# Intrinsic origin of the two-dimensional electron gas at polar oxide interfaces

**ABSTRACT** The predictions of the polar catastrophe scenario to explain the occurrence

of a metallic interface in heterostructures of the solid

solution(LaAlO$_3$)$_{x}$(SrTiO$_3$)$_{1-x}$ (LASTO:x) grown on (001) SrTiO$_3$

were investigated as a function of film thickness and $x$. The films are

insulating for the thinnest layers, but above a critical thickness, $t_c$, the

interface exhibits a constant finite conductivity which depends in a

predictable manner on $x$. It is shown that $t_c$ 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.

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**ABSTRACT:**We review the recent developments in the electric field control of magnetism in multiferroic heterostructures, which consist of heterogeneous materials systems where a magnetoelectric coupling is engineered between magnetic and ferroelectric components. The magnetoelectric coupling in these composite systems is interfacial in origin, and can arise from elastic strain, charge, and exchange bias interactions, with different characteristic responses and functionalities. Moreover, charge transport phenomena in multiferroic heterostructures, where both magnetic and ferroelectric order parameters are used to control charge transport, suggest new possibilities to control the conduction paths of the electron spin, with potential for device applications.Journal of Physics Condensed Matter 07/2012; 24(33):333201. · 2.22 Impact Factor

Page 1

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 [13]: LAO has a formal po-

larization P0

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 [14].

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

tc=ε0εLAO∆E

eP0

LAO

, (1)

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 [12], 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 [19], although recent sur-

face x-ray diffraction measurements revealed an atomic

rumpling in the LAO layer, a clear signature of an elec-

tric field [20], as well as an expansion of the LAO c-axis

in very thin layers, compatible with an electrostrictive

effect produced by ELAO[21].

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

LASTO:x= xP0

LAO.For instance, for

arXiv:1112.3532v1 [cond-mat.mtrl-sci] 15 Dec 2011

Page 2

2

∆

LAOSTO

VB

CB

E = eVc

tc

φn

Vc

t

(1)

tc

tc

(2)

LAO charge

distribution

−1

+1

V

charge distribution

LAO STO0.50.5

−0.5

+0.5

TiLa AlO La/SrSr Al/Ti

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.

c

and t(2)

c

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 [17]) 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 [22]). 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,

tLASTO:x

c

= tLAO

c

/x. (2)

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

(see [22]).

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

Page 3

3

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 [22].

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 [23], which

FIG. 3:

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 [24]. 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

Page 4

4

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. [3] 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

c

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,we have

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.

c

between 6 and 7 unit

shownthat inhet-

∗philip.willmott@psi.ch

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