first principles computational study on ferroelectricity ... · committee members: dr. avinash...

First Principles Computational Study on Ferroelectricity in Hafnia (HfO2) and Beyond

Rohit Batra

Department of Materials Science and Engineering,University of Connecticut, USA

Principal Adviser: Dr. Rampi RamprasadAssociate Advisers: Dr. George Rossetti, Jr., Dr. Serge M. NakhmansonCommittee Members: Dr. Avinash Dongare, Dr. Pu-Xian Gao

Proposal Defense17 July, 2017

Linear Dielectric vs. Ferroelectric

2

Linear dielectric

Ein∝-EP∝E

Ferroelectric

EinPPr =

Ferroelectric: Presence of a polar phase with switchable polarization

Example: BaTiO3, PZT

P

E

P

EPPb

O

Electric field (E)

PPb

O

Ti/Zr

Linear dielectric

P

E

Hafnia: Dielectric or Ferroelectric

3

• High-k material• Used as SiO2 replacement• Vital part of commercially available

electronic devices

• Observations in hafnia films• New opportunities due to

promising FE properties

Hafnia

Until 2010

Ferroelectric

P

E

Since 2010

Applications of Ferroelectric (FE) Materials

4Varghese et al. J. Mater. Chem. C, 1, 2618(2013)

P

E

PO

PO

‘Bit 0’

‘Bit 1’

https://dx.doi.org/10.1039/2050-7534/2013

Exciting Properties of Hafnia

Hafnia can assist miniaturization of electronic devices!!

However…

5

Substantial polarization at small thickness

Funakubo et al., Sci. Rep., 32931(2016)

Size reduction

Source: http://www.electronics-eetimes.com/Park et al., APL, 107,19(2015)

1 order smaller than perovskite-

based FE materials

Ohtaka et al., J. Am. Cream. Soc. 84, 1369 (2001)

OB

OA

P-T phase diagram of hafnia

“Known” Hafnia PhasesAll known equilibrium phases are non-polar, can’t display FE behavior

Which polar phase of hafnia causes ferroelectricity?6

Processing conditions of hafnia films

Monoclinic(M)

(P21/c)

Tetragonal (T)

P42/nmc

Orthorhombic(OA)Pbca

(100) projections of hafnia phasesHfO

Mnemonic 1

OA P-O1 P-O2 T C0

102030405060708090

Ea�

EM

(meV

/ato

m)

Computational

ΔEn

ergy

(w.r.

t M)

Huan et al., PRB 90, 064111 (2014)

FE Phase of Hafnia?

Potential FE phases identified, but which conditions stabilize it? 7

Difficult to characterize FE

hafnia phase due to:

1. Small film thickness2. Structural similarity

Potential FE phase

(100) projections of hafnia phases

Orthorhombic(P-O2)Pmn21

Tetragonal(T)

P42/nmc

Orthorhombic(P-O1)Pca21

Experimental: XRD

MT

P-O1P-O2OA

Pbcm

Schenk, T. Ph. D. dissertation thesis (2017) Mnemonic 2Mnemonic 3

E-field 4

External Factors in FE Hafnia Films

Overall GOAL: How these factors combine to induce FE behavior in hafnia films?

8

• Other factors: Oxygen vacancies• Empirical results indicate critical role of these factors

HfO2

Bottom electrode

Top electrode

Si substrate

10-30 nm

Dopant2

Stress3

Surface/interface energy

1

Typical FE hafnia film

Grimley et al., Adv. Electron. Mater. 2: 1600173 (2016)

Research Objectives

9

Com

plet

ed

B. Combined influence of extrinsic factors1. Establish origin of ferroelectricity in hafnia films2. Electric-field induced T to P-O1 phase

transformations?Prop

osed ElectricfieldDopants

Stra

in Surfaceenergy

A. Individual influence of extrinsic factors1. Surface energy2. Dopants3. Mechanical stress4. Electric field

Dopants

Stre

ss Surfaceenergy

Electricfield

C. New opportunities beyond hafnia1. Search other potential FE simple binary oxides

Prop

osed

Methodology: DFT

10Using DFT compute energy of a given hafnia system

Using DFT compute energy of different hafnia phases in:• bulk or slab form• pure or doped state• under hydrostatic or biaxial stress state

Ground state energy?

𝚿E[𝚿]

Schrödinger equation

3 x No. of e-No. of variables

Density functional theory

⍴

3

E[⍴(r)]

e- charge density

Objective A

11



transformations?


Com

plet

edPr

opos

edPr

opos

ed

Dopants

Stre

ss Surfaceenergy

Electricfield

ElectricfieldDopants

Stra

in Surfaceenergy

Expe

rimen

tA.1: Surface Energy

For most orientations, T phase has the lowest surface energy

Polakowski-Müller, APL 106, 232905 (2015)

Hoffmann et al., J. Appl. Phys., 118(2015)

DFT computed surface energies

(110)

P-O2P-O1

Batra et al., APL 108, 172902 (2016) 12

A.1: Surface Energy

Surface energy does not explain observed ferroelectricity

a[100]

b[010]

c[001]

Schematic of hafnia particle

[100] = 12.8 Å [100] = 27.4 Å

P-O2

P-O1

Batra et al., APL 108, 172902 (2016)

Stabilization of T or P-O2 phase due to surface energy

• Results consistent with studies on ultra-thin hafnia films and nanotubes

13

A.2: Dopants — The Strategy

Identify dopants that promote polar phases the most

Incr

easi

ng co

st/a

ccur

acy

Observations of ferroelectricity in diverse dopants(Si, Al, Gd, La, Sr, and more…)

14

OA P-O1 P-O2 T C0

102030405060708090

Ea�

EM

(meV

/ato

m) Pure

ΔEn

ergy

OA P-O1 P-O2 T C0

102030405060708090

Ea D�

EM D

(meV

/ato

m)

Dopant addition

ΔEn

ergy

selection

selection

Batra et al., arXiv:1707.04211 (2017)

�50

0

50

100

150D

Ea�

MD

(meV

/f.u

.) Ca (a) Sr (b)

M P-O2 OA T P-O1

Ba (c)

0 3 6 12% doping conc.

�50

0

50

100

150

DEa

�M

D(m

eV/f

.u.) Y (d)


La (e)


Gd (f)

�50

0

50

100

150

DEa

�M

D(m

eV/f

.u.) Ca (a) Sr (b)

M P-O2 OA T P-O1

Ba (c)


�50

0

50

100

150

DEa

�M

D(m

eV/f

.u.) Y (d)


La (e)


Gd (f)

A.2: Dopants — Results Stage 3

Open symbols: (a) phase relaxed into other phase, (b) phase cannot be classified

Dopants promote P-O1 phase, but alone do not stabilize it

Monoclinic

T to P-O1

15

Phase cannot be classified

Mnemonic 4

Similar results for Ca, Sr, Ba, Y and Gd

Batra et al., arXiv:1707.04211 (2017)

A.2: Dopants — Insights & Validation

Theoretical results on dopants match experiments

Dopants that stabilize P-O1:1. Larger radius2. Lower electronegativity

Pola

rizat

ion(

µC/c

m2 )

Ionic radius (pm)

Boettger et al., J. Mater. Chem. C, 5(2017)

Empirical observations of larger Pr for larger dopants

Divalent

16

Batra et al., arXiv:1707.04211 (2017)

120 125 130 135 140 145 150

Volume (Å3)

0

20

40

60

80

100

120

Ea�

EM 0

(meV

/ato

m)

Hydrostatic

(a)MT

P-O1P-O2

OA

23 24 25 26 27 28 29

Area (Å2)

Equibiaxial

(b)

-11.5 -7.8 -4.1 -0.4 3.3 6.9 10.6e(%)

-10.5 -6.7 -2.8 1.1 5.0 8.9 12.8e(%)

(001)

120 125 130 135 140 145 150

Volume (Å3)

0

20

40

60

80

100

120

Ea�

EM 0

(meV

/ato

m)

Hydrostatic

(a)MT

P-O1P-O2

OA

23 24 25 26 27 28 29

Area (Å2)

Equibiaxial

(b)

-11.5 -7.8 -4.1 -0.4 3.3 6.9 10.6e(%)

-10.5 -6.7 -2.8 1.1 5.0 8.9 12.8e(%)

120 125 130 135 140 145 150

Volume (Å3)

0

20

40

60

80

100

120

Ea�

EM 0

(meV

/ato

m)

Hydrostatic

(a)MT

P-O1P-O2

OA

23 24 25 26 27 28 29

Area (Å2)

Equibiaxial

(b)

-11.5 -7.8 -4.1 -0.4 3.3 6.9 10.6e(%)

-10.5 -6.7 -2.8 1.1 5.0 8.9 12.8e(%)

A.3: Mechanical Stress

Compressive stress favor P-O1 phase, but alone fails to stabilize it

Polar P-O1 phase stable relative to M phase in compressed state

17

Equilibrium M phase

Experiments: The capping electrode necessary to induce ferroelectricity

TensionCompression

Batra et al., J. Phys. Chem. C, (2017)

A.4: Electric field

E-field promotes P-O1 phase, but alone fails to stabilize it18

E↵ = E↵DFT � V ↵0 (✏↵r ✏0 ~E + ~P↵) ~E

Schenk, T. et al. Appl. Mater. Inter., 6(22), 19744–19751 (2014)

Wake up


stress-free

Energy change due to electric field

(Not first principles)

Electric field significantly alters the phase stability

Recap

19

• Each of these factors promote the polar P-O1 phase• However, no factor alone stabilizes the P-O1 as the ground state

Can combination of these factors explain observed ferroelectricity?

120 125 130 135 140 145 150

Volume (Å3)

0

20

40

60

80

100

120

Ea

�E

M 0(m

eV/

atom

)

Hydrostatic

(a)MT

P-O1P-O2

OA

23 24 25 26 27 28 29

Area (Å2)

Equibiaxial

(b)

-11.5 -7.8 -4.1 -0.4 3.3 6.9 10.6e(%)

-10.5 -6.7 -2.8 1.1 5.0 8.9 12.8e(%)

Stress

Area

Electric field

Electric field (MV/cm)

�50

0

50

100

150D

Ea�

MD

(meV

/f.u

.) Ca (a) Sr (b)

M P-O2 OA T P-O1

Ba (c)


�50

0

50

100

150

DEa

�M

D(m

eV/f

.u.) Y (d)


La (e)


Gd (f)Dopant

Dopants

% doping conc.

stress-free equibiaxial

A: Combined Stress and Electric Field

Multiple factors, operating jointly, may be responsible for FE

• In-plane stress “de-stabilize” the M phase, and• Electric field “stabilize” the polar phase

20

Stabilization of P-O1 phase due to stress and

electric fieldelastic energy


Objective B

21



transformations?


Com

plet

edPr

opos

edPr

opos

ed

Dopants

Stre

ss Surfaceenergy

Electricfield


Stra

in Surfaceenergy

Remaining Work: Objective B

22Improved models to better understand ferroelectricity in hafnia

Conditions to be modeledaccurately

Limitation: Phenomenological E-fieldSolution: DFT-based E-field (only hafnia films)

Carefully chosen parameter space

E

Electric field from first principles

Ps’

(111) P-O1 slab

OHf

Remaining Work: Objective B

23

• More realistic models• Possibly electric field induced T to P-O1 transformations (Mnemonic 4)

Further extension

Improved models to better understand ferroelectricity in hafnia

Non-zero temperatures(DFT-based MD simulations)

Carefully chosen parameter space

Doped (111) P-O1 slab

Sr/La

Ps’ E

Objective C

24



transformations?


Com

plet

edPr

opos

edPr

opos

ed

Dopants

Stre

ss Surfaceenergy

Electricfield


Stra

in Surfaceenergy

Tool Example of HfO2

Remaining Work: Objective C

25

Structure search algorithm

Point group

Minimum energy pathway

M, T, OAP-O1 and P-O2

T parent phaseof P-O1 and P-O2

Switching barrier:P-O1: 30 meVP-O2: 10 meV

Hafnia is potentially ferroelectric

Search for low energy structures

Identify polar phase and respective parent phase

Compute polarization and switching energy barrier

Propose potential FE materials

Search Steps1

2

3

Is hafnia unique, or are there more FE binary oxides?

Key insight: (1) low energy polar phase and (2) small switching barrier

Remaining Work: Objective C

26

Initial set criteria:1) Insulator2) Simple binary oxide3) Non-magnetic

Promising Stage 1 results for few oxides

Timeline

27

Objective 2017 2018Fall Spring Summer

B Phase stability in hafnia films

C Search for other potential FE binary oxides

FE materials in Non-volatile Memories

28

Non-volatile RAM

???

Future?

CPU

1980

Tape

Disk

CPU

RAM

Present

Disk

Tape

Flash drive

CPU

RAM

Accesstime

1 ns —

1 µs —

1 ms —

1 s —

Solution: FE materials (Hafnia and

others)

Source: Schenk, T. Ph. D. dissertation thesis (2017)

Volatile

Non-volatile

Summary and Impact

29

Extrinsic factors promoting ferroelectricity in hafnia

New potential FE materials

Insights on origins of FE behavior in hafnia films

Better FE devices!!

A

B

C

Acknowledgements

30

Puneet BatraBrother

Prof. Rampi Ramprasad

AdviserKhushboo Mittal

Wife

Acknowledgements

31

Committee members:Prof. Serge M. Nakhmanson, Prof. Avinash Dongare and Prof. Pu-Xian Gao

Group members and friends:Garvit, Lihua, Dr. Satyesh Yadav , Dr. Venkatesh Botu , Deepak, Dr. Chiho Kim and Sergey

Computational resources:UCONN Hornet clusters, XSEDE

Funding Agency:Army Research Office

U.S. Army

Collaborators:Prof. Jacob L. Jones, NCSU, USAProf. Dr. Uwe Schröder, Namlab, Germany

Special thanks to:Prof. George Rossetti, Jr. and Dr. Huan Doan Tran

DeepakSriram

HarishKaleelMasabKhushboo

& Rohit

Yupeng

XinHamzaTaraSumairaKamran

Paritosh

Alex

Thanks!!

33

first principles computational study on ferroelectricity ... · committee members: dr. avinash...

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