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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