Correlations between structure and
transport in BaTiO3
Santosh Raghavan
Materials Department, University of California, Santa Barbara
Materials-286K
15th December, 2014
BaTiO3
d
http://www.mdpi.com/sensors/sensors-1001935/article_deploy/html/images/sensors-10-01935f2-1024.png
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Ferroelectric perovskite at RT (TC = 120 °C)
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Used in capacitors and piezo applications
A. Von Hippel, Reviews of Modern Physics, 22, 221 (1950)
B. Sarkar et al, J. Phys D: App Phys, 45, 505304 (2012)
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Local Ti distortions toward <111> octahedral faces
BaTiO3
3
Q. Zhang, T. Cagin and W. A. Goddard, PNAS, 103, 14695 (2006)
Local Ti distortions toward <111> octahedral faces
BaTiO3
Vacancy formation
Carrier transport mechanism
Metal – Insulator transition
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Q. Zhang, T. Cagin and W. A. Goddard, PNAS, 103, 14695 (2006)
1. Vacancy formation in Sr1-xBaxTiO3
In SrTiO3,
La + SrTiO3  LaSr + VSr’’ + TiTi+ 3OO + 1eA-site substitution  A-site vacancy formation!
In BaTiO3,
4La + 4BaTiO3  4LaBa + VTi’’’’+ 4BaBa+ 3TiTi + 12OO
A-site substitution  B-site vacancy formation!
But easier to dope the B-site with Nb instead…
In Sr1-xBaxTiO3, both A-site and B-site vacancies!
H.M. Chan, M.P. Harmer, D. M. Smyth, J. Am. Ceram. Soc., 69, 507 (1986)
D. Makovec, Z. Samardzija, U. Delalut and D. Kolar, J. Am. Ceram. Soc., 78, 2193 (1995)
L. Wang, Y. Sakka, Y. Shao, G.A. Botton, T. Kolodiazhnyi, J. Am. Ceram. Soc., 93, 2903 (2010)
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1. Vacancy formation in Sr1-xBaxTiO3
28% La-doped Sr1-xBaxTiO3
VTi’’’’ – Most unlikely, highly
energetic, major perturbation to
the lattice
Why does it form instead of VBa’’?
Reason  Ti <111> displacement,
Ti—O hybridisation
Off-center Ti covalently bonds to
Oxygen  Stabilises VTi’’’’
Excess charge can be transferred
to nearby partial covalent Ti—O
bonds
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L. Wang, Y. Sakka, Y. Shao, G.A. Botton, T. Kolodiazhnyi, J. Am. Ceram. Soc., 93, 2903 (2010)
2. BaTiO3 – Polaron hopping or Band transport?
Holstein’s small polaron
(SP)
model
μho – SP hopping
μb – SP band transport
μH – SP Hall transport
Measured μHall and μdrift are
supposed to be different
In BaTiO3, experimentally measured μHall and μdrift are comparable!
T. Holstein, Annals of Physics, 8, 325 (1959)
J.P. Boyeaux and F.M. Michel-Calendini, J. Phys. C: Solid State Phys.,12, 545 (1979)
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2. BaTiO3 – Polaron hopping or Band transport?
Ba0.996Y0.004TiO3
• Most recent Y-doped BaTiO3 samples
showed mobility as high as 12 cm2/Vs at
120K! – Large polarons?
• Measured μHall and μdrift are supposed to
be different but are comparable
• Band transport with a very heavy mass
and phonon scattering?
• Correlated small polaron hopping theory
can account for comparable μHall and μdrift?
Temperature – dependant mobility values in BaTiO3 from literature all over the map…
T. Kolodiazhnyi, A. Pedric, N. Niewczas, C. Bridges, A. Safa-Sefat and J.E. Greedan, PRB. 68, 085205 (2003)
D. Emin, PRL, 25, 1751 (1970)
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2. BaTiO3 – Polaron hopping or Band transport?
A. Verma, A.P. Kajdos, T.A. Cain, S. Stemmer and D. Jena, PRL, 112, 216601 (2014)
• No last word in transport mechanisms even in the easier SrTiO3 system
• Debate on exact BaTiO3 transport mechanisms expected to continue…
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3. BaTiO3 – Metal-Insulator-Transition
In SrTiO3,
La + SrTiO3  LaSr + VSr’’ + TiTi+ 3OO + 1eSrTiO3  SrSr + VO’’+ TiTi + 2OO + ½O2 + 2e-
nc1/3aH ~ 0.25
For SrTiO3
Mott criterion for MIT at nc ~ 4×1010cm-3
SrTiO3-δ
Compensated carriers Mott criterion for
MIT at nc ~ 1015cm-3
For BaTiO3
Mott criterion for MIT at nc ~ 1×1020cm-3
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A. Spinelli, M. A. Torija, C. Liu, C. Jan, C. Leighton, PRB, 81, 155110 (2010)
3. BaTiO3 – Metal-Insulator-Transition
In BaTiO3, BaTiO3  BaBa + VO’’+ TiTi + 2OO + ½O2 + 2e-
nc1/3aH ~ 0.25
For SrTiO3
Mott criterion for MIT at nc ~ 4×1010cm-3
Compensated carriers Mott criterion for
MIT at nc ~ 1015cm-3
BaTiO3-δ
For BaTiO3
Mott criterion for MIT at nc ~ 1×1020cm-3
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T. Kolodiazhnyi, PRB, 78, 045107 (2008)
3. BaTiO3-δ – Ferroelectric metal?
Low symmetry phases seen even in metallic BaTiO3-δ
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T. Kolodiazhnyi, M. Tachibana, H. Kawaji, J. Hwang and E. Takayama-Muromachi, PRL, 104, 147602 (2010)
3. BaTiO3-δ – Ferroelectric metal?
• Low symmetry phases seen in
metallic BaTiO3-δ
• Tc (CT) reduces as [VO’’] increases
• Change in slope of Tc near the MIT
• Itinerant electrons seem to screen the
destabilising effect of VO’’ to preserve
low symmetry phases?
• Slope says n > nc (1.9×1021 cm-3 )
needed to destroy the lower symmetry
states
• Not possible to achieve nc with VO’’
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T. Kolodiazhnyi, M. Tachibana, H. Kawaji, J. Hwang and E. Takayama-Muromachi, PRL, 104, 147602 (2010)
3. BaTiO3-δ – Ferroelectric metal?
Highly Nb doped BaTiO3
• n ~ 2×1021 cm-3
• Sample retains long
range cubic symmetry
at all temperatures
• Local Ti <111>
displacements still
persist in the sample at
all temperatures!!
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3. BaTiO3-δ – Ferroelectric metal?
Highly Nb doped BaTiO3
• n ~ 2×1021 cm-3
• Sample retains long
range cubic symmetry
at all temperatures
• Local Ti <111>
displacements still
persist in the sample at
all temperatures!!
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K. Page, T. kolodiazhnyi, T. Proffen, A.K.Cheetham and R. Seshadri, PRL, 101, 205502 (2008)
3. BaTiO3-δ – Ferroelectric metal?
Mixture of 40% tetragonal FE phase and
60% metallic cubic phases
 Claim no co-existence of metallicity and
ferroelectricity?
• PDF still shows 2 Ti-O distances,
albeit reduced
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I-K. Jeong, S. Lee, S-Y Jeong, C. J. Won, N. Hur and A. Llobet, PRB, 84, 064125 (2011)
3. MIT due to e- doping or donor-lattice distortion?
DFT says pure electron doping can
cause CT transition to vanish!
Claim local Ti <111> displacements
vanish as well by pure electron doping
Calculated nc ~ 1.36×1021 cm-3
Donors like Nb or VO’’ only
accelerate the disappearance of the
CT transition
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Y. Iwazaki, T. Suzuki, Y. Mizuno and S. Tsuneyuki, PRB, 86, 214103 (2012)
Integration of BaTiO3 with RTiO3/SrTiO3 interfaces
Study of the BaTiO3 – RTiO3 interface
R+3Ti+3O-23
• Will there still be a 2DEG at the
interface?
• What will happen to the insulating
BaTiO3 films?
???
Ba2+O2-
• Similar interface between SrZrO3
and SmTiO3 has no 2DEG!
5 nm SmTiO3
Ba2+O2-
x nm BaTiO3
Ba+2Ti+4O-23
20 nm SrTiO3
LSAT
• Start by inserting
thin BaTiO3
layers in
between SrTiO3
and SmTiO3
A. Ohtomo and H. Y. Hwang, Nature, 427, 423 (2004)
R. Ohtsuka, M. Matvejeff, K. Nishio, R. Takahashi, and M. Lippmaa, Appl. Phys. Lett., 96,192111 (2010)
P. Moetakef, T. A. Cain, D. G. Ouellette, J. Y. Zhang, D. O. Klenov, A. Janotti, C. G. Van de Walle,
S. Rajan, S. J. Allen, and S. Stemmer, Appl. Phys. Lett. 99 (2011) 232116
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Integration of BaTiO3 with RTiO3/SrTiO3
SrTiO3
[100]
[110]
[100]
[110]
[100]
[110]
BaTiO3
SmTiO3
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Integration of BaTiO3 with RTiO3/SrTiO3
17 nm BaTiO3 / 5 nm SmTiO3
1 BaO
2 BaO
3 BaO
4 BaO
5 BaO
8 BaO
14 BaO
5 nm SmTiO3
x BaO layers
20 nm SrTiO3
LSAT
• Hall coefficient indicates presence of space charge layer
with ~3×1014 cm-2 of electrons similar to RTiO3/SrTiO3
• Increasing BaTiO3 film thickness, the films switch from
metallic to insulating behaviour at 5 BaO (or 4 u.c. BaTiO3)
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Integration of BaTiO3 with RTiO3/SrTiO3
17 nm BaTiO3 / 5 nm SmTiO3
1 BaO
2 BaO
3 BaO
4 BaO
5 BaO
8 BaO
14 BaO
5 nm SmTiO3
x BaO layers
20 nm SrTiO3
LSAT
• If all the electrons are in the BaTiO3, the critical carrier concentration
(remote doping) for metallic BaTiO3 is n3D ~ 1.2×1021 cm-3 (for 5 BaO)
T. Kolodiazhnyi et al., PRL 104,147602 (2010)
V. Fritsch et al., PRB 64, 045113 (2001)
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Integration of BaTiO3 with RTiO3/SrTiO3
1 BaO
2 BaO
3 BaO
4 BaO
5 BaO
8 BaO
14 BaO
5 nm SmTiO3
x BaO layers
20 nm SrTiO3
LSAT
• Mobility of the space charge layer shows a sudden
drop around 3 to 5 BaO layers
• Possible that BaTiO3 switches from tetragonal to
cubic around 4 u.c. due to pure electron doping?
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Summary
BaTiO3
Vacancy formation
Carrier transport mechanism
Metal – Insulator transition
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Q. Zhang, T. Cagin and W. A. Goddard, PNAS, 103, 14695 (2006)