Nanostructure of amorphous films
The paper presents results of experimental and theoretical investigations of thin chalcogenide films at the nanostructure level. Transmission electron microscopy demonstrated an amorphous cluster structure. The equations for order parameters in cluster boundaries have been obtained and analyzed.
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
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| author | Dyakonenko, N.L. Lykah, V.A. Sinelnik, A.V. Korzh, I.A. Bilozertseva, V.I. |
| author_facet | Dyakonenko, N.L. Lykah, V.A. Sinelnik, A.V. Korzh, I.A. Bilozertseva, V.I. |
| citation_txt | Nanostructure of amorphous films / N.L. Dyakonenko, V.A. Lykah, A.V. Sinelnik, I.A. Korzh, V.I. Bilozertseva // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 199-203. — Бібліогр.: 10 назв. — англ. |
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| description | The paper presents results of experimental and theoretical investigations of thin chalcogenide films at the nanostructure level. Transmission electron microscopy demonstrated an amorphous cluster structure. The equations for order parameters in cluster boundaries have been obtained and analyzed.
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| first_indexed | 2026-03-18T23:47:45Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 199-203.
doi: https://doi.org/10.15407/spqeo20.02.199
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
199
PACS 81.07.-b, 81.15.-z
Nanostructure of amorphous films
N.L. Dyakonenko1, V.A. Lykah2, A.V. Sinelnik3, I.A. Korzh4, V.I. Bilozertseva5
National Technical University “Kharkiv Polytechnic Institute”
2, Kirpichov str., 61002 Kharkiv, Ukraine,
E-mail: dnina490@gmail.com1, lykahva@yahoo.com2,
sinelnikav@gmail.com3, korira2542@gmail.com4, bilozv@gmail.com5
Abstract. The paper presents results of experimental and theoretical investigations of
thin chalcogenide films at nanostructure level. Transmission electron microscopy
demonstrated amorphous cluster structure. The equations for order parameters in cluster
boundaries have been obtained and analyzed.
Keywords: chalcogenide thin film, nanocluster, cluster bond, order parameters, potential
relief.
Manuscript received 13.01.17; revised version received 24.04.17; accepted for
publication 14.06.17; published online 18.07.17.
1. Introduction
Amorphous chalcogenide films have a wide range of
varying physical and chemical properties, which find
applications in electronics and optoelectronics [1-5].
Functionality of thin films obtained from glassy
materials often derives from their structure at different
length scales. Nevertheless, the structural character
investigations of these materials are carried out rarely
without a significant opportunity to obtain systematic
information. Most glasses have structures dominated by
network in which bonding is predominantly covalent and
have been described in terms of the random network
model. Network glasses are the physical prototype for
many self-organized systems, ranging from proteins to
computer science. Cluster appearance in the non-
crystalline objects is associated with partial self-
organization of matter under chemical bonds influence
[6, 7]. There are general cluster formation conformities
in different amorphous substances irrespective of their
composition, preparation method, kind of conductivity
and other properties. Conventional theories of gases,
liquids, and crystals do not account the character of the
glass-forming tendency, the phase diagrams of glasses
[8] or their optimizable properties.
The degree of self-organization depends on
preparation conditions (the substrate material and
temperature). As the result, the breach of statistically
homogeneous atomic distribution of nanosized
irregularities (clusters) appears. In contrast to the
crystalline state characterized by long-range order
(LRO), i.e., by existence of correlations between the
positions of every two atoms situated as far as possible
one from another, the non-crystalline state is
characterized by the absence of the LRO. The remnant is
not total disorder but a certain limited order called as
short-range order (SRO) defined by the inter-atomic
correlations in the first coordination spheres of an
arbitrary atom, i.e., up to the maximum distance where
the bonding forces are active. In chalcogenide glasses,
the order extends up to interatomic distances. On this
basis, a new type of order was defined: the medium-
range order (MRO). It is known that glasses and liquids
exhibit the first sharp diffraction peak that is evidence
for intermediate range order caused by regularities in the
packing of structural units.
This communication presents results of
experimental and theoretical investigations of thin
amorphous films of different chalcogenide systems at
nanostructural level.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 199-203.
doi: https://doi.org/10.15407/spqeo20.02.199
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
200
2. Experimental results
The thin films of chalcogenide glass compounds
A1BiСV1 (A1-Li, K, Na, Rb, СV1-S, Se) were evaporated
from the resistant-heated tungsten boat onto a relatively
cold glass substrate (300 K) in vacuum 1 mPa. The
results of TEM investigations are represented in Fig. 1.
All these chalcogenide films have an amorphous
structure. Amorphous layers have not an atomic-smooth
surface, but consist of clusters from 5 to 15 nm in size.
The contrast on the electron-microscopic images of
clusters is supposed to be caused by material density
changes. The absence of contact between clusters is their
specific feature. There are regions of low density
between clusters 1-2 nm in size for different films.
Distribution of the relative frequency N of clusters (a)
and cluster boundaries (b) dimensions for KBi3S5 films
are shown in Fig. 2.
In the ideal crystal, chalcogen compounds form a
plane triangular subgrate with the six-coordinated
covalent bond. These planes interchange with bismuth
layers (semimetal) and alkali that have the metal bond.
That is, in the ideal crystal A1BiСV1 chalcogen layers
with covalent directional bonds are interchanged with
Bi, alkali metallic (isotropic) bonds. The bond between
layers does not seem to be covalent and metallic. It may
be, to a large degree, ionic and unidirectional.
When condensing, the atoms are deposited in a
uniform layer, in which they are placed in disorder, the
stoichiometry of the compound being saved. As the
result of disturbing the atom order, the lengths and
orientation of chemical bonds are broken.
In low temperature experiments, atoms solidify in
random positions. Homogeneous amorphous phase with
full disordering the covalent bond lengths and
orientations is realized through the homogeneous
inversion of the covalent, metallic and ionic bonds order.
If the substrate temperature is high, the diffusion of
atoms and crystal phase formation during deposition
process are possible. In this way, the atomic system
energy is minimized.
Fig. 1. Structure of KBi3S5 films: thickness h = 40 nm, vacuum
level P = 10–3 Pa, rate of condensation 0.1–0.5 nm/s, substrate
temperature Ts = 300 K. A – clusters, B – cluster boundaries.
In our experiments, the substrate temperature was
less than the temperature of crystallization, that is the
atoms order changing processes were not realized. But it
was formed the structure with interchanging regions of
low and high density of the film. The present
measurements agree satisfactorily with following the
theoretical analyses.
3. Theoretical analysis
Two mutually related order parameters have been
chosen for description of an amorphous film structure:
the mean deviation of angle from the optimal average
value in covalent bond φ and the average interatomic
distance r. The spatial change of the order parameters is
assumed to be slow.
There are various microscopic descriptions of
interatomic interaction: Morse potential, model potential
for Van der Waals and Lenard–Jones type interactions.
Parameter φ should well describe bad ordering. The
Fig. 2. Distribution of the relative frequency N of cluster (a) and cluster boundaries (b) dimensions for KBi3S5 films.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 199-203.
doi: https://doi.org/10.15407/spqeo20.02.199
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
201
sharp orientation of the bond and their periodicity, appa-
rently, are well described by elliptic functions. The most
sharp orientation among elliptic function is elliptic cosine
cn(x, k), where k is the elliptic module, x is variable. In the
limit case k = 0, elliptic functions turn in trigonometrically
sin x, cos x, and at k→1 they turn in hyperbolic ones:
( ) ( )xkx tanh,sn → , ( ) ( )xkx hcos1,cn → [9].
The free energy density of the system
hominh wwVWw +== consists of homogeneous whom
and inhomogeneous winh parts. Let’s write down the free
energy density with the obvious account of angular
dependence
222
inh 22
⎟
⎠
⎞
⎜
⎝
⎛
∂
ϕ∂
+⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
=
z
Gl
z
xEw ,
( )
mnn x
c
x
baw ++
χ−χ⋅−
−= 0
hom
sn , (1)
where x is the average interatomic distance. The letters
a, b, c stand for average energy parameters of
microscopic potential of interaction, they depend on
average quantity of neighbours with different type of
bound and effective radius. E, G are effective Young and
shear modules and l is the effective length for angular
deformation; z is the coordinate along which there are
changes of parameters of the system. φ is the average
angle of the bond calculated from an optimal value Ф0,
0Φ−Φ=ϕ . The angle is also normalized by period:
...,4,2,000 KKkd =Φ=χ the elliptic function period
4K(k), where K(k) is the full elliptic integral of the first
kind. ( )kkd ,sn Φ is the Jacobi elliptic function, it sets
periodicity of the bound change depending on the angle
Ф. k is the elliptic module, d – angular period of
covalent bond (in section).
The sharp orientation of the covalent bond falls
with increase in the distance and ionic rate [6]. The
repulsion of atomic shells dominates at strong approach
between them. According to it, we shall choose the
elementary function having a maximum at the optimum
bond length rc.. So, nx1 and mnx +1 are contributions
to potential of Lenard–Jones type. The covalent bond is
directed and strong. The sharp minimum of potential
corresponds to ( ) 0,sn 2 =Φ kkd .
With increasing the interatomic distance, the ionic
component of the bond increases, the depth of potential
decreases. It corresponds to ( ) 1,sn 2 =Φ kkd .
The free energy variation with the order parameters
leads to the system of Lagrange-type equations:
.
0
0
⎪
⎪
⎭
⎪⎪
⎬
⎫
⎪
⎪
⎩
⎪⎪
⎨
⎧
=
ϕ∂
∂
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ϕ′∂
∂
⋅
∂
∂
=
∂
∂
−⎟
⎠
⎞
⎜
⎝
⎛
′∂
∂
⋅
∂
∂
ww
z
r
w
r
w
z (2)
Here and somewhere further, r = x. The integral of
the equations’ system is:
C
x
c
x
ba
z
Gl
z
xE
mnn =
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
χ−
−−⎟
⎠
⎞
⎜
⎝
⎛
∂
ϕ∂
+⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
+
2222 sn
22
. (3)
The homogeneous part is the effective “potential
energy” (Fig. 3) of the system. Let’s introduce
dimensionless parameters: x = γrс, cb=β , where
( )m
n
c a
cmnxr +
== 0 (4)
is the equilibrium distance for covalent bond at
( ) 0,sn 2 =Φ kkd ;
( )
m
cnr
cmna +
= , 22
r
nm
c
c l
c
rEr ==
+
, 22
ϕ
+
== l
c
r
Gl
nm
c ,
rl
z
=ς . (5)
Then, the integral in dimensionless variables will
become
( )( )
C
n
mn
mnn
=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
γ
+
γ
χβ−+
−−
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ς∂
ϕ∂λ
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ς∂
γ∂
+
1sn1
22
1
2
222
. (6)
Fig. 3. Potential relief for the density of free energy w. φ is the
average angle of covalent bond, r = x – average length of the
bonds between atoms, rc corresponds to the minimum energy
within clusters. Different minima correspond to different
clusters. Level lines are shown.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 199-203.
doi: https://doi.org/10.15407/spqeo20.02.199
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
202
Boundary conditions in domains are:
( ) 0,sn 2 =Φ kkd , γ' = 0, φ' = 0 (γ = 1, x = rc), it
defines the integral value
( )( )
011sn1
22
1 222
=−
γ
−
γ
χβ−+
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ς∂
ϕ∂λ
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ς∂
γ∂
+mnnn
mn
(7)
( ) ( )ςϕςγ , – (functions) dimensionless parameters of
interatomic distance and the bond angle (parameters of
interatomic interaction); n, m are powers in the potential
of Lenard–Jones type; β is the parameter responsible for
depth of modulation of covalent bond; λ – parameter
equal to the relation of the angle and length scales of the
bond.
It is obvious that the system is transformed into a
state with reoriented bonds and decreased their average
lengths to minimize energy. In a three-dimensional case,
this process, probably, is possible with reduction of total
volume of a sample. Under condensation on a substrate
for strong connection of the sample atoms with a
substrate, the average (not reoriented) values of the bond
lengths should be kept, and after formation of several
layers their local reorientation is possible. Qualitatively,
this process is similar to that of formation of discrepancy
dislocations. The experiment shows saving the initial
stratified structure for the films, which thickness is
larger than the average cluster sizes.
To considerate spatial changes of the order
parameters (average interatomic distance r and average
angle ϕ), we have assumed their slow change in space.
The problem of the variables splitting is old and hard
[10]. Here, we choose a rectangle way. This path is
shown in Fig. 4, it goes between two potential minima
(a, e) that correspond to two neighbor clusters. Besides,
it requires the energy minimum (saddle point c) at the
maximum interatomic distance. So, the path has two
regions where only the distance changes (a-b and d-e)
and one region where only the angle changes (b-c-d).
Boundary conditions for single boundary between
clusters (point 0 corresponds to 2K in Figs. 3 and 4):
±∞=z , 0=
∂
ϕ∂
z
,
2
d
±=ϕ . (8)
The choice of an integration contour, i.e., transfer
from one domain (cluster) to another, splits variables
x = r and ϕ. Optimization of the domain boundary
depends on choice of an integration contour. For
variables splitting, we’ll choose a contour shown in
Figs. 4 and 5. The coordinate dependence of the angle
distance breaks up into two sites. This contour
corresponds to a rigid angular dependence of potential
and soft dependence of the interatomic distance.
Fig. 4. The levels of the potential w(r, φ) at r-φ plane (compare
with Fig. 3). Solid line with straight parts is the integration
pathway through a cluster boundary on the r-φ plane.
At the first step, let us consider the change of bond
angles at the fixed bond lengths r = rcs = const, which
corresponds to the saddle point c of the effective
potential. Figs. 4 and 5 show the integration path along
the r-φ plane and in r-w cross-section as well as the
saddle point c at φ = K and r = rcs. Then, the latter
integral of the equation will have a form:
( ) C
n
mn
n =
γ
χβ+
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ς∂
ϕ∂λ 222 sn
2
. (9)
Variable data are separated, and the solution can be
obtained by integration
( )KC
dCd
,sn2
1
20
ϕ−
ϕ
=ς−ς=ς ∫∫ , (10)
where functions C1, C2 depend on parameters rcs, β, γ, λ,
m, n. The obvious coordinate dependence of the angle
φ(z) is shown in Fig. 5 as the curve b-c-d.
Fig. 5. Curve 1 is cross-section of w(r, φ) at φ = 0; i.e.
sn(φ) = 0 (absolute min). Curve 2 is the cross-section of
w(r, φ) at φ = K(k), i.e., sn(φ) = 1. Thick line is the path for the
cluster boundary on the r-φ plane. Letters a–e correspond to
the same points in Fig. 4.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 199-203.
doi: https://doi.org/10.15407/spqeo20.02.199
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
203
e
d
c
b
a 2d
d
rc
rcs
r
ϕ
z
Fig. 6. Change of the parameters r, φ in dependence on the
space coordinate z. Letters and points a–e correspond to the
same objects in Figs. 4 and 5. The points b and d need tailoring
because of break shape of the path.
At the second step, let us consider the bond length
change in the range [ ]csc rr , at the fixed angles bond
φ = 0, 2K. Integration and the coordinate dependence of
the bond length r(z) = x(z) are obtained using the same
way as for the angle. The obvious coordinate
dependence of the bond length is shown in Fig. 5, 6 as
the line segments a-b and d-e.
The cluster boundary gives positive contribution to
the general energy (see Fig. 5). The found long bonds
inside the cluster boundaries correspond to lower density
and the experimentally found better electron transition in
TEM. Clusters have negative contribution to the energy
of an initial strongly disordered system. The reason is
that the energy level decreases, which is caused by some
reorientation and shortening the covalent bonds inside
the clusters.
4. Conclusions
The free energy that describes atomic interaction in
disordered state was introduced. The order parameters,
angles and lengths of covalent bonds were introduced.
The equations for cluster boundary were derived. The
dependence of the order parameters on coordinates
within the cluster boundaries was found. TEM results
are found to be in reasonable agreement with theoretical
estimates. The cluster is noncrystalline due to disordered
atomic bonds with different lengths and angles. The
cluster boundaries contain enlarged disordered bonds.
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|
| id | nasplib_isofts_kiev_ua-123456789-214932 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-18T23:47:45Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Dyakonenko, N.L. Lykah, V.A. Sinelnik, A.V. Korzh, I.A. Bilozertseva, V.I. 2026-03-04T12:52:47Z 2017 Nanostructure of amorphous films / N.L. Dyakonenko, V.A. Lykah, A.V. Sinelnik, I.A. Korzh, V.I. Bilozertseva // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 199-203. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS: 81.07.-b, 81.15.-z https://nasplib.isofts.kiev.ua/handle/123456789/214932 https://doi.org/10.15407/spqeo20.02.199 The paper presents results of experimental and theoretical investigations of thin chalcogenide films at the nanostructure level. Transmission electron microscopy demonstrated an amorphous cluster structure. The equations for order parameters in cluster boundaries have been obtained and analyzed. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Nanostructure of amorphous films Article published earlier |
| spellingShingle | Nanostructure of amorphous films Dyakonenko, N.L. Lykah, V.A. Sinelnik, A.V. Korzh, I.A. Bilozertseva, V.I. |
| title | Nanostructure of amorphous films |
| title_full | Nanostructure of amorphous films |
| title_fullStr | Nanostructure of amorphous films |
| title_full_unstemmed | Nanostructure of amorphous films |
| title_short | Nanostructure of amorphous films |
| title_sort | nanostructure of amorphous films |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214932 |
| work_keys_str_mv | AT dyakonenkonl nanostructureofamorphousfilms AT lykahva nanostructureofamorphousfilms AT sinelnikav nanostructureofamorphousfilms AT korzhia nanostructureofamorphousfilms AT bilozertsevavi nanostructureofamorphousfilms |