Optical anisotropy in self-assembled InP quantum dots

Abstract

Strong optical anisotropy is observed in the photoluminescence (PL) bands of both the InP self-assembled quantum dots and the Ga0.5In0.5P matrix. From the linearly polarized PL spectra measured under weak excitation, we found that large size quantum dots show strong anisotropy. The luminescence from a single quantum dot observed by the micro-PL technique revealed a doublet fine structure of the exciton levels that obey the linear polarization selection rule. The observed fine structure is shown to arise from an interplay of the electron-hole exchange interaction and the asymmetric crystal structure of the InP/Ga0.5In0.5P system.

Full text

Optical anisotropy in self-assembled InP quantum dots
Mitsuru Sugisaki,*Hong-Wen Ren, and Selvakumar V. Nair
Single Quantum Dot Project, ERATO, JST, Tsukuba Research Consortium, 5-9-9 Tokodai, Tsukuba, Ibaraki 300-2635, Japan
Kenichi Nishi
Optoelectronics and High Frequency Device Research Laboratories, NEC Corporation, 34 Miyukigaoka,
Tsukuba, Ibaraki 305-8501, Japan
Shigeo Sugou
Single Quantum Dot Project, ERATO, JST, Tsukuba Research Consortium, 5-9-9 Tokodai, Tsukuba, Ibaraki 300-2635, Japan
and Optoelectronics and High Frequency Device Research Laboratories, NEC Corporation, 34 Miyukigaoka,
Tsukuba, Ibaraki 305-8501, Japan
Tsuyoshi Okuno
Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
Yasuaki Masumoto
Single Quantum Dot Project, ERATO, JST, Tsukuba Research Consortium, 5-9-9 Tokodai, Tsukuba, Ibaraki 300-2635, Japan
and Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
~Received 22 October 1998!
Strong optical anisotropy is observed in the photoluminescence ~PL!bands of both the InP self-assembled
quantum dots and the Ga0.5In0.5P matrix. From the linearly polarized PL spectra measured under weak exci-
tation, we found that large size quantum dots show strong anisotropy. The luminescence from a single quantum
dot observed by the micro-PL technique revealed a doublet fine structure of the exciton levels that obey the
linear polarization selection rule. The observed fine structure is shown to arise from an interplay of the
electron-hole exchange interaction and the asymmetric crystal structure of the InP/Ga0.5In0.5P system.
@S0163-1829~99!50608-5#
Recently there has been strong interest in low-
dimensional semiconductor structures such as quantum
wells, wires, and boxes. From the basic physics viewpoint,
an exciton confined in a zero-dimensional system is an at-
tractive subject because of interesting physical properties re-
flecting dimensionality such as
d
-function-like density of
states, enhanced oscillator strength, and strong optical non-
linearity. In the past few years, the self-assembled quantum
dots ~SAD’s!have emerged as an attractive system for such
studies.1–3
Theoretically, the electronic structures of the InP ~Ref. 4!
and ~Ga!InAs ~Refs. 5–7!SAD’s have been studied. A sym-
metric shape of the quantum dot is usually assumed to sim-
plify the calculations. However, since the quantum dots
grown under the Stranski-Krastanov mode are highly
strained due to the lattice mismatch between the matrix and
the SAD’s, the energy levels of the confined exciton are
influenced by the matrix in addition to the shape of the quan-
tum dots. In real systems, therefore, the electronic levels of
the confined excitons suffer perturbations due to strain and
possible structural anisotropies of the matrix, and the elec-
tron states eventually become asymmetric. The asymmetry
would manifest as energy splittings and optical anisotropy of
the confined exciton states. In this paper, we report the opti-
cal anisotropy in the InP SAD’s observed using conventional
and microphotoluminescence systems, hereafter referred to
as macro- and
m
-PL, respectively.
InP quantum dots embedded in Ga0.5In0.5P were grown
on a Si-doped ~001!oriented GaAs substrate by means of a
gas-source molecular beam epitaxy.8After an undoped
Ga0.5In0.5P~lattice matched to the GaAs substrate!buffer
layer 160 nm thick was grown on the substrate, the self-
assembled InP islands were formed at 480°C ~sample 1!or
520°C ~sample 2!by deposition of nominally 4 monolayers
InP. In order to investigate their optical properties, these is-
lands were buried by a Ga0.5In0.5P layer 160 nm thick. The
average size of the SAD’s are estimated by cross-sectional
transmission electron microscopy ~TEM!~see Table I!, and
from atomic force microscopy, the size dispersions of the
SAD’s are estimated to be less 30%. For photoluminescence
~PL!measurements, an Ar-ion laser was used as the excita-
tion light source. An edge of the sample was glued on the
cold finger of the sample holder and the sample was cooled
by cold helium gas in a flow-type cryostat. The PL was led to
a 50-cm single monochromator using an optical fiber, and
detected by a charge coupled device camera. The spectral
resolution of this system is better than 0.3 meV. In order to
measure the PL spectra from a single quantum dot, micro-
patterns with 10
m
m310
m
m square were drawn on the
sample by means of photolithography. After wet etching by
HCl:H2O52:1 at 30°C, the mesa size was reduced to less
than 4
m
m34
m
m. For the measurement of the polarization
dependence of
m
-PL, a microscope objective lens was used
to reduce the PL coming from outside of the mesa and a film
polarizer was set inside the microscope.9
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The solid and the dotted curves in Fig. 1~a!show the PL
spectra at4Kofsample 1 polarized along the @11
¯
0#and
@110#directions of the GaAs substrate, respectively. The PL
bands observed at 1.52 eV and 1.94 eV arise from the GaAs
substrate and the Ga0.5In0.5P matrix, respectively. The PL
peak coming from the SAD’s was observed at 1.67 eV. Even
when the excitation power is decreased to 100 times weaker
than this, the peak energy, the bandwidth, and the shape of
this PL band are the same. Thus, the spectrum reflects the
size distribution of the SAD’s, and the luminescence arises
from the radiative decay of the confined excitons in the
ground state.
The PL peaks from the GaAs substrate do not show any
polarization dependence as expected for cubic symmetry.
The PL peaks from the Ga0.5In0.5P matrix and the InP
SAD’s, however, show clear polarization dependence, al-
though both bulk Ga0.5In0.5P and bulk InP have the same
symmetry as GaAs. The PL spectrum was not sensitive to the
polarization of excitation under band-to-band excitation, im-
plying that the memory of polarization is lost before the
carriers excited in Ga0.5In0.5P matrix relax into the quantum
dots. The peak intensity of the luminescence band observed
for @11
¯
0#polarization, which is parallel to the long axis of
the SAD’s, is more than twice as strong as that observed for
@110#polarization.
The degree of linear polarization Pdefined by
P5I[11
¯
0]2I[110]
I[11
¯
0]1I[110] ~1!
is plotted in Fig. 1~b!, where I[11
¯
0] and I[110] are the PL
intensities observed for the @11
¯
0#and @110#polarizations,
respectively. It has a peak at 1.63 eV, which is at the lower
energy edge of the PL band from the InP SAD, and gradually
decreases with increasing the photon energy. This suggests
that large size quantum dots have stronger optical anisotropy
than small ones. The degrees of polarization at PL peaks of
the InP SAD’s and the Ga0.5In0.5P matrix are 44% and 83%,
respectively.
The peak intensity of the PL bands of the InP SAD’s and
the Ga0.5In0.5P matrix are plotted in Fig. 1~c!as a function
of the polarization angle of observation
u
. Both bands exhibit
a twofold symmetry and have a maximum value for @11
¯
0#
polarization. They are fitted by
I5Asin2
u
1Bcos2
u
,~2!
where Aand Bcorrespond to the peak intensities of the PL
bands observed for @11
¯
0#and @110#polarizations, respec-
tively. This relation was found in the ordered Ga0.5In0.5Pby
Wei et al.10 As shown by the solid lines in Fig. 1~c!, not only
the PL from the Ga0.5In0.5P matrix but also that from the InP
SAD’s can be fitted by Eq. ~2!. This suggests that the InP
SAD’s have a twofold symmetric structure with symmetry
axes along @110#and @11
¯
0#directions.
The inset of Fig. 1~a!shows the normalized PL spectra at
the peaks of each InP SAD band. The PL peak observed for
@11
¯
0#polarization is shifted to the lower energy side of that
observed for @110#polarization by about 5 meV.
The polarization dependence of the PL spectra in
~Ga!InAs SAD’s has been earlier reported as summarized in
Table I, and the anisotropy was attributed to the anisotropic
TABLE I. Growth temperature, size, and the optical properties of the InP SAD’s in the Ga0.5In0.5P
matrix. For comparison, those of ~Ga!InAs/GaAs are also summarized.
Growth Size of SAD’s Degree of polarization in
Sample No. temperature ~°C!~nm3!matrix ~%!SAD’s ~%!
InP ~Sample 1!480 353453683 44
InP ~Sample 2!520 403483540 13
In0.5Ga0.5Asa520 173333316
InAsb480 133153332
InAs on ~311!A GaAsc500 13
aSee Ref. 11.
bSee Ref. 12.
cSee Ref. 13.
FIG. 1. ~a!Polarization dependence of the PL spectra under
weak excitation at 4 K observed for @11
¯
0#~solid line!and @110#
~dotted line!polarization. The polarization dependence appears in
the PL bands of the InP SAD’s and the Ga0.5In0.5P matrix. Inset:
The normalized PL spectra of the InP SAD’s bands. The energy
separation of the peaks is 5 meV. ~b!Degree of polarization of the
PL spectra shown in Fig. 1~a!. At the PL peaks of the InP SAD and
the Ga0.5In0.5P matrix, it is 44% and 83%, respectively. ~c!Polar
plots of the polarized PL peak intensities from Ga0.5In0.5P matrix
~open circles!and the InP SAD’s ~closed squares!. They show two-
fold symmetry, and can be fitted by Eq. ~2!.
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shape of the SAD’s.11–13 The optical anisotropy of sample 2,
which was grown at a higher temperature than sample 1, was
very weak in comparison with sample 1, although the differ-
ence of the size and the shape of the SAD’s between these
samples is small ~see Table I!. Therefore, the observed
strong optical anisotropy in sample 1 is not mainly due to the
anisotropic shape of the SAD’s. TEM study suggests that the
optical anisotropy in the Ga0.5In0.5P matrix could be due to
the formation of composition modulation planes along the
@11
¯
0#and @001#directions.8We found that the degree of
modulation in Ga0.5In0.5P grown at lower temperature is
stronger, and then InP SAD’s show the stronger optical an-
isotropy. In this case, since Ga0.5In0.5P matrix has C2v or
lower symmetry, the optical anisotropy of the PL from
Ga0.5In0.5P is observed. SAD’s are thus embedded in an
anisotropic matrix that would be subjected to an anisotropic
strain.14 An anisotropic lattice structure of the SAD’s is the
most probable origin for their optical anisotropy. To clarify
this further, we studied the luminescence from individual
quantum dots by
m
-PL.
Figure 2 shows the comparison of the typical PL spectra
of sample 1 at 8 K measured by means of the macro-PL
system ~the main spectrum of Fig. 2!and the
m
-PL system
@insets ~a!and ~b!#.Inthe
m
-PL spectra, many sharp PL lines
were observed at the higher energy side of the PL peak of the
SAD’s band, as shown in Fig. 2~a!. Each PL peak corre-
sponds to the radiative annihilation of the exciton confined in
a single quantum dot and reflects
d
-function-like density of
states. The envelopes of the PL spectra measured by means
of macro- and
m
-PL system are almost the same. Thus, most
of the sharp lines observed in
m
-PL are considered to arise
from the ground state of confined excitons.
The
m
-PL measurements were also made for the energy
range between the PL peak of the SAD’s and the PL band of
Ga0.5In0.5P matrix, as shown in Fig. 2~b!. Although the
macro-PL intensity is weak under weak excitation, the
m
-PL
lines coming from single quantum dots were clearly ob-
served. In the energy region shown in Fig. 2~b!, the number
of the PL lines is reduced because the areal density of the
small sized SAD’s is low. Thus the polarization dependence
of the PL from a single quantum dot was studied in this
region.
The spectra ~a!and ~d!in Fig. 3 are observed without the
polarizer, while the spectra ~b!and ~e!are observed for the
@11
¯
0#polarization, and ~c!and ~f!for the @110#polarization.
The most important feature seen in the
m
-PL spectrum is the
doublet nature of each peak. Each constituent of the doublet
is fully polarized, i.e., one is along @110#and the other is
along @11
¯
0#. For example, a doublet with an energy separa-
tion of DE.400
m
eV at 1.851 eV is clearly resolved in the
polarized spectrum @Figs. 3~b!and 3~c!#. Theoretical analysis
described below shows that the fine splitting arises from the
electron-hole exchange interaction in the presence of struc-
tural asymmetry.
When the symmetry is lowered from Tdto C2v , the single
particle levels will lose all degeneracies except that due to
spin. Thus, the hole levels would be twofold degenerate with
the Bloch part of the wave functions, written in terms of the
X,Y, and Zvalence-band orbitals of the original cubic ma-
terial, given by
u
h1
&
5~ei
f
u
X
&
2ie2i
f
u
Y
&
)↑1c
u
Z
&
↓~3a!
u
h2
&
5~e2i
f
u
X
&
1iei
f
u
Y
&
)↓2c
u
Z
&
↑,~3b!
where
f
and care constants. The electron levels are also
twofold degenerate but s-like, and may be written as
u
e1
&
5
u
S
&
↑and
u
e2
&
5
u
S
&
↓. Consequently, the electron-hole pair
states are fourfold degenerate unless the electron-hole ex-
change interaction is taken into account. The interband ex-
change splits each fourfold degenerate exciton state, in C2v
symmetry, into four states consisting of a dark state ~pure
triplet!, two states optically excited by x- and y-polarized
FIG. 2. Below: Macro-PL spectra at 8 K. Insets ~a!and ~b!:
m
-PL spectra of the mesa processed sample. Each
d
-function-like
PL line arises from the radiative decay of the confined exciton.
FIG. 3. Normalized
m
-PL spectra at 8 K obtained without @spec-
tra ~a!and ~d!# and with polarizer along the @11
¯
0#@~b!and ~e!# and
@110#@~c!and ~f!# directions. The solid lines are guides to the eyes.
The separation of the broken lines are 400
m
eV ~left!and 190
m
eV
~right!. Each spectrum is normalized at the peak.
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light, and one state excited only by z-polarized light. The
x-ypolarized states, observed in our setup, are given by
u
x6
&
5
u
h1
&
u
e2
&
6i
u
h2
&
u
e1
&
.~4!
As may be easily verified, the states x1and x2are fully
polarized along the @110#and @11
¯
0#directions, respectively.
It can be shown that
u
x1
&
and
u
x2
&
are separated in energy
by DE}sin2
f
. The constant of proportionality is of the or-
der of the exchange energy that in bulk InP is less than 100
m
eV, but would be enhanced in SAD’s because of the strong
confinement along the growth direction, as is seen in quan-
tum wells. The observed energy splitting suggests a reason-
able exchange energy of the order of 1 meV. A more accu-
rate quantitative analysis that takes into account the detailed
structure of the envelope wave functions is made difficult by
the complicated nature of the hole confinement potential in
InP/Ga0.5In0.5P systems.4The difference in oscillator
strength between the constituents of a doublet, Df, is also
proportional to sin2
f
and thus to DE. This is qualitatively
in agreement with the observed spectrum.15 It is important to
note that the energy splitting between the @110#and @11
¯
0#
polarized exciton emissions is caused by the combined effect
of the exchange interaction and the asymmetric strain; the
latter causes the symmetry reduction. This effect is similar
to the stress exchange interplay observed in bulk
semiconductors.16
We found that the observed splitting energy differs from
dot to dot. For example, even if the PL is observed at 1.870
eV as a single peak in Fig. 3~d!, it is composed of two con-
stituents and they are selected by using a polarizer @see Figs.
3~e!and 3~f!#. Such a fine splitting resolved by polarization
is also observed at the lower energy edge of the PL band
(;1.64eV). On the other hand, the polarization-dependent
energy shifts of some PL peaks marked by open and closed
triangles were not observed within our resolution limit. As
mentioned before, the actual magnitude of the splitting
would depend on the electron-hole envelope functions and
hence on the size and strain distribution of each SAD. The
observed dispersion in the energy splitting, therefore, implies
that the structure of the SAD’s is affected by the long range
inhomogeneities in the composition modulated Ga0.5In0.5P
matrix. It may be noted that a fine splitting of the exciton
level is also observed in the PL and the PL excitation spectra
of excitons trapped by potential minimum induced by the
fluctuation of the width of a quantum well.17
In summary, we observed optical anisotropy in the PL
spectra of the InP SAD grown in Ga0.5In0.5P. The optical
anisotropy is observed in the PL bands of both the InP
SAD’s and the Ga0.5In0.5P matrix. By comparing the PL
spectra of the samples grown at different temperatures, we
found that the optical anisotropy is not related to the shape of
the SAD’s, but results from the anisotropy in the micro-
scopic structure of the SAD’s. This is consistent with the
expected symmetry reduction of a cubic unit cell under lat-
eral stress. In the
m
-PL spectra we observed a fine splitting
~doublet structure!of the exciton states in single quantum
dots. This fine structure arises from the electron-hole ex-
change interaction in the presence of structural asymmetry. It
is demonstrated that each peak in the doublet can be selected
by a polarizer set inside the microscope. The energy separa-
tions of the doublet lines differ from dot to dot. This suggests
that the anisotropy of the confined exciton states is influ-
enced by the structure of the matrix.
*Electronic address: mitsuru@sqdp.trc-net.co.jp
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