Origin of the 2DEG at the LAO/STO Interface

S. Amoruso, C. Aruta, R. Bruzzese, E. Di Gennaro, A. Sambri, X. Wang and F. Miletto Granozio

University FEDERICO II & CNR-SPIN, Napoli (Italy)

D. Maccariello, P. Perna

IMDEA, Madrid (Spain)

C. Cantoni , J. Gazquez , M. P. Oxley , M. Varela , A.R. Lupini , S.J. Pennycook

Oak Ridge National Laboratory

1

Umberto Scotti di Uccio

This presentation regards the still open issue of the origin of the two dimensional

electron gas at the LAO/STO interface. I will show some experimental data and make

comments on this subject, but I’d like to state that my contribution is not completely

general because it is limited to epitaxial samples. I will not speak of amorphous LAO

samples, that have very different fabrication procedure and structure.

donors

2D Electron Gas in semiconductors

1. Introduction

2

Main ingredients:

• Quantum well

• Donor states

2deg’s are observed in several different systems, such as for instance semiconducting

structures based on gallium compounds. But in any cases they share two main

ingredients, that are the existence of a quantum well and of donor states that populate

the well with charge carriers. In the case of STO/LAO interfaces everybody agrees that

the quantum well is formed within STO, close to the interface. So when I say “origin of

the 2deg” I specifically refer to the nature and location of the donor states.

Two alternative mechanisms for crystalline STO/LAO

Oxygen vacancies

VB

CB

VB

e-

STO LAO

Electronic reconstruction

TiO2 (0)

SrO (0)

TiO2 (0)

LaO (+1)

AlO2 (-1)

LaO (+1)

AlO2 (-1)

charge(Sr+2) (Ti+4) (O-2)3

( ) ••× ++ → O2reduction

O V'e2gO2

1O

LaAlO3

SrTiO3

VV

V

- - - - - -e-

O (g)

3

1. Introduction

3

Grossly speaking, there are two alternative models. The first one

is the electronic reconstruction model. Instead, one may consider

defects as donors, such as oxygen vacancies, or some kind of

cation intermixing at the interface.

Two alternative mechanisms for crystalline STO/LAO

Electronic reconstruction

SrTiO3

LaAlO3

+ + + + + + +

--

--

--

-

Donors are on the top of LAO

Oxygen vacancies/ intermixing

SrTiO3

LaAlO3

- - -- - - -+ + + + + + +

LaAlO3

--

--

--

-

++

+

+

+

++

SrTiO3

Donors are at the interface Donors are within STO

1. Introduction

4

Different local electric field expected

One interesting difference between the models is the location of donors. In the

electronic reconstruction case they are on the top of LAO, in the other cases they are at

the interface or within STO. And as a consequence of the different location, different

local electric fields are expected.

An HRTEM+EELS experiment to probe local fields

+ + + + + + +

--

--

--

-

SrTiO3

Injected charge

Polar state

Polar state

Can we directly determine E ? Not so easy.

But we can measure:

• the injected charge σ• the polarization of both layers

1. Introduction

5

Unfortunately, the direct determination of the local electric field is not that easy. As I

will show, we can instead measure the injected charge and the polarization of both

layers.

Preliminary considerations: Simple electrostatics

TiO2

SrO

TiO2

LaO

AlO2

LaO

AlO2-

-

+

+

oPr

1. Introduction

STO

High-k dielectric

( ) E1'kP oOST

rr−ε= DP OST

rr≈

6

LAOHigh-k dielectric

plus topological polar state

( ) ooOLA PE1kPrrr

+−ε=k

PDP o

OLA

rrr

+≈

An HRTEM+EELS experiment to probe local fieldsThe electric displacement DDDD depends on the injected charge (i.e., the free charge)(see, e.g., M. Stengel, PRL 2011)

However, this is enough, because based on the theoretical work by Stengel we can

define the microscopic electrical displacement in STO/LAO, and the displacement is

directly connected to the injected charge. Then we can write electrostatics equations

that directly connect displacement and polarization. The case of STO is simple. STO is a

high-k dielectric and we immediately get that the displacement is approximately equal

to the polarization. The epitaxial layer of LAO is different, because it possesses a built-in,

topological polar state, with polarization Po. Besides, it can also react to the field, and

this gives a dielectric polarization. But again it is easy to find out a relation between

polarization and displacement. Now we have a theoretical framework and we can look

at experiment.

RHEED-assisted PLDKrF Excimer laser λ = 248 nm, 1 Hz, 2 J cm-2

Ts = 800 °C Buffer Gas: P(O2) = 10-3 mbar Thickness 5-10 u.c. LAO

2. Experimental

7

Conducting samples were fabricated by PLD at 10-3 mbar oxygen pressure at Napoli. I

skip the details…

Electron Energy-Loss Spectroscopy with atomic-scale resolution in the aberration corrected microscope

STEM + EELS

5 u.c. LAO – 10-3 P(O2)Conducting sample

C. Cantoni, et al. ADV. MAT. 2012 8

2. Experimental

…and analyzed by Scanning Tunneling Electron Microscopy and Electron Energy Loss

Spectroscopy in an aberration corrected microscope. This slide shows the

microstructure of the interface and an EELS scan across the interface to show the

sample quality and the capability of EELS to determine the local chemical composition

with atomic resolution.

2DEG DOS: free charge injection

Ti 2p 1/2

Ti 3d eg

Ti 3d t2g

Ti 2p 3/2

dc

baE

E-∆E

|ψ>

|ψ’> CB

Core level

• Energy loss � Ti 2p-3d excitation

• Peak intensity decreases when the final state is occupied

Information from EELS Ti L2,3 lines

9

2. Experimental

EELS also allows one to determine the occupancy of the conduction band. To this aim

we can investigate the Ti L2,3 lines

Ti 2p 1/2

Ti 3d eg

Ti 3d t2g

Ti 2p 3/2

dc

ba

Energy (eV)

c/d decreases if the CB is occupied

Information from EELS Ti L2,3 lines

10

2. Experimental2DEG DOS: free charge injection

LA

O

STO

…doing that at different distance from the interface

∆E decreases if the CB is occupied

a decreases if the CB is occupied

O 1s

O 2p + Ti 3d t2g

O 2p + Ti 3d eg

ba

Information from EELS O K lines

multiple scattering

da b c

11

2. Experimental2DEG DOS: free charge injection

LA

O

STO

We can also investigate the O K line…

2DEG confinement within STO

• depth of confinement: ≈ 1 nm

• integral: 0.3 e- / square unit cell

ρ

ρ

ρ

ρ

(e-/ u

. c.)

12

LAO STO

(u.c.)depth

FabricationP(O2) = 10-3 mbar

Ts = 800 °C

2. Experimental

…and this is the summary. From the map we extract the plot of the injected charge

density vs. distance from the interface. The main results are the depth of confinement,

that is about 1 nm, and the total injected charge, amounting to 0.3 electrons per unit

square cell.

TiO2

SrO

TiO2

LaO

AlO2

LaO

AlO2 Al

La

Ti Sr

interface

C. Cantoni, et al. ADV. MAT. 2012

Polarization measurement

∑=cellunit

j

jj

i

z zqP.

• Assuming the formal charge of ions• Neglecting the deformation of valence orbitals

13

2. Experimental

Let’s come now to the measurement of polarization. We determine from STEM the

average position of each cation and define the polarization in a classical way, assuming

the formal charge of ions and neglecting the deformation of valence orbitals.

STO Polarization

measurement

Sr

Ti

O

14

2. Experimental

LA

O

ST

O

Here are the results for STO. We observe the rumpling of each crystal plane and a

polarization close to the interface and quickly approaching to zero when moving toward

the bulk.

LAO Polarization LAO Polarization

Al

La

O

measurement

Al

La

O

15

2. Experimental

LA

O

ST

O

In LAO, instead, the polarization is uniform.

16

Discussion1. The STO side

3. Discussion

• depth of confinement: ≈ 1 nm

• integrated charge

σo ≈ 0.3 e- / square u.c.

• PSTO ≈ D

Impossible, the polarization has the wrong sign

0 2 4 6 8

-0.1

0.0

0.1

0.2

0.3

0.4

Ti3

+ f

ractio

nP

ST

O

distance (u.c.)

-0.1

0.0

0.1

0.2

0.3

0.4

electrostatics

So we can now discuss the results. Let’s first consider the STO side. Here we roughly see

the same length-scale for both charge and polarization. And we also see that the

displacement calculated by the integrated injected charge corresponds to the measured

polarization at the surface. This confirms the correctness of the approach based on

classical electrostatics. There is a second consequence. We can exclude that the donors

are deep within STO, because in that case we would have found a different orientation

of polarization.

17

Discussion1. The STO side

Conducting LAO/STO has efficient SHG

3. Discussion

Second harmonic generation

RequirementBreaking of the centro-symmetry E

r

After charge injection, the lattice is deformed

A. Rubano, et al. PRB 2011

Since we have a strong polarization, we have a strong deformation of unit cells. But if

the cubic environment is distorted, also the 3d orbitals of Ti atoms are deformed. This

breaking of symmetry explains why STO/LAO interfaces emit so strongly in second

harmonic, as we observed for our samples.

Discussion2. The LAO side

3. Discussion

18

No electric displacement

the dielectric response almost conceals

the topological polarization Po

oo

OLA Pk

PP

rr

r<<≈

k

PDP o

OLA

rrr

+≈

Add electric displacement

the dielectric response decreases

k

PDP o

OLA

rrr

+≈

Now let’s come to the LAO side. Let’s start from the characteristic equation in the green

square. If we have no electric displacement, the equation foresees a strong suppression

of the topological polarization, due to the dielectric polarization. But if we have electric

displacement, the dielectric polarization decreases and the net polarization increases.

Discussion2. The LAO side

3. Discussion

19

k

PDP o

OLA

rrr

+≈

Add electric displacement

the dielectric response decreases

…but we do observe

a large polarization!

So, there is a finite displacement

In fact, we do observe a large net polarization. Then we conclude that there is a

displacement in LAO…

Discussion2. The LAO side

3. Discussion

20

…but we do observe

a large polarization!

So, there is a finite displacement

P ≈ 0.32 e-/u.c.

D ≈ 0.3 e-/u.c.

k ≈ 20Po ≈ 0.5 e-/u.c.

Consistent explanation of LAO state

PLAO ≈ 0.35 e-/u.c.

and based on a few simple assumptions we deduce that it is about 0.3 electronic

charges per square unit cell.

3. Discussion

21

P ≈ 0.32 e-/u.c.

D ≈ 0.3 e-/u.c.

k ≈ 20Po ≈ 0.5 e-/u.c.

Consistent explanation of LAO state

PLAO ≈ 0.35 e-/u.c.

Experiment + simple electrostatics

The electric displacement is continuous at the interface

Most donors are on the top of LAO

Discussion3. Where are the donors?

So, the estimated displacement in LAO is the same as in STO. In other terms, D is

continuous. This brings us back to the question: Where the donors are? Well, they can’t

accumulate at the interface, or we would not observe the displacement continuity. They

must be on the top of LAO. This is consistent with the electronic reconstruction. Can we

exclude at all that some donors are at the interface? Well we can’t, the experimental

errors are large enough to allow for a fraction of donors to be there. But most of them

must be far away in LAO.

Conclusions

22

1. LAO/STO Interfaces “with a lot of” V(O) do conduct

2. LAO/STO Interfaces “with negligible” V(O) content do conduct

3. Different types of donors bring to essentially the same 2DEG

a) In amorphous samples, V(O) are the donor states

b) In samples with negligible V(O), the polarization state of LAO

is compatible with the electronic reconstruction

Conclusions

23

1. LAO/STO Interfaces “with a lot of” V(O) do conduct

2. LAO/STO Interfaces “with negligible” V(O) content do conduct

3. Different types of donors bring to essentially the same 2DEG

Thank you for your attention!

a) In amorphous samples, V(O) are the donor states

b) In samples with negligible V(O), the polarization state of LAO

is compatible with the electronic reconstruction