Imaging of Point Defects in ... - Susanne Stemmer Group talk 2018.pdfAllen, S. Stemmer, Phys. Rev. B...

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).


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∑


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


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




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



Variable Angle HAADF STEM - Simulated Configurations

Certain configurations are more distinguishable in one detector range but not the other


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)





















Certain configurations are more distinguishable in one detector range but not the other One detector is not uniformly better than another










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


#

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





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).


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


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


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


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


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


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





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


• 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)


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


Use STEM to quantify local octahedral distortions Successive Sm displacements to quantify “deviation angles”



• 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



• No local distortions around the dopant atoms • Large fraction of the image contains no Sr • Long-range structural effects, which are uniform



• 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

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Imaging of Point Defects in ... - Susanne Stemmer Group talk 2018.pdfAllen, S. Stemmer, Phys. Rev. B...

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