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Imaging of Point Defects in Complex Oxides Using Quantitative STEM
Honggyu Kim, Jack Zhang, and Susanne Stemmer
Materials Department, University of California, Santa Barbara, USA
19th International Microscopy Congress September 10, 2018 Sydney, Australia
Funding:
Outline
• Quantitative STEM for three-dimensional imaging of dopant atoms and point defects
• Improving contrast and interpretability: variable-angle HAADF-STEM
• Vacancies and local structure relaxations around point defects
• Doping a Mott insulator
Quantitative HAADF/STEMJ. M. LeBeau, S. D. Findlay, L. J Allen, S. Stemmer,
Phys. Rev. Lett. 100, 206101 (2008). J. M. LeBeau, S. Stemmer, Ultramicroscopy 108, 1653 (2008).
J. M. LeBeau, S. D. Findlay, X. Wang, A. J. Jacobson, L. J. Allen, S. Stemmer, Phys. Rev. B 79, 214110 (2009).
• Quantify atom column intensities (relative to incident probe intensity)
• Compare with simulated column intensities
• Obtain meaningful and quantifiable information from HAADF image intensities
For a tutorial see: http://www.mrl.ucsb.edu/~stemmer/main_pdfs/STEM%20Tutorial.pdf
Three-Dimensional Imaging of Individual Dopant Atoms
Quantitative STEM from a single image to: • Determine the number of dopant atoms in each column • Determine the dopant depth position for each dopant atom
1 2 3 4 5
Top
Bottom
Gd
Sr
Gd-doped SrTiO3
J. Hwang, J. Y. Zhang, A. J. D’Alfonso, L. J. Allen, and S. Stemmer, Phys. Rev. Lett. 111, 266101 (2013).
Three-Dimensional Imaging of Individual Dopant Atoms
Gd-doped SrTiO3ISr
ITi-O
Column averaged intensities (insensitive to spatial incoherence)* Haibo et al., Ultramicroscopy 133, 109 (2013)
0.0080.0060.0040.002 0.0060.0040.002
ISr map ITi-O map
Need to establish a visibility criterion
• Thickness variations
• ISr is sampled only if the standard deviation of four neighboring ITi-O is 4% or less
Three-Dimensional Imaging of Individual Dopant Atoms0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000
I Sr
0.0040.0030.0020.001ITi-O
Undoped SrTiO3 Sim. Exp. raw Exp. background
subtracted
5 u.c.
6 u.c.
0.0030.0020.001ITi-O
Undoped SrTiO3 exp. fit
Undop
ed S
rTiO 3
exp.
error
cutof
f
Gd doped SrTiO3 exp.
-0.001
0.000
0.001
I Sr
0.0005-0.0005ITi-O
0.0070
0.0065
0.0060
0.0055
0.0050
0.0045
0.0040
0.0035
0.0030
I Sr
0.00260.00250.0024ITi-O
Gd doped SrTiO3 exp. Gd doped SrTiO3 sim.
A
B
C
D
H
GF
5
43
21
5,45,3
5,2
5,1
4,34,2
4,13,23,1
2,1
Undoped SrTiO3 exp.
Undoped SrTiO3
exp. error cutoff
E
1 2 3 4 5
Top
Bottom
Gd
Sr
pi =erfi t( )erfn t( )
n∑
Probability of configuration
σ = pi zi − µ( )2i∑
Expectation Value Uncertainty
µ = zi pii∑
J. Hwang, J. Y. Zhang, A. J. D’Alfonso, L. J. Allen, and S. Stemmer, Phys. Rev. Lett. 111, 266101 (2013).
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000
I Sr
0.0040.0030.0020.001ITi-O
Undoped SrTiO3 Sim. Exp. raw Exp. background
subtracted
5 u.c.
6 u.c.
0.0030.0020.001ITi-O
Undoped SrTiO3 exp. fit
Undop
ed S
rTiO 3
exp.
error
cutof
f
Gd doped SrTiO3 exp.
-0.001
0.000
0.001
I Sr
0.0005-0.0005ITi-O
Three-Dimensional Imaging of Individual Dopant Atoms
A B x
y D C E
F
C A B
4.4±0.6
2.0±0.7
3.8±0.7
1.8±0.8
y x
z
1
2
3
4
5
D C E
3.3±1.0 3.3±0.7
1.5±0.6
2.7±0.7
1.2±0.4 1
2
3
4
5
y x
z
• Quantitative information of expectation values and dopant visibility • Determined complete 3D configuration from a single STEM image • Sufficiently thin TEM foils are key
J. Hwang, J. Y. Zhang, A. J. D’Alfonso, L. J. Allen, and S. Stemmer, Phys. Rev. Lett. 111, 266101 (2013).
Three-Dimensional Imaging of Individual Dopant Atoms
J. Hwang, J. Y. Zhang, A. J. D’Alfonso, L. J. Allen, and S. Stemmer, Phys. Rev. Lett. 111, 266101 (2013).
0.0070
0.0065
0.0060
0.0055
0.0050
0.0045
0.0040
0.0035
0.0030
I Sr
0.00260.00250.0024ITi-O
Gd doped SrTiO3 exp. Gd doped SrTiO3 sim.
A
B
C
D
H
GF
5
43
21
5,45,3
5,2
5,1
4,34,2
4,13,23,1
2,1
Undoped SrTiO3 exp.
Undoped SrTiO3
exp. error cutoff
E
1 2 3 4 5
Top
Bottom
Gd
Sr
• Certain dopant atom configurations are indistinguishable
• General problem: uniquely identify a structure from the measured intensities
• How to improve contrast in STEM?
Variable Angle HAADF STEM
• Use angular resolved information • In certain angular regions, the red dopant has a higher scattering
power than the blue dopant • Do not have a detector with angular segments • Use two camera lengths instead Detector 1 (60-390 mrad) Detector 2 (47-306 mrad)
Integrated intensities in 30 mrad segments
J. Y. Zhang, J. Hwang, B. J. Isaac, and S. Stemmer, Sci. Rep. 5, 12419 (2015).
Variable Angle HAADF STEM - Experimental
Detector 1 Detector 2
• Simulate all possible dopant configurations for both detectors
• Determine standard deviation from undoped sample for both detectors
Detector 1 Detector 2
J. Y. Zhang, J. Hwang, B. J. Isaac, and S. Stemmer, Sci. Rep. 5, 12419 (2015).
Variable Angle HAADF STEM - Simulated Configurations
Certain configurations are more distinguishable in one detector range but not the other
Detector 1 Detector 2
All possible simulated configurations for 1 or 2 dopants
Examples • Configuration 4,5 and 3,5
(much better with detector 2) • Configuration 1,5 and 2,5
(better with detector 1)
• Configuration 5 (much better with detector 2)
J. Y. Zhang, J. Hwang, B. J. Isaac, and S. Stemmer, Sci. Rep. 5, 12419 (2015).
Variable Angle HAADF STEM - Simulated Configurations
Certain configurations are more distinguishable in one detector range but not the other
Detector 1 Detector 2
All possible simulated configurations for 1 or 2 dopants
Examples • Configuration 4,5 and 3,5
(much better with detector 2) • Configuration 1,5 and 2,5
(better with detector 1)
• Configuration 5 (much better with detector 2)
J. Y. Zhang, J. Hwang, B. J. Isaac, and S. Stemmer, Sci. Rep. 5, 12419 (2015).
Variable Angle HAADF STEM - Simulated Configurations
Certain configurations are more distinguishable in one detector range but not the other
Detector 1 Detector 2
All possible simulated configurations for 1 or 2 dopants
Examples • Configuration 4,5 and 3,5
(much better with detector 2) • Configuration 1,5 and 2,5
(better with detector 1)
• Configuration 5 (much better with detector 2)
J. Y. Zhang, J. Hwang, B. J. Isaac, and S. Stemmer, Sci. Rep. 5, 12419 (2015).
Variable Angle HAADF STEM - Simulated Configurations
Certain configurations are more distinguishable in one detector range but not the other One detector is not uniformly better than another
Detector 1 Detector 2
All possible simulated configurations for 1 or 2 dopants
Examples • Configuration 4,5 and 3,5
(much better with detector 2) • Configuration 1,5 and 2,5
(better with detector 1)
• Configuration 5 (much better with detector 2)
J. Y. Zhang, J. Hwang, B. J. Isaac, and S. Stemmer, Sci. Rep. 5, 12419 (2015).
Variable Angle HAADF STEM - Simulated Configurations
J. Y. Zhang, J. Hwang, B. J. Isaac, and S. Stemmer, Sci. Rep. 5, 12419 (2015).
Determining the number of dopant atoms in a column
Some ambiguous configurations can only be determined with both detectors (2,3 and 1,3) Combined detector information always improves accuracy
Variable Angle HAADF STEM - Experiment
J. Y. Zhang, J. Hwang, B. J. Isaac, and S. Stemmer, Sci. Rep. 5, 12419 (2015).
#
Dopants
Detector
1
Detector
2 Combined
Detector 1 Detector 2 Combined
Position Probability Position Probability Position Probability
0 5.1% 0% 0% 5 0.0279 5 0.4179 5 0.0742
1 64.9% 49.5% 78.7% 4 0.2491 4 0.5311 4 0.8429
2 30.1% 50.5% 21.3% 3 0.2734 3 0.0340 3 0.0592
2 0.2607 2 0.0071 2 0.0118
1 0.1889 1 0.0099 1 0.0119
Region
1 2.67±1.12 4.34±0.67 3.96±0.53
0 1.5% 4.8% 0.2% 5 0.0692 5 0.0026 5 0.0008
1 57.3% 63.8% 73.1% 4 0.2978 4 0.0441 4 0.0605
2 41.1% 31.3% 26.8% 3 0.2861 3 0.3489 3 0.4599
2 0.2202 2 0.2929 2 0.2970
1 0.1267 1 0.3115 1 0.1818
Region
2 2.96±1.14 2.21±0.92 2.40±0.85
Region 1: • Detector 2 unable to distinguish
number of dopants, but better at distinguishing the position!
• Combined detector converges on position
Variable Angle HAADF-STEM
• Three-dimensional dopant atom configurations determined by quantitative STEM
• Variable angle HAADF results in improvement in precision and accuracy in obtaining 3D dopant configurations
• One particular angular range not unilaterally better than the other
• Using multiple angle ranges and compound probabilities improve depth quantification
• Can be extended to include additional angular ranges
• Parallel data acquisition would be highly desirable
Outline
• Quantitative STEM for three-dimensional imaging of dopant atoms and point defects
• Improving contrast and interpretability: variable-angle HAADF-STEM
• Vacancies and local structure relaxations around point defects
• Doping a Mott insulator
Imaging of Point Defects in STEM
So far have considered only relatively heavy dopant atoms in lighter matrix
Less visible defects, such as vacancies?
Structure relaxation around individual point defects
Determines “electrical activity” of a point defect
Small polaron formation: “self-trapping” of carriers by lattice distortion
Charge states of point defectsMater. Res. Express 1 025905
Imaging of Point Defects in STEM
So far have considered only relatively heavy dopant atoms in lighter matrix
Less visible defects, such as vacancies?
Structure relaxation around individual point defects
Determines “electrical activity” of a point defect
Combine variable angle HAADF with rigid registration
Variable Angle HAADF-STEM for Vacancy Detection
0.002 0.008 0.014 0.020 0.020 0.007 0.012
A B
Detector 1
A B
Detector 2 0.005 0.011 0.017 0.023 0.040 0.010 0.016
A B C
D E F
Intentionally non-stoichiometric (Sr-deficient) SrTiO3 film grown by MBE Columns containing Sr-vacancies can be identified H. Kim, J. Y. Zhang, S. Raghavan, and S. Stemmer, Phys. Rev. X 6, 041063 (2016).
Variable Angle HAADF-STEM for Vacancy Detection
The number of vacancies in a column can be determined
0.020
0.015
0.010
0.005
0.000
I Sr
0.0150.0100.0050.000ITi-O
SrTiO3 (sim.) SrTiO3 with vacancy (sim.) Column A (exp.) Column B (exp.)
Detector1
6 u.c.
8 u.c.
0.025
0.020
0.015
0.010
0.005
0.000
I Sr
0.0150.0100.0050.000ITi-O
SrTiO3 (sim.) SrTiO3 with vacancy (sim.) Column A (exp.) Column B (exp.)
Detector 2
6 u.c.
8 u.c.
A
B
0.020
0.015
0.010
0.005
0.000
I Sr
0.0150.0100.0050.000ITi-O
SrTiO3 (sim.) SrTiO3 with vacancy (sim.) Column A (exp.) Column B (exp.)
Detector1
6 u.c.
8 u.c.
0.025
0.020
0.015
0.010
0.005
0.000
I Sr
0.0150.0100.0050.000ITi-O
SrTiO3 (sim.) SrTiO3 with vacancy (sim.) Column A (exp.) Column B (exp.)
Detector 2
6 u.c.
8 u.c.
A
B
Column A Column BThickness
(u.c.) # Vacancies Probability (%) Thickness (u.c.) # Vacancies Probability (%)
Detector 1 Detector 2 Combined Detector 1 Detector 2 Combined
8 2 0.78 1.17 0.02 6 0 27.52 5.06 4.11
8 3 71.19 68.19 92.6 6 1 4.06 7.02 0.84
8 4 8.71 19.37 3.22 7 1 24.95 3.29 2.43
9 4 19.32 11.29 4.16 7 2 43.39 72.29 92.59
7 3 0.08 12.01 0.03
All possible vacancy
configurations
Detector 1 Detector 2
H. Kim, J. Y. Zhang, S. Raghavan, and S. Stemmer, Phys. Rev. X 6, 041063 (2016).
Variable Angle HAADF-STEM of Lattice Relaxations
2.65 2.75 2.85 2.95
Distance (Å)
Avg.: 2.76 Å Std.: 1.5 pm
Column distances in stoichiometric SrTiO3
Variable Angle HAADF-STEM for Vacancy Detection
A
2.65 2.75 2.85 2.95 Distance (Å)
C
B
D
2.88
2.85
• Neighboring Ti columns move away from the Sr-vacancy containing columns
• Consistent with XRD showing lattice expansion
• Not consistent with published DFT*
• Correlation effects?
*T. Tanaka, et al., Phys. Rev. B 68, 205213 (2003); A. Janotti, et al., Phys. Rev. B 90, 085202 (2014); D. A. Freedman, D. Roundy, and T. A. Arias, Phys. Rev. B 80, 064108 (2009).
Average distance in stoichiometric SrTiO3: 2.76 Å ± 1.5 pm
H. Kim, J. Y. Zhang, S. Raghavan, and S. Stemmer, Phys. Rev. X 6, 041063 (2016).
Outline
• Quantitative STEM for three-dimensional imaging of dopant atoms and point defects
• Improving contrast and interpretability: variable-angle HAADF-STEM
• Vacancies and local structure relaxations around point defects
• Doping a Mott insulator
Doping a Mott Insulator
SrTiO3 SmTiO3
c
b a
SmxSr1-xTiO3
x 1.00
Pm3m Non-magnetic Band insulator
Pbnm Antiferromagnetic Mott insulator
Add rare earth Electron doping
Add Sr Hole doping
• What happens when the Mott gap collapses on doping is one of the most fundamental questions in condensed matter physics
• Quantitative STEM allows us to investigate the local scale (around the doping atom) and longer length scale (phase separation...)
Mott InsulatorMetal
Doping a Mott Insulator
• Prototypical Mott insulators: one electron in t2g • Filling induced MIT upon hole doping • Critical concentration for MIT depends on degree of octahedral distortions • Not consistent with ideal Mott insulator that only exists at half-filling • Disorder of the dopant atoms (i.e., Sr) localizing electrons • First order, band-width controlled MIT that requires percolation of the metallic regions* • Other?
• How strongly is this MIT coupled to the lattice?
TNTc
InsulatorFM
AFM
Metal
Hole do
ping
Octahedral distortions
Band width
c
a b
Band-width controlled, first order phase transition?
*C.-H. Yee, L. Balents, Phys. Rev. X 5, 021007 (2015)
RTiO3 (R = rare earth ion)
Doping a Mott Insulator
101
102
103
104
105
She
et re
sist
ance
(Ohm
/sq.
)
300250200150100500
Temperature (K)
Sr0.05Sm0.95TiO3 Sr0.10Sm0.90TiO3 Sr0.15Sm0.85TiO3 Sr0.20Sm0.80TiO3
• 50 nm, epitaxial SmTiO3 films grown by MBE and doped with Sr
• Sample with ~ 5% Sr is at the MIT boundary
• SmTiO3 too insulating to measure
• Atomic resolution STEM of octahedral distortions → how uniform?
MIT
Mott insulator
H. Kim, P. B. Marshall, K. Ahadi, T. E. Mates, E. Mikheev, and S. Stemmer, Phys. Rev. Lett. 119, 186803 (2017).
Pbnm Antiferromagnetic Mott insulator
Sr:SmTiO3
Doping a Mott Insulator
Use STEM to quantify local octahedral distortions Successive Sm displacements to quantify “deviation angles”
H. Kim, P. B. Marshall, K. Ahadi, T. E. Mates, E. Mikheev, and S. Stemmer, Phys. Rev. Lett. 119, 186803 (2017).
Doping a Mott Insulator
• Octahedral distortions decrease as Sr is added
• The metallic film (x = 0.1) still shows substantial octahedral distortions
• The MIT is not strongly coupled to the lattice
• Sr-doping changes the structure uniformly: there is no phase separation
• No local distortions around the dopant atoms
• Long-range structural effects
H. Kim, P. B. Marshall, K. Ahadi, T. E. Mates, E. Mikheev, and S. Stemmer, Phys. Rev. Lett. 119, 186803 (2017).
Doping a Mott Insulator
• No local distortions around the dopant atoms • Large fraction of the image contains no Sr • Long-range structural effects, which are uniform
H. Kim, P. B. Marshall, K. Ahadi, T. E. Mates, E. Mikheev, and S. Stemmer, Phys. Rev. Lett. 119, 186803 (2017).
Doping a Mott Insulator
• The MIT in the RTiO3 is not strongly coupled to the symmetry of the lattice
• Not first order, no phase separation
• Disorder remains as a possible explanation for the large hole doping required
• However: no local distortions around Sr atoms, only global, uniform response
• Sr doping globally affects the structure and electronic properties → long range strong correlation effects drive the transition
Variable Angle HAADF-STEM of Point Defects in Oxides
• Variable angle HAADF-STEM can identify columns containing point defects with very high degree of confidence
• “Low visibility defects” such as vacancies can be identified
• Atom relaxations around the vacancies are clearly visible
• What happens around individual point defects determines their electrical activity, strong correlation physics, ...
Future developments:
• Variable angle HAADF-STEM of displacements
• Combine with low-angle data*
*J. Johnson, S. Im, W. Windl, and J. Hwang, Ultramicroscopy 172, 17 (2017).
Thank you for your attention