Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology
The calculations of intensity ratio of both the main and additional lines, the energy differences between which are fulfilled for quantum well (QW) with asymmetrical potential profile, are presented here. It is grounded on the basis of this calculation that additional line in exciton spectrum of QW...
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Інститут фізики конденсованих систем НАН України
1999
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| Цитувати: | Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology / S.M. Ryabchenko, F.V. Kirichenko, Yu.G. Semenov, V.G. Abramishvili, A.V. Komarov // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 543-552. — Бібліогр.: 6 назв. — англ. |
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irk-123456789-1205462017-06-13T03:05:48Z Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology Ryabchenko, S.M. Kirichenko, F.V. Semenov, Yu.G. Abramishvili, V.G. Komarov, A.V. The calculations of intensity ratio of both the main and additional lines, the energy differences between which are fulfilled for quantum well (QW) with asymmetrical potential profile, are presented here. It is grounded on the basis of this calculation that additional line in exciton spectrum of QW can be explained by transitions between the confined states of valence and conductivity electrons with different parity, which ceases to be forbidden in the presence of asymmetry of QW potential profile caused by technology of growth. It is shown that e1-hh2 additional exciton line is more intensive in most of the actual cases. In particular, it is shown that the additional exciton line, which was observed in the laser ablation grown structures with QW, may be explained as e1-hh2 transition. The calculations show the substantial sensitivity of the results not only to the parameter of widening of the interface, but to the detailed type of the interface profile function. It is concluded that the laser ablation method of heterostructure growth leads to a larger asymmetry of QW potential profile caused by technology than MBE potential profile. Проведенi розрахунки вiдношення iнтенсивностей основної i додаткової лiнiй, енергетичної вiдстанi мiж ними для квантових ям (КЯ) з асиметричним потенцiальним профiлем. Обгрунтовано, що додаткова лiнiя у екситонному спектрi КЯ може бути пояснена переходами мiж утримуваними в КЯ станами валентних електронiв i електронiв провiдностi з рiзною парнiстю, якi перестають бути забороненими у присутностi асиметрiї потенцiального профiлю, спричиненої технологiєю вирощування КЯ. Показано, що додаткова екситонна лiнiя типу e1-hh2 є бiльш iнтенсивною в бiльшiй частинi актуальних випадкiв. Зокрема, показано, що додаткова екситонна лiнiя в структурах вирощених методом лазерної абляцiї, може бути пояснена як e1-hh2 перехiд. Розрахунки показують суттєву чутливiсть не лише до параметру розширення iнтерфейсу, але й до функцiї його профiлю. Зроблено висновок, що метод лазерної абляцiї призводить до бiльшої асиметрiї КЯ, нiж метод молекулярно-пучкової епiтаксiї. 1999 Article Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology / S.M. Ryabchenko, F.V. Kirichenko, Yu.G. Semenov, V.G. Abramishvili, A.V. Komarov // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 543-552. — Бібліогр.: 6 назв. — англ. 1607-324X DOI:10.5488/CMP.2.3.543 PACS: 78.55.Et http://dspace.nbuv.gov.ua/handle/123456789/120546 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The calculations of intensity ratio of both the main and additional lines, the
energy differences between which are fulfilled for quantum well (QW) with
asymmetrical potential profile, are presented here. It is grounded on the
basis of this calculation that additional line in exciton spectrum of QW can
be explained by transitions between the confined states of valence and
conductivity electrons with different parity, which ceases to be forbidden in
the presence of asymmetry of QW potential profile caused by technology
of growth. It is shown that e1-hh2 additional exciton line is more intensive
in most of the actual cases. In particular, it is shown that the additional
exciton line, which was observed in the laser ablation grown structures
with QW, may be explained as e1-hh2 transition. The calculations show the
substantial sensitivity of the results not only to the parameter of widening
of the interface, but to the detailed type of the interface profile function. It is
concluded that the laser ablation method of heterostructure growth leads
to a larger asymmetry of QW potential profile caused by technology than
MBE potential profile. |
| format |
Article |
| author |
Ryabchenko, S.M. Kirichenko, F.V. Semenov, Yu.G. Abramishvili, V.G. Komarov, A.V. |
| spellingShingle |
Ryabchenko, S.M. Kirichenko, F.V. Semenov, Yu.G. Abramishvili, V.G. Komarov, A.V. Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology Condensed Matter Physics |
| author_facet |
Ryabchenko, S.M. Kirichenko, F.V. Semenov, Yu.G. Abramishvili, V.G. Komarov, A.V. |
| author_sort |
Ryabchenko, S.M. |
| title |
Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology |
| title_short |
Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology |
| title_full |
Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology |
| title_fullStr |
Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology |
| title_full_unstemmed |
Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology |
| title_sort |
additional lines in quantum wells excitonic spectra connected with qw asymmetry caused by technology |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
1999 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120546 |
| citation_txt |
Additional lines in quantum wells excitonic spectra connected with QW asymmetry caused by technology / S.M. Ryabchenko, F.V. Kirichenko, Yu.G. Semenov, V.G. Abramishvili, A.V. Komarov // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 543-552. — Бібліогр.: 6 назв. — англ. |
| series |
Condensed Matter Physics |
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| first_indexed |
2025-07-08T18:06:43Z |
| last_indexed |
2025-07-08T18:06:43Z |
| _version_ |
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| fulltext |
Condensed Matter Physics, 1999, Vol. 2, No. 3(19), pp. 543–552
Additional lines in quantum wells
excitonic spectra connected with QW
asymmetry caused by technology
S.M.Ryabchenko 1 , F.V.Kirichenko 2 , Yu.G.Semenov 2 ,
V.G.Abramishvili 1 , A.V.Komarov 1
1 Institute of Physics of the National of Academy Sciences of Ukraine,
46 Nauki Avenue, Kiev, Ukraine
2 Institute of Semiconductors Physics
of the National of Academy Sciences of Ukraine,
45 Nauki Avenue, Kiev, Ukraine
Received July 7, 1998
The calculations of intensity ratio of both the main and additional lines, the
energy differences between which are fulfilled for quantum well (QW) with
asymmetrical potential profile, are presented here. It is grounded on the
basis of this calculation that additional line in exciton spectrum of QW can
be explained by transitions between the confined states of valence and
conductivity electrons with different parity, which ceases to be forbidden in
the presence of asymmetry of QW potential profile caused by technology
of growth. It is shown that e1-hh2 additional exciton line is more intensive
in most of the actual cases. In particular, it is shown that the additional
exciton line, which was observed in the laser ablation grown structures
with QW, may be explained as e1-hh2 transition. The calculations show the
substantial sensitivity of the results not only to the parameter of widening
of the interface, but to the detailed type of the interface profile function. It is
concluded that the laser ablation method of heterostructure growth leads
to a larger asymmetry of QW potential profile caused by technology than
MBE potential profile.
Key words: quantum well, asymmetrical potential, interface profile
function, additional exciton transitions, semimagnetic semiconductors
PACS: 78.55.Et
1. Introduction
The heterostructures with quantum wells (QW) are very interesting objects for
both practical applications and for scientific investigations. Most part of scientific
and applied interest to QW is connected with the energy of dimensionally quantized
c© S.M.Ryabchenko, F.V.Kirichenko, Yu.G.Semenov, V.G.Abramishvili, A.V.Komarov 543
S.M.Ryabchenko et al.
states, with penetration of wave function of electrons in these states into barrier and
possibility of tunnelling of electrons between a different QW in the structure.
The magnetically mixed (or diluted magnetic, or semimagnetic) semiconductors
(DMS) are unique materials with possibilities for giant spin splitting (GSS) of energy
positions of the carriers by the external magnetic field. In many cases this splitting
reaches the values comparable with (or larger than) a bonding energy of the states
of a coupled electron (or exciton). A role of an antiferromagnetic ion-ion exchange
interaction in DMS is substantial as well in the case of a high enough content
of magnetic ions. In A2
1−x MxB
6 DMS materials (M is 3d group magnetic ion) it
decreases a x-dependence of magnetization in comparison with the linear growth and
for x > 0.15 the dependence turns into falling but not increasing. These materials
have also got a lot of other interesting peculiarities, which are, in the main, specified
by the carrier-ion exchange interaction as well. It is the main reason for a wide
spreading of preparations and studies of structures with a QW based on the DMS.
There are several different types of such structures depending on using DMS as a
QW or as a barrier material. In the case of QW formed from a usual semiconductor
and of barrier formed from a DMS, a GSS should take place for barrier carriers
only. But the exchange induced splitting of energy positions of in-well levels of
confined carriers in the external magnetic field H takes place too, and it arises from
penetrating of the wave function of these carriers in the barrier.
The effect of “paramagnetic enhancement” of confined excitons GSS was found
on such a QW as an interesting and unexpected peculiarity of the discussed QW
excitonic spectra. It was established experimentally in cases of high content of mag-
netic ions in DMS material of the barrier that this GSS is noticeably stronger than
the one calculated for corresponding rectangular QW with sharp interfaces.
Two main reasons were considered to explain the effect. The first of them is a
surface effect of interface for the antiferromagnetically coupled magnetic ions in the
monolayers of DMS in the barriers close to the interface. The number of magnetic
neighbours in these monolayers is reduced due to the lack of magnetic ions in usual
semiconducting material of QW.
The second mechanism is connected with intermixing of QW and barrier materi-
als in the region close to the interface due to the growth process and interdiffusion.
The analysis of these mechanisms contribution to the effect value (see, for in-
stance, [1,2]) has showed that the second of them is determinant. The numerical
solution of Schroedinger equation for a one-dimensional motion of electron in ar-
bitrary profile QW potential was used in [1,2]. A simple approach based on the
perturbation theory (see for instance [3]) confirmed this conclusion as well.
The experiments with especially grown “normal” and “inverted” interfaces on
the structures of Cd1−xMnxTe/CdTe/Cd1−yMgyTe have shown that a real profile
of x(z) and y(z) in the regions close to the interfaces is asymmetrical due to the
peculiarities of the QW growth technology.
In a such a case the parity of QW potential will be broken, and it should cause a
permission of optical transitions between the confined states with different parity of
wave functions of valence and conductivity electrons in QW. The observation of such
544
Additional lines in quantum wells excitonic spectra
transitions in the case of asymmetry caused by the growth technology may provide
the information about the real component distribution at the interface region and
control the growth technology in this way.
2. Theory
The optical transitions in QW are permitted in the usual case between the states
with the same numbers n of spatial quantization for valence and conductivity elec-
trons respectively. But transitions between the states with different n of the same
parity are weakly permitted too, due to the difference of effective masses of con-
ductivity and valence electrons as well as due to the difference of QW deepness for
them. As a result, the overlap integrals of envelope of wave functions of these states
are not equal to zero and it is the reason for permitting the transitions.
The loss of QW potential symmetry due to asymmetrical interface intermixing
should result in nonzero values of the mentioned overlap integrals for the states with
different parity as well. It will give rise to the transitions between the states of a
different parity, for instance of type e1-hhn (or en-hh1) with an even n. In the exper-
iments with asymmetrical half-parabolic QW on the Cd1−x(z)Mnx(z)Te base [4] both
e1-hh2 and e2-hh1 optical transitions were observed and it enabled us to determine
the value of valence band offset (VBO) for Cd1−xMnxTe/CdTe heterostructures as
VBO = 0.45.
In many cases only the states with n = 1 (the type of e1 and hh1 or lh1) are
present in QWs of a given width and deepness for electrons of conductivity and
holes (“heavy”-hh and “light”-lh respectively). But for QW, it is necessary to take
into account the possibility for two types of exsitons. One of them is “usual” and
is formed by electron and hole both of which are confined into QW for them. The
second one is “unusual” and it is formed by one of the carriers which is confined
into its QW potential and by the second carrier which is in over-well state and is
confined by the Coulomb attraction of the first carrier only. Both electron and hole
should be considered as a “first” and a “second” carrier and two different excitons
of such a type may exist.
For the excitons of similar type the motion of the carrier in the over-well state
should be considered in a joined potential of QW and an effective potential of
Coulomb interaction of the carriers averaged with the wave function of the “first”
carrier in a confined state and with the exciton function of relative motion of an
electron and a hole. At the large distance (z − zw0) from the centre of QW position
(zw0), the Coulomb correction is decreasing as (z− zw0)
−1 and it results in the pres-
ence of states with n > 1 in a joined potential. The wave functions of all states in
this potential should be orthogonal to one another.
The similar approach was used in [5] for interpreting the additional line in the
excitonic spectrum of light reflection in Cd0.88Mn0.12Te/CdTe/Cd 0.88Mn0.12Te. This
line was arising in σ+ GSS spectrum only at a magnetic field H > 2T and was
explained by the authors of [5] as e1-hh3 additional exciton. The relative intensity
of such excitons in case of symmetrical rectangular QW potential may be substantial
545
S.M.Ryabchenko et al.
for providing agreement with the experiment in the case of H-field induced type I –
type II transition in QW potential. For the carrier spin sublevels which are connected
with σ+ optical transition it is possible for Cd0.88Mn0.12Te/CdTe/Cd0.88Mn0.12Te
structure at H=2T if VBO = 0.15. The authors of [5] treat the arising additional
line in σ+ spectrum as the evidence of type I – type II transition in their sample
and as the evidence of VBO=0.15. This value is in contradiction with the data of
[4].
The analysis of intermixing effect on “paramagnetic enhancement” of GSS of e1-
hh1 excitons in QW [1,2] showed that VBO value 0.3 – 0.4 is more preferable than
the 0.15 value. At the same time studies of Cd1−xMnx Te/CdTe/Cd1−yMgxyTe QW
with “normal” and “inverted” interfaces distinctly show that a potential profile of
“rectangular” QW which was grown using the MBE method has got an asymmetry
caused by the technology.
An asymmetry of QW may cause the arising of “forbidden” transitions such as
e1-hh2 or e2-hh1. The overlapping integrals for such transitions should depend on
the asymmetry parameters and may turn out to be large enough for observing these
lines.
In many cases the deepness of QW is sufficient for the presence of hh2 or e2
states in QW even without taking into account a Coulomb transformation of hole
or electron QW potential.
In the present investigation we consider the additional lines in QW exciton spec-
tra connected with optical transitions between the states with different parity, which
arise due to the asymmetry of QW potential. We will consider the case of “usual”
excitons in QW only, where both of the carriers are confined by the initial QW
potential without Coulomb corrections.
For the quantitative analysis of this problem we carried out the numerical solving
of Schroedinger equation for a one-dimensional motion of electrons and holes (with
effective masses m∗
e and m∗
hh respectively) in the arbitrary “sabre-like” potentials
Ue(hh)m(z). The index m determines the spin (moment) projection of an electron
(±1/2) or of a heavy hole (±3/2) respectively.
To describe Ue(hh)m(z) we used the approach proposed by the authors of [1,2]
with determining the potential as a function of the value of Mn fractional content
x(z). To expose x(z) for QW we used the next expression:
x(z) = xw + (xb − xw) {F (z − z0) + [1− F (z − z0−Lw)]} , (1)
where xb and xw are the nominal contents of Mn in the barrier and QW respectively
(we considered the case of xw = 0 only); z0 and Lw is the left interface nominal
position and a nominal QW width respectively. The interface profile function F(z)
is used to replace the stepped function which is used in the rectangular QW case. The
F (z) have a trend to 1 and 0 for the left and the right sides afar from the interface
region. In the case of symmetric intermixing the [F (z) − 1/2] is an antysymmetric
function and it hasn’t got a definite symmetry in the other cases.
We use the different probe functions F (z) for modelling the real profile of the
546
Additional lines in quantum wells excitonic spectra
-6 -4 -2 0 2 4 6
0,06
0,07
0,08
0,09
0,10
0,11
0,12
0,13
m*
e
=0.09, m*
hh
=0.65
L
w
=26 Å
σ -
σ +
L
w
=28 Å
L
w
=25 Å
L
w
=27 Å
LD/Lw=0.148
VBO=0.45
s1=1
T=2K
x=0.11
ra
tio
I(
e1
hh
2)
/I(
e1
hh
1)
H (T)
Figure 1. The H-field dependencies of R of e1-hh2 and e1-hh1 transitions at
different values of Lw and fixed of LD/Lw and VBO calculated for σ+ and σ−
GSS components (H > 0 and H < 0 parts of dependencies respectively).
interface. For instance, a function of “power” type was used:
F (z) =
{
1 for z < 0
[1 + (z/LD)
s1]−1 for z > 0
(2)
or an “exponential” function:
F (z) =
{
1 for z < 0
exp(−z/LD) for z > 0
, (3)
where LD is a parameter of width of the intermixing region. The more complicated
multi-parametrical modelling functions were tested as well. For instance, functions
of a two-stage type were used which were similar to (1,2), but consisted of two parts:
“fast” and “slow” with weight coefficients (f) and (1-f) respectively. Each of them
was characterized by its parameters such as s1, s2, LD1, LD2.
The calculations of the same type were carried out for the systems of two wells
with the barrier width Lb between them for modelling the superlattice (SL). Both
electron and hole inter-well tunnelling was taken into account. The tunnel splitting
of in-well states was used to evaluate the miniband width in SL with the same Lw
and Lb as in the two-well system.
The calculation of the main (e1-hh1) and the additional (e1-hh2) exciton line
energies as well as of the ratio of intensities (R) of these lines was carried out for a
number of possible parameters of structure materials (x, VBO) of QW (Lw, Lb) and
for different types of F (t) or parameters of it (LD, s1, etc). The R was calculated
as the square of a corresponding overlapping integral ratio. The dependence of it on
the H was considered for σ+ and σ− components of GSS.
The calculations for a e2-hh1 optical transition were fulfilled as well. It was shown
that e2-hh1 exciton line might be observable for a strong enough QW asymmetry
but in all the cases examined it will be weaker than the e1-hh2 exciton line.
The results of a part of such calculations are shown on the figures 1–4 in the form
of dependencies from the different QW and F (z) (in the form of (2)) parameters.
547
S.M.Ryabchenko et al.
-6 -4 -2 0 2 4 6
0,05
0,06
0,07
0,08
0,09
0,10
0,11
0,12
0,13
0,14
m*
e
=0.09, m*
hh
=0.65
σ - σ +
L
D
/L
w
=0.111
L
D
/L
w
=0.185
L
D
/L
w
=0.222
L
D
/L
w
=0.148
Lw=27 Å T=2 K
VBO=0.45
s1=1
x=0.11
ra
tio
I(
e1
hh
2)
/I(
e1
hh
1
H (T)
-6 -4 -2 0 2 4 6
0,04
0,06
0,08
0,10
0,12
m*
e
=0.09, m*
hh
=0.65
VBO=0.4
VBO=0.45
VBO=0.5
Lw=27 Å LD/Lw=0.148
s1=1
T=2 K
x=0.11
σ
- σ
+
ra
tio
I(
e1
hh
2)
/I(
e1
hh
1)
H(T)
Figure 2. The calculated H-field de-
pendencies of R of e1-hh2 and e1-
hh1 transitions at different values of
LD/Lw and fixed of Lw and VBO.
Figure 3. The calculated H-field de-
pendencies of R of e1-hh2 and e1-hh1
transitions at different values of VBO
and fixed of Lw and LD/Lw.
-6 -4 -2 0 2 4 6
0,05
0,06
0,07
0,08
0,09
0,10
0,11
0,12
m*
e
=0.09, m*
hh
=0.65
σ
+
σ
-
s1=1.1
s1=0.9
s1=1
x=0.11 LD/Lw=0.148
VBO=0.45
Lw=27 Å
T=2 K
ra
tio
I(
e1
hh
2)
/I(
e1
hh
1)
H (T)
Figure 4. The calculated H-field dependencies of R of e1-hh2 and e1-hh1 transi-
tions at different values of s1 parameter of F (z). Other parameters are fixed.
One can see that in cases of strong QW asymmetry (LD/Lw up to 1), the ratio
of integral intensities of additional (e1-hh2) and main (e1-hh1) lines may be large
enough (up to 10–15%)
It is interesting to analyze the dependence of R on the H field for σ+ and σ−
components of GSS. The deepness of QW decreases with H for spin components
of valence and conductivity electrons which are connected with σ+ transition and
it increases for the ones connected with σ− transition. From this point of view this
dependence reflects the changing of the ratio with QW deepness. One can see in
figures 1–4 that this dependence has got a maximum and it may take place both in
H > 0 and in H < 0 region depending on QW and F (z) parameters.
3. Comparison with the experiment
Light reflection spectrum measurements were fulfilled on the samples which had
been grown by J.J.Dubowski (Ottawa, Canada) using the Pulsed Laser Evaporation
548
Additional lines in quantum wells excitonic spectra
0 1 2 3
1,70
1,75
1,80 b)
CCM-207
E
(
eV
)
H (T)
0 1 2 3
1,70
1,75
1,80 a)
CCM-205
E
(
eV
)
H (T)
Figure 5. The H-field dependencies of energy of σ+ (full symbols) and σ− (open
symbols) components of GSS in CCM 205 (a) and CCM 207 (b) exciton reflection
lines. Main line – squares, additional – triangles, barrier exciton – circles.
and Epitaxy (laser ablation) method. One of them (CCM 205) has got 6 CdTe QW
with the width Lw (the value of Lw = 20 Å was planned in the process of the
sample grown) separated by Cd0.89Mn0.11Te barrier with the width Lb = 165 Å. The
tunnelling of carriers across this barrier is small and the approach of a single quantum
well (SQW) may be used in this case. Another structure (CCM 207) involves 41 CdTe
QW with the same Lw as in CCM 205, with the barrier of the same material, but
with Lb = 45 Å. This barrier is narrow enough for inter-well tunnelling of both the
conductivity electrons and the heavy holes, and the formation of a miniband results.
So, this sample may be considered as a superlattice (SL). The photoluminescence
measurements on these samples were carried out in [6]. The evidence of SL effects
occurring was obtained. The authors of [6] suppose that the real value of Lw in these
samples is rather 27 Å than 20 Å. Detailed data on the sample parameter are given
in the mentioned reference as well.
The light reflection spectrum of these samples show the presence of additional
exciton lines shifted in the high-energy side on 20 ± 5 meV compared to the main
e1-hh1 QW exciton. This shift is stronger for CCM 205 sample than in CCM 207
sample. The GSS of the additional line is a little larger than it is for the main line
and hasn’t got a substantial contribution which would be proportional to H 2. It
gives no possibility to connect this line to the excited states of the main exciton.
On the figures 5a, b the dependencies of energies of σ+ and σ− components of
the main, the additional and the barrier excitons from H at temperature 2 K are
shown.
The additional line was distinctly observable at H=0 in both samples. Its in-
tensity was up to 5–15% from the main line. The intensity of σ+ component of
the additional line slightly increased with H growth and that of σ− component
decreased.
One can conclude from comparing with the dependencies which are shown on
figures 1–4 that these experimental data may be explained based on the mechanism
549
S.M.Ryabchenko et al.
-4 -3 -2 -1 0 1 2 3 4
-120
-100
-80
-60
-40
-20
0
CCM-205
experiment
e1hh2
e1hh1
L
D
/L
w
=0.2
1
5
L
D
/L
w
=5
1
0.2 f=0.7 Lw=27 Å
T=2K
x=0.11
H (T)
E
-
E
ex
c.
b
ar
.
(m
eV
)
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8
-120
-110
-100
-90
-80
-70
-60
-50
L
w
=27 Å, L
b
=45 Å, T=2 K, x=0.11
expiriment CCM-207
e1hh2
e1hh1
f=0.4
f=0.2
f=0
f=0
f=0.2
f=0.4
E
-
E
ex
c.
ba
r
[m
eV
]
LD/Lw
Figure 6. Comparison of CCM 205
data (stars) and calculated energy
of e1-hh1 (full symbols) and e1-hh2
(open symbols) excitons versus H.
The positions of σ+ and σ− compo-
nents corresponded to H > 0 and
H < 0 parts of dependencies re-
spectively. The Eexc.bar. is the bar-
rier exciton energy at H = 0. The
two-stage F (z) (2)-like function with
s1=2, LD1/Lw = 0.01, s2 = 1, f =
0.7 is used.
Figure 7. Comparison of CCM
207 data and energies of excitons
calculated for transitions between
permutative-symmetrical states into
two-well potential at H = 0 de-
pending on LD2/Lw. The transitions,
which are equivalent to e1-hh1 (full
symbols) and e1-hh2 (open symbols)
excitons, are taken into account. The
two-stage F (z) (2)-like function with
s1 = 2, LD1/Lw = 0.01, s2 = 1 is
used.
discussed. We should suppose that the laser ablation method leads to a strong
enough asymmetry of QW profile with LD/Lw up to 1 for Lw ∼ 20 − 30 Å. In
the MBE grown DMS based QW with close parameters the additional lines are not
observable or they are weaker. It may be explained by sharper interfaces of QW
grown by this method.
The calculation of the energy of the main (e1-hh1), the additional (e1-hh2) and
the barrier excitons as well as of their GSS components were fulfilled in the frame-
work of the discussed model. The best agreement with the experiment was achieved
at VBO value up to 0.45 and with F (z) parameters which corresponded to a strong
QW asymmetry. Some results of comparing the calculations with the experiment are
shown on the figures 6,7. It’s necessary to note that the calculated values of GSS,
both main and additional lines, were a little larger than it was observed experimen-
tally. It may indicate that the real intermixing of QW and the barrier material in the
near interface region is a little less than it follows from the chosen F (z) parameters.
The calculations carried out showed that their results are very sensitive not only
to the choice of F (z) parameters but to the type of this function as well. Taking
into account Coulomb corrections of confining potential together with a detailed
selection of F (z) may be important for a more complete agreement of calculations
with the experiment.
The smaller energy distance between the e1-hh1 and e1-hh2 lines in CCM 207
structure in comparison with CCM 205 is in a qualitative agreement with calculation
results for a two-well model and is connected with miniband formation.
550
Additional lines in quantum wells excitonic spectra
4. Conclusion
The calculations of intensity ratio of both the main and additional lines are pre-
sented. Energy differences between them are fulfilled for QW with the asymmetrical
potential profile. It is grounded on the basis of this calculation that additional line in
exciton spectrum of QW can be explained by transitions between the confined states
of valence and conductivity electrons which ceases to be forbidden in the presence
of asymmetry of QW potential profile caused by technology of growth. It is shown
that e1-hh2 additional exciton line is more intensive in most of the actual cases.
The calculations showed the substantial sensitivity of results not only to LD
parameter, but to the detailed type of F (z) function. It is distinct from the situation
using the intermixing model for explaining a “paramagnetic enhancement” of GSS
effects [1,2] where only LD value was really important. Such a situation gives us an
expectation to use the analysis of additional lines observed to obtain the information
regarding the detailed interface structure at different growth technologies.
It is shown that the laser ablation method of heterostructure growth leads to a
larger asymmetry of QW potential profile caused by technology than MBE potential
profile.
The authors are grateful to J.J.Dubowski for providing samples of the structures
for measurements as well as for a helpful discussion.
This investigation was partly supported by INTAS grant N 93–3657ext. and by
the grant of State Fundamental Research Foundation of Ukraine NF4/346-97.
References
1. Gaj J.A., GrieshaberW., Bodin-Deshays C., Cilbert J., Feuillet G., Merle d’Aubigne Y.,
Wasiela A. Magneto-optical study of interface mixing in the CdTe-(Cd,Mn)Te system.
// Phys. Rev B, 1994, vol. 50, No. 8, p. 5512–5527.
2. GrieshaberW., Haury A., Cibert J., Merle d’Aubigne Y., Wasiela A., Gaj J.A. Magneto-
optical study of the interface in semimagnetic semiconductor heterostructures: Intrinsic
effect and interface profile in CdTe - Cd1−xMnxTe. // Phys. Rev B, 1996, vol. 53, No. 8,
p. 4891–4904.
3. Abramishvili V.G., Komarov A.V., Ryabchenko S.M., Sugakov V.I., Vertsimakha A.V.
Influence of interfaces on the paramagnetic enhancement of giant spin splitting of ex-
citonic states in structures of Cd1−xMnxTe/CdTe/Cd1−xMnxTe. // Ukr. Fiz. Zhurn.,
1998, vol. 43, No. 8, in press (in Ukrainian).
4. Kutowski M., Wojtowicz T., Grywinski G., Karczewski G., Janik E., Dynowska E., Kos-
sut J. Half-parabolic quantum wells of diluted magnetic semiconductor Cd1−xMnxTe.
// Acta Phys. Polonica A, 1997, vol. 92, No. 5, p. 887–890.
5. Ribayrol A., Couillat D., Lascaray J.P., Kavokin A.V., Ashenford D.E. Flare-up of the
e1-hh3 exciton oscillator strength in quantum well structure under type I – type II
transition. // Phys. Rev B, 1995, vol. 51, p. 7882–7890.
6. Roth A.P., Benzaquen R., Finnie P., Berger P.D., Dubowski J.J. Excitonic recombina-
tion in Cd0.90Mn0.10Te/CdTe heterostructures grown by Pulsed Laser Evaporation and
Epitaxy. // Proc. SPIE, 1994, vol. 2045, p. 322–327.
551
S.M.Ryabchenko et al.
Додатковi лiнiї в екситонних спектрах квантових ям,
пов’язанi з технологiчно обумовленою асиметрiєю
С.М.Рябченко 1 , Ф.В.Кириченко 2 , Ю.Г.Семенов 2 ,
В.Г.Абрамiшвiлi 1 , А.В.Комаров 1
1 Iнститут фiзики НАН України, Київ, просп. Науки, 46
2 Iнститут фiзики напiвпровiдникiв НАН України, Київ, просп. Науки, 45
Отримано 7 липня 1998 р.
Проведенi розрахунки вiдношення iнтенсивностей основної i додат-
кової лiнiй, енергетичної вiдстанi мiж ними для квантових ям (КЯ) з
асиметричним потенцiальним профiлем. Обгрунтовано, що додатко-
ва лiнiя у екситонному спектрi КЯ може бути пояснена переходами
мiж утримуваними в КЯ станами валентних електронiв i електронiв
провiдностi з рiзною парнiстю, якi перестають бути забороненими у
присутностi асиметрiї потенцiального профiлю, спричиненої техно-
логiєю вирощування КЯ. Показано, що додаткова екситонна лiнiя ти-
пу e1-hh2 є бiльш iнтенсивною в бiльшiй частинi актуальних випадкiв.
Зокрема, показано, що додаткова екситонна лiнiя в структурах виро-
щених методом лазерної абляцiї, може бути пояснена як e1-hh2 пе-
рехiд. Розрахунки показують суттєву чутливiсть не лише до параме-
тру розширення iнтерфейсу, але й до функцiї його профiлю. Зробле-
но висновок, що метод лазерної абляцiї призводить до бiльшої аси-
метрiї КЯ, нiж метод молекулярно-пучкової епiтаксiї.
Ключові слова: квантова яма, асиметричний потенцiал, функцiя
профiлю iнтерфейсу, додатковi екситоннi переходи, напiвмагнiтнi
напiвпровiдники
PACS: 78.55.Et
552
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