The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation
In the paper, the effect of the electric field on the conditions of formation and on the period of the surface superlattice of adatoms in n-GaAs semiconductor is investigated. It is established that in GaAs semiconductor, an increase in the electric field strength, depending on the direction, leads...
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Інститут фізики конденсованих систем НАН України
2019
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| Цитувати: | The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation / R.M. Peleshchak, O.V. Kuzyk, O.O. Dan'kiv, S.K. Guba // Condensed Matter Physics. — 2019. — Т. 22, № 1. — С. 13801: 1–15. — Бібліогр.: 26 назв. — англ. |
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Peleshchak, R.M. Kuzyk, O.V. Dan'kiv, O.O. Guba, S.K. 2019-06-20T03:52:47Z 2019-06-20T03:52:47Z 2019 The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation / R.M. Peleshchak, O.V. Kuzyk, O.O. Dan'kiv, S.K. Guba // Condensed Matter Physics. — 2019. — Т. 22, № 1. — С. 13801: 1–15. — Бібліогр.: 26 назв. — англ. 1607-324X PACS: 81.07.Bc, 66.30.Lw DOI:10.5488/CMP.22.13801 arXiv:1903.11601 https://nasplib.isofts.kiev.ua/handle/123456789/157479 In the paper, the effect of the electric field on the conditions of formation and on the period of the surface superlattice of adatoms in n-GaAs semiconductor is investigated. It is established that in GaAs semiconductor, an increase in the electric field strength, depending on the direction, leads to an increase or decrease of the critical temperature (the critical concentration of adatoms), at which the formation of self-organized nanostructure is possible. It is shown that in strongly alloyed n-GaAs semiconductor, an increase of the electric field strength leads to a monotonous change (decrease or increase depending У роботi дослiджено вплив електричного поля на умови формування та перiод поверхневої надгратки адсорбованих атомiв у напiвпровiднику n-GaAs. Встановлено, що у напiвпровiднику GaAs збiльшення напруженостi електричного поля залежно вiд напрямку призводить до збiльшення або зменшення критичної температури (критичної концентрацiї адатомiв), при якiй можливе формування самоорганiзованої наноструктури. Показано, що у сильнолегованому напiвпровiднику n-GaAs збiльшення напруженостi електричного поля призводить до монотонної змiни (зменшення чи збiльшення залежно вiд напрямку електричного поля) перiоду самоорганiзованих поверхневих наноструктур адатомiв. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation Вплив електричного поля на нуклеацiю нанометрової перiодичної структури адатомiв у напiвпровiднику GaAs пiд впливом лазерного опромiнення Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation |
| spellingShingle |
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation Peleshchak, R.M. Kuzyk, O.V. Dan'kiv, O.O. Guba, S.K. |
| title_short |
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation |
| title_full |
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation |
| title_fullStr |
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation |
| title_full_unstemmed |
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation |
| title_sort |
effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in gaas semiconductor under the action of laser irradiation |
| author |
Peleshchak, R.M. Kuzyk, O.V. Dan'kiv, O.O. Guba, S.K. |
| author_facet |
Peleshchak, R.M. Kuzyk, O.V. Dan'kiv, O.O. Guba, S.K. |
| publishDate |
2019 |
| language |
English |
| container_title |
Condensed Matter Physics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| format |
Article |
| title_alt |
Вплив електричного поля на нуклеацiю нанометрової перiодичної структури адатомiв у напiвпровiднику GaAs пiд впливом лазерного опромiнення |
| description |
In the paper, the effect of the electric field on the conditions of formation and on the period of the surface superlattice of adatoms in n-GaAs semiconductor is investigated. It is established that in GaAs semiconductor, an
increase in the electric field strength, depending on the direction, leads to an increase or decrease of the critical
temperature (the critical concentration of adatoms), at which the formation of self-organized nanostructure is
possible. It is shown that in strongly alloyed n-GaAs semiconductor, an increase of the electric field strength
leads to a monotonous change (decrease or increase depending
У роботi дослiджено вплив електричного поля на умови формування та перiод поверхневої надгратки
адсорбованих атомiв у напiвпровiднику n-GaAs. Встановлено, що у напiвпровiднику GaAs збiльшення
напруженостi електричного поля залежно вiд напрямку призводить до збiльшення або зменшення критичної температури (критичної концентрацiї адатомiв), при якiй можливе формування самоорганiзованої наноструктури. Показано, що у сильнолегованому напiвпровiднику n-GaAs збiльшення напруженостi
електричного поля призводить до монотонної змiни (зменшення чи збiльшення залежно вiд напрямку
електричного поля) перiоду самоорганiзованих поверхневих наноструктур адатомiв.
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/157479 |
| citation_txt |
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation / R.M. Peleshchak, O.V. Kuzyk, O.O. Dan'kiv, S.K. Guba // Condensed Matter Physics. — 2019. — Т. 22, № 1. — С. 13801: 1–15. — Бібліогр.: 26 назв. — англ. |
| work_keys_str_mv |
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| first_indexed |
2025-11-27T01:40:38Z |
| last_indexed |
2025-11-27T01:40:38Z |
| _version_ |
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| fulltext |
Condensed Matter Physics, 2019, Vol. 22, No 1, 13801: 1–9
DOI: 10.5488/CMP.22.13801
http://www.icmp.lviv.ua/journal
The effect of the electric field on the nucleation of
the nanometer periodic structure of adatoms in GaAs
semiconductor under the action of laser irradiation
R.M. Peleshchak1, O.V. Kuzyk1, O.O. Dan’kiv1∗, S.K. Guba2
1 Drohobych Ivan Franko State Pedagogical University, 24 Franko St., 82100 Drohobych, Ukraine
2 Lviv National Polytechnic University, 12 Bandera St., 79013 Lviv, Ukraine
Received August 27, 2018, in final form December 9, 2018
In the paper, the effect of the electric field on the conditions of formation and on the period of the surface su-
perlattice of adatoms in n -GaAs semiconductor is investigated. It is established that in GaAs semiconductor, an
increase in the electric field strength, depending on the direction, leads to an increase or decrease of the critical
temperature (the critical concentration of adatoms), at which the formation of self-organized nanostructure is
possible. It is shown that in strongly alloyed n -GaAs semiconductor, an increase of the electric field strength
leads to a monotonous change (decrease or increase depending on the direction of the electric field) of the
period of self-organized surface nanostructures of adatoms.
Key words: nucleation, electric field, adatom, surface superlattice, diffusion, deformation
PACS: 81.07.Bc, 66.30.Lw
1. Introduction
Recently, the possibility of obtaining semiconductor structures with self-organized nanoclusters using
methods of molecular-beam epitaxy [1, 2], ion implantation [3, 4] and under the action of laser irradia-
tion [5, 6], as well as the ability to control their physical properties, have become the subject of intense
research. In particular, laser-induced periodic surface nanostructures can be generated practically on any
material (metals, semiconductors, dielectrics) at linearly polarized irradiation and are formed in a wide
range of intervals of impulses, ranging from continuous wave radiation to several femtoseconds [7–10].
In the experimental work [6] it was shown that their formation is caused by the effect of a long-range
action of a laser pulse and is explained by the effect of the pressure gradient of the surface acoustic
wave. The data on nucleation (incipient state of the formation) of periodic nanostructures of adsorbed
atoms (adatoms) and implanted impurities are important for optimization of the technological process
and for a predictable control of the physical parameters of semiconductor structures with nanoclusters. In
particular, in order to calculate the symmetry, the period and the formation time of surface structures, it is
sufficient to analyze only the initial (linear) stage of the development of the defect-deformation instability.
In [10], there was developed a theory of spontaneous nucleation of the surface nanometer lattice
which is due to instability in the system of adatoms interacting with self-consisting surface acoustic wave
(SAW). Within this theory, the conditions of formation of nanoclusters on the surface of solids and the
periods of nanometer lattice as a function of concentration of adatoms and temperature are defined.
In the experimental works [11, 12] the effect of the external electric field on the formation of self-
organized nanostructures was investigated. In particular, in [12] it is shown that the external electric field
increases the density and changes the size of the CuO quantum wires.
∗E-mail: dankivolesya@ukr.net
This work is licensed under a Creative Commons Attribution 4.0 International License . Further distribution
of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
13801-1
https://doi.org/10.5488/CMP.22.13801
http://www.icmp.lviv.ua/journal
http://creativecommons.org/licenses/by/4.0/
R.M. Peleshchak, O.V. Kuzyk, O.O. Dan’kiv, S.K. Guba
The elastic fields created by defects turn out to be a determining factor in the formation of the surface
superlattice of adatoms. In works [13–17] it is shown that external hydrostatic pressure, ultrasonic wave
and doping with isovalent impurities should contribute to the improvement of the conditions for the
formation of surface nanostructures. The periodic deformation arising on the surface of a semiconductor
leads to the modulation of the bottom of the conduction band and, consequently, to the modulation of
electronic density. The arising nonuniform electric field leads to a nonuniform displacement of the nodes
of the crystal lattice and, consequently, to the change in the amplitude of the SAW [18, 19]. Therefore, it
can be expected that when placing a semiconductor in the external electric field, it is possible to change
the conditions of the formation of laser-induced periodic surface nanostructures and predictably control
their parameters due to the interaction of the electric field with nonuniformly distributed free current
carriers on the surface.
Due to the high mobility of charge carriers, gallium arsenide is widely used in the production of
quantum-sized structures and high-frequency lasers on their basis. Considerable attention of researchers
is paid to laser modification of the morphology of near-surface layers of GaAs, in which the conditions
of the formation of nanoclusters are a controlled process [8, 20]. In addition, gallium arsenide has one
of the largest constants of the deformation potential of the conduction band (greater only in Ge) [21],
which makes the conduction band and the electronic subsystem sensitive to deformation. Therefore, it
is expected that the interaction of the electric field with periodic deformation will be quite significant.
In this paper, the effect of the external electric field perpendicular to the SAW on the nucleation of the
nanometer periodic structure of adatoms in GaAs semiconductor is investigated.
2. The model
The equations for the displacement vectors ®u of an elastic medium are of the form [22]:
∂2 ®u
∂t2 = c2
t ∆®u + (c
2
l − c2
t ) grad (div ®u) , (2.1)
where cl and ct are the longitudinal and transversal sound velocities, respectively.
Let the surface of semiconductor coincide with the plane z = 0 (z-axis is directed into the crystal
depth), and assume that along the x-axis there is a surface perturbation of the elastic medium, which
is given in the form of a static SAW which quickly fades into the depth of a semiconductor and has an
amplitude rowing with time [10]:
ux = −iqReiqx+λt−klz − iktQeiqx+λt−ktz, (2.2)
uz = klReiqx+λt−klz + qQeiqx+λt−ktz, (2.3)
where k2
l,t = q2 + λ2
c2
l,t
; λ is the increment of defect-deformation instability; R and Q are SAW amplitudes.
Then, deformation ε on the semiconductor surface (z = 0) is of the form
ε =
∂ux
∂x
+
∂uz
∂z
= −
λ2
c2
l
Reiqx+λt . (2.4)
Consider the case where the semiconductor contains impurities — ionized donors, free electrons and
neutral adatoms. The electroneutrality condition will look as follows:
n0 = N+d , (2.5)
where N+d and n0 are the surface concentration of ionized donors and the spatially homogeneous values
of the surface concentration of electrons, respectively.
Periodic surface deformation leads to spatial nonuniform redistribution of adatoms N(x), the modu-
lation of the bottom of the conduction band and, respectively, to redistribution of the concentration of
conduction electrons n(x) and the electrostatic potential ϕ(x):
N(x) = N0 + N1(x) = N0 + N1(q)eiqx+λt, (2.6)
13801-2
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs
n(x) = n0 + n1(x) = n0 + n1(q)eiqx+λt, (2.7)
ϕ(x) = ϕ(q)eiqx+λt, (2.8)
where N1(q), n1(q) and ϕ(q) are the amplitudes of the corresponding periodic perturbations; N0 is the
spatially homogeneous values of the surface concentration of adatoms.
The Poisson equation, taking into account (2.5), (2.7) and (2.8), will take the form:
− q2ϕ(q) =
e
ε0ε̃a
n1(q) , (2.9)
where ε0 and ε̃ are dielectric constant and dielectric permittivity of the medium, respectively; a is a
lattice constant.
The equations for concentration of adatoms can be presented as follows:
∂N
∂t
= Dd
∂2N
∂x2 − Dd
θd
kBT
∂
∂x
[
N
∂
∂x
(
ε + l2
d
∂2ε
∂x2
)]
, (2.10)
where Dd is the surface diffusion coefficient; kB is Boltzmann constant; T is temperature; θd is the
deformation potential; ld is the characteristic length of interaction of adatoms with lattice atoms. The
second term expresses the interaction of adatoms with the deformation field, taking into account the
nonlocal interaction [10]. The defect which enters the surface of semiconductor leads to a change in
its volume and energy, and the initial fluctuation of deformation under certain conditions causes the
emergence of deformation-induced flows of adatoms. In nonuniform deformation-concentration field
there are forces proportional to gradients of concentration and deformation.
Taking into account (2.4), (2.6) and in the approximation of N1 � N0, the equation (2.10) is written
in the form:
λN1(q) = −Ddq2N1(q) −
DdN0θd
kBT
[
λ2
c2
l
Rq2 (1 − q2l2
d
) ]
. (2.11)
The density of the electron current:
j = − jel = nµn
dχ
dx
, (2.12)
where jel is the flow of electrons; µn is the mobility of electrons; the electrochemical potential χ is
defined by the relation
χ(x) = kBT ln
n(x)
Ni
− eϕ(x) + acε(x) , (2.13)
where Ni is the effective density of states; Ni = 2
(
2πmkBT
h2
)3/2
; ac is the constant of hydrostatic deforma-
tion potential of the conduction band. Then, taking into account (2.12), (2.13), the continuity equation
can be written in the form:
e
∂n
∂t
= kBT µn
∂
∂x
(
n
∂
∂x
ln
n
Ni
)
− eµn
∂
∂x
(
n
∂ϕ
∂x
)
+ acµn
∂
∂x
(
n
∂ε
∂x
)
. (2.14)
Taking into account (2.4), (2.7) – (2.9), the equation (2.14) can be presented as follows:
n1(q)
(
eλ + kBT µnq2 +
e2n0µn
ε0ε̃a
)
= acn0µnq2 λ
2
c2
l
R. (2.15)
From (2.11) and (2.15), we obtain expressions for the amplitudes of the surface concentration of
adatoms N1(q) and conduction electrons n1(q):
N1(q) = −
DdN0θd
kBT
(
λ + Ddq2) [
λ2
c2
l
Rq2 (1 − q2l2
d
) ]
, (2.16)
13801-3
R.M. Peleshchak, O.V. Kuzyk, O.O. Dan’kiv, S.K. Guba
n1(q) =
acn0µnq2
eλ + kBT µnq2 +
e2n0µn
ε0ε̃a
λ2
c2
l
R. (2.17)
Thus, on the surface of semiconductor, there is not only a periodic modulation of the surface relief
with the accumulation of adatoms in the maxima or minima of deformation (depending on the sign of the
deformation potential θd), but also the surface modulation of the electronic density [figure 1 (a)]. As can
be seen from the formulae (2.4), (2.6), (2.7), (2.16) and (2.17), the periodically distributed deformation
ε(x), the surface concentration of adatoms N1(x) and the concentration of electrons n1(x) are in the
same phase at θd > 0 (the condition qld < 1 is fulfilled) and ac < 0. For θd < 0, the distribution of the
surface concentration of the adatoms N1(x) and the concentration of electrons n1(x) are in the opposite
phase. Moreover, since for GaAs, the constant of the hydrostatic deformation potential of the conduction
band ac < 0, an excess of electrons will be observed in those areas of the surface where adatoms are
accumulated, which are the centers of stretching (θd = K∆Ω > 0, ∆Ω is the change in the volume of
the crystal by one adsorbed atom, K is comprehensive compression module), and conversely, in those
areas of the surface where adatoms are accumulated, which are the centers of compression, there will be
a shortage of electrons in comparison with the mean value [figure 1 (a)]. That is, the defects of the type
of the centers of stretching and the electrons accumulate in the deformation maxima. On the contrary,
the defects of the type of the centers of compression accumulate in the deformation minima and there
is a decrease in the concentration of electrons in comparison with their spatially uniform value. This
is explained by the fact that the deformation flow of electrons ( jel = −acnµn ∂ε∂x ) is directed toward an
increase of deformation and the electrons are localized in the region with a lower potential energy (there
is a local shift of the bottom of the conduction band by the value of ∆Ec = acε ). At the same time, the
deformation flow of adatoms [the second term in the formula (2.10)], which are the centers of stretching,
is also directed toward an increase of deformation, and the centers of compression are directed towards the
reduction of deformation. The controlled parameter N0 is determined by the intensity of laser irradiation.
By placing the semiconductor in the electric field, perpendicular to the direction of propagation of
the acoustic wave [figure 1 (b), (c)], an additional pressure on the surface of semiconductor is created:
σel
zz = en (x) Eel. (2.18)
Moreover, in the case where the vector of the electric field strength ®Eel is directed into the crystal
depth [figure 1 (b)], the surface area where the adatoms accumulate, which are the centers of stretching,
and, respectively, electrons accumulate, is exposed to additional stretching. The surface area in which the
adatoms of type of the compression centers accumulate and there is a shortage of electrons, is exposed to
additional compression. This, in turn, leads to the emergence of additional deformation-diffusion flow of
adatoms (for defects of type of the centers of stretching in the direction of an increasing deformation, for
defects of type of the compression centers — in the opposite direction). At change of the direction of the
electric field [figure 1 (c)], an additional pressure caused by the external electric field leads to a decrease
in the deformation gradients on the surface of a semiconductor and, accordingly, to the delocalization of
adatoms.
Figure 1. The geometric model of formation of the surface superlattice of adatoms under the influence of
the electric field. Here, black circles are the defects of type of the centers of stretching; white circles are
the defects of type of the compression centers.
13801-4
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs
The spatial nonuniform distribution of adatoms modulates the surface energy F(x), which leads to
the appearance of lateral mechanical tension σxz =
∂F(N (x))
∂x , which is compensated by a shift tension in
the medium [10]:
F(N(x)) ≈ F(N0) +
∂F
∂N
��
N=N0
N1(x), ∂F
∂N
��
N=N0
≈
θ2
dN0
aK [23].
The boundary condition expressing the balance of lateral tensions is as follows:
E
2 (1 + ν)
(
∂ux
∂z
+
∂uz
∂x
)
z=0
=
∂F(N(x))
∂x
=
∂F
∂N
∂N1(x)
∂x
, (2.19)
where E and ν are Young’s modulus and Poisson’s ratio, respectively.
Besides, the interaction of adatoms with atoms of a semiconductor results in the emergence of the
normal mechanical tension on the surface, and the corresponding boundary condition is of the form:
E (1 − ν)
(1 + ν) (1 − 2ν)
(
∂uz
∂z
+
ν
1 − ν
∂ux
∂x
)
z=0
=
θd
a
N1(x) + en (x) E . (2.20)
Thus, a system of homogeneous linear equations (2.19) and (2.20) for amplitudes R and Q is obtained
and the dispersion dependences λ(q) can be obtained from the condition of non-triviality of solutions
(from the condition of equality to zero of the determinant of this system).
3. Calculation results and their discussion
The calculations of λ(q) were carried out for GaAs semiconductor at the following values of para-
meters: N0 = 2 · 1012 cm−2; ld = 2.9 nm; a = 0.565 nm; cl = 3500 m/s; ct = 2475 m/s; ρ = 5320 kg/m3;
ac = −7.17 eV; θd = 10 eV; Dd = 107 exp
(
− 5.6 eV
kBT
)
cm2/s [24]; ε̃ = 12. Mobility of electrons as
function of temperature and concentration was determined by the technique given in work [25].
Figure 2 shows the results of calculation of the dependence of the increment of defect-deformation
instability on themodule of the wave vector at various values of the concentration of conduction electrons,
temperature and electric field strength (Eel+) with the direction shown in figure 1 (b). Such a dependence
has a maximum, which is shifted towards great values of the module of the wave vector with an increase in
the electric field strength. The formation of the surface superlattice of adatoms is possible only at positive
values of the increment of defect-deformation instability λ. As seen from figure 2, the formation of the
superlattice is possible only at a temperature lower than a certain critical value Tc. The formation of the
surface superlattice is defined by the ratio between the ordinary diffusion flow of adatoms [the first term
of equation (2.10)] and the deformation flow [the second term of equation (2.10)]. At high temperatures,
the first term is decisive and over time the concentration of adatoms on the surface is levelled, and the
formation of the surface superlattice is impossible (λ < 0). As the temperature decreases, the contribution
of the deformation flow of adatoms increases, which becomes decisive at values of temperature less than
the critical value of Tc. In this case, the defects accumulate in the maxima (minima) of deformation and
the surface superlattice is formed. In particular, at a temperature of 100 K [figure 2 (b)], in the absence
of the electric field, the formation of the surface superlattice at a given intensity of laser irradiation
is impossible. However, an increase in the electric field strength leads to a change in the sign of the
increment of defect-deformation instability λ [figure 2 (b), curve 3], which makes the formation of the
superlattice of adatoms possible. Reducing the electron concentration at a constant temperature leads
to a decrease in the value of the increment of defect-deformation instability [figure 1 (c)]. Thus, in a
semiconductor with a higher degree of doping with donor impurities, the processes of the formation of
nanometer periodic structures should be faster.
The value of qmax, atwhich the increment of defect-deformation instability has amaximum, determines
the period of the dominant structure d = 2π
qmax
(figure 3). Figure 3 shows the dependence of the period
of the surface superlattice of adatoms on the electric field strength at various values of the electron
concentration, temperature and various directions of the electric field. An increase in the electric field
strength leads to a decrease [figure 3 (a), (c)] and increase [figure 3 (b)] of the period of the surface
superlattice of adatoms, depending on the direction of the electric field. The effect of the electric field on
13801-5
R.M. Peleshchak, O.V. Kuzyk, O.O. Dan’kiv, S.K. Guba
Figure 2. Dependence of the increment of defect-
deformation instability on the wave vector at the
following values of parameters: T = 70 K [(a), (c)];
T = 100 K (b); n0 = 1012 cm−2 [(a), (b)]; n0 =
109 cm−2 (c); 1 − Eel = 0; 2 − Eel+ = 30 kV/cm;
3 − Eel+ = 80 kV/cm.
Figure 3. Dependence of the period of the surface
defect-deformation structure on the electric field
strength at its various directions and at various va-
lues of the electron concentration: T = 70 K [(a),
(b)]; T = 100 K (c); 1 − n0 = 1012 cm−2;
2 − n0 = 109 cm−2.
the period of the surface defect-deformation structure manifests only in strongly alloyed semiconductors.
In particular, in GaAs semiconductor with the surface electron concentration of n0 = 1012 cm−2, at a
temperature of 70 K, when the electric field strength increases to 60 kV/cm, the period of the superlattice
changes by 2.5 nm. In a semiconductor with the surface electron concentration of n0 = 109 cm−2, the
period of the superlattice practically does not change [figure 3 (a), (b)].
At temperatures that are insignificantly higher than the critical temperature Tc [figure 3 (c)], there
is a significant effect of the electric field, and the direction of the electric field (Eel+) corresponds
to figure 1 (b). In this case, in the absence of the electric field, the defect-deformation structures do not
arise at the given intensity of laser irradiation. However, there is some critical value of the electric field
strength Eel
c , at the excess of which the formation of the surface periodic structure of adatoms is possible.
Otherwise, it can be interpreted as expansion of temperature intervals under the action of the electric
field, within which the formation of the surface superlattice is possible.
13801-6
The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs
Figure 4. Dependence of the critical temperature (critical concentration) on the electric field strength at
different values of the electron concentration: 1 − n0 = 1012 cm−2; 2 − n0 = 109 cm−2.
Changing the direction of the electric field [figure 1 (c)] leads to deterioration of the conditions of
the formation of self-organized nanostructures, irrespective of the sign of the deformation potential θd,
in particular, it leads to a decrease in the critical temperature and to an increase of the period of the
surface superlattice [figure 3 (b)]. This is explained by the fact that in this case, the local deformation
caused by the action of the electric field bears the character opposite to the deformation created by
adatoms (figure 1).
The intensity of laser irradiation (the average concentration of adatoms) is another parameter that
determines the conditions for the nucleation of the surface superlattice of adatoms. Figure 2 shows the
dependence of the increment of defect-deformation instability on the wave vector at different values
of temperature and at the fixed value of N0 = 2 · 1012 cm−2. Similar dependencies can be obtained at
various values of N0, having fixed a certain value of temperature. In this case, there is a critical value of
the concentration of adatoms Nc. For concentrations less than Nc, the formation of the periodic surface
structure is impossible. Figure 4 shows the dependence of the critical temperature Tc (the critical value of
the concentration of adatoms 1/Nc) on the electric field strength at different values of the concentration of
electrons. The area under the curves is the area in which there is formed a periodic structure of adatoms.
The electric field, whose direction corresponds to figure 1 (b), allows one to reduce the critical value
of the concentration of adatoms (the intensity of laser irradiation) or to increase the temperature below
which the formation of the surface superlattices occurs. The effect of the electric field is more significant
for highly doped semiconductors.
In the framework of this model, the initial (linear) stage of the formation of a surface superlattice
is considered (t < 1/λ). Due to an increase of the amplitude of deformation, nonlinear effects become
significant, which leads to its saturation (the amplitude no longer increases). In this case, in order to
calculate the amplitude in the energy of elastic interaction, it is necessary to take into account the
anharmonic terms [23], or to consider the nonlinearity in the boundary conditions. Except the structure
dominating in the linear approximation with an increment λmax(qmax), the whole continuum of structures
with λ > 0 intensifies (figure 2). At an exit to the stationary regime, an increase of the amplitude of the
dominant structure will reach saturation due to elastic nonlinearity, but the amplitudes with a smaller
increment will continue to increase [26]. Thus, the spectrum of the generatedmodes can extend. However,
it is shown in [26] that in solids with defects which are the centers of tension ( θd > 0), only single-mode
generation with qmax is most frequently realized.
4. Conclusions
1. The theory of nucleation of the surface superlattice of adatoms in GaAs semiconductor under
the effect of laser irradiation at the action of electric field, directed perpendicular to the direction of
13801-7
R.M. Peleshchak, O.V. Kuzyk, O.O. Dan’kiv, S.K. Guba
propagation of the SAW, is developed. The proposed theory takes into account the interaction of adatoms
and conduction electrons with self-consistent SAW. The semiconductor can be located both in the external
electric field and internal one, created, for example, by a hetero-borders. The electric field, transverse
to the direction of propagation of the SAW, creates an additional non-uniform mechanical tension.
Depending on the direction of the electric field, it is possible to increase or decrease the deformation
flows of adatoms.
2. The formation of the superlattice is possible if the average concentration of adatoms exceeds
a certain critical value (or the temperature is less than a certain critical value). The concentration of
adatoms is defined by the intensity of laser irradiation. It is established that in GaAs semiconductor, an
increase of the electric field strength, depending on the direction, leads to an increase or to a decrease of
the critical temperature (the critical concentration of adatoms), at which the formation of self-organized
nanostructure is possible. It is shown that the effect of the electric field is more significant in highly doped
semiconductors as well as in semiconductors with a high value of the constant of hydrostatic deformation
potential of the conduction band and electron mobility. GaAs semiconductor is the most optimal for these
parameters.
3. It is shown that in strongly alloyed n-GaAs semiconductor, an increase of the electric field strength
leads to a monotonous change (decrease or increase depending on the direction of the electric field) of
the period of self-organized surface nanostructures of adatoms.
4. It is established that the effect of the electric field on the conditions of formation and on the period
of the surface superlattice does not depend on the sign of the deformation potential of adatoms.
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Вплив електричного поля на нуклеацiю нанометрової
перiодичної структури адатомiв у напiвпровiднику GaAs пiд
впливом лазерного опромiнення
Р.М. Пелещак1, О.В. Кузик1, О.О. Данькiв1, С.К. Губа2
1 Дрогобицький державний педагогiчний унiверситет iменi Iвана Франка,
вул. Iвана Франка, 24, 82100 Дрогобич, Україна
2 Нацiональний унiверситет “Львiвська полiтехнiка”, вул. Степана Бандери, 12, 79013 Львiв, Україна
У роботi дослiджено вплив електричного поля на умови формування та перiод поверхневої надгратки
адсорбованих атомiв у напiвпровiднику n -GaAs. Встановлено, що у напiвпровiднику GaAs збiльшення
напруженостi електричного поля залежно вiд напрямку призводить до збiльшення або зменшення кри-
тичної температури (критичної концентрацiї адатомiв), при якiй можливе формування самоорганiзова-
ної наноструктури. Показано,що у сильнолегованому напiвпровiднику n -GaAs збiльшення напруженостi
електричного поля призводить до монотонної змiни (зменшення чи збiльшення залежно вiд напрямку
електричного поля) перiоду самоорганiзованих поверхневих наноструктур адатомiв.
Ключовi слова: нуклеацiя, електричне поле, адатом, поверхнева надгратка, дифузiя, деформацiя
13801-9
https://doi.org/10.5488/CMP.18.43801
https://doi.org/10.1088/0957-4484/22/32/325701
https://doi.org/10.1103/PhysRevB.39.1871
https://doi.org/10.5488/CMP.17.23601
https://doi.org/10.1063/1.348589
https://doi.org/10.1134/1.1641133
https://doi.org/10.1070/QE1999v029n07ABEH001533
Introduction
The model
Calculation results and their discussion
Conclusions
|