Low-temperature photoluminescence and reflectance measurements were employed to study the optical transitions present in two-dimensional electron systems confined at Mg_xZn_(1–x)O/ZnO heterojunctions. Transitions involving A- and B-holes and electrons from the two lowest subbands formed within the confinement potential are detected. In the studied density range of 2.0–6.5 × 10¹¹ cm⁻², the inter-subband splitting is measured and the first excited electron subband is shown to be empty of electrons

Falson, J.

Kawasaki, M.

Kozuka, Y.

Kukushkin, I. V.

Maryenko, D.

Smet, J. H.

Solovyev, V. V.

Tsukazaki, A.

Van'kov, A. B.

Zhang, D.

English

Caltech Authors - Main

Appl. Phys. Lett. 106, 082102 (2015); https://doi.org/10.1063/1.4913313 106, 082102
© 2015 AIP Publishing LLC.
Optical probing of MgZnO/ZnO
heterointerface confinement potential
energy levels
Cite as: Appl. Phys. Lett. 106, 082102 (2015); https://doi.org/10.1063/1.4913313
Submitted: 25 December 2014 . Accepted: 10 February 2015 . Published Online: 23 February 2015
V. V. Solovyev, A. B. Van'kov, I. V. Kukushkin, J. Falson, D. Zhang, D. Maryenko, Y. Kozuka, A. Tsukazaki, J.
H. Smet, and M. Kawasaki
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Optical probing of MgZnO/ZnO heterointerface confinement potential
energy levels
V. V. Solovyev,1,2 A. B. Van’kov,1,2 I. V. Kukushkin,1,2 J. Falson,3 D. Zhang,2 D. Maryenko,4
Y. Kozuka,3 A. Tsukazaki,5,6 J. H. Smet,2 and M. Kawasaki3,4
1Institute of Solid State Physics, RAS, Chernogolovka 142432, Russia
2Max-Planck-Institut f€ur Festk€orperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
3Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo,
Tokyo 113-8656, Japan
4RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
5Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
6PRESTO, Japan Science and Technology Agency (JST), Tokyo 102-0075, Japan
(Received 25 December 2014; accepted 10 February 2015; published online 23 February 2015)
Low-temperature photoluminescence and reflectance measurements were employed to study the
optical transitions present in two-dimensional electron systems confined at MgxZn1–xO/ZnO hetero-
junctions. Transitions involving A- and B-holes and electrons from the two lowest subbands formed
within the confinement potential are detected. In the studied density range of 2.0–6.5 1011cm2,
the inter-subband splitting is measured and the first excited electron subband is shown to be empty of
electrons.VC 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4913313]
Wide direct band gap semiconductor materials such as
ZnO, GaN, and BN offer improved performance for future
photonic and electronic power devices due to higher optical
transition energies, electric breakdown field, and saturation
velocity compared with Si and GaAs.1 In the case of ZnO,
progress in crystal growth techniques now enables the devel-
opment of high quality MgxZn1–xO/ZnO heterojunctions
(HJ) which host high mobility two-dimensional electron sys-
tems (2DES).2–5 In contrast to the AlxGa1–xAs/GaAs
(x> 0.2) heterointerface where the presence of a large barrier
height in combination with modulation doping determines
both the energy band diagram and electron distribution
between different quantized subbands of the 2DES,6,7 it is
the discontinuity in internal polarization at the MgxZn1–xO/
ZnO heterointerface that naturally induces a 2DES.8 The
charge density (n) is therefore determined by the discontinu-
ity in electric field, which is a monotonic function of
Mg-fraction.2 However, the barrier height too grows linearly
with Mg-content x. It is therefore unclear a priori what elec-
tron distribution is realized at the HJ for each particular
value of Mg.
Here, we investigate the energy levels formed at the
MgxZn1–xO/ZnO HJ through optical measurements. A series
of 2DES covering the electron density range from 2.0 to
6.5 1011cm2 with varying x¼ 0.014–0.045 were studied
by means of photoluminescence (PL) and reflectance meas-
urements at temperatures of 0.5K and in perpendicular mag-
netic fields up to B¼ 14 T. A number of optical transitions
show periodic oscillations in energy with B and can be asso-
ciated with the Landau level spectrum of a 2DES. They
involve the two lowest subbands of the confinement potential
in the conduction band as well as two branches of the
valence-bands. It is possible to quantify the splitting of the
two lowest electron subbands. It grows monotonically with
density. For all heterostructures, only the lowest electron
subband is occupied. Calculations of the confinement
potential suggest that the full-width-half-maximum of the
wavefunction is less than 10 nm.
The MgxZn1–xO/ZnO heterostructures were grown by
ozone-molecular beam epitaxy.3 Low temperature (T¼ 0.5K)
transport measurements (not shown) as well as the optical
experiments described below yield the electron mobility, lt,
and density, nt and no, respectively (see Table I). These sam-
ples are much lower in density and higher in quality than
those of previous optical studies.9,10 Photoluminescence and
reflectance measurements were conducted in a two-fiber ge-
ometry. PL spectra were recorded by exciting the sample with
the continuous-wave output of a 325 nm He-Cd laser, while
the light from a commercial 365 nm light emitting diode was
employed to detect reflectance spectra. The excitation power
density was below 30lW/mm2. PL and reflectance spectra
were obtained in one cooldown using a Monospec spectrome-
ter with a linear dispersion of 5 A˚/mm and a spectral resolution
of 0.3 A˚.
Both the PL and reflectance spectra contain a multitude
of features mostly stemming from optical transitions in bulk
ZnO and MgxZn1–xO. We concentrate on features near the
ZnO fundamental gap energy and investigate their origin.
They are marked with triangles, circles, and squares in
Fig. 1. A hallmark of feature associated with 2D electrons is
oscillating behavior periodic in 1/B, as a result of the saw-
tooth motion of the chemical potential in a Landau quantized
2DES of fixed density. All features highlighted in Fig. 1
TABLE I. The electron mobility lt and density from transport (nt) and opti-
cal studies (no) of the investigated samples.
Sample nt (10
11cm2) no (10
11 cm2) lt (10
3 cm2/V s)
282 1.9 2.0 270
244 2.3 2.3 400
202 3.5 3.6 300
302 6.2 6.5 160
0003-6951/2015/106(8)/082102/4/$30.00 VC 2015 AIP Publishing LLC106, 082102-1
APPLIED PHYSICS LETTERS 106, 082102 (2015)
show such periodicity. In Fig. 2, the B-field dependence of the
PL intensity recorded on sample 302 (no¼ 6.5 1011cm2) at
the fixed energies of 3.3675 eV and 3.3755 eV is shown. These
energies correspond to the triangles and circles in Fig. 1, and
features are observed in both PL and reflectance. The most
prominent oscillations in intensity occur at the 3.3675 eV PL-
band. The locations of the intensity minima correspond closely
to integer fillings ¼ 1, 2, 3,…( ¼ hneB) of Landau levels. We
therefore associate them with PL recombination of 2D elec-
trons at the heterointerface. The intensity oscillations of the
spectral line at 3.3755 eV are in anti-phase with the lower
energy band at 3.3675 eV. The reasons will be discussed later.
The optical oscillations11 allow the quantification of the charge
density (no) under illumination, which is slightly enhanced in
comparison with values from transport data (see Table I).
Fig. 3 displays examples of the B-dependent behavior in the re-
flectance spectrum of sample 244. The center-of-mass energy
values of the three spectral features marked in Fig. 1 with a tri-
angle, circle, and square plotted as a function of B. Again, the
observed maxima correlate with integer fillings.
The lowest energy line in the reflectance spectra,
marked by triangles in Fig. 1, is attributed to optical transi-
tions from the top valence band state (A-band) to just above
the Fermi energy EF of the electrons in the lowest subband
of the conduction band (see Fig. 2(c)). This assignment is
supported through a comparison with the PL spectrum,
which is plotted above each reflectance spectrum. The line
coincides with the abrupt termination of the PL-band of
highest intensity. The energy span of the PL-band for the
FIG. 1. Reflectance (bottom) and photoluminescence (top) spectra for the
samples in Table I with density no. The evolution with density of three
2DES-related optical transitions in the reflectance are marked with triangles,
squares, and circles. Transitions marked by circles and triangles are corre-
lated with PL features (dotted lines).
FIG. 2. (a) Magnetic field dependence of the PL-signal at a photon energy
of 3.3675 eV corresponding to EF. Features associated with integer filling of
the Landau levels are marked and enable the extraction of the carrier den-
sity: no¼ 6.5 1011cm2. (b) Same for photon energy 3.3755 eV, corre-
sponding to line E1 in Fig. 1. The oscillations at this energy are synchronous
(but anti-phase) with oscillations at EF, i.e., 3.3675 eV. (c) Schematic draw-
ing of the optical transitions between the electron subbands and two
branches of the valence band. Upward and downward arrows depict transi-
tions active in reflectance and PL experiments, respectively.
FIG. 3. Magnetic field dependence of the center-of-mass of the three fea-
tures in the reflectance spectrum of sample 244 (no¼ 2.3 1011cm2) origi-
nating from 2D electrons. They are marked by a triangle, circle, and square
in Fig. 1.
082102-2 Solovyev et al. Appl. Phys. Lett. 106, 082102 (2015)
highest density sample is marked by a double arrow. It grows
with density, so that it can be related to the Fermi energy of
the 2DES.12 The high energy edge experiences a red-shift at
higher densities presumably due to the dependence of the
electron-hole energy separation on band bending near the
HJ. Every interband transition involves the creation (for re-
flectance) or annihilation (for PL) of a valence band hole
located at some distance from the HJ. The total energy of a
hole reaches a minimum at some distance as it experiences
the Coulombic attraction to the 2DES, but also the repulsive
action from the built-in electric field near the HJ. This last
energy term grows with the electron density resulting in a
larger separation of the hole from the 2D channel. Hence, the
optical transitions from and to the lowest electron subband
redshift with density.
The assignment of both higher energy spectral lines in
the reflectance spectra is more complex. Higher lying electron
subbands at the heterointerface may possibly contribute.
Alternatively or in addition, these features may be associated
with the close energetic proximity of the heavy and light hole
branches (A- and B-branches) in the ZnO valence band. The
crystal-field splitting is only about 5meV.13–15 The density
dependence of the spectral features is summarized in Fig. 4(a)
using the same symbols as in Fig. 1. There is an apparent cor-
relation between the previously identified feature at EF (trian-
gles) with the feature marked by squares. A monotonic
decrease in energy is observed for both with increasing den-
sity. They are offset by 5.5meV. Hence, we can attribute
them to optical transitions from the crystal field split A- and
B-valence bands to the lowest electronic subband of the
2DES. This interpretation is also supported by the absence of
the transition involving the B-holes in the PL spectra in the
three lowest density samples (Fig. 1), since recombination
occurs predominantly with thermalized A-holes in the top va-
lence band states. For the sample no¼ 6.5 1011cm2, a PL
peak appears at the same position as the square in the reflec-
tance spectrum; however, this is coincidental. The PL peak is
insensitive to B and is therefore ascribed to bulk PL.
The remaining spectral line is marked by circles in
Figs. 1 and 4. As opposed to the other spectral lines, it dis-
plays a blue shift with increasing density. Upon increasing the
density, the confinement potential in the conduction band is
expected to narrow down and the subband spacing will go up
accordingly. In MgZnO/ZnO HJ, this is not only caused by
the density increase but also by an enlargement of the conduc-
tion band offset with increasing Mg-content. It is therefore
natural to attribute this spectral line to non-equilibrium recom-
bination of electrons in the first excited subband (E1) with
photo-excited holes.16 The E1 line (circle) is well above the
EF line (triangle) for all samples, and in PL spectra, the inten-
sity of this line is one order of magnitude weaker than that of
the PL-band involving the lowest subband and terminating at
EF. This assignment would also account for the out-of-phase
behavior highlighted in Fig. 2 of these two spectral features.
Since the 2DES resides in the lowest subband only, at integer
fillings, screening is entirely suppressed and the probability
for recombination of electrons excited up into the second
subband with valence band states is highest. The PL signal
reaches its maximum and weakens again away from integer
filling due to screening of the attraction between the
photo-excited electrons and holes. To ensure that for the high-
est density sample the E1 spectral feature is properly assigned,
it is verified whether the photoluminescence intensities of the
lines at EF and E1 oscillate anti-phase in a 1/B–periodic fash-
ion as for all other samples. Further supporting evidence for
proper assignment is obtained by tracing the behavior of the
optical transitions as in Fig. 4(a) with density. We conclude
that the spectral line marked by circles corresponds to the
recombination of electrons from the first excited electron sub-
band and holes in the A-branch of the valence band.
From Fig. 4(a), it follows that at all densities, the second
subband is located above EF of the 2D electrons and it is pos-
sible to estimate the energy splitting between the bottom of
the second subband, E1, and the EF high energy edge. EF itself
can be estimated from the density using the band mass17 value
m*¼ 0.3m0. Combining this information yields an estimate of
the intersubband splitting E10. It is plotted as a function of
density in Fig. 4(b) and exhibits a linear dependence. For the
sake of completeness, we note that intersubband splittings
extracted from electron-hole transition energies may include
corrections from excitonic binding energies, as previously
observed in GaAs-based heterostructures with empty excited
subbands.16 Hence, the data in Fig. 4(b) somewhat underesti-
mate the single-particle splitting E10.
Finally, we utilize the experimentally extracted E10 and
no to guide calculations of the wavefunctions confined at the
FIG. 4. (a) Density dependence of the 2DES-related spectral features from
Fig. 1. The spectral lines marked by triangles and squares are split by
5.5meV, while exhibiting the same red-shift. They are attributed to optical
recombination of electrons near EF in the lowest electron subband to holes
residing in the A- and B-branch of the valence bands. The circles correspond
to a blue-shifting optical transition from the A-valence band branch to the
first excited electron subband. (b) The estimated intersubband splitting (E10)
between the lowest and the first excited subband (solid line) and the esti-
mated EF (dotted line). (c) Full-width half-maximum of the 2DES wave-
function at the heterointerface. The inset shows the wavefunction for
no¼ 2.0 1011cm2, x¼ 0.014.
082102-3 Solovyev et al. Appl. Phys. Lett. 106, 082102 (2015)
heterointerface. Using the surface potential of MgZnO and
ZnO as adjustable parameters, the Schr€odinger-Poisson
equation is solved self-consistently so that the calculated
energy levels E0 and E1 agree with the experimentally quan-
tified values. A representative wavefunction for sample 282
(n¼ 2.0 1011cm2) is shown in the inset to Fig. 4. The cal-
culations in panel c suggest that across the charge density
range studied, the full-width half-maximum (FWHM) of the
wavefunction is less than 10 nm, in agreement with previous
experiments and theoretical calculations.8,18,19
In summary, low temperature PL and reflectance spectra
of MgxZn1–xO/ZnO HJ reveal several interband optical tran-
sitions connected with the lowest two 2DES subbands and
the A- and B-valence bands. In the studied 2DES density
range of 2.0–6.5 1011 cm2, the first excited electron sub-
band was shown to lie above EF of the 2DES, and therefore,
electrons reside only in the lowest subband. The intersub-
band energy splitting E10 has been estimated in this range of
electron densities and grows linearly with increasing density,
or alternatively, Mg content. The FWHM of the 2DES wave-
function varies between 8 and 4 nm.
V.V.S., A.B.V., and I.V.K. thank the Russian Scientific
Foundation (Grant No.14-12-00693) for support in developing
reflectance measurements on ZnO heterostructures. This work
was partly supported by Grant-in-Aids for Scientific Research
(S) No. 24226002 from MEXT, Japan, “Funding Program for
World-Leading Innovative R&D on Science and Technology
(FIRST),” Program from the Japan Society for the Promotion
of Science (JSPS) initiated by the Council for Science and
Technology Policy.
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Optical probing of MgZnO/ZnO heterointerface confinement potential energy levels

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Optical probing of MgZnO/ZnO heterointerface confinement potential energy levels

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