Weak antilocalization and zero-field electron spin splitting in AlGaN/AlN/GaN heterostructures with a polarization induced two-dimensional electron gas

Abstract

Spin-orbit coupling is studied using the quantum interference corrections to conductance in AlGaN/AlN/GaN two-dimensional electron systems where the carrier density is controlled by the persistent photoconductivity effect. All the samples studied exhibit a weak antilocalization feature with a spin-orbit field of around 1.8 mT. The zero-field electron spin splitting energies extracted from the weak antilocalization measurements are found to scale linearly with the Fermi wavevector with an effective linear spin-orbit coupling parameter 5.5x10^{-13} eV m. The spin-orbit times extracted from our measurements varied from 0.74 to 8.24 ps within the carrier density range of this experiment. Comment: 16 pages, 4 figures

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Weak antilocalization and zero-field electron spin splitting in AlGaN/AlN/GaN
heterostructures with a polarization induced two-dimensional electron gas

Ç. Kurdak(1), (2), N. Biyikli(2), Ü. Özgür(2), H. Morkoç(2), and V. I. Litvinov(3)

(1) Physics Department, University of Michigan, Ann Arbor, MI 48109
(2) Department of Electrical Engineering, Virginia Commonwealth University,
Richmond VA 23284
(3) WaveBand/Sierra Nevada Corporation, 15245 Alton Parkway, Suite 100
Irvine, CA 92618

Spin-orbit coupling is studied using the quantum interference corrections
to conductance in AlGaN/AlN/GaN two-dimensional electron systems
where the carrier density is controlled by the persistent photoconductivity
effect. All the samples studied exhibit a weak antilocalization feature with
a spin-orbit field of around 1.8 mT. The zero-field electron spin splitting
energies extracted from the weak antilocalization measurements are found
to scale linearly with the Fermi wavevector ( ESS= 2αkf) with an effective
linear spin-orbit coupling parameter α = 5.5×10−13eV⋅m. The spin-orbit
times extracted from our measurements varied from 0.74 to 8.24 ps within
the carrier density range of this experiment.

PACS Numbers: 71.70.Ej, 73.20.Fz, 73.40.Kp

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Following the advances in magnetic semiconductors, there has been growing interest in
spin-based electronics (spintronics).1 Realization of useful spintronic devices requires
controlled spin polarization, spin transport, and spin detection. These are particularly
challenging tasks. Unlike charge, the spin of an electron in a semiconductor system is a
nonconserved quantity mainly due to spin-orbit coupling. Spin-orbit interaction in
zincblende III-V semiconductor quantum wells manifests itself in the Dresselhaus2 and
Rashba3 effects arising from bulk inversion asymmetry of the crystal and the structural
inversion asymmetry of the confinement potential, respectively. The spin-splitting that
arises from the Rashba effect is isotropic and scales linearly with the Fermi wavevector
kF whereas there are two terms for spin-splitting associated with the Dresselhaus effect;
one scales as
f k and the other scales as
3
f k but is anisotropic in the plane of the quantum
well. The Rashba coupling is of particular interest for spin transistor applications, as it
can be controlled by a gate potential.4

Both low and high bandgap semiconductors are currently being considered for spintronic
applications. In low bandgap semiconductors, such as InAs, the Rashba coupling is
known to be strong, which is desirable for spin transistor applications. On the other hand,
dilute magnetic semiconductors based on low bandgap semiconductors exhibit low Curie
temperatures above which ferromagnetism is lost. In contrast, it has been suggested that
at room temperature, or even above, ferromagnetism can be achieved in high bandgap
semiconductors such as GaN and ZnO.5,6 Within this context, there has been recent
interest in exploring AlGaN/GaN heterostructures for spintronic applications.

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Spin-orbit interaction and the associated spin-splitting in zincblende III-V semiconductor
heterostructures have been studied for more than a decade and are relatively well
understood.7 In addition to Rashba and Dresselhaus terms for spin-splitting there is an
additional term for wurtzite quantum well structures that arises from bulk inversion
asymmetry with a functional form identical to that of the Rashba term.8 These terms have
not been measured independently in the wurtzite system. Moreover, recent experiments
based on Shubnikov-de Haas (SdH),9,10 weak antilocalization (WAL),11,12,13 and circular
photogalvanic14 measurements have given conflicting results for the spin splitting in
wurtzite AlGaN/GaN heterostructures. In particular, spin-splitting energies extracted
from the beat pattern of SdH measurements are found to be as large as 9 meV, which is
about an order of magnitude larger than the theoretical estimates based on the Rashba
coupling mechanism for this material system.15 To account for the discrepancy, Lo et al.
have proposed an additional spin splitting mechanism for wurtzite structures16 and Tang
et al. proposed an alternative interpretation of such data based on magneto-intersubband
scattering.17

To help resolve these issues, we have performed WAL and SdH measurements on three
AlxGa1-xN/AlN/GaN samples with different Al concentrations. We used the persistent
photoconductivity effect to vary the carrier density of the two-dimensional electron gas
(2DEG).18 The electron spin splitting energies extracted from our weak antilocalization
measurements varied from 0.3 to 0.7 meV. Consistent with such small spin splitting

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energies, we have not seen any beat feature in the SdH oscillations. More importantly, the
measured spin splitting energies are found to scale linearly with the Fermi wavevector.

The three heterostructures used in this study were grown by metalorganic vapor phase
epitaxy on c-plane sapphire substrates and consist of the following layers: a 3 µm thick
GaN buffer layer, a 1 nm thick AlN interfacial layer, a 25 nm thick AlxGa1-xN layer, and
3 nm of GaN cap layer where x =0.1, 0.15, and 0.25 for heterostructures A, B, and C,
respectively. All layers were undoped and the 2DEG is formed as a result of spontaneous
and piezoelectric polarization effects just below the AlN interfacial layer. An AlN
interfacial layer between the GaN and AlGaN layers was used to suppress alloy
scattering.19 600 µm long 100 µm wide Hall bar structures were fabricated by
photolithography followed by dry etching. Ti/Al/Ti/Au contacts annealed at 900 °C were
then used to form ohmic contacts to the 2DEG.

Magnetoresistance and Hall measurements were performed in a variable temperature
cryostat with a base temperature of 1.6 K. The samples exhibited SdH oscillations and
integer quantum Hall effect at high magnetic fields. As expected, the carrier density of
the sample with the highest Al fraction (Sample C) had the highest carrier density. To
change the carrier density of the samples, we have illuminated the top surface of the
samples through the optical access port of the cryostat via a flashlight. After each
illumination the carrier density of the sample increases and does not drop to its
equilibrium concentration, unless the sample is warmed up to room temperature.20 By
using the persistent photoconductivity effect we were able to vary the carrier density of

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the samples in a controllable manner over the ranges of 0.8-1.3×1012 cm-2, 1.7-
4.9×1012 cm-2, and 3.1-6.7×1012cm-2 for samples A, B, and C, respectively. Sample B
had the highest electron mobility of µ =20,300 cm2/V⋅s at a carrier concentration of
n = 4.9×1012 cm-2. Consistent with previous studies based on gated structures, at low
carrier densities the electron mobility is found to be decreasing with decreasing carrier
density.21 Typical high field magnetoresistivity traces obtained from these three samples
are shown in Fig. 1. From the temperature dependence of SdH oscillations, we extracted
an effective electron mass of m*= 0.23me. We could not resolve any beat feature in the
SdH oscillations even at high carrier densities where the onset of SdH is around 2 Tesla.
The SdH oscillations also indicate that only a single subband of the quantum well is
occupied by the 2DEG. Furthermore, at high carrier densities, we could resolve SdH
oscillations corresponding to filling fractions above 100 which implies that the carrier
density was uniform throughout our device even after illumination.

The absence of any beat feature in the SdH oscillations prevented us from extracting
spin-splitting energies from high magnetic field measurements. An alternative method,
however, was employed to extract the spin-orbit coupling and the associated spin-
splitting energies from the measurements of quantum corrections to conductance. Hikami
et al. first predicted that in the limit of large spin-orbit interaction the quantum correction
to conductance changes sign.22 Experimentally the quantum interference corrections are
typically studied by performing high accuracy magnetoconductance measurements at low
magnetic fields where the sign of the magnetoconductance is either positive or negative
depending on the size of spin-orbit coupling. If a negative magnetoconductance near zero