Supporting information
The role of quantum confinement in optical anisotropy
of a-plane Cd0.06Zn0.94O/ZnO quantum wells
Hiroaki Matsui 1, 2 and Hitoshi Tabata 1, 2
1
Department of Bioengineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
2
Department of Electronics Engineering, The University of Tokyo, Bunkyo-ku,
Tokyo 113-8656, Japan
1
1. Polarized photoluminescence of QWs with an LW of 4.8 and 2.0 nm at various temperatures
1
Polarization ()
PL intensity (a.u.)

(a)
E⊥c
E //c
0.5
LW = 4.8 nm
100
200
Temperature (K)
PL intensity (a.u.)

300
0
1
(b)
Polarization ()
0
E⊥c
E //c
0.5
LW = 2.0 nm
0
100
200
Temperature (K)
300
0
Figure S1. (a) PL intensity of E⊥c (closed circles) and E//c (open circles) and their polarization
ratio (blue circles) as a function of T for a QW with (a) LW = 4.8 nm and (b) LW = 2.0 nm.
Figure S1(a) shows the PL intensity and polarization ratio () as a function of temperature (T) for an
a-plane Cd0.06Zn0.94O/ZnO QW with LW = 4.8 nm. At 300 K, carriers were sufficiently distributed in
the Z -like state, resulting in a low value. However,  gradually increased with decreasing T
because of a higher thermal distribution of holes in the Y -like state compared to the Z -like state.
As a consequence, a high  value was achieved at 200 K by negligible carrier distribution in the
Z -like state. The value of  remained unchanged at temperatures below 200 K. The same behavior
was also observed for LW = 2.0 nm. The value of  at 300 K was 0.71 and gradually increased to 0.88
at 200 K, and then remained almost constant below 200 K [Fig. S1(b)]. These phenomena are a result
of the weak mixing between the two topmost VB levels, indicating an increase in the carrier
distribution in the Z -like state, and is in agreement with both the theoretical estimation, and
2
experimental results derived from m-plane MgxZn1-xO/ZnO and CdxZn1-xO/ZnO QWs
1, 2, 4
. Therefore,
PL peak energy (eV)
excitonic localization did not adhere to the polarization rules at low temperature.
(a)
3.05
E //c
3
E⊥c
2.95
0
LW = 4.8 nm
100
200
300
PL peak energy (eV)
Temperature (K)
(b)
3.15
E⊥c
3.1
E //c
LW = 2.0 nm
Energy separation
E (meV)
0
50
100
200
Temperature (K)
▲ LW = 4.8 nm
300
(c)
▲ LW = 2.0 nm
25
0
0
100
200
Temperature (K)
300
Figure S2. PL peak energies of E⊥c (closed circles) and E//c (open circles) as a function of T
for a QW with (a) LW = 4.8 nm and (b) LW = 2.0 nm. (c) Energy separation (E) between PLO
peak energies for E⊥c (green triangles) and E//c (red triangles).
The PL peak energies of a-plane Cd0.06Zn0.94O/ZnO QWs with LW = 4.8 and 2.0 nm and the energy
separation (E) between them are plotted as a function of T [Figs. S2(a) - S2(c)]. For both QWs,
temperature-dependent PL peak energies showed a typical S-shaped shift, which is closely related to
excitonic localization 5. The first redshift from 10 K is due to the trapping of carriers into the lowest
3
energy states of the potential minima. In this regime, E was almost zero for E⊥c and E//c. The strong
confinement of excitons destroys the optical polarization because of the increased mixing of excitons
that possess different VB states 6. However, the value of E increased in the temperature range above
150 K for both QWs, and then acquired a constant value around room temperature. The final redshift
of the PL peak in the temperature range from 200 to 300 K reflects temperature-induced band gap
shrinkage, which indicates that excited carriers do not localize in the potential minima by thermal
energy. Therefore, the distribution of excited carriers in the two topmost VB states ( Y - and Z -like
states) obeys a Boltzmann-like distribution at room temperature. Therefore, the polarized PL spectra at
300 K for QWs with LW = 4.8 and 2.0 nm obey the excitonic polarization rule. In contrast, a breaking
of the optical polarization rules due to excitonic localization was observed in the temperature region
below 200 K, which was also clarified from Figs. S1 and S2.
4
(a)
E //c
3.05
3
0
E⊥c
LW = 2.8 nm
(c)
100
200
300
Temperature (K)
E⊥c
1
Polarization ()
3.1
PL intensity (a.u.)
PL peak energy (eV)
2. Polarized photoluminescence of QWs with an LW of 6.0 and 2.8 nm at various temperatures

0.5
E //c
LW = 2.8 nm
0
100
200
Temperature (K)
300
0
E //c
2.95
E⊥c
LW = 6.0 nm
0
100
200
E⊥c

Temperature (K)
0.5
E //c
LW = 6.0 nm
0
300
Polarization ()
(b)
3
PL intensity (a.u.)
PL peak energy (eV)
1
(d)
100
200
300
0
Temperature (K)
Figure S3. PL peak energies of E⊥c (closed circles) and E//c (open circles) as a function of T for
a QW with (a) LW = 2.8 nm and (b) LW = 6 nm. PL intensity of E⊥c (closed circles) and E//c
(open circles) and their polarization ratio (blue circles) as a function of T for a QW with (c) LW =
2.8 nm and (d) LW = 6 nm.
Figures S3(a) and S3(b) show the temperature dependence of PL peak energy for a-plane
Cd0.06Zn0.94O/ZnO QWs with LW = 2.8 nm and 6.0 nm. For both QWs, PL peak energy exhibited a
typical S-shaped temperature dependence 4, which was derived from excitonic localization induced at
low temperatures below 200 K. Figures S3(c) and S3(d) show the PL intensity and polarization ratio
() as a function of T for QWs with LW = 2.8 nm and LW = 6.0 nm. The temperature dependence of PL
intensity and polarization for QWs with LW = 2.8 nm and LW = 6.0 nm were similar to those of QWs
with LW = 2.0 nm and LW = 4.8 nm. When T decreased to 200 K,  systematically increased because of
negligible carrier distribution in the Z -like state. At low temperatures below 200 K, the value of 
5
remained unchanged. This was due to an increase in the carrier distribution in the Z -like state as a
consequence of weak mixing between the two topmost VB states. In Figs. S1 - S3, the PL peak energy
and PL intensity of all QW samples with different well widths exhibited similar temperature
dependence.
6
3. Degree of excitonic localization of a-plane Cd0.06Zn0.94O/ZnO QWs with different LW.
E(0) = 3.207 eV, a = 0.90 meV
 = 780 K,  = 9.4 meV
PL peak energy (eV)
3.15
(a)
3.125
3.1
3.1
E(0) = 3.168 eV, a = 1.1 meV
 = 780 K,  = 9.6 meV
(d)
3.05
3.05
PL peak energy (eV)
3.175
E(0) = 3.126 eV, a = 1.3 meV
 = 780 K,  = 10.2 meV
(b)
E(0) = 3.073 eV, a = 0.97 meV
 = 780 K,  = 9.8 meV
(c)
3
2.95
3
2.975
2.95
3
0
100
200
Temperature (K)
300
2.925
0
100
200
300
Temperature (K)
Figure S4. PL peak energy versus temperature for QWs with LW = 2.0 nm (a), 2.8 nm (b), 4.8
nm (c) and 6.0 nm (d). The solid lines are fitting curves based on the band-tail model of Eq. (1).
The degree of excitonic localization by alloy disorder and interface fluctuation can be estimated
from temperature-dependent PL. Excitonic localization was well reflected in the PL signal because the
PL peak energy of both layers showed an S-shaped temperature dependence that is based on thermal
activation of excitonic dynamics. The S-shape shift is interpreted as a temperature-sensitive
redistribution process that is related to the transfer of excited carrier high-energetic and low-energetic
localized states. The band-tail model is suitable for an analysis of the localization for excitons. If the
density of states for the conduction and valence bands is assumed to have a Gaussian-like distribution,
the S-shaped shift can be estimated as -2/ kBT, where  is the standard deviation of the potential
fluctuations. The temperature dependence of the PL peak energy is described by the following
expression 7:
E (T )  E 
T 2  2

T   k BT
(1)
where E represents the energy gap at 10 K, and  and  are known as Varshini’s parameters. Figures
S4(a) - 4(d) show the PL peak energy as a function of temperature. The fitting parameters of Eq. (1)
are given in Fig. 7. The  and  Varshini constants were 0.94-1.3 meV/K and 780 K, respectively. The
7
values of  for QWs with LW = 2.0, 2.8, 4.8 and 6.0 nm were 9.4, 9.6, 10.2 and 9.8 meV, respectively.
The  value, which reflects the degree of excitonic localization, was not related to the well width.
Thus, excitonic localization is related to alloy disorder of the Cd atom in the well layer because the Cd
content in the well layer was 6% in all QWs. Therefore, excitonic localization did not affect the
polarized PL properties at 300 K. Energy separation (E) and polarization () of the polarized PL were
only dependent on the well width, which originated from strain-induced modification of VB levels.
8
4. Determination of the absorption edge of strained a-plane Cd0.06Zn0.94O layers
Absorption ()
○ Experiment data
2.2
Calculation
2.4 2.6 2.8
3
Photon energy (eV)
3.2
Figure S5. Absorption spectrum of a strained Cd0.06Zn0.94O layer on an a-plane ZnO substrate. A
red line indicates a theoretical curve fitted by Eq. (2).
The absorption edge of Cd0.06Zn0.94O was estimated from a strained Cd0.06Zn0.94O layer on a-plane
ZnO substrates, as confirmed by an optical absorption measurement at 300 K. The layer shows
spectral broadening at the band edge because of spatial fluctuations of Cd atoms. We therefore made a
determination using the effective band gap (Eg) and broadening factor (E) that were derived from a
sigmoidal absorption approximation given by the following equation 8:
 (E) 
0
(2)
 Eg  E 

1  exp 
 E 
where absorption is obtained from transmission through the relation a(E) versus –ln (T), which
neglects interface reflection losses and optical scatter. The value of Eg was determined as 2.940 eV
with a E value of 28 meV.
9
5. Histograms of RSD spots obtained by a Fast-Fourier transform (FFT) analysis
RSD patterns were obtained by a two-dimensional fast Fourier transform (2-D FFT) from the TEM
images of Figs. 4(a) and 4(d). Figures S6 and S7 show histograms of different spots (A-D) in the RSD
patterns of QWs with LW = 4.8 nm and 2.0 nm, respectively. All histograms were analyzed by the
Gaussian distribution, which is generally described the following expression:
f ( x) 
 ( x   ) 2 

exp

2
2  2

 2
1
(3)
where f is a frequency function, and  and  represent the average and variance, respectively. From
the estimated  and  values, the distributions of plane intervals of well and barrier layers were within
0.2 to 0.4%. Furthermore, we estimated a plane interval along the x-axis. As a consequence, the plane
intervals along the x-axis were 1.65 nm and 1.66 nm for the QWs with LW = 4.8 and 2.0 nm,
respectively, which corresponded to expansions of 1.4 and 1.8% along the x-axis, respectively.
Therefore, the basal hexagon of the Cd0.06Zn0.94O well layers clearly had anisotropic lattice distortions,
which were related to anisotropic compressive strains on the growing surface planes (y-z planes).
dC
(D)
dD
Spot (C)
Spot (D)
 = 2.806 Å
 = 0.008 Å
 = 2.871 Å
 = 0.013 Å
0.287 nm
(C)
0.281 nm
Well
(B) 0.283 nm
(A)
0.281 nm
Barrier
2.77 2.81 2.85
2.88 2.92
2.96
3
2.77
2.82
2.87
2.92
dB
dA
Spot (A)
Spot (B)
 = 2.828 Å
 = 0.008 Å
 = 2.808 Å
 = 0.006 Å
2.77
2.97
Plane internal (Å)
Plane internal (Å)
2.81
2.85
2.88
2.92
2.96
3
Plane internal (Å)
2.77
2.82
2.87
2.92
2.97
Plane internal (Å)
Figure S6. Histograms of different RSD spots (A-D) of well and barrier layers in a QW with LW
= 4.8 nm. Red lines are fitted by the Gaussian distribution.
10
(D) 0.289 nm
dD
dC
Spot (D)
Spot (C)
(C)
0.281 nm
Well
(B)
(A)
0.281 nm
Barrier
 = 2.887 Å
 = 0.012 Å
 = 2.807 Å
 = 0.007 Å
0.282 nm
2.77 2.81 2.85 2.88 2.92 2.96
3
Plane internal (Å)
3
dB
dA
2.77
2.77 2.81 2.85 2.88 2.92 2.96
Plane internal (Å)
2.81
Spot (A)
Spot (B)
 = 2.812 Å
 = 0.005 Å
 = 2.833 Å
 = 0.009 Å
2.85 2.88 2.92 2.96
Plane internal (Å)
3
2.77
2.81
2.85
2.88
2.92
2.96
Plane internal (Å)
Figure S7. Histograms of different RSD spots (A-D) of well and barrier layers in a QW with LW
= 2.0 nm. Red lines are fitted by the Gaussian distribution.
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