Post on 06-Jul-2020
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
A. Individual influence of extrinsic factors1. Surface energy2. Dopants3. Mechanical stress4. Electric field
B. Combined influence of extrinsic factors1. Establish origin of ferroelectricity in hafnia films2. Electric-field induced T to P-O1 phase
transformations?
C. New opportunities beyond hafnia1. Search other potential FE simple binary oxides
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)
0 3 6 12% doping conc.
La (e)
0 3 6 12% doping conc.
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)
0 3 6 12% doping conc.
�50
0
50
100
150
DEa
�M
D(m
eV/f
.u.) Y (d)
0 3 6 12% doping conc.
La (e)
0 3 6 12% doping conc.
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
Batra et al., J. Phys. Chem. C, (2017)
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)
0 3 6 12% doping conc.
�50
0
50
100
150
DEa
�M
D(m
eV/f
.u.) Y (d)
0 3 6 12% doping conc.
La (e)
0 3 6 12% doping conc.
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
Batra et al., J. Phys. Chem. C, (2017)
Objective B
21
A. Individual influence of extrinsic factors1. Surface energy2. Dopants3. Mechanical stress4. Electric field
B. Combined influence of extrinsic factors1. Establish origin of ferroelectricity in hafnia films2. Electric-field induced T to P-O1 phase
transformations?
C. New opportunities beyond hafnia1. Search other potential FE simple binary oxides
Com
plet
edPr
opos
edPr
opos
ed
Dopants
Stre
ss Surfaceenergy
Electricfield
ElectricfieldDopants
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
A. Individual influence of extrinsic factors1. Surface energy2. Dopants3. Mechanical stress4. Electric field
B. Combined influence of extrinsic factors1. Establish origin of ferroelectricity in hafnia films2. Electric-field induced T to P-O1 phase
transformations?
C. New opportunities beyond hafnia1. Search other potential FE simple binary oxides
Com
plet
edPr
opos
edPr
opos
ed
Dopants
Stre
ss Surfaceenergy
Electricfield
ElectricfieldDopants
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
32
DeepakSriram
HarishKaleelMasabKhushboo
& Rohit
Yupeng
XinHamzaTaraSumairaKamran
Paritosh
Alex
Thanks!!
33