Intrinsic origin of the two-dimensional electron gas at polar oxide interfaces
M.L. Reinle-Schmitt,1C. Cancellieri,1D. Li,2D. Fontaine,3M. Medarde,1E. Pomjakushina,1
C.W. Schneider,1S. Gariglio,2Ph. Ghosez,3J.-M. Triscone,2and P.R. Willmott1, ∗
1Paul Scherrer Institut, CH-5232 Villigen, Switzerland
2DPMC, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Gen` eve 4, Switzerland
3Physique Th´ eorique des Mat´ eriaux, Universit´ e de Li` ege, B-4000 Li` ege, Belgium
(Dated: December 16, 2011)
The predictions of the polar catastrophe scenario to explain the occurrence of a metallic interface
in heterostructures of the solid solution(LaAlO3)x(SrTiO3)1−x (LASTO:x) grown on (001) SrTiO3
were investigated as a function of film thickness and x. The films are insulating for the thinnest
layers, but above a critical thickness, tc, the interface exhibits a constant finite conductivity which
depends in a predictable manner on x. It is shown that tc scales with the strength of the built-in
electric field of the polar material, and is immediately understandable in terms of an electronic
reconstruction at the nonpolar-polar interface. These results thus conclusively identify the polar-
catastrophe model as the intrinsic origin of the doping at this polar oxide interface.
Conductivity at the LaAlO3/SrTiO3(LAO/STO) in-
terface was originally explained in terms of the so-called
polar-catastrophe scenario [1–3]. In this model, an in-
trinsic electronic reconstruction at the interface is ex-
pected from the buildup of an internal electrical potential
in LAO as the film thickness t increases, due to the polar
discontinuity at the interface between LAO, which con-
sists of alternating positively and negatively charged lay-
ers, (LaO)+and (AlO2)−, and STO, with charge-neutral
layers. However, models explaining the conductivity in
terms of extrinsic effects caused by structural deviations
from a perfect interface have also been proposed [4–12].
The intrinsic doping mechanism, illustrated in Fig. 1,
was elegantly reformulated in the framework of the mod-
ern theory of polarization : LAO has a formal po-
the unit-cell cross-section in the plane of the interface),
while in nonpolar STO, P0
STO= 0. The preservation
of the normal component of the electric displacement
field D along the STO/LAO/vacuum stack in the ab-
sence of free charge at the surface and interface (D = 0)
requires the appearance of a macroscopic electric field
ELAO. Due to the dielectric response of LAO, this field
is ELAO= P0/ε0εLAO= 0.24 V˚ A−1, where εLAO≈ 24 is
the relative permittivity of LAO .
The electric field in LAO will bend the electronic bands
as illustrated in Fig. 1. At a thickness tc, the valence
O 2p bands of LAO at the surface reach the level of
the STO Ti 3d conduction bands at the interface and
a Zener breakdown occurs. Above this thickness, elec-
trons will be transferred progressively from the surface to
the interface, which hence becomes metallic. This simple
electrostatic model not only explains the conduction, but
also links the formal polarization of LAO, its dielectric
constant, and tcsuch that
LAO= e/2S = 0.529 Cm−2(where S is
where ∆E ≈ 3.3 eV is the difference of energy between
the valence band of LAO and the conduction band of
STO and e is the electron charge. This yields an estimate
of tc≈ 3.5 monolayers (MLs).
The main success of the polar-catastrophe scenario
is that it very accurately predicts the critical thick-
ness tcoriginally observed experimentally by Thiel et al.
[3, 15], a very robust result which has been replicated
in several laboratories [4, 16] and also predicted from
first-principles calculations on ideal STO/LAO/vacuum
stacks [17, 18]. However, the surface of LAO and its in-
terface with STO are far from ideal and alternative, ex-
trinsic, effects have been invoked to explain the observed
conductivity, such as oxygen vacancies [5–7], adsorbates
at the LAO surface , or intermixing between LAO and
STO at the interface [8–11]. The presence of an electric
field within the LAO layer, expected to produce the Zener
breakdown, was also questioned , although recent sur-
face x-ray diffraction measurements revealed an atomic
rumpling in the LAO layer, a clear signature of an elec-
tric field , as well as an expansion of the LAO c-axis
in very thin layers, compatible with an electrostrictive
effect produced by ELAO.
In this Letter we describe experiments performed to
further assess the relative importance of the intrinsic
polar-catastrophe scenario and the extrinsic intermix-
ing model to explain the origin of the conductivity. To
achieve this, we replaced pure LAO with ultrathin films
of LAO diluted with STO [(LaAlO3)x(SrTiO3)1−x, or
LASTO:x] for different values of x. This system is both
intermixed and has a formal polarization different to that
of pure LAO. In this manner, we could observe whether
tcproperly evolves with the formal polarization and di-
electric constant of this material, as predicted by Eq. (1),
while also investigating the possible role of intermixing.
Varying the composition of the LASTO:x films (i.e.,
x) allows one to tune continuously the formal polariza-
tion such that P0
x = 0.5, the random solid solution has alternating planes
with +0.5 and −0.5 formal charges, compared to +1 and
LAO.For instance, for
arXiv:1112.3532v1 [cond-mat.mtrl-sci] 15 Dec 2011
E = eVc
FIG. 1: (color online) Schematic showing the buildup of potential in a polar layer as a function of its thickness t for LAO and
LASTO:0.5, assuming the same relative permittivity but different formal polarization P0induced by the charge of the successive
A-site and B-site sublayers. The critical thicknesses for the electronic reconstruction are labeled t(1)
LASTO:0.5, respectively. The band-level scheme shows band bending in the pure LAO layer of the valence band (VB) and
conduction band (CB), and the critical thickness tc and potential buildup eVc required to induce the electronic reconstruction.
φn is the valence-band offset between STO and LAO.
for LAO and
−1 charges in pure LAO (see Fig. 1). One must, how-
ever, also consider possible changes of the other funda-
mental quantities determining the critical thickness ex-
pressed in Eq. (1).The energy gap ∆E formally de-
pends on the electronic bandgap of STO and the valence-
band offset φn (see Fig. 1) between the two materials,
which can evolve with x. In practice, however, the O 2p
valence bands of STO and LAO (x = 1) are virtu-
ally aligned (φn = 0.1 eV ) and φn further dimin-
ishes with x, so that we can confidently approximate
∆E ≈ Eg
electric constants of STO and LAO, however, differ sig-
nificantly (εSTO= 300,εLAO= 24 at room temperature)
and it is not obvious a priori how the dielectric constant
of the solid solution will evolve with composition. To
clarify this point, we performed first-principles calcula-
tions on bulk compounds of different compositions using
a supercell technique (see ). Although the dielectric
constant of the LASTO:x evolves slightly with the atomic
arrangement, we observe that it remains essentially con-
stant for x = 1, 0.75 and 0.5. This result may initially
seem surprising; however, the large dielectric constant of
pure STO is mainly produced by a low-frequency and
highly polar phonon mode related to its incipient ferro-
electric character. This mode, absent in LAO, is very sen-
sitive to atomic disorder and is stabilized at much larger
frequencies through mixing with other modes for x > 0.5
without contributing significantly to the dielectric con-
stant. Hence, from the discussion above, it appears that
STO, irrespective of the composition. The di-
varying the composition of the LASTO:x films allows one
to tune the formal polarization while keeping the other
quantities in Eq. (1) essentially constant, that is,
Based on this argument, we therefore predict that tc=
7 ML and 5 ML for x = 0.5 and 0.75, respectively, a result
confirmed for x = 0.50 from first-principles calculations
Two independent series of LASTO:x films were pre-
pared by pulsed laser deposition (PLD) using two dif-
ferent sets of growth parameters. The first set of films,
produced at the Paul Scherrer Institut, was grown on
both native and TiO2-terminated (001) STO substrates
using two different PLD sintered targets, with x = 0.50
and 0.75. Neither target (> 85 % dense) was conduct-
ing. Growth conditions using 266-nm Nd:YAG laser ra-
diation were: pulse energy = 16 mJ (≈ 2 Jcm−2), 10 Hz;
T = 750◦C, pO2= 2.5 × 10−8mbar; sample cooled
after growth at 25◦C min−1and postannealed for one
hour in 1 atm. O2 at 550◦C. The second set of films
was grown on TiO2-terminated STO at the University
of Geneva using standard growth conditions: KrF laser
(248 nm) with a pulse energy of 50 mJ (≈ 0.6 Jcm−2),
1 Hz; T = 800◦C, pO2= 1 × 10−4mbar; sample cooled
after growth to 550◦C in 200 mbar O2 and maintained
at this temperature and pressure for one hour before
being cooled to room temperature in the same atmo-
sphere. The stoichiometries of the films from both sets
FIG. 2: (color online) (a) Sheet carrier density and (b) mo-
bility as a function of temperature and film thickness for pure
LAO and LASTO:0.5.
were shown by Rutherford backscattering (RBS) to be
equal to the nominal PLD-target compositions of 0.5 and
0.75 to within the experimental accuracy of 1.5 %. In-
situ reflection high-energy electron-diffraction (RHEED)
measurements, and x-ray diffraction measurements con-
firming perfectly strained growth are detailed in .
Neither of the mixed-composition film stoichiometries
investigated produce layers which increase in conduc-
tance with thickness, as one might otherwise expect for
intermixed materials which were intrinsically electrically
conducting. In addition, none of the films are conduct-
ing at the top surface, but instead require careful bonding
at the interface to exhibit conductivity. These metallic
interfaces were characterized by transport properties us-
ing the van der Pauw method. All samples remained
metallic down to the lowest measured temperature of
1.5 K. The sheet carrier densities ns estimated from
the Hall effect at low magnetic field for interfaces with
LAO and with LASTO:0.5 of different thicknesses are
shown in Fig. 2(a). The value of ns is in the range 3
to 15 × 1013cm−2, though with no obvious dependence
on composition or thickness of the layers. According to
the polar-catastrophe model, we should expect LASTO:x
samples to exhibit a lower carrier density, as the screening
charge scales as x·e/2S, whereby S is the unit-cell surface
area. However, as already observed for LAO/STO inter-
faces, the estimation of the carrier density from the Hall
effect yields values up to one order of magnitude smaller
than those predicted from theory, possibly suggesting a
large amount of trapped interface charges. Figure 2(b)
shows the Hall mobility µ of the same interfaces mea-
sured as a function of temperature. Note that interfaces
with LAO and LASTO:x display similar values, with µ
larger for samples with low ns.
To probe experimentally the dielectric constant, capac-
itors were fabricated with different thicknesses of pure
LAO and the x = 0.5 films, using palladium as the top
electrode.A serious complication in measurements of
such ultrathin films is the significant contribution of the
electrode–oxide interface on the capacitance , which
LASTO:x films for x = 1, 0.75 and 0.50. The dashed ver-
tical lines for x = 1.0 and 0.75 indicate the experimentally
determined threshold thicknesses tc, which for x = 0.5, is
represented by a band for the more gradual transition. All
values were obtained after ensuring that the samples had re-
mained in dark conditions for a sufficiently long time to avoid
any photoelectric contributions.
(color online) Room-temperature conductance of
means the results can only be viewed semi-quantitatively.
We observe that the dielectric constant of the LASTO:0.5
and LAO display values in the range of 20 to 30, and
are in good agreement with previous reports on ceramic
solid-state solutions, where no large enhancement of the
relative permittivity was observed for the solid solution
up to 80 % STO . Measurements of the temperature
dependence and the electric-field tunability confirm that
LASTO:x behaves like LAO rather than STO. Cooling
the films to 4 K produces a small change of the dielectric
constant, in sharp contrast with the low-temperature di-
vergence of STO. These experimental results show that
there is no large enhancement of the dielectric constant
in LASTO:0.5 with respect to pure LAO, as predicted by
our first-principles calculations.
Figure 3 is the central result of this work. The con-
ductance of the interface as a function of the LASTO:x
film thickness is shown for x = 1.0 (pure LAO, lower
panel), x = 0.75 (middle panel), and x = 0.50 (top
4 Download full-text
panel). The conductivity is given in sheet conductance
(left axis) and/or conductance (right axis). The step in
conductance for x = 1.0 is observed at 4 unit cells, as
first observed by Thiel et al.  and reproduced by sev-
eral groups. For x = 0.75 and 0.50, the data unambigu-
ously demonstrate that the critical thickness increases
with STO-content in the solid solution, with tLASTO:0.75
close to 5 unit cells, and tLASTO:0.5
cells. This striking result demonstrates that the critical
thickness depends on x, increasing as the formal polariza-
tion decreases. Although the critical thicknesses obtained
from the experimental data are marginally smaller than
predicted by theory, this can easily be attributed to the
uncertainty in the dielectric constants of the solid solu-
tions. The overall agreement, however, with the polar-
catastrophe model described by Eq. (1) is remarkable.
In conclusion, wehave
erostructures of ultrathin films of the solid solution
(LaAlO3)x(SrTiO3)1−x grown on (001) SrTiO3, the
critical thickness at which conductivity is observed
scales with the strength of the built-in electric field of
the polar material. These results test the fundamental
predictions of the polar-catastrophe scenario and con-
vincingly demonstrate the intrinsic origin of the doping
at the LAO/STO interface.
Support of this work by the Schweizerischer National-
fonds zur F¨ orderung der wissenschaftlichen Forschung,
in particular the National Center of Competence in
Research, Materials with Novel Electronic Properties,
MaNEP, and by the European Union through the project
OxIDes. The staff of the Swiss Light Source is grate-
fully acknowledged. The authors also thank Dr. Max
D¨ obeli for the RBS measurements and Dr. Pavlo Zubko
for assistance in the capacitance measurements. Ph.G. is
grateful to the Francqui Foundation.
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