Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers
Effects of the presence of isolated disordered layers on the exciton scattering by compositional fluctuations in double semiconductor quantum wells have been studied. In the structures containing both ordered and disordered layers, the probability of the scattering depends on the degree of the excit...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2015
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irk-123456789-1207382017-06-13T03:06:27Z Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers Vertsimakha, G.V. Effects of the presence of isolated disordered layers on the exciton scattering by compositional fluctuations in double semiconductor quantum wells have been studied. In the structures containing both ordered and disordered layers, the probability of the scattering depends on the degree of the exciton wavefunction localization in the disordered layers, where it interacts with the fluctuations. For some parameters of the structure the exciton wavefunction can penetrate deeply into the ordered layers of the structure, which leads to a sharp drop of the probability of the scattering and, consequently, to the narrowing of the optical exciton bands. It has been shown that for heterostructures containing diluted magnetic semiconductor layers, the probability of the scattering can be tuned by external magnetic field. 2015 Article Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers / G.V. Vertsimakha // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 1. — С. 110-114. — Бібліогр.: 13 назв. — англ. 1560-8034 DOI: 10.15407/spqeo18.01.110 PACS 71.22.+i, 71.23.-k, 71.35.Cc, 73.21.Fg, 75.50.Pp http://dspace.nbuv.gov.ua/handle/123456789/120738 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Effects of the presence of isolated disordered layers on the exciton scattering by compositional fluctuations in double semiconductor quantum wells have been studied. In the structures containing both ordered and disordered layers, the probability of the scattering depends on the degree of the exciton wavefunction localization in the disordered layers, where it interacts with the fluctuations. For some parameters of the structure the exciton wavefunction can penetrate deeply into the ordered layers of the structure, which leads to a sharp drop of the probability of the scattering and, consequently, to the narrowing of the optical exciton bands. It has been shown that for heterostructures containing diluted magnetic semiconductor layers, the probability of the scattering can be tuned by external magnetic field. |
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Article |
| author |
Vertsimakha, G.V. |
| spellingShingle |
Vertsimakha, G.V. Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Vertsimakha, G.V. |
| author_sort |
Vertsimakha, G.V. |
| title |
Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers |
| title_short |
Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers |
| title_full |
Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers |
| title_fullStr |
Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers |
| title_full_unstemmed |
Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers |
| title_sort |
peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2015 |
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http://dspace.nbuv.gov.ua/handle/123456789/120738 |
| citation_txt |
Peculiarities of the exciton scattering in double semiconductor quantum wells with disordered layers / G.V. Vertsimakha // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 1. — С. 110-114. — Бібліогр.: 13 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT vertsimakhagv peculiaritiesoftheexcitonscatteringindoublesemiconductorquantumwellswithdisorderedlayers |
| first_indexed |
2025-07-08T18:29:42Z |
| last_indexed |
2025-07-08T18:29:42Z |
| _version_ |
1837104505141854208 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 110-114.
doi: 10.15407/ spqeo18.01.110
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
110
PACS 71.22.+i, 71.23.-k, 71.35.Cc, 73.21.Fg, 75.50.Pp
Peculiarities of the exciton scattering in double semiconductor
quantum wells with disordered layers
G.V. Vertsimakha
Institute for Nuclear Research, NAS of Ukraine
47, prospect Nauky, 03680 Kyiv, Ukraine,
Phone: +380 (44) 525-2349; e-mail: avertsim@kinr.kiev.ua
Abstract. Effects of the presence of isolated disordered layers on the exciton scattering
by compositional fluctuations in double semiconductor quantum wells have been studied.
In the structures containing both ordered and disordered layers, the probability of the
scattering depends on the degree of the exciton wavefunction localization in the
disordered layers, where it interacts with the fluctuations. For some parameters of the
structure the exciton wavefunction can penetrate deeply into the ordered layers of the
structure, which leads to a sharp drop of the probability of the scattering and,
consequently, to the narrowing of the optical exciton bands. It has been shown that for
heterostructures containing diluted magnetic semiconductor layers, the probability of the
scattering can be tuned by external magnetic field.
Keywords: double quantum well, diluted magnetic semiconductor, exciton scattering.
Manuscript received 16.10.14; revised version received 23.12.14; accepted for
publication 19.02.15; published online 26.02.15.
1. Introduction
The extensive use of semiconductor heterostructures in
modern optoelectronic devices spurred to study factors
influencing broadening the exciton bands in these
systems [1-3]. In semiconductor quantum wells, the
bandwidth is conditioned by various factors: fluctuations
in the well thickness, interface roughness, various kinds
of macroscopic inhomogeneities etc. In semiconductor
alloys, like to Cd1–xMnxTe, AlxGa1–xAs, Zn1–xMnxSe, in
addition to these technological factors, there is another
mechanism of the band broadening caused by the
microscopic compositional disorder – the exciton
scattering by fluctuations in the crystal composition.
Ions of components of an alloy are randomly distributed
across the crystal lattice, which creates rapid oscillations
in the space potential for carriers. This potential arises
from different values of electron densities of the
substitutional atom and that of the crystal (for small
contents of these atoms, one can say about “impurity
atoms” and “host atoms”), deformation of the lattice in
the vicinity of substitutional atoms and so on. This
disorder is always present in the semiconductor alloys,
and it is especially important for high-quality samples. It
must be noted that calculations of the effect of this
scattering mechanism on the bandwidth don’t tolerate
uncertainties related to unknown values of parameters, in
contrast to mechanisms caused by technological defects.
In diluted magnetic alloys, like to Cd1–xMnxTe,
Zn1–xMnxSe, excitons scatter also by magnetic ion spin
projection fluctuations. Calculations and experimental
study demonstrate some interesting manifestations of
this scattering: for example, the strong magnetic field
dependence of the optical exciton bandwidths is
observed in diluted magnetic semiconductors [4-7].
In the present paper, the exciton scattering by
fluctuations in composition in double quantum well
structures has been studied. Very often in such hetero-
structures some layers are formed by semiconductor
alloys, and others – by pure semiconductor crystals, for
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 110-114.
doi: 10.15407/ spqeo18.01.110
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
111
example, CdTe/(Cd,Mn)Te, (Al,Ga)As/GaAs etc. It
means that in these systems only some of the layers are
essentially disordered, and the probability for exciton to
be scattered by the fluctuations depends on the
probability for carriers to be in the disordered layers or,
in other words, on the spatial distribution of the exciton
wavefunction over the ordered and disordered layers. It
leads, for example, to extremely low broadening of
exciton bands in shallow GaAs/(In,Ga)As/GaAs single
quantum wells [3] due to strong penetration of the
wavefunction from the disordered In1–xGaxAs region into
the GaAs barriers, where compositional disorder is
absent. In the case of double quantum wells, the spatial
distribution of the wavefunction over the structure
essentially depends on the parameters of the whole
system, which, as it will be shown, causes some
interesting peculiarities in the exciton scattering. Also,
the magnetic field dependence of the probability of the
exciton scattering in the structure with magnetic
impurities in one of the quantum well layers has been
considered.
2. Model of the system and methods of calculations
The methods used for calculating the probability of the
exciton scattering by the fluctuations of distribution and
spin projections of the impurities in diluted magnetic
semiconductors are similar to those described in the
work [7] in detail. So, in this paper, consideration will be
confined to a short description of the basic theoretical
methods and discussion of the obtained results.
Let us consider a double quantum well with the
impurities localized in the well layers (Fig. 1). In the
studied system, Hamiltonian of exciton can be written as
int0 HHH , (1)
where H0 is typical free exciton Hamiltonian, including
the kinetic energy of electron, hole and Coulomb
interaction; Hint – Hamiltonian of interaction between
carriers and impurities.
Hamiltonian of exciton interaction with magnetic
impurity ions Hint can be written as
.
1
0
int
nhnhhh
eneee
n
xnrSSJ
nrSSJ
N
H
(2)
Here, N0 is the concentration of cation lattice sites, n
–
coordinate of the cation lattice site, her
– position of
electron (hole), e(h) – potential of the nonmagnetic
interaction of electron (hole) with impurity ion, nx
describes occupation of cation sites by impurity
ions: 0nx if there is host ion in the n
lattice site, and
1nx if the site is occupied by substitutional ion, Je(h) –
exchange integral for electron (hole), heS
– spin of
electron (hole), nS
– spin of magnetic ion.
The numbers of the site occupation can be
expressed as
nn xxx , nznznz SSS
,,, . (3)
Here, x denotes the average value of the relative
concentration of ions in a certain layer of the structure,
1
zS is the average value of the single spin projection on
the direction of magnetic field, coinciding with the
direction of the structure growth along the axis z (this
average value can be easily obtained in the mean field
approximation [9]), nx
and nzS
,
denote the
fluctuations of the corresponding values, which lead to
the scattering of exciton.
To describe this scattering, perturbation
Hamiltonian may be introduced:
intint HHH , (4)
Where
intH
determines the profile of quantum wells for
electron and hole in the mean field approximation (see
[8, 9] for the detail description). For calculations, the
following form of the variational wavefunction of
exciton in the double quantum well was used:
ezfzfe
S
rr hhee
Rki
hek 2
21
,
, (5)
where hehe zf is the one-particle wavefunction of
electron (hole) in the double quantum well,
hehehe zr ,
, k
and R
are the wave vector and
position of the exciton center of masses in the plane of
layers, z is the direction of crystal growth. The
fluctuations lead to the elastic exciton scattering with the
change of the two-dimensional wave vector k
. The
reverse relaxation time can be calculated using the
formula:
k
kk
k
W
,
1
, (6)
where
kk
W
,
is the probability of the exciton scattering
from k
state to k
state calculated with the wave-
function (5) and perturbation Hamiltonian (4) [7]. The
obtained relaxation time was averaged with respect to
the impurity concentration and spin projection
distributions assuming the latter to be chaotic:
mnmn xxxx
,1, , mnzmznz SSS
,
2
,, , . (7)
The scattering of exciton should manifest itself in
the broadening of exciton optical bands. The reverse
relaxation time ħ
/τE(ω), where E(ω) is the exciton energy
on the frequency ω, determines the contribution of the
scattering to the damping of the excitonic resonance and,
consequently, the shape of the exciton absorption
bands [10].
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 110-114.
doi: 10.15407/ spqeo18.01.110
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
112
a
b
Fig. 1. A schematic illustration of the structure (a) and
corresponding band edge profiles (b) of a double-well
heterostructure containing ordered (dark grey) and disordered
(light grey with circles) semiconductor layers. Impurity ions
are placed in the layers forming potential wells for electrons
and holes in the conduction and valence bands. Dashed lines
depict one-particle energy levels in the quantum wells.
Calculations were performed for the ZnTe/
Cd1–xMnxTe
/ZnTe/Cd1–yMnyTe/ZnTe double quantum
well. The following parameters were used [9, 11-13]: the
total energy band gap for Cd1–xMnxTe Eg(Cd1–xMnxTe) =
= 1.606 + eVMn xdEg , xdEg
Mn
= 1.592x eV,
,1
Mn
xd
xdEg
e
xd
xdEg
h
Mn
, α = 0.4, the
total energy band gap for ZnTe Eg (ZnTe) = 2.35 eV, the
valence band offset on the interfaces ZnTe/(Cd, Mn)Te
was chosen to be equal to α' = 0.2, the effective masses
of electron and heavy hole were considered as the same
for all layers and are equal to me =0.096m0, mhh
=0.6m0,
where m0 is the mass of free electron, the dielectric
constant ε = 9.7, Je
= 0.22 eV, Jh
= – 0.88/3 eV, and the
concentration of cation lattice sites N0 = 4/ 3
0a , where
a0
=6.48 Å is the lattice parameter in CdTe.
The calculated dependence of the reverse relaxation
time ħ
/τk for k = 0 on the barrier width for the quantum
wells of the same width and concentration of impurities
in ZnTe/Cd1–xMnxTe/ZnTe/Cd1–xMnxTe/ZnTe in the
absence of external magnetic field (H = 0) is depicted in
Fig. 2. The thick lines correspond to the ground exciton
state 1e – 1hh, and the thin lines correspond to the
excited state 2e – 2hh. To explain the obtained depen-
dence for the ground state, we have to take into account
distribution of the wavefunction over the layers of the
structure containing and not containing the impurities. In
single and double well structures with a very thin barrier,
the wavefunctions of electron and hole are localized in
the well layer, where the impurities are placed. For
exciton that corresponds to a high probability to be
scattered by concentration fluctuations of the impurities.
As the thickness of the barrier layer rises, the wave-
function of the exciton begins to penetrate into the
barrier layer, which leads to decrease in the probability
of the scattering. When the barrier becomes thick
enough, penetration of the wavefunction into the barrier
layer becomes weaker, and the probability of the
scattering rises a little. Regarding the excited state for
very thin as well as for thick barriers, its wavefunction
penetrates deeper into barriers than the function of the
ground state, and the probability of the scattering for the
excited state is less than for the lowest one. It can be
seen that there is the region of barrier widths, where the
probability to be scattered for the ground state decreases
so essentially (due to penetration of the wavefunction
into the ordered barrier layer) that it turns out to be less
than that for the excited state.
In Fig. 3, the reverse relaxation time ħ
/τk for k = 0
for the same structure in the absence of external
magnetic field and for the first well width L1 =3.5 nm as
a function of the second well width L2 is shown for a few
values of the barrier widths. The curves have a well-
defined drop when the well widths are equal. This effect
is also associated with the redistribution of the
wavefunction between the layers containing and not
containing the impurities. Again, the part of the
wavefunction in the barrier layer (where impurities are
absent) is maximal for the wells of the same width when
localization of the particles in the disordered well layer
is the weakest one.
Fig. 2. The reverse relaxation time as a function of the barrier
width for k = 0 and various values of the well widths in the
symmetrical structure L1 = L2, x = y = 0.03, H = 0 for the
ground state (thick lines) and excited (thin lines) exciton states.
To illustrate, depicted at the bottom of the figure are schematic
pictures of the one-particle wavefunction (solid curve) for the
ground state of carriers in the structure with an absent barrier
layer Lb = 0 (left), a thin barrier layer (centre) and thick (right)
barrier layer. Dark grey with hatch line marks the regions of
penetration of the wavefunction into the barrier layers (grey),
where impurities are absent, which decreases the probability of
the exciton scattering.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 110-114.
doi: 10.15407/ spqeo18.01.110
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
113
Fig. 3. The reverse relaxation time as a function of the right
well width L2 for k = 0 for the first well width L1 = 3.5 nm,
x = y = 0.03, and various values of the barrier widths. To
illustrate, depicted at the bottom of the figure are schematic
pictures of the one-particle wavefunction (solid curve) for the
ground state of carriers in the structure with different (left) and
equal (right) well widths. Dark grey line marks the regions of
penetration of the wavefunction into the barrier layers. This
penetration is much more essential in the case of equal wells
(right).
Fig. 4. The reverse relaxation time as a function of external
magnetic field for k = 0 for the system with one magnetic well
for a few values of the barrier widths. The left well is non-
magnetic with the well width L1 = 2 nm, and the right well is
magnetic with the width L2 = 4 nm and magnetic ion
concentration x = 0.03, temperature T = 4.2 K. To illustrate,
depicted at the bottom of the figure are schematic pictures of
the one-particle wavefunction for the ground state of carriers in
the structure without magnetic field (left) and under external
magnetic field (right) for the –-transition. In the absence of
magnetic field, the lowest state of carriers corresponds to
localization of carriers in the wider well, where magnetic
impurities are placed and, therefore, to the high probability of
the scattering. Under high magnetic field, the band gap in the
magnetic layer rises, which leads to transition of carriers to the
non-magnetic layer and, respectively, to drop of the scattering.
Both the considered above effects should take place
in similar structures formed by any semiconductor
alloys, both magnetic and non-magnetic. At the same
time, in diluted magnetic semiconductors, parameters of
the structure can be tuned by external magnetic field. It
is known [5, 6] that in diluted magnetic semiconductors,
the bandwidth increases with increase of the magnetic
field for the
–
-component of the exciton transition,
while it decreases for the
+
-component. Suppose, in
contrast to the previous cases, only one of the quantum
well layers contains magnetic ions. External magnetic
field influences the depths of the quantum wells for
electron and hole formed by the diluted magnetic layer.
It can change drastically the wavefunction of the system,
i.e. there is the probability for the carrier to be found in
the certain layer of the structure. Suppose also that the
magnetic layer is rather wide, and in the absence of
external magnetic field the ground state of the system
corresponds to the carriers localized in the magnetic
layer (Fig. 4). Under magnetic field for the
–
-
component of the exciton transition, the quantum well
depths for both carriers decrease as the intensity of the
field rises [9]. Simultaneously, the probability of exciton
to be scattered by the fluctuations rises because of
strengthening the magnetic part of interaction with ions.
As it can be seen from Fig. 4, in our system the
probabilty of the scattering also rises as the magnetic
field rises in low fields. It takes place until the carriers
are localized in the magnetic layer. When achieving a
certain some value of the magnetic field, the potential
wells become too shallow, and it becomes energetically
advantageous for carriers to transit to the non-magnetic
well, which results in sharp drop of the probability of the
scattering.
3. Conclusions
In the paper, the exciton scattering in double quantum
wells, some layers of which are formed by ternary
semiconductor alloys, has been considered. In these
disordered layers, the scattering is caused primarily by
the interaction of carriers with fluctuations in the
impurity concentration and (in the case of diluted
magnetic semiconductors) fluctuations of magnetic ion
spin projections. It has been shown that the probability
of the scattering depends essentially on those of the
system’s parameters that determine the degree of the
exciton wavefunction localization in the disordered
layers. Particularly, the probability of the scattering in
the system with quantum wells of equal widths
essentially drops: in this case, penetration of the
wavefunction in the ordered barrier layers of the
structure is maximal, which decreases the effect of the
fluctuations in the disordered layers and, as a result,
decreases the excitonic optical bandwidth. The same
effect can be reached by tuning one of the particle levels
in the quantum wells by external magnetic field, which
also leads to delocalization of the wavefunction and
narrowing the optical bands.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 110-114.
doi: 10.15407/ spqeo18.01.110
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
114
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