Electric properties of the interface quantum dot — matrix
A theoretical research is presented concerning the potential distribution and electric field intensity in the InAs/GaAs nanoheterosystem with InAs QDs within the framework of self-consistent electron-deformation model. It is shown that at the strained border between a quantum dot and matrix there...
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Інститут фізики конденсованих систем НАН України
2009
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| Цитувати: | Electric properties of the interface quantum dot — matrix / R.M. Peleshchak, I.Ya. Bachynsky // Condensed Matter Physics. — 2009. — Т. 12, № 2. — С. 215-223. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-1199892017-06-11T03:04:26Z Electric properties of the interface quantum dot — matrix Peleshchak, R.M. Bachynsky, I.Ya. A theoretical research is presented concerning the potential distribution and electric field intensity in the InAs/GaAs nanoheterosystem with InAs QDs within the framework of self-consistent electron-deformation model. It is shown that at the strained border between a quantum dot and matrix there is a double electric layer, that is n⁺ - n junction. У межах моделi самоузгодженого електрон-деформацiйного зв’язку, теоретично дослiджено розподiл потенцiалу та напруженостi електричного поля в напруженiй наногетеросистемi InAs/GaAs з квантовими точкам InAs. Показано, що на напруженiй межi квантова точка – матриця виникає подвiйний електричний шар, тобто n⁺ - n перехiд. 2009 Article Electric properties of the interface quantum dot — matrix / R.M. Peleshchak, I.Ya. Bachynsky // Condensed Matter Physics. — 2009. — Т. 12, № 2. — С. 215-223. — Бібліогр.: 16 назв. — англ. 1607-324X PACS: 68.65.Hb, 73.21.La, 73.63.Kv DOI:10.5488/CMP.12.2.215 http://dspace.nbuv.gov.ua/handle/123456789/119989 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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A theoretical research is presented concerning the potential distribution and electric field intensity in the
InAs/GaAs nanoheterosystem with InAs QDs within the framework of self-consistent electron-deformation
model. It is shown that at the strained border between a quantum dot and matrix there is a double electric
layer, that is n⁺ - n junction. |
| format |
Article |
| author |
Peleshchak, R.M. Bachynsky, I.Ya. |
| spellingShingle |
Peleshchak, R.M. Bachynsky, I.Ya. Electric properties of the interface quantum dot — matrix Condensed Matter Physics |
| author_facet |
Peleshchak, R.M. Bachynsky, I.Ya. |
| author_sort |
Peleshchak, R.M. |
| title |
Electric properties of the interface quantum dot — matrix |
| title_short |
Electric properties of the interface quantum dot — matrix |
| title_full |
Electric properties of the interface quantum dot — matrix |
| title_fullStr |
Electric properties of the interface quantum dot — matrix |
| title_full_unstemmed |
Electric properties of the interface quantum dot — matrix |
| title_sort |
electric properties of the interface quantum dot — matrix |
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Інститут фізики конденсованих систем НАН України |
| publishDate |
2009 |
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http://dspace.nbuv.gov.ua/handle/123456789/119989 |
| citation_txt |
Electric properties of the interface quantum dot — matrix / R.M. Peleshchak, I.Ya. Bachynsky // Condensed Matter Physics. — 2009. — Т. 12, № 2. — С. 215-223. — Бібліогр.: 16 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT peleshchakrm electricpropertiesoftheinterfacequantumdotmatrix AT bachynskyiya electricpropertiesoftheinterfacequantumdotmatrix |
| first_indexed |
2025-07-08T17:02:08Z |
| last_indexed |
2025-07-08T17:02:08Z |
| _version_ |
1837098995541868544 |
| fulltext |
Condensed Matter Physics 2009, Vol. 12, No 2, pp. 215–223
Electric properties of the interface quantum dot – matrix
R.M.Peleshchak, I.Ya.Bachynsky
Drohobych Ivan Franko state pedagogical University, 82100 Drohobych, 24 I.Franko Str., Ukraine
Received March 31, 2009, in final form May 13, 2009
A theoretical research is presented concerning the potential distribution and electric field intensity in the
InAs/GaAs nanoheterosystem with InAs QDs within the framework of self-consistent electron-deformation
model. It is shown that at the strained border between a quantum dot and matrix there is a double electric
layer, that is n
+ − n junction.
Key words: quantum dots, electron-deformation and electrostatic potentials
PACS: 68.65.Hb, 73.21.La, 73.63.Kv
1. Introduction
At present, the study of electric properties of stressed heteroborder between a quantum dot(QD)
(InAs, CdTe) and matrix (GaAs, ZnTe) is of great interest [1]. This interest is related to the devel-
opment of new approaches to the creation of p-n structures on QDs, specifically tunnel diodes [2],
quantum transistors [3], elements of one-electronic memory [4]. Stresses that arise in nanoheterosys-
tems with QDs both in the process of growth and temperature changes, and during fabrication on
their basis of opto- and nanoelectronics devices, effect the shape and the potential barrier height
at the border between a QD and a matrix, the band-gap energy, a discrete spectrum of energy
states of the electrons localised in a QD, the charge emission from the QD into the corresponding
bands of the semiconductor, the barrier capacity of the structure and the width of the space charge
region.
Electrical and optical properties of nanoheterostructures with QDs are defined, mainly, by an
energy distribution of charge carriers. Therefore, such properties should be sensitive to the sizes,
to the shape, to the composition of nanocluster InAs(CdTe) and strains of materials of nanocluster
and the surrounding matrix GaAs(ZnTe), since deformation effects the depth and the character
of quantizing potential of a quantum dot. In particular,nanoclusters InAs (CdTe) create in matrix
GaAs (ZnTe) the potential wells for electrons and holes, which can be negatively or positively
charged, capturing electrons and holes from the surrounding volume of a matrix. The degree of
charging of a QD by carriers and their emission will depend on the character and size of deformation
of nanocluster and matrices materials, which effects both the energy location of local levels in a
QD and the location of electrochemical potential in a nanoheterostructure.
In papers [5,6], the authors have explored, for the one-dimensional case, a potential distribution
in the field of a spatial charge in the vicinity of the boundary of the contact between metal and
semiconductor GaAs with a layer of quantum dots InAs [5], capacitance-voltage characteristics [5],
potential distribution and transport processes in silicon Shottki diodes, which contain an array
of germanium nanoclusters [6]. Theoretical research in articles [5,6] was done without taking into
account the deformation effects, which essentially effect the transport properties of the carriers in
nanoheterosystems with quantum dots.
The purpose of the given paper is to study the potential distribution and electric field at the
strained boundary between a QD (InAs, CdTe) and the matrix (GaAs, ZnTe) within the framework
of self-consistent electron-deformation model [7]. Thus, knowing the mechanism of changing the
character of a potential distribution and an electric field in nanoheterosystem with an array of
quantum dots, under the effect of deformation fields, it is possible to predict and control electrical
c© R.M.Peleshchak, I.Ya.Bachynsky 215
R.M.Peleshchak, I.Ya.Bachynsky
properties of p–n structures, which are created on the basis of strained nanoheterosystems with an
array of QDs.
2. Model of the potential and electric field distribution in a spherical QD
InAs and in the matrix GaAs
In this formulation of the problem, nanoheterosystems InAs/GaAs (001) with coherently strained
InAs quantum dots without a precisely determined crystallographic facet are considered. Techno-
logically, such QDs can be obtained if the thickness of the InAs growing layer becomes of the order
of 2 monolayers (ML) [8]. Therefore, in what follows, both the contribution of the island edges to
the elastic deformation energy and, correspondingly, the jump of the strain tensor at the island
edges can be neglected.
We consider the InAs/GaAs heterosystem with coherently stressed spherical InAs QDs. In
order to reduce the problem with a large number of QDs to the problem with one QD, we use the
following approximation. The energy of the pairwise elastic interaction between the QDs can be
replaced by the energy of interaction of each QD with the averaged elastic strain field σef(N−1) of
all other (N − 1) QDs [9]. Thus, QD InAs in matrix n-GaAs creates a potential well for electrons,
and in p-GaAs – a potential well for holes, accordingly (see figure 1). The given potential wells can
be charged with the negative or positive charge.
Figure 1. Geometry model (a) and zone scheme (b) of a InAs/GaAs nanoheterosystem with InAs
QDs (solid line without taking into account deformation effects, dashed line -with deformation
effects).
Under the effect of inhomogeneous deformation of compression of QD InAs material and inho-
mogeneous deformation of tension of matrix GaAs material, which surrounds a quantum dot, the
band structure of the nanoheterosystem with QDs locally changes (see figure 1b). Such a change,
as a result of self-compounding of an electron-deformation framework, leads to redistribution of
electronic density in the surroundings of strained boundary between a quantum dot and matrix.
Therefore, in the material of a QD, near heteroboundary, there is a surplus of negative charge
216
Electric properties of the interface quantum dot – matrix
while in the matrix material there is a shortage. Thus, at the strained heteroboundary between a
quantum dot and the matrix there arises n+ − n junction (electron-deformation dipole ~Pel.−def.).
The mathematical model featuring a potential distribution at the strained heteroboundary
between QD and matrix consists of the following self-compounded combined equations:
the Schrodinger equation
[
~
2
2m∗
i
∆~r + V
(i)
def (~r) − eϕi(~r)
]
ψ(i)
n (~r) = Ẽnψ
(i)
n (~r), i =
{
1 ≡ InAs,
2 ≡ GaAs,
(1)
V
(i)
def (~r) =
{
−
(
|∆Ec| −
∣
∣
∣a
(1)
c ε1
∣
∣
∣ −
∣
∣
∣a
(2)
c ε2
∣
∣
∣
)
,
0.
(2)
here ∆Ec – is the depth of the potential well for electrons in the QD in a non-deformed het-
erostructure InAs/GaAs; Ẽn = En − λ0 is eigenvalues Schrodinger functional; λ0 is the energy of
the bottom of non-deformed allowed band; a
(i)
c – is the constant of the hydrostatic deformation
potential of the conduction band; εi(~r) = Sp ε̂i is deformation parameter, which is defined through
displacement of atoms ~ui, which are taken from the equilibrium equation:
~∇div~ui = −D(i) · ~F (i) (~r) , (3)
where ~F (i)(~r) = −eδ ~E(i), D(i) = (1+νi) (1−2νi)
(a(i))3Ei (1−νi)
here δ ~E is redundant electric field, which arises
at the strained interface between quantum dot and matrix, the intensity of which is determined
through a gradient of electrostatic potential
(
δE(i) = −dϕ(i)(~r)
dr
)
; a(i) is lattice parameter; νi are
Poisson coefficients; Ei is Young modulus of the QD and surrounding matrix materials; e is ele-
mentary electronic charge.
From the Poisson equation we find electrostatic potential ϕ(i) (~r):
∆ϕi(~r) =
e
ε
(i)
d ε0
∆ni(~r), (4)
where ε
(i)
d is relative dielectric constant; ∆ni(~r) is the change of electron density at the interface
between QD and matrix and can be obtained through superposition of wave function multiplication,
which are solutions of the Schrodinger equation(1):
ni(r) =
∑
n
ψ
∗(i)
n (~r)ψ
(i)
n (~r)
exp(β(Ẽn − µi)) + 1
, (5)
where µi is chemical potential; and equation for defining the electrochemical potential:
1
Ω0
∫
n(~r)d~r = n0 , (6)
here Ω0 is the volume of unit cell, n0 is the average electron density in nanoheterostructure with
QDs.
Since in the task there is considered a spherically – symmetrical nanoheterosystem, the system
of equations (1)–(6) will take the following form:
[
− ~
2
2m∗
i
(
d2
dr2
+
2
r
d
dr
− l(l+ 1)
r2
)
+ V
(i)
def (r) − eϕi(r)
]
R
(i)
nl (r) = Enr
R
(i)
nl (r) , (7)
where R
(i)
nl (r) is radial wave function of electrons. Radial wave functions R
(i)
nl are the solutions of
the radial Schrodinger equation(7) with deformation potential(2):
R
(1)
nl (r) = Ajl(knlr) +Bnl(knlr), 0 6 r 6 R0 ,
R
(2)
nl (r) = Ch
(1)
l (iχnlr) +Dh
(2)
l (iχnlr) , R0 6 r 6 R1 , (8)
217
R.M.Peleshchak, I.Ya.Bachynsky
where
k2
nl =
2m∗
1
~2
(∣
∣
∣V
(1)
def
∣
∣
∣− |Enl|
)
,
χ2
nl =
2m∗
2
~2
|Enl| . (9)
The continuity conditions for the wave functions and density of the flow of probability at the
QD-matrix interface,
R
(1)
nl (r) |r=R0 = R
(2)
nl (r) |r=R0 ,
1
m∗
1
dR
(1)
nl (r)
dr |r=R0 = 1
m∗
2
dR
(2)
nl (r)
dr |r=R0
(10)
along with the regularity condition of the function R
(1)
nl (r) at r → 0, zero equality of the function
R
(2)
nl (r) at r → R1
(
R
(2)
nl (r) |r=R1 = 0
)
and with normalization, determine the energy spectrum Enl
and wave functions of the electron in the InAs/GaAs heterosystem with the InAs QD. Therefore, the
energy of the ground state of the electron in the QD is determined from the following transcendental
equation[9]:
k tg
(
kR0 − n
π
2
)
= χ
m∗
1
m∗
2
ctgh(χ(R1 −R0)) +
m∗
1 −m∗
2
R0m∗
2
, n = 1. (11)
In case of spherical symmetry, the equilibrium equation(3) can be presented in the form:
d2u
(i)
r
dr2
+
2
r
du
(i)
r
dr
− 2
r2
u(i)
r = D(i)e
dϕ(i)(r)
dr
(12)
here u
(i)
r is radial component of displacements of atoms. General solution of the heterogeneous
equation(12) is presented in the form of the sum of mechanical u
(i)
r mech(r) and electron-deformation
u
(i)
rel−def(r) displacements components:
u(i)
r (r) = u
(i)
r mech(r) + u
(i)
rel−def(r), (13)
where u
(i)
r mech(r) = C
(i)
1 r +
C
(i)
2
r2 , u
(i)
rel−def(r) = −D(i)e
r2
∫
r2ϕ(i)(r) dr. For insignificant conduction
electron concentrations in a matrix of the nanoheterosystem (n0 < 1018 sm−3), the value of the
electron-deformation component of displacements u
(i)
rel−def(r) in QD is one order smaller than the
mechanical component of displacements u
(i)
r mech(r). Therefore, in the first approximation we ignore
the electron-deformation component of displacements u
(i)
rel−def(r)
The field of displacements determines the following components of the strain tensor:
ε(1)rr = ε(1)ϕϕ = ε
(1)
θθ = C
(1)
1 , (14)
ε(2)rr = C
(2)
1 − 2C
(2)
2
r3
, (15)
ε(2)ϕϕ = ε
(2)
θθ = C
(2)
1 +
C
(2)
2
r3
. (16)
The coefficients C
(1)
1 , C
(2)
1 , C
(2)
2 are determined from the solution of the following combined
equations :
u
(2)
r |r=R0 − u
(1)
r |r=R0 = fR0,
σ
(1)
rr |r=R0 = σ
(2
rr|r=R0 + PL|r=R0 , PL = 2α
R0−
∣
∣
∣
u
(1)
r
∣
∣
∣
,
σ
(2)
rr |r=R1 = −σef(N − 1),
(17)
218
Electric properties of the interface quantum dot – matrix
α – is the surface energy of the InAs QD [10], f – is the lattice mismatch of the materials of
the QD and the matrix:f = a(1)
−a(2)
a(1) ≈ 7% ; σ
(i)
rr are radial components of the mechanical strain
tensor [11].
Poisson equation(4) can be presented in the form:
d2ϕ(i)
dr2
+
2
r
dϕ(i)
dr
=
e
ε
(i)
d ε0
(ni(r) − n0) . (18)
The charge density in a strained nanoheterostructure with a quantum dot was calculated with δ
– similar density of electronic state in QD δ (E ′ −En) ≈ 1√
π/2 ∆E
exp
(
−2(E′
−En)2
∆E2
)
. Specifically,
at the T = 0K temperature in the QD (0 6 r 6 R0) and matrix (R0 6 r 6 R1), the charge
density ni(r) can be obtained from the following formula :
ni (r) =
∫ µ−λ
(i)
0 −a(i)
c ε(i)
rr +eϕi(r)
0
2NQD
a(i)
√
π/2∆E
e
−2(E′
−E1)
2
∆E2
∣
∣
∣ψ
(i)
nlm
∣
∣
∣
2
dE′
=
∣
∣
∣ψ
(i)
nlm
∣
∣
∣
2 NQD
a(i)
(
erf
( √
2
∆E
E1
)
+ erf
√
2
∆E
(
µ−E1 − λ
(i)
0 − a(i)
c ε(i)rr + eϕi (r)
)
)
, (19)
where NQD surface density of quantum dots, which is equal in nanoheterostructure InAs/GaAs
with QDs InAs ≈ 3× 1010 sm−2 [12]; ∆E – half-width of Gauss line;E1 – energy of an electron at
the first localized level in a quantum well; ψ
(i)
nlm (r, θ, ϕ) = R
(i)
nl (r) · Ylm(θ, ϕ) – the solution of the
Schrodinger equation (1) in the spherical system of coordinates; Ylm(θ, ϕ) – the spherical Legendre
functions [13].
The Poisson equation (18) concentration of charge carriers ni(r)(19) is a nonlinear function
from ϕi(r). Therefore, first of all we linearize it, i. e., we substitute Taylor expansion for expression
(18) in the Poisson equation:
ni(r) ≈
∣
∣
∣
ψ
(i)
nlm
∣
∣
∣
2 NQD
a(i)
[
erf
( √
2
∆E
E1
)
+ erf
( √
2
∆E
(
µ−E1 − λ
(i)
0 − a(i)
c ε(i)rr
)
)
+
√
8
π
e
∆E
e
−2(µ−E1−λ
(i)
0
−a
(i)
c ε
(i)
rr )
2
∆E2 × ϕ i (r)
]
. (20)
The solution of the Poisson equation (18) in the QD and matrix, taking into account the
expression for an electron concentration(20), with an average frequency function
∣
∣ψ̄i
∣
∣
2
has the
following form:
ϕ1(r) = A1
sinh
(√
1
a1
r
)
r
− a1b1 , (21)
ϕ2(r) = B1
exp
(
−
√
1
a2
r
)
r
+B2
exp
(√
1
a2
r
)
r
− a2b2 −
d2
2r
×
[
exp
(
−
√
1
a2
r
)
×Ei
(
√
1
a2
r
)
+ exp
(
√
1
a2
r
)
×Ei
(
−
√
1
a2
r
)]
, (22)
where
Ei (z) = −
∫
∞
−z
exp (−t)
t
dt,
1
a1
=
e2
ε
(1)
d ε0a(1)
∣
∣ψ̄1
∣
∣
2
NQD
√
8
π
∆E
exp
−2
(
µ−E1 − λ
(1)
0 − a
(1)
c C
(1)
1
) 2
∆E2
,
219
R.M.Peleshchak, I.Ya.Bachynsky
1
a2
=
e2
ε
(2)
d ε0a(2)
∣
∣ψ̄2
∣
∣
2
NQD
√
8
π
∆E
exp
−2
(
µ−E1 − λ
(2)
0 − a
(2)
c C
(2)
1
) 2
∆E2
,
d2 =
2a
(2)
c C
(2)
2 e
ε
(2)
d ε0a(2)
∣
∣ψ̄2
∣
∣
2
NQD
√
8
π
∆E
exp
−2
(
µ−E1 − λ
(2)
0 − a
(2)
c C
(2)
1
) 2
∆E2
,
b1 =
e
ε
(1)
d ε0a(1)
∣
∣ψ̄1
∣
∣
2
NQD
[
erf
( √
2
∆E
E1
)
+ erf
( √
2
∆E
(
µ−E1 − λ
(1)
0 − a(1)
c C
(1)
1
)
)
− a(1)n0
∣
∣ψ̄1
∣
∣
2
NQD
]
,
b2 =
e
ε
(2)
d ε0a(2)
∣
∣ψ̄2
∣
∣
2
NQD
[
erf
( √
2
∆E
E1
)
+ erf
( √
2
∆E
(
µ−E1 − λ
(2)
0 − a(2)
c C
(2)
1
)
)
− a(2)n0
∣
∣ψ̄2
∣
∣
2
NQD
]
.
Accordingly, the expression for an electric field intensity in quantum dots and a matrix will
look like this:
E1(r) = A1
√
1
a1
r cosh
(√
1
a1
r
)
− sinh
(√
1
a1
r
)
r2
, (23)
E2(r) = −d2
r2
+
e
−
√
1
a2
r
r
(
d2
2
Ei
(
√
1
a2
r
)
−B1
)(
1
r
+
√
1
a2
)
+
e
√
1
a2
r
r
(
d2
2
Ei
(
−
√
1
a2
r
)
−B2
)(
1
r
−
√
1
a2
)
. (24)
The coefficients A1, B1, B2 in expressions (21)–(24) are determined from requirements of a
continuity of potentials ϕ1(r) and ϕ2(r) at the strained heteroboundary, normal component of a
vector of an electric displacement and the condition of neutrality.
ϕ(1)(r)|r=R0 = ϕ(2)(r)|r=R0 ,
ε1
dϕ(1)(r)
dr |r=R0 = ε2
dϕ(2)(r)
dr |r=R0 ,
R0
∫
0
r2∆n1(r)dr+
R1
∫
R0
r2∆n2(r)dr = 0.
(25)
3. Numerical calculations and discussion of results
Further, we present the results of theoretical research of the dependence of the electrostatic
potential and electric field intensity in the InAs QD and in the matrix within the framework
of self-consistent electron-deformation model. The calculations were performed for the following
parameters ([10,14,15]): a(1) = 6.08 Å; a(2) = 5.65 Å; C
(1)
11 = 0.833 Mbar; C
(1)
12 = 0.453 Mbar;
C
(2)
11 = 1.223 Mbar; C
(2)
12 = 0.571 Mbar; ∆Ec (0) = 0.83 eV; a
(1)
c = −5.08 eV; a
(2)
c = −7.17 eV;
E
(1)
g (0) = 0.36 eV; E
(2)
g (0) = 1.452 eV; R1 = 1000 Å; σef = 109N/m2; m
(e)
1 = 0.057m0; m
(e)
2 =
0.065m0; α = 0.657 H/m.
Figure 2–4 shows the dependence of electrostatic potential ϕ (r) (figure 2), electric field intensity
(figure 3) and charge density ∆n (r) (figure 4) in a InAs/GaAs nanoheterosystem with InAs QDs
size : R0 = 50 Å, R0 = 100 Å.
220
Electric properties of the interface quantum dot – matrix
(a) (b)
Figure 2. Coordinate dependence of the electrostatic potential ϕ (r) in the InAs/GaAs
nanoheterosystem with InAs QDs; (a) R0 = 50 Å, (b) R0 = 100 Å.
(a) (b)
Figure 3. Coordinate dependence of the electric field intensity E (r) in the InAs/GaAs
nanoheterosystem with InAs QDs; (a) R0 = 50 Å, (b) R0 = 100 Å.
(a) (b)
Figure 4. Coordinate dependence of the charge density ∆n (r) in the InAs/GaAs nanoheterosys-
tem with InAs QDs; (a) R0 = 50 Å, (b) R0 = 100 Å.
It is evident from figure 2 that electrostatic potential ϕ (r), in such nanoheterosystem, deflates
when the size of QD increase. In particular, the increase of the QD radius R0 from 50 to 100 Å
results in a decrease of the electrostatic potential at the interface between QD and matrix by about
206 meV.
Potential distribution ϕ (r) , in such nanoheterosystem, subject to the size of a QD has a
monotonous (figure 2a) or a nonmonotonous character (figure 2b). Specifically, coordinate depen-
dence of the electrostatic potential for QDs at the sizes 20 Å 6 R0 6 70 Å is monotonous, and
at the sizes R0 > 70 Å it is nonmonotonous, the maximum location of which is defined by radius
of a QD. Such a character of electrostatic potential ϕ (r) distribution in QDs of different sizes is
221
R.M.Peleshchak, I.Ya.Bachynsky
defined by redistribution of an electronic density of charge ∆n = ∆n (~r) (see figure 4) at the QD –
matrix interface. At the QD – matrix interface, electrostatic potential ϕ (r) is changed and moving
from boundary (r → R1) the potential goes to the value ϕ (r) |r=R1 ≈ B2
e
√
1
a2
R1
R1
− a2b2 .
Figure 3 shows the electric field intensity distribution in the QD and in the matrix. As numerical
calculations show the electric field intensity deflates with an increase of the QD size, and it is
maximal at the QD – matrix interface. Specifically, for a QD at the size 50 Å E(r)
∣
∣
r=R0 = 66kV
sm
and at the size 100 Å − E(r)
∣
∣
r=R0 = 49kV
sm . The decrease of the electric field intensity when the
size of QD increases is specified by a decrease of the deformation potential. With a distance from
the boundary, the electric field intensity in QD wanes and is equal to zero at the center of QD,
and in the matrix it has a nonmonotonous character and approaching the matrix edge it wanes to
zero.
As it is shown in the figures (figures 4a,b) at the QD – matrix interface, spatial redistribution
of electrons takes place: the electrons are excessive near the interface in the QD InAs(CdTe), and
they are depleted in the matrix GaAs(ZnTe). The effect of electrostatic interaction of charges
leads to such a redistribution of electronic density that at the strained border between quantum
dot and matrix there arises a double electric layer, i. e., n+ − n junction. It is possible to control
the electrical properties of n+ − n junction at the expense of the surface densityNQD variation
of QDs. Observationally, it is possible to define the concentration profile of the majority carriers
of a charge in such a nanoheterosystem with QDs by differentiating the C–V [16] characteristic:
n(i)(r) = 2
[
ε
(i)
d ε0S
2 d
dV
(
1
C2
)
]
−1
(S are contact surfaces between a quantum dot and a matrix, r
is a moving coordinate of the boundary space-charge region).
References
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222
Electric properties of the interface quantum dot – matrix
Електричнi властивостi межi подiлу квантова точка –
матриця
Р.М.Пелещак, I.Я.Бачинський
Дрогобицький державний педагогiчний унiверситет iменi Iвана Франка,
Дрогобич 82100, вул. Iвана Франка 24, Україна
Отримано 31 березня 2009 р., в остаточному виглядi – 13 травня 2009 р.
У межах моделi самоузгодженого електрон-деформацiйного зв’язку, теоретично дослiджено роз-
подiл потенцiалу та напруженостi електричного поля в напруженiй наногетеросистемi InAs/GaAs з
квантовими точкам InAs. Показано, що на напруженiй межi квантова точка – матриця виникає по-
двiйний електричний шар, тобто n
+ − n перехiд.
Ключовi слова: квантовi точки, електрон-деформацiйний та електростатичний потенцiали
PACS: 68.65.Hb, 73.21.La, 73.63.Kv
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