD β= , where β0 is the diffusion
constant (for metals Al, Bi, the diffusion coefficient
depending on temperature D = 10–10…10–15 cm2/s,
β0 ≈ 0.2, a = (2…4)·10–8 cm [8, 17].
The change dynamics in the number of particles of
the components of the system modifier Nmod under the
action of source G during time τp is considered in the
following part. The change in the number of particles in
the size interval dLLL +, is determined by correlation
),,()( trLgLV
r
and the total number of particles
( ) ( )∫
∞
π
0
2 ,,4 dLtrLgLVL
r
. The atomic particles flux
)exp(source mzgG −⋅= . gsource, m are constants of particle
source; here, the transition from time dependence to
space dependence is taken into account according to
correlation Vzt ⇒ (V is the velocity of layer growth)
that may change with time according to a certain law (in
this case, an exponential change law is considered) [18-
20]. Thus, the dynamics of changing the number of
particles is given in the equation:
( ) ( )∫
∞
∇+π−=
∂
∂
0
mod
22mod ,,4 NDdLtrLgLVLG
t
N
a
r
. (3)
The equation of continuity
0,0, mod
0
mod
mod0mod =
∂
∂
=
∂
∂
= === dzzsz
z
N
z
N
NN (d is
the layer thickness). The first summand in (3) determines
the change in the number of components of the modifier
due to the source of the molecular flow, the second – due
to structural inhomogeneity (available vacancies,
micropores), the third one – the diffusion of particles.
Equations (2) and (3) enable describing the dynamics of
system behavior. The following part of the paper
considers the cases of homogeneous and inhomogeneous
sources.
SPQEO, 2018. V. 21, N 4. P. 365-373.
Yurkovych N.V., Mar’yan M.I., Seben V. Synergetics of the instability and randomness in formation of gradient …
368
0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
t
m
=20s
t
m
=50s
t
m
=100s
t
m
=120s
N
m
o
d
/
4
.5
4
⋅1
0
1
1
,a
t.
z, µm
Fig. 3. Modification of modifier distribution with temperature
change for Ві from Тevap = 750 °С till Т = 730 °С during the
time intervals tm (tm1 = 20 s, m1 = 0.27029, g1 = 2.786⋅1011;
tm2 = 50 s, m2 = 0.67572, g2 = 2.786⋅1011; tm3 = 100 s,
m3 = 1.35143, g3 = 2.786⋅1011; tm4 = 120 s, m4 = 1.62172,
g4 = 2.786⋅1011).
The equations (2) and (3) in the stationary case
=
∂
∂
=
∂
∂
0,0mod
t
g
t
N
acquire the following form:
( ) ( )[ ] ( ) ( ) 0,,,, 2 =∇+
∂
∂
− trLgLDtrLgLV
L
sss
, (4)
( ) ( ) .0,,4
)exp(
0
mod
22
source
=∇+π−
−−⋅
∫
∞
sass NDdLtrLgLVL
mzg
The stationary solutions of the equation (4) in the
homogeneous case (G = gsource) are determined by the
correlations:
( )2
source
hom
mod 4const LDgN ass πρ≈= ,
( )LLLg ss −δ⋅ρ=hom . (5)
In the inhomogeneous case )exp(source mzgG −⋅= ,
taking into account that φ = const and solutions of the
equation )()(,mod zZRgN ρ≈ , the following equations
are obtained:
( )zNN ss γ−⋅= exphom
mod
inhom
mod
,
( )zgg ss γ−⋅= exphomhomin
,
( ) asas DGNDL −πρ=γ hom
mod
22 4 . (6)
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0
t
m
=2s
t
m
=6s
t
m
=10s
t
m
=15s
N
m
o
d
/
1
.2
5
⋅1
0
1
2
a
t.
z, µm
Fig. 4. Changing the modifier distribution when changing
temperature for Al from Тevap = 765 °С till Т = 740 °С during
time intervals tm (tm1 = 2 s, m1 = 0.03323, g1 = 2.786⋅1011;
tm2 = 6 s, m2 = 0.09968, g2 = 2.786⋅1011; tm3 = 10 s,
m3 = 0.16613, g3 = 2.786⋅1011; tm4 = 15 s, m4 = 0.24919,
g4 = 2.786⋅1011).
The equations (6) describe formation of amorphous
structures of inhomogeneous thicknesses. In particular,
the inhomogeneous distribution of the modifier
component at z causes formation of a structure with the
gradient of the distribution function of the modifier
domains according to sizes in the spatial scales
γ
∝
1
[19]. In this case, the atomic flow of the modifier is
described by the expression:
[ ]12
evapevap
evap122 scm10513.3 −−⋅=
ТM
Pa
GN , (7)
where Pevap is the equilibrium saturated vapor pressure of
the evaporated substance (Al, Bi, Pb, Te),
Pevap ≈ 10-4 mmHg, a1 – evaporation coefficient (in case
of a clean surface of the evaporating substance a1 = 1)
[21, 22], Mevap – molecular weight of evaporated
elements – modifiers, Tevap – evaporation temperature. In
order for the vapour molecules to freely evaporate, the
pressure Pevap should not exceed ≈10–2 mmHg, and the
area of evaporator should be no more than several square
centimeters (in our case, the area of the evaporator
depends on the modifier type and is approximately
10-4 cm2) [2, 14].
To determine the parameter m of an inhomogeneous
source of the atomic flow of the modifier (see Eq. (6)),
the following approximation is used. Supposing at time
t = 0, the source of the atomic flow of the modifier is
determined by the temperature of the modifier
vaporization: ( )evap11 TGG = . In the interval of time t = tm,
when the evaporation temperature changes from Тevap to
T, the source of the modifier’s atomic flow will be equal
to ( ) mmt
eTGTG
−⋅= evap12 )( . Hence, the parameter m is
determined in the following way:
SPQEO, 2018. V. 21, N 4. P. 365-373.
Yurkovych N.V., Mar’yan M.I., Seben V. Synergetics of the instability and randomness in formation of gradient …
369
0 %
1 0 %
2 0 %
3 0 %
4 0 %
5 0 %
6 0 %
7 0 %
8 0 %
9 0 %
1 0 0 %
5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0
Sі
Ge
S
Al
co
nc
en
tr
at
io
n
λ, nm
Fig. 5. Distribution of elements over the thickness of the film:
〈Ge2S3:Al〉.
( )
)(
ln
1
2
evap1
TG
TG
t
m
m
= .
Otherwise, taking into account the correlation (7), the
following equation is obtained:
evap
ln
2
1
T
T
t
m
m
= [s-1]. (8)
From the correlations (6) to (8), calculation has been
performed of the atom distribution of modifiers Ві and
Al according to the thickness of the inhomogeneous films
based on the vitreous Ge2S3 by changing the source of
the modifier’s atomic flow, structural inhomogeneity
(vacancy, micropores), and particle diffusion. Figs. 3 and
4 show the dependence of the change, calculated in
accordance to (6), in the number of atoms Ві and Al in
the action of the source of atomic flow at time intervals
(tm1 to tm4), during which the temperature changes from
Тevap to Т.
4. Gradient thin-film structures: obtaining and
determining the concentric distribution of
components
The obtainment of gradient films based on vitreous Ge2S3
with modifiers Al, Bi, Pb, Te has been carried out by the
method of thermal evaporation in a vacuum using the
results of computer modeling [12, 22]. Due to the change
of the constant control parameter (evaporation
temperature) a necessary flow of the modifying element
(Al, Bi, Pb, Te) has been created. The dynamics of the
particle number of the modifier components Nmod under
the influence of the inhomogeneous source of atomic
flow G (see the formula (6)) provides the required
distribution of introduced modifier over the thickness of
deposited film within 0.5…3 µm (see Figs. 3 and 4).
The studied films were deposited on glass and
silicon substrates. The control of the chemical and
quantitative composition of the obtained gradient films
〈Ge2S3:Х〉 (X = Al, Ві, Pb, Te) was performed using the
method of mass-spectrometry with post-ionized neutral
particles. The quantitative analysis enabled to construct
the distribution of elements over the thickness of film
(Fig. 5). The ordinate axis corresponds to the atomic
percent of components, and the abscissa axis manifests
the value of depth from the surface of the film.
As it can be seen from the diagrams, the films
〈Ge2S3:Al〉 (Al – 2 at.%), 〈Ge2S3:Ві〉 (Ві – 14 at.%) have
an alternating composition with a continuous distribution
of constituent components over the thickness. The
repeatability of the results concerning the distribution of
the introduced modifier over the thickness of the film is
satisfactory dependent on the type and concentration of
the introduced chemical element (Al, Bi, Pb, Te) and
comprises ~90%. In addition, technological regimes of
obtaining thin-film inhomogeneous structures with
different modifiers (evaporation temperature,
condensation rate, fluctuations of technological
environment) play an important constructive role in the
repeatability of the results.
5. Calculation of distribution of composite
components in modified structures: comparison with
experimental data
In order to check the correctness of the chosen approach
that allows calculating the critical values of parameter
fluctuations, in which the structural characteristics of the
studied layers are not sensitive to changing conditions for
their obtaining and to predict formation of qualitatively
new structures at allocated intensities of noise,
calculation of the distribution of constituent components
over the thickness of the film and comparison with
experimental data has been performed.
The difference between internal system fluctuations
and external environmental fluctuations should be noted.
Unlike internal fluctuations, the stochastic nature of the
environment does not have the microscopic origin; the
intensity of environmental fluctuations can be increased
in a controlled manner in order to investigate its
influence on the system behavior. With the
corresponding experimental modification of the
conditions for obtaining inhomogeneous structures, the
noise level can be reduced but it is impossible to
eliminate it completely. It constitutes another difference
of noise from internal fluctuations, which makes it more
flexible guided in the hands of the experimenter. The
external noise is never strictly equal to zero, and
therefore it must be taken into account: either the
presence or absence of the influence.
SPQEO, 2018. V. 21, N 4. P. 365-373.
Yurkovych N.V., Mar’yan M.I., Seben V. Synergetics of the instability and randomness in formation of gradient …
370
Table 1. Technological parameters for obtaining modified
structures.
Compo-
sition
Thick-
ness
z, µm
Conden-
sation
velocity
υ, Å/s
συ,
Å/s
Тevap,
°С
σТ,
°С
〈Ge2S3:Te〉 1.03 2.70 0.02 726 ±5
〈Ge2S3:Pb〉 2.26 5.84 0.02 747 ±5
〈Ge2S3:Bi〉 1.26 3.50 0.02 750 ±5
〈Ge2S3:Al〉 2.4 6.20 0.02 765 ±5
Table 1 represents the technological parameters of
obtaining modified structures (condensation velocity,
evaporation temperature, thickness) and the values of
fluctuations of the condensation velocity συ and the
evaporation temperature of the layer σТ.
Two-parameter approximation of the data of
experimental curves was carried out, and parameters m, g
were calculated for experimentally obtained dependences
of the concentration distribution of constituent
components over the thickness of film (Fig. 5), taking
into account the equations (6) which describe the
formation of amorphous structures with inhomogeneous
thicknesses.
The following part of the paper considers the two-
parameter dependence mzgey −= , where m, g are
constant parameters [12]. Consequently, the values of the
constant can be calculated (Fig. 5). The concentration
distribution of modifier Bi over the film thickness
〈Ge2S3:Ві〉 (Ві – 14 at.%) parameters m, g that
correspond to the experimental dependences (Fig. 5). As
a result of parameters calculation, the following values of
constant parameters were obtained: for the composition
〈Ge2S3:Al〉 m = 0.66142, g = 3.85894, for the
composition 〈Ge2S3:Bi〉 m = 0.85772, g = 10.47423.
Figs. 6 and 7 represent the dependences of the
atomic distribution for modifiers Al (2 at.%) and Ві
(14 at.%) over the film thickness and compositions
〈Ge2S3:Al〉 and 〈Ge2S3:Bi〉, calculation of which was
carried out from the correlations (6) to (8) (theoretical
curve), the approximation of the two-parameter
dependence distribution of the modifier atomic flow
(approximation) and the comparison with the
experimental curves (exp. curve), which are obtained
using the method of mass spectrometry of post-ionized
neutral particles. As it can be seen from Figs. 6 and 7,
satisfactory approximation of the exponential distribution
of the two-parameter dependence of the modifier atomic
flow over the film thickness is observed. Consequently,
the given approach to calculating the distribution of
introduced elements (Al, Bi, Pb, Te) and the calculation
program of constant m and g allows to check the
experimental distribution of the modifier on the film
thickness by using the set of programs and to determine
the constants of this distribution with the given accuracy
[13].
0.0 0.5 1.0 1.5 2.0 2.5
-2
0
2
4
6
8
10
12
14
exper.
approx.
theor.
n
,а
т
.%
z,µm
Fig. 6. Concentration distribution of modifier Bi over the film
thickness 〈Ge2S3:Ві〉 (Ві – 14 at.%).
0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
exper.
approx.
theor.
n
,а
т
.%
z,µm
Fig. 7. Concentration distribution of modifier Al over the film
thickness 〈Ge2S3:Al〉 (Al – 2 at.%).
6. Research of film surface morphology
Figs. 8 to 11 illustrate morphology of investigated
surfaces of inhomogeneous structures 〈Ge2S3:Х〉 (Х = Al,
Ві, Pb, Te). The results show that surface morphology of
the films is quite complex and depends on the type of the
introduced modifier. Therefore, the results of studies of
inhomogeneous layers 〈Ge2S3:Bi〉 (Bi – 14 at.%) are
shown in Fig. 8.
It has been found that with introduction of
elements-modifiers of bismuth and lead, the condensate
formation occurs in the form of vapor-liquid-solid phase
with coalescence. It is characterized by formation of
channels and merging of small islets into larger ones.
Table 2 presents the main parameters characterizing the
surface of the films. The height of the surface roughness
of the gradient structure with the bismuth is within the
range of 0.4…2.5 nm [8, 23, 24].
Fig. 9 shows the axonometric image and the
structural analysis of the inhomogeneous film 〈Ge2S3:Pb〉
(Pb – 12 at.%).
Similar to Ві, the mechanism of condensate
formation occurs in the form of vapour-liquid-solid phase
with coalescence. The height of surface roughness
reaches 1.2…5.4 nm.
SPQEO, 2018. V. 21, N 4. P. 365-373.
Yurkovych N.V., Mar’yan M.I., Seben V. Synergetics of the instability and randomness in formation of gradient …
371
Fig. 8. Axonometric image and sectional analysis of the
gradient film surface 〈Ge2S3:Bi〉 (Bi – 14 at.%), obtained using
AFM.
Fig. 9. Axonometric image and sectional analysis of the
gradient film surface 〈Ge2S3:Pb〉 (Pb – 12 at.%), obtained using
AFM.
Table 2. Main parameters characterizing the film surface.
Composition
RMS,
nm
Ra,
nm
Rmax,
nm
h, nm
Ge2S3 0.62 0.1 0.99 0.4–0.5
〈Ge2S3:Bi〉 (14 at.%) 0.80 0.22 3.34 0.4–2.5
〈Ge2S3:Те〉 (30 at.%) 6.93 5.45 21.84 2.3–36.9
〈Ge2S3:Al〉 (2 at.%) 1.53 1.03 8.07 1.4–6.3
〈Ge2S3:Pb〉 (12 at.%) 2.44 2.06 11.06 1.2–5.4
RMS – mean-square deviation vertically,
Ra – arithmetic mean deviation,
Rmax – maximum deviation,
h – roughness height.
Having analyzed Fig. 10 for the structure
〈Ge2S3:Те〉 (Те – 30.7 at.%), it is clear that the
parameters characterizing the roughness value are
significantly different from the previous results [24]. This
difference in the values for structures with Te is
explained by the presence of two halogens with different
structural parameters in the film, resulting in possible
substitution of sulfur by tellurium, which leads to a
partial disordering of an amorphous matrix frame on the
basis of vitreous Ge2S3, formation of obtained
condensates at given concentrations of solid solutions
according to the mechanism of vapor-solid phase, with
formation of a large number of large-sized islets. The
height of the roughness reaches 37 nm.
Analyzing Fig. 11 for the structure 〈Ge2S3:Al〉 (Al –
2 at.%), it has been established that formation of
condensate occurs according to the vapor-solid phase
mechanism with densely filled islets of small sizes,
which is not observed in structures with modifiers Bi, Pb.
Thus, the main feature of obtaining amorphous
gradient structures in the solid phase with modifying
elements is that they are always formed in non-
equilibrium conditions, in which the minimum potential
energy of the system is not achieved. The high energy of
an amorphous state affects the values of ionic or atomic
radii and the bond angles, but, first of all, on the methods
of stacking structural units of solids, which are extremely
large in this case [24]. The process of growth and the
structure of amorphous condensates of inhomogeneous
modified structures is significantly influenced by the
vapor composition, energy state of its particles,
condensation rate, temperature of the substrate, and
evaporator.
Thus, as it can be seen from the AFM figures, the
surface roughness of the studied films is negligible
(Table 2), it lies within 1…7 nm at the thicknesses of
structures of 500…3000 nm, and only for Те the
roughness reaches the values of 37 nm, that is, the film
surface is rather smooth. It is an important conclusion for
the following interpretation of optical film research data.
SPQEO, 2018. V. 21, N 4. P. 365-373.
Yurkovych N.V., Mar’yan M.I., Seben V. Synergetics of the instability and randomness in formation of gradient …
372
Fig. 10. Axonometric image and sectional analysis of the
gradient film surface 〈Ge2S3:Те〉 (Те – 30.7 at.%).
Fig. 11. Axonometric image and sectional analysis of the
gradient film surface 〈Ge2S3:Al〉 (Al – 2 at.%).
7. Conclusions
Computer simulation of the source of the atomic flow of
the modifier has been carried out, which makes it
possible to form gradient structures with the predicted
distribution of chemical elements accord to the film
thickness. The equations describing formation of
inhomogeneous amorphous structures and taking into
account the dynamics of the number of modifier particles
owing to the source of the atomic flow of a chemical
element, structural heterogeneity (availability of
vacancies, micropores and particle diffusion) have been
obtained.
The criteria for formation of an inhomogeneous
structure on the basis of vitreous Ge2S3 with modifiers
Al, Bi, Pb, Te that are identified due to changes in the
condensed medium (evaporation temperature,
condensation velocity, increasing or decreasing the
intensity of the fluctuations of the active fields) have
been investigated. The possibility of obtaining qualitative
modified gradient structures with a given distribution of
components by the method of thermal deposition in
vacuum and the possibility of studying the concentration
thickness distribution by using mass spectrometry of
post-ionized neutral particles has been shown.
The mechanism of interaction of the selected
chemical modifiers (Al, Bi, Pb, Te) of the determined
maximum concentration with the glassy matrix Ge2 S3
has been established. Morphology of the surfaces of the
gradient structures Ge2S3:X (X = Al, Bi, Pb, Te) has also
been investigated. It has been found that the film surfaces
are quite smooth, i.e., reflection of light from them can
be described on the basis of the scattering theory of
Kirchhoff’s diffraction.
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Authors and CV
Nataliya Yurkovych, PhD (Physics
& Mathematics), Ass. Prof. of the
Department of solid-state electronics
& information security of Faculty of
Physics, Uzhgorod National
University, Uzhgorod, Ukraine. The
area of scientific interests covers
computer modeling in the diagnostics,
formation, and modifications of
different kinds of the thin film gradient modified
semiconductor structures.
Uzhgorod National University, Uzhgorod, Ukraine
E-mail: yurkovich@ukr.net
Mykhaylo Mar’yan, Doctor of
Sciences (Physics & Mathematics),
Professor of Department of Solid-
State Electronics & Information
Security, Faculty of Physics
Uzhgorod National University,
Uzhgorod, Ukraine. The scientific
interests are associated with studies and implementation
of the self-organization processes in the synergetics
systems of the different nature (non-crystalline state,
fractal structures, information and stochastic systems).
Uzhgorod National University, Uzhgorod, Ukraine
E-mail: mykhaylo.maryan@uzhnu.edu.ua
Vladimir Seben, PhD, Head of the
Department of Physics, Mathematics
& Technics, Faculty of Humanities
and Natural Science University of
Presov, Presov, Slovak Republic. A
sphere of the scientific interests is
associated with research of stochastic
processes.
University of Presov, Presov, Slovak
Republic
E-mail: vladimir.seben@unipo.sk
|
| id | nasplib_isofts_kiev_ua-123456789-215325 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-23T18:47:45Z |
| publishDate | 2018 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Yurkovych, N.V. Mar'yan, M.I. Seben, V. 2026-03-12T08:55:13Z 2018 Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures / N.V. Yurkovych, M.I. Mar'yan, V. Seben // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 365-373. — Бібліогр.: 24 назв. — англ. 1560-8034 PACS: 78.66.Jg, 68.35.bj, 89.75.Fb https://nasplib.isofts.kiev.ua/handle/123456789/215325 https://doi.org/10.15407/spqeo21.04.365 The criteria for formation of an inhomogeneous structure based on vitreous Ge₂S₃ with modifiers Al, Bi, Pb, and Te that are identified due to changes in the condensed medium (evaporation temperature, condensation velocity, increasing or decreasing the intensity of the fluctuations of the active field) have been determined. The article analyzes the obtained equations describing the formation of inhomogeneous amorphous structures and taking into account the dynamics of the concentration of the modifier owing to the source of the atomic flow of a chemical element, structural heterogeneity (availability of vacancies, micropores), and particle diffusion. Computer simulation of the source of the atomic flow of the modifier has been carried out, which makes it possible to form gradient structures with the predicted distribution of the chemical element according to the film thickness. Morphology of gradient structure surfaces and the mechanism of condensation of modifiers Al, Bi, Pb, Te with the amorphous matrix of Ge₂S₃ have been ascertained. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Semiconductor physics Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures Article published earlier |
| spellingShingle | Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures Yurkovych, N.V. Mar'yan, M.I. Seben, V. Semiconductor physics |
| title | Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures |
| title_full | Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures |
| title_fullStr | Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures |
| title_full_unstemmed | Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures |
| title_short | Synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures |
| title_sort | synergetics of the instability and randomness in the formation of gradient-modified semiconductor structures |
| topic | Semiconductor physics |
| topic_facet | Semiconductor physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215325 |
| work_keys_str_mv | AT yurkovychnv synergeticsoftheinstabilityandrandomnessintheformationofgradientmodifiedsemiconductorstructures AT maryanmi synergeticsoftheinstabilityandrandomnessintheformationofgradientmodifiedsemiconductorstructures AT sebenv synergeticsoftheinstabilityandrandomnessintheformationofgradientmodifiedsemiconductorstructures |