Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs)
The analytical and numerical calculations of electron and hole spectra renormalised by L- and I-phonons taking into account the configurational interaction are performed for the QD embedded into semiconductor medium exemplified by GaAs/AlxGa₁₋xAs nanoheterosystems. It is established that for the...
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| Опубліковано в: : | Condensed Matter Physics |
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| Дата: | 2001 |
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Інститут фізики конденсованих систем НАН України
2001
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| Цитувати: | Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) / M.V. Tkach, M.Y. Mikhalyova, O.M. Voitsekhivska, R.B. Fartushinsky // Condensed Matter Physics. — 2001. — Т. 4, № 3(27). — С. 579-589. — Бібліогр.: 16 назв. — англ. |
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Tkach, M.V. Mikhalyova, M.Y. Voitsekhivska, O.M. Fartushinsky, R.B. 2017-06-12T07:58:44Z 2017-06-12T07:58:44Z 2001 Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) / M.V. Tkach, M.Y. Mikhalyova, O.M. Voitsekhivska, R.B. Fartushinsky // Condensed Matter Physics. — 2001. — Т. 4, № 3(27). — С. 579-589. — Бібліогр.: 16 назв. — англ. 1607-324X PACS: 79.60.Jv, 63.20.Dj DOI:10.5488/CMP.4.3.579 https://nasplib.isofts.kiev.ua/handle/123456789/120473 The analytical and numerical calculations of electron and hole spectra renormalised by L- and I-phonons taking into account the configurational interaction are performed for the QD embedded into semiconductor medium exemplified by GaAs/AlxGa₁₋xAs nanoheterosystems. It is established that for the nanosize QDs the shifts of electron and hole ground levels are created by the interaction of these quasiparticles with Land I-phonons due to all the states of discrete and continuous spectrum. For the small QDs, the shifts of ground energy levels have strong nonlinear dependences while for the big QDs, they almost do not depend on QD radius and have the magnitude close to the shifts of ground levels in massive crystal creating QD. Due to the different effective masses of light and heavy holes, the splittings of their ground levels are the complicated functions on QD radius and Al concentration in AlxGa₁₋xAs medium. У роботі виконано аналітичний і чисельний розрахунки перенормування L- та I-фононами електронного та діркового спектрів з повним врахуванням конфігураційної взаємодії у квантовій точці, що вміщена в напівпровідникове середовище. Конкретний розрахунок виконано для гетеросистеми GaAs/AlxGa₁₋xAs. Установлено, що зсуви основних рівнів електрона та дірки формуються взаємодією цих квазічастинок як з L-, так і з I-фононами за участю всіх станів дискретного та неперервного спектрів. При малих розмірах КТ зсуви основних енергетичних рівнів квазічастинок мають сильно нелінійну залежність, а при великих радіусах КТ вони практично не залежать від розміру КТ та близькі за величиною до зсувів основних рівнів у масивному кристалі, з якого утворена КТ. Через різницю ефективних мас важкої та легкої дірок розщеплення їх основних рівнів має складну залежність від радіуса КТ та концентрації Al (x) у середовищі AlxGa₁₋xAs. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) Взаємодія електронів та дірок з фононами у квантовій точці, що вміщена в напівпровідникове середовище (GaAs/AlxGa₁₋xAs) Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) |
| spellingShingle |
Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) Tkach, M.V. Mikhalyova, M.Y. Voitsekhivska, O.M. Fartushinsky, R.B. |
| title_short |
Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) |
| title_full |
Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) |
| title_fullStr |
Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) |
| title_full_unstemmed |
Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) |
| title_sort |
electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (gaas/alxga₁₋xas) |
| author |
Tkach, M.V. Mikhalyova, M.Y. Voitsekhivska, O.M. Fartushinsky, R.B. |
| author_facet |
Tkach, M.V. Mikhalyova, M.Y. Voitsekhivska, O.M. Fartushinsky, R.B. |
| publishDate |
2001 |
| language |
English |
| container_title |
Condensed Matter Physics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| format |
Article |
| title_alt |
Взаємодія електронів та дірок з фононами у квантовій точці, що вміщена в напівпровідникове середовище (GaAs/AlxGa₁₋xAs) |
| description |
The analytical and numerical calculations of electron and hole spectra
renormalised by L- and I-phonons taking into account the configurational
interaction are performed for the QD embedded into semiconductor medium
exemplified by GaAs/AlxGa₁₋xAs nanoheterosystems.
It is established that for the nanosize QDs the shifts of electron and hole
ground levels are created by the interaction of these quasiparticles with Land
I-phonons due to all the states of discrete and continuous spectrum.
For the small QDs, the shifts of ground energy levels have strong nonlinear
dependences while for the big QDs, they almost do not depend on QD radius
and have the magnitude close to the shifts of ground levels in massive
crystal creating QD. Due to the different effective masses of light and heavy
holes, the splittings of their ground levels are the complicated functions on
QD radius and Al concentration in AlxGa₁₋xAs medium.
У роботі виконано аналітичний і чисельний розрахунки перенормування L- та I-фононами електронного та діркового спектрів з повним
врахуванням конфігураційної взаємодії у квантовій точці, що вміщена
в напівпровідникове середовище. Конкретний розрахунок виконано
для гетеросистеми GaAs/AlxGa₁₋xAs.
Установлено, що зсуви основних рівнів електрона та дірки формуються взаємодією цих квазічастинок як з L-, так і з I-фононами за участю всіх станів дискретного та неперервного спектрів. При малих розмірах КТ зсуви основних енергетичних рівнів квазічастинок мають сильно нелінійну залежність, а при великих радіусах КТ вони практично
не залежать від розміру КТ та близькі за величиною до зсувів основних рівнів у масивному кристалі, з якого утворена КТ. Через різницю
ефективних мас важкої та легкої дірок розщеплення їх основних рівнів має складну залежність від радіуса КТ та концентрації Al (x) у середовищі AlxGa₁₋xAs.
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/120473 |
| citation_txt |
Electron- and hole-phonon interaction in quantum dot embedded into semiconductor medium (GaAs/AlxGa₁₋xAs) / M.V. Tkach, M.Y. Mikhalyova, O.M. Voitsekhivska, R.B. Fartushinsky // Condensed Matter Physics. — 2001. — Т. 4, № 3(27). — С. 579-589. — Бібліогр.: 16 назв. — англ. |
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2025-11-26T00:18:46Z |
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2025-11-26T00:18:46Z |
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| fulltext |
Condensed Matter Physics, 2001, Vol. 4, No. 3(27), pp. 579–589
Electron- and hole-phonon interaction
in quantum dot embedded into
semiconductor medium
(GaAs/AlxGa1−xAs)
M.V.Tkach, M.Y.Mikhalyova, O.M.Voitsekhivska,
R.B.Fartushinsky
Chernivtsi State University,
2 Kotsiubinsky Str., 274012 Chernivtsi, Ukraine
Received May 24, 2001
The analytical and numerical calculations of electron and hole spectra
renormalised by L- and I-phonons taking into account the configurational
interaction are performed for the QD embedded into semiconductor medi-
um exemplified by GaAs/AlxGa1−xAs nanoheterosystems.
It is established that for the nanosize QDs the shifts of electron and hole
ground levels are created by the interaction of these quasiparticles with L-
and I-phonons due to all the states of discrete and continuous spectrum.
For the small QDs, the shifts of ground energy levels have strong nonlinear
dependences while for the big QDs, they almost do not depend on QD ra-
dius and have the magnitude close to the shifts of ground levels in massive
crystal creating QD. Due to the different effective masses of light and heavy
holes, the splittings of their ground levels are the complicated functions on
QD radius and Al concentration in AlxGa1−xAs medium.
Key words: nanoheterosystem, interaction, electron, hole, phonon
PACS: 79.60.Jv, 63.20.Dj
1. Introduction
Numerous theoretical and experimental investigations [1–3] during the past de-
cade are devoted to the theory of electron-phonon interaction in low-dimensional
systems. Nevertheless, the problem of spectral parameters dependence on the ge-
ometrical parameters of nanosystems is discussed up till now. Different physical
models and mathematical approximations [4] are used for the description of the
above mentioned systems.
It is known [4] that the main model for studying the electron-phonon interaction
in the simplest heterosystems (plane quantum wells [5–6], quantum wires (QW) [7–
c© M.V.Tkach, M.Y.Mikhalyova, O.M.Voitsekhivska, R.B.Fartushinsky 579
M.V.Tkach et al.
8] and quantum dots (QD) [9–12]) is the dielectric continuum model. It gives rather
exact results compared to the Huang-Zhu microscopic model [4]. The calculation of
electron (hole) energy renormalised due to the interaction with phonons is a sophis-
ticated mathematical problem even within the framework of dielectric continuum
model. The reasons of these difficulties are the multilevel and multiband electron
(hole) spectrum and the presence of several modes of phonon spectrum.
In order to simplify the problem some authors [9–10] considered only the inter-
level interaction between electron and optical phonons assuming the other types of
interaction as secondary. At this approximation, the interlevel interaction through
the continuous states is not taken into account, as well as the interaction with inter-
face phonons which are absent in spherical QDs only for the spherically-symmetric
states (l = 0). It is true only for the small QDs when there is a ground energy level
in the potential well or the excited levels are located quite far away. But in [13] it
was shown that for the plane QWs the interlevel interaction becomes essential for
the big QWs. When the QW width increases from zero to the infinity, the shift of
the band bottom and the electron effective mass smoothly vary in the limits close
to the corresponding three-dimensional magnitudes.
The other group of authors [7, 11–12] have used the approximation of infinitely
deep potential well in the media interface, justifying such mathematical simplifica-
tion by the small difference between electron wave functions in the potential well
of infinite and finite depth. Herein, there is not taken into account the shift of the
external medium phonons which is rather big for the small radii of a heterosystem
and the real shift of interface phonons is essentially smaller as well.
In this paper the different types of electron, light and heavy hole interaction with
optical and interface phonons through the discrete and continuous states of GaAs
spherical QD embedded into GaxAl1−xAs massive external medium are investigated
in detail.
2. Electron-phonon Hamiltonian in spherical nanohetero-
system
The renormalization of the electron (hole) ground level due to the interaction
with phonons is under study for the semiconductor QD embedded into a massive
semiconductor sphere. According to the general theory [14], the Hamiltonian of
electron interacting with phonon in the representation of the second quantization
over all the variables of nanoheterosystem has the following form
Ĥ = Ĥe + ĤL + ĤI + Ĥe−L + Ĥe−I , (1)
where
Ĥe =
∑
plm
Eplâ
+
plm ˆaplm (2)
is the Hamiltonian of the electron subsystem. Here p is the set of two radial quantum
numbers (n, k) denoting the states of discrete and continuous spectra, respectively;
580
Electron- and hole-phonon interaction in quantum dot
l, m are orbital and magnetic quantum numbers. The discrete spectrum energies
Enl are defined by the solutions of the dispersion equations [14] and the continuous
spectrum energies are fixed by the expression
Ekl =
~
2k2
2m1
, (3)
where m1 is the quasiparticle effective mass in the external medium.
ĤL =
1
∑
i=0
∑
silm
ΩLi
(
b̂+silmb̂silm +
1
2
)
, (4)
ĤI =
∑
lms=±
Ω
(s)
l
(
b̂+slmb̂slm +
1
2
)
(5)
are the Hamiltonians of confined and interface phonons, respectively. The energies of
confined phonons (ΩLi
) are equal to the corresponding energies of the longitudinal
optical vibrations of the massive crystals, and the energies of interface phonons
(Ω
(s)
l ) are given by the dispersion equations [14]. Index si=0,1 corresponds to the
radial quantum numbers of the confined polarizational vibrations and s = ± –
numerates two modes of interface vibrations.
Ĥe−L =
1
∑
i=0
∑
p1l1m1
p2l2m2
∑
silm
Φp2l2m2
p1l1m1
(silm)â+p2l2m2
âp1l1m1
(b̂+silm + b̂sil−m), (6)
Ĥe−I =
∑
p1l1m1
p2l2m2
∑
slm
Φp2l2m2
p1l1m1
(slm)â+p2l2m2
âp1l1m1
(b̂+slm + b̂sl−m) (7)
are the Hamiltonians of interaction between electron and L-, I-phonons, respective-
ly. The expressions for the binding functions Φp2l2m2
p1l1m1
(silm) and Φp2l2m2
p1l1m1
(slm) are
presented in [14].
Finally, the Hamiltonian given by equation (1) makes it possible to use the Greens
function method for the investigation of electron (hole) spectrum renormalized due
to the interaction with phonons.
3. Calculation and analysis of the ground electron level renor-
malization due to the interaction with optical and interface
phonons
It is known [15–16], that in the case of QD with multilevel electron spectrum,
the Fourier image of Green’s function is connected with mass operator (MO) of the
system by Dyson equation
Gµµ
′ (ω) = G0
µµ
′ (ω)δµµ′ +G0
µ(ω)
∑
µ1
Mµµ
′Gµ1µ
′ (ω), (8)
581
M.V.Tkach et al.
Table 1. Values of physical parameters used in numerical calculations.
GaAs AlxGa1−xAs
me 0.067 0.067 + 0.083x
mlh 0.08 0.08 + 0.1x
mhh 0.035 0.35 + 0.05x
ǫ0 10.6 10.9− 2.8x
ǫ∞ 12.5 13.2− 3.1x
ΩLo (meV) 36.2 50.1
Eg 1.42 1.42 + 1.155x+ 0.37x2
where
G0
µ(ω) = (ω − Eµ + iη)−1 (9)
and µ = n, l,m is the set of all quantum numbers characterizing the electron states
of the discrete spectrum.
According to [15], in case of the weak binding which is realised for the researched
GaAs/AlxGa1−xAs nanoheterosystem, the MO describing the ground state (µ =
100) renormalization, has the form
M100,100(ω) = M(ω) =
1
∑
i=o
∑
plm
∑
Si
|(FSil)
pl
10|
ω −Epl − ΩLi
+
∑
splm
∑
|(F
(s)
l )pl10|
ω − Epl − Ωl
, (10)
where Epl,ΩLi
,Ω
(s)
l are the energies of electron and phonon subsystems and (FSil)
pl
10,
(F
(s)
l )pl10 are the radial parts of binding functions of these quasiparticles obtained in
[14].
The pole of the Greens function Fourier image brings to the dispersion equation
defining the energy (Ẽ10) of the electron ground level renormalized due to phonons
as
Ẽ10 = E10 +∆, (11)
where according to the MO structure (10) the shift ∆ is given by the sum of partial
shifts
∆ = ∆L0d +∆L1d +∆I+d +∆I−d +∆L0c +∆L1c +∆I+c +∆I−c (12)
due to the respective phonon modes through the states of discrete (d) and continuous
(c) parts of electron spectrum.
The numerical calculation of electron, light and heavy holes ground level total
and partial shifts was performed for the QD with physical parameters listed in
table 1. The dependences of the electron and hole ground level total and partial shifts
on QD radius are qualitatively the same, and therefore, the analysis is performed
for the electron only.
Figures 1–4 present the total and partial shifts of electron ground level (in di-
mensionless units of optical phonon energy of GaAs crystal) determined by different
582
Electron- and hole-phonon interaction in quantum dot
types of interaction with phonons as functions of QD radius (in units of GaAs lattice
constant).
Figure 1a shows the picture of the formation of GaAs QD and phonons of the
AlxGa1−xAs external medium between the electron and the confined optical phonons
through all the discrete states (d). Namely: ∆e
L1d
is the shift produced by the in-
teraction with phonons of the external medium, ∆e
L0d
(nl) – by phonons of internal
medium through the nl-th state,
∑′
nl ∆
e
L0
(nl) – by phonons of internal medium
through all excited states, ∆e
Ld – the sum partial shift due to the interaction with
the confined phonons through all the states of a discrete spectrum. From the figure
it is clear that when the energy level appears in GaAs well, its shift is formed by
the intralevel interaction ∆e
L0d
(10) + ∆e
L1d
. When the QD radius (r0) increases, the
partial shift ∆e
L0d
produced by the intralevel interaction with Lo-phonons, reach-
es its maximum and then slowly decreases. For the big QD there are the excited
electron states in the well (n 6= 1, l 6= 0). Their interaction with phonons gives
the corresponding partial shifts ∆e
L0d
(nl). The dependences of these shifts on r0 are
qualitatively the same – after the appearance of the respective state in the well their
magnitude smoothly increases, reaches their maximum and then slowly decreases.
After the appearance of every new bound states in QD, the absolute magnitude of
the partial shifts becomes smaller. Thus, for the fixed QD radius the shift produced
by the intralevel interaction is bigger than the shift formed due to every excited
state. But for rather big sizes of the internal medium there is a big number of en-
ergy levels in GaAs well, thus the sum shift due to interlevel interaction is much
bigger than the intralevel one. The interlevel interaction becomes more essential for
the bigger QD radii. It increases at bigger r0, reaches the magnitude of intralevel
interaction and then becomes a basic one.
In figure 1a the dependence of ∆e
Ld partial shift on r0 is shown by a dashed
curve. It is clear that this therm is essential only for the small QD radii and has
a sharp minimum vanishing at r0 > 20aGaAs. Such a behaviour of the curve is
explained by the fact that only for the small QDs the probability of electron location
in AlxGa1−xAs barrier is bigger than the probability of its location in GaAs well.
The ∆e
Ld magnitude is comparable to the ∆e
L0d
(10). When the QD radius increases,
the electron is “involved” into GaAs which corresponds to the vanishing of ∆e
L1d
shift, formed by the phonons of the external medium.
In figure 1b the partial shifts caused by the interaction of electron with interface
phonons through all the states of discrete spectrum are presented as the functions
of QD radius. Namely: ∆e
I±d(nl) is the shift produced by I±-phonons through the
nlth-state, ∆e
I±d
is the shift produced by I±-phonons through all the excited states,
∆e
Id is total partial shift due to the interaction with interface phonons through all
the states of discrete spectrum.
Thus in the central-symmetric states (l = 0) there are no interface phonons
[9,14], it is natural that in the figure, the shifts are presented formed by the interlevel
interaction only. Thus, the shifts caused by interface phonons start to arise at such
QD radius when the first excited level appears in the well. It is clear that for the
arbitrary radius of the internal medium the partial shifts ∆ e
I+d (dotted curve) are
583
M.V.Tkach et al.
Figure 1. Dependences of partial shifts caused by electron interaction with con-
fined (a) and interface (b) phonons through the discrete states on QD radius.
584
Electron- and hole-phonon interaction in quantum dot
Figure 2. Dependences of partial shifts caused by electron interaction with con-
fined (a) and interface (b) phonons through the continuous states on QD radius.
bigger than ∆e
I−d (dashed curve). When r0 increases, the partial shift of every level,
after its appearance, rapidly increases to its maximum magnitude and then slowly
vanishes. Therefore, the total shift caused by the interaction with interface phonons
reaches its maximum at r0 ≈ 15 and then slowly decreases.
In figure 2 the picture of the formation of ground electron level shift caused
by the interaction with all phonons through all the continuous states is presented.
From the figure one can see that when the QD radius increases the partial shift of
L-phonons into ∆e
Lc magnitude slowly decreases after reaching the maximum. The
partial shifts ∆e
I+c and ∆e
I−c are formed at such QD radius, when it appears that the
dependence of these partial shifts on r0 is qualitatively the same but quantitatively
|∆e
I+c| is several times bigger than |∆e
I−c| at any r0 values.
The reason of sharp minimum in ∆e
I±d
curve lies in the fact that the magnitude of
electron-interface phonons interaction is proportional to the density of probability of
electron location in the vicinity of media interface, where the potential of I-phonon
field has its maximum. When the QD radius increases, the probability reaches its
maximum (the electron is “involved” from the barrier into the well) and the inter-
action with interface phonons becomes bigger. At further increasing of the radius
the probability vanishes and, as a result, |∆e
I±d
| decreases.
In figures 3a,b the total (∆e,h) and partial (∆e,h
L ,∆e,h
I ) shifts produced due to the
electron (figure 3a) and hole (figure 3b) interaction with confined (L) and interface
(I) phonons through all the states of discrete spectrum are shown as functions of QD
radius. The partial shifts ∆e,h
l,Ic, caused by the interaction with all phonons through
585
M.V.Tkach et al.
Figure 3. Dependences of partial shifts of ground electron (a) and heavy hole (b)
energy levels due to the interaction with interface and confined phonons on QD
radius.
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Electron- and hole-phonon interaction in quantum dot
Figure 4. Dependence of splitting between total shifts of light and heavy holes
on QD radius.
the states of continuous (c) spectrum are presented as well. The light hole has the
effective mass close to the mass of electron, since the behaviour of its total and
partial shifts is almost the same as for the electron.
In the curve (∆e) in the vicinity r0 = 4 one can see the sharp minimum pro-
duced by the interaction with the confined phonons of the external medium (L1).
Further, the curve smoothly limits to the saturation. The shift (∆e
Id), formed by
the interaction with interface phonons through the discrete states, tends to vanish.
As a result, the total shift depends on r0 only for small QD radii. For the big QDs
the magnitude of the shifts is close to its value (∆3De,hh,lh
GaAS ) in an analogue massive
crystal creating the QD. The small difference between these shifts arises due to the
neglecting of non-diagonal terms of higher order MO.
Figure 3b proves that the behaviour of heavy hole shifts is qualitatively equivalent
to the behaviour of electron shifts.
Due to the difference between light and heavy hole effective masses, the interac-
tion with the phonons eliminates the degeneration of these quasiparticles energies
in ground states. The magnitude of splitting (Dh) of light and heavy hole ground
levels is determined by the difference of their shifts
Dh = Ehh −Elh = ∆hh −∆lh (13)
thus Dh, in general case, depends on the radius and on Al concentration (x) in a
nanosystem.
In figure 4, the dependence ofDh splitting on Al concentration (x) in AlxGa1−xAs
medium is shown for the different QD radii (r0). From the figure one can see that
for the small QDs (r0 < 15aGaAs), the Dh(x) dependence is nonlinear, for the big
587
M.V.Tkach et al.
QDs (15aGaAs < r0 < 20aGaAS) it is linear and at further r0 increasing, Dh does
not depend on x. It is caused by the fact that the shifts are very sensitive (strongly
nonlinear) to the varying of QD radius for the small radii, and almost not sensitive
for the big QD radii.
Finally, the main conclusion is that for the nanosize QDs, the shifts of electron
and hole ground levels are created by the interaction of these quasiparticles with
L- and I-phonons due to all the states of discrete and continuous spectrum. For the
small QDs, the shifts of ground energy levels have a strong nonlinear dependence and
for the big QDs, they almost do not depend on QD radius and have the magnitude
close to the shifts of ground levels in a massive crystal creating QD. Due to different
effective masses of light and heavy holes, the splittings of their ground levels are
complicated functions of QD radius and Al concentration in AlxGa1−xAs medium.
References
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Взаємодія електронів та дірок з фононами у
квантовій точці, що вміщена в напівпровідникове
середовище (GaAs/AlxGa1−xAs)
М.В.Ткач, М.Я.Міхальова, O.M.Войцехівська,
Р.Б.Фартушинський
Чернівецький національний університет,
58005 Чернівці, вул. Коцюбинського, 2
Отримано 24 травня 2001 р.
У роботі виконано аналітичний і чисельний розрахунки перенорму-
вання L- та I-фононами електронного та діркового спектрів з повним
врахуванням конфігураційної взаємодії у квантовій точці, що вміщена
в напівпровідникове середовище. Конкретний розрахунок виконано
для гетеросистеми GaAs/AlxGa1−xAs.
Установлено, що зсуви основних рівнів електрона та дірки формую-
ться взаємодією цих квазічастинок як з L-, так і з I-фононами за учас-
тю всіх станів дискретного та неперервного спектрів. При малих роз-
мірах КТ зсуви основних енергетичних рівнів квазічастинок мають си-
льно нелінійну залежність, а при великих радіусах КТ вони практично
не залежать від розміру КТ та близькі за величиною до зсувів основ-
них рівнів у масивному кристалі, з якого утворена КТ. Через різницю
ефективних мас важкої та легкої дірок розщеплення їх основних рів-
нів має складну залежність від радіуса КТ та концентрації Al (x) у се-
редовищі AlxGa1−xAs.
Ключові слова: наногетеросистема, взаємодія, електрон, дірка,
фонон
PACS: 79.60.Jv, 63.20.Dj
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