Electrostatic charging and redox effects in oxide heterostructures

Peter Littlewood1,2,3 Nick Bristowe3 & Emilio Artacho3,6

Miguel Pruneda4 and Massimiliano Stengel5

1Argonne National Laboratory 2University of Chicago

3University of Cambridge 4Centre d'Investigacion en Nanociencia i Nanotecnologia, Barcelona

5Institut de Ciencia de Materials, Barcelona 6CIC Nanogune, and DIPC, San Sebastian

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Bristowe et al., PRB 80, 45425 (2009); 83,20545 (2011); 85, 021406 (2012); JPCM 23, 081001 (2011); PRL 108, 166802 (2012)

• Transition metal oxides are responsible for some interesting and useful physics and materials science: magnetism, superconductivity, ferroelectricity, ...

• We use oxides to make batteries, capacitors, photovoltaics, ... • Physically, these are systems where the carriers are “small” (strongly

correlated). Strong correlations means high energy density and therefore “useful”

• Control of doping by chemistry is the usual route, and it’s challenging • In semiconductors, we have learned to modulation dope, and this has

been responsible for much modern semiconductor technology and essentially ALL of modern semiconductor physics

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Why are heterostructure oxides interesting?

• LaAlO3/SrTiO3 (polar-insulator) • Introduction: interface 2DEG, “polar catastrophe” argument • Net interface charges – formal argument • Model test – n-p superlattices • Origin of 2DEG in reality – surface redox?

• BaTiO3/La0.7Sr0.3MnO3 (ferroelectric-half metal) • Introduction: ferroelectric screening • Redox calculations • Magnetoelectric and tunneling electroresistance

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Outline

An example: LaAlO3 / SrTiO3

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Whence the carriers? Two (at least) points of view

Ideal interface is charged (polar catastrophe) produces electrical potential attracts (mobile?) carriers Charged interfaces may destabilise growth produces (neutralising) charged defects also generates carriers

A Ohtomo & H Hwang, Nature 427, 423 (2004) Interface between two band insulators is (sometimes) conducting

LaAlO3 / SrTiO3

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Sheet resistance of n-type SrTiO3/LaAlO3 interfaces. Temperature dependence of the sheet resistance for SrTiO3/LaAlO3 conducting interfaces, grown at various partial oxygen pressures A. Brinkman et al Nat.Mater. 2007, 6, 493

.

Ohtomo and Hwang Nature 427, 423 2004

Surface polar adsorbates • Carrier density and conductivity depends on details of

growth and also (reversibly) on surface adsorbates • AFM used to modulate buried interface layer conduction

e.g. Cen et al. Nature Mater. 7, 298-302 (2008).

• Carrier density at buried interface in LAO/STO is modulated by surface adsorption of polar molecules

Xie et al Arxiv1105:3891

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Counting charge and polarisation

• How to count charge at an interface? – Remember: dopants in a semiconductor, eg P (group V) in Si (group IV) – P adds 5 valence electrons and +5 charge to core – Compared with Si +1 impurity and 1 extra electron – in this case

weakly bound – In compound semiconductors, it is possible to separate the charge

from the impurity and capture it in a quantum well – modulation doping

– Is this the correct picture in oxides ?

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Modulation doping

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(a) Two semiconductors not in electrical contact

(b) In electrical contact, chemical potentials balance

(c) Donors added to wide gap material ionise and populate

interfacial electron layer

Capacitor Plate Model for STO/LAO

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σc is the chemical charge density – formal ionic charges

12x 12 superlattice of LaAlO3 / SrTiO3

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Bristowe et al PRB 80, 045425 (2009)

• Linear shift of potential with distance from interface • Quantitative agreement of DFT results with capacitor

plate model – including lattice relaxation – including a non-linear dielectric response P as function of electric

field and strain – NB contribution to P from ferroelectricity of strained SrTiO3

• But not with experiment .... see later

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.... science fiction interlude ....

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Self- modulation doping: Mobile charges in coupled valence and conduction bands

Once E > Egap /d , mobile (?) carriers appear at the two interfaces.

Beyond a critical spacing dc ~ 5 unit cells the charge transferred compensates the formal ionic charge

The potential difference between the interfaces is pinned approximately at the gap (owing to large DoS).

Carrier density grows with d but is generally quite small, for example

n12/12 = 0.073 e/unit cell In LAO/STO strong screening -> large effective

Bohr radius Potentially interesting Coulomb correlations –

Mott transition for excitons; superfluids and solids etc.

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e/cell

Ultracapacitor / Photovoltaic • Excitons: add electrons

and holes in pairs • Energy cost = Energy gap –

binding energy + interaction energy – Tuned by external bias ~ 0

• Capacitance is theoretically very large – Store one exciton/Bohr

radius (Mott density)

• Intrinsic photovoltaic – Enormous internal field ~

V/nm

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Energy per pair (in exciton Rydberg) as a function of density

Zhu et al, PRB 54, 13575 (1996)

... back to reality ....

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Not particularly consistent with experiments

Problems: • Strong dependence of carrier density on growth conditions

(particularly oxygen pressure) – more metallic when grown in lower oxygen pressures

• Model critical thickness (>6 u.c.) > observed ( <4 u.c.) • No mobile holes seen at surface • XPS measures no internal field • HAXPS see electrons at interface before onset of conduction Resolution? • Defects (bulk/surface) contribute to carriers ....

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Resolution ? • Several suggested mechanisms: (Review: Schlom & Mannhart 2010)

• STO oxygen vacancies • Ionic intermixing (La-Sr) • La doping • Hard to explain MIT of 4 u.c. consistently measured by

several groups using various growth techniques • None aid LAO screening • Surface redox reactions stabilised under growth conditions

by generating screening charge

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Bristowe et al, arXiv:1008:1951; Stephenson and Highland, arXiv:1101.0298

Surface redox reactions generated under growth conditions

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E.g. Oxygen vacancy – creates (double) donor Electrons transfer to interface Thermodynamically stable for a thick enough layer – transferred charges lower capacitive energy that grows with thickness Energy cost to create vacancy balanced against Coulomb

Surface donor states stabilised by Coulomb?

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Free energy cost to create vacancy balanced against Coulomb

Critical separation

n = defect density d = film thickness Defect creation energy Defect interactions

Electrostatic energy

Intrinsic charge density

Reconstructed charge density

Field energy if interface partially screened

Surface redox reactions and 2DEGs

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Bristowe et al. PRB 83, 205405 (2011)

• LaAlO3/SrTiO3 (polar-insulator) • Introduction: interface 2DEG, “polar catastrophe” argument • Net interface charges – formal argument • Model test – n-p superlattices • Origin of 2DEG in reality – surface redox?

• BaTiO3/La0.7Sr0.3MnO3 (ferroelectric-half metal) • Introduction: ferroelectric screening • Redox calculations • Magnetoelectric and tunneling electroresistance

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Outline

Surprising stability of domains in thin BTO films

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Source of screening • Conventional view : charged species and metallic

screening -“accidental” charged species • Redox reaction freeing charge to the interface ?

thermodynamic equilibrium established in writing/growth

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In context of ferroelectrics, see e.g. Stephenson and Highland, arXiv:1101.0298

Methods

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Bristowe et al PRB 85, 024106 (2012)

Atomic displacements

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• No polarisation in pristine film • Bulk P (up/down) stabilised by compensating charges

from (adatom/vacancy) [~1/2 per unit cell] – Not surprising since it slightly overscreens the bulk polarization

• Needs further work to establish equilibrium density • In addition

– Large magneto-electric effect – Large tunnelling electroresistance – See also Burton and Tsymbal Phys. Rev. B 82, 161407 (2010);

Phys. Rev. Lett. 106, 157203 (2011) – mechanism slightly different but principles the same

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Substantial magnetoelectric effect

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Electroresistance • Perfect screening of surface redox • Imperfect screening in LSMO • Interface dipole shifts with polarisation state

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Tunnelling electroresistance

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There are other mechanisms for TER and ME effects involving changed magnetic ground states of the LSMO (Tsymbal 2010/2011)

Electrochemistry?

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Spectroscopy of adatom/vacancy in manganites

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Bryant et al, Nat. Commun. 2:212 (2011)

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Bryant et al, Nat. Commun. 2:212 (2011)

Electrochemical Strain Microscopy on LAO/STO

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1V

30V

Apply a tip bias, and measure both the topographic changes and the elastic response – ramp up voltage in a sequence

Conclusions • Centrosymmetric materials can have a (non-switchable)

polarization e.g. LAO – The polarization is precisely half a quantum

• Heterostructures require polarization screening – Either by internal charge transfer “self modulation doping” – Or by charged defects

• Surface oxygen/vacancies plausible candidates? • Can we control surface electrochemistry with

nanoelectrodes? • Is O vacancy a double donor? – correlation effects?

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Collaborators: Nick Bristowe, Emilio Artacho, Miguel Pruneda, Massimiliano

Stengel, Sergei Kalinin

Discussions: Mineral Sciences group, G Catalan, J Scott, N Mathur, X

Moya, V Garcia, M Bibes, J Junquera, J Iniguez, P Ordejon, H Hwang, W Pickett, D Vanderbilt, F Schoofs, T Fix, M Blamire

Funding:

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