Ph.D. Dissertation Proposal
First Principles Studies of Defects in HfO2
and at Si:HfO2 Heterojunctions
Chunguang Tang (唐春光)
(Bachelor Eng.: Univ. Sci. Tech. Beijing)
(Master. Sci.: NUS)
Chemical, Materials & Biomolecular Engineering
Institute of Materials Science
University of Connecticut
Principal Advisor: Prof. R. Ramprasad
Associate Advisor: Prof. L. Shaw
Associate Advisor: Prof. P. S. Alpay
# of transistors
Introduction: device miniaturization
First transistor radio: 4 transistors.
Quad core processor contains
820 million transistors
high k (dielectric constant) transistor
K~4
K ~ 30
High k issues
• Formation of interface phases (SiOx, silicate, Hf-Si)
Wong et al,
Microelectronic
Eng. (2006)
Locquet et al,
JAP (2006);
Stemmer et al
– Effects of oxygen point defects*
• Point defects migration may contribute to interfacial phase formation
• High oxygen pressure favors silica & low pressure favors Hf silicide
* D. Y. Cho et al, APL, 86, 041913 (2005); X. Y. Qiu et al,
APL, 88, 072906 (2006); S. Stemmer, JBSTB, 22, 791
(2004)
High k issues
• High leakage currents and low dielectric
constant due to crystallization
– As-deposited: amorphous (preferred)
– Crystallizes at 400~500 °C
amorphous
k ~ 30
cubic
k ~ 29
tetragonal
k ~ 70
– Doped HfO2 with alloying elements.
• Si, Y, La, F, N
• Increase crystallization temperatures
• Stabilize higher k phases
monoclinic
k ~ 16
Proposed research plan
• Undoped HfO2
– The formation and migration of O vacancies,
O interstitials and Hf vacancies.
– Their contribution to the interfacial phases.
• Doped HfO2
– Dopants: Si, Y, La, F, N.
– Effects of dopants on relative stabilities of
various phases of HfO2.
– Effects of dopants on O defect chemistry.
Computational Methods
• Density Functional Theory (DFT)
– Many nuclei-many electron problem  one electron problem
 2 2






V
r
eff

  i r    i  i r 
 2m

– Supercell approach
– Phase and structure information, defect energies
• Computational times
– Defect formation energies  16 days in one AMD 2.0 GHz
processor (Supercell of ~230 atoms).
– Migration energy calculation  45 days.
0
E
1
2
Emigr.
3
4
Reaction path
Completed Research
• Bulk HfO2 results
Table I: relative energies (eV) and lattice constants (Å) of bulk HfO2
DE/HfO2
a (calc./expr.)
b (calc./expr.) c (calc./expr.)
c-HfO2
0.25
5.06/5.08*
=a
=a
t-HfO2
0.16
5.06/5.15**
=a
5.14/5.29
m-HfO2
0
5.14/5.12***
5.19/5.17
5.30/5.29
*
J. Wang, H. P. Li, and R. Stivens, J. Mater. Sci. 27, 5397 (1992)
** D. M. Adams, S. Leonard, D. R. Russel, and R. J. Cemik, J. Phys. Chem. Solids 52, 1181 (1991)
*** J. Adam and M. D. Rodgers, Acta Crystallogr. 12, 951 (1959)
Defects in bulk HfO2
Eform
+ 1 O atom
Eform = Evac+ (EO2)/2 - Eperf
Table II: Formation energies (eV) of point defects in bulk HfO2
3-fold site
4-fold site
O interstitial
1.7
2.5
O vacancy
6.6
6.5
Hf vacancy
6.1
O interstitial Formation and Migration*
Si
HfO2
Hf
O
Interfacial segregation:
Thermodynamic driving
force (decreasing Eform as
interface is approached)
Kinetic driving force, and
O penetration into Si
(decreasing Emigr as
interface is approached)
Experimental Emigr. of O
interstitial in bulk Si: 2.44
eV** (2.26 eV, calculated)
O interstitials could
lead to the formation
of SiOx
* C. Tang & R. Ramprasad, Phys. Rev. B 75, 241302 (2007);
** J. C. Mikkelsen, Appl. Phys. Lett. 40, 336 (1981).
O Vacancy Formation and Migration*
Si
HfO2
Hf
O
Interfacial segregation:
Aided by thermodynamic &
kinetic driving forces
O vacancies could
lead to the formation
of Hf silicide
* C. Tang, B. Tuttle & R. Ramprasad, Phys. Rev. B 76, 073306 (2007)
Hf Vacancy Formation and Migration*
Hf
O
Si penetration
•
Hf vacancies prefer
the interface
•
Si strongly prefers to
penetrate into HfO2
Hf vacancies could
lead to the formation
of Hf silicate
* C. Tang & R. Ramprasad, Appl. Phys. Lett., 92, 152911 (2008)
Accumulation of O Point Defects*
Thermodynamics favors
accumulation of point
defects at interface, and
consequently, the
creation of Hf silicide or
SiOx
Abrupt Interface
“SiOx”
Interface
* C. Tang & R. Ramprasad, Appl. Phys. Lett., 92, 182908 (2008)
“Hf-Si”
Interface
Si doped HfO2 (SDH)
C-SDH
(1-x) HfO2 + xSiO2 + Ef = Hf1-xSixO2
t-SDH
m-SDH
1. If Si > 12%  t-HfO2 most
stable
2. The local chemistry of Si
prefers SiO2 configuration
c-SDH
m-SDH
t-SDH
Y doped HfO2 (YDH)
(1-x) HfO2+(x/2)Y2O3+Ef=Hf1-xYxO2-x/2
m-YDH
c-YDH
Charge neutrality  2 Y atoms & 1 O
vacancy
t-YDH
1. If Y > 12%, t-HfO2 and c-HfO2
more stable.
2. Similar stabilization phenomenon
in c-YSZ for fuel cell application.
3. Instead of Y, positively charged O
vacancies are identified as the
major stabilizing factor.
Remaining research
• Undoped HfO2
– Amorphous HfO2 and Si heterojunction;
• Lower leakage current
• High dielectric constant
– Various charged states of O defects (VO0, VO+1,
VO+2, iO0, iO-1, iO-2);
• Formation energies
Remaining research
• Doped HfO2
– Effects of dopants on HfO2 stabilities (La, F,
N);
– Formation and migration energies of O
defects close to and far away the dopants.
• How they influence the behaviors of defects in
HfO2 and Si heterojunctions
Publication list
1. C. Tang and R. Ramprasad, "Oxygen defect accumulation at Si:HfO2
interfaces" , Appl. Phys. Lett., 92, 182908 (2008).
2. C. Tang and R. Ramprasad, "A study of Hf vacancies at Si:HfO2
heterojunctions" , Appl. Phys. Lett., 92, 152911 (2008).
3. C. Tang and R. Ramprasad, "Oxygen pressure dependence of HfO2
stoichiometry: An ab initio investigation" , Appl. Phys. Lett., 91, 022904 (2007).
4. C. Tang, B. R. Tuttle and R. Ramprasad, "Diffusion of O vacancies near Si:HfO2
interfaces: An ab initio investigation", Phys. Rev. B, 76, 073306 (2007).
5. C. Tang and R. Ramprasad, "Ab initio study of O interstitial diffusion near
Si:HfO2 interfaces", Phys. Rev. B, 75, 241302(R) (2007).
6. B. R. Tuttle, C. Tang and R. Ramprasad, "First-principles study of the valence
band offset between silicon and hafnia", Phys. Rev. B, 75, 235324 (2007).
7. R. Ramprasad and C. Tang, "Circuit elements at optical frequencies from first
principles: a synthesis of electronic structure and circuit theories", J. Appl. Phys.
100, 034305 (2006).
8. Tang CG, Li Y, Zeng KY, Mater. Lett., 59, 3325, (2005).
9. Tang CG, Li Y, Zeng KY, Mater. Sci. Eng. A, 384, 215, (2004).
10. Li Y, Cui LJ, Cao GH, Ma QZ, Tang CG, Wang Y, Wei L, Zhang YZ, Zhao ZX, Baggio-Saitovitch E,
Physica C, 314, 55, (1999).
11. Li Y, Wang YB, Tang CG, Ma QZ, Cao GH, SCI CHINA SER A, 40, 978, (1997).
12. Li Y, Tang CG, Ma QZ, Wang YB, Cao GH, Wei T, Wang WH, Zhang TB, Physica C, 282, 2093,
(1997).
Acknowledgment
Committee members:
Profs. Rampi Ramprasad, Leon L. Shaw and Pamir S. Alpay
Profs. Puxian Gao and George A. Rossetti
Group students:
Ning, Luke, Tom, Ghanshyam and Hong
Computational resources:
IMS computation clusters; SGI supercomputer in SoE
Funding:
NSF & ACS-PRF
Backup slides
(P, T) dependence of O defects
•
DFT computations of O vacancy & interstitial formation energies as a function of defect
concentration … combined with … thermodynamic model yields (P,T) dependence of
stoichiometry
formation
E defect
 E defect  E perfect 

 
1 0
 O  kT ln PO2
2 2
Jiang et al
Appl. Phys. Lett. 87, 141917 (2005)
Pick up T, find P to
make formation energy
0, corresponding to
equilibrium condition.
C. Tang & R. Ramprasad
Appl. Phys. Lett. 91, 022904 (2007)
(P, T) dependence of interface morphology
T = 1200 K
T = 400 K
formation
coverage
E
N
 Ecoverage  Eabrupt  O2
2
P (coverage) 
e
rma tio n
 Ecofovera
g e / kT
e
rma tio n
 Ecofovera
g e / kT
coverage
“Hf-Si”
Interface
Abrupt Interface
“SiOx”
Interface
•
Pressure changes
could stabilize
silicide or SiOx
•
Increase in T
makes abrupt
Si:HfO2 interface
less stable
Si doped HfO2 (SDH)
(1-x) HfO2+xSiO2+Ef=Hf1-xSixO2
a1
a2
c-SDH
m-SDH
The local chemistry of Si
prefers SiO2 configuration
t-SDH
Y doped HfO2
Density Functional Theory
Hˆ i (r )   i i (r )
 (r ' )
1 2
ˆ
H     v pseudopot(r )  
d 3r '  XC [  (r )]
2
r  r'
occ
 (r )   i (r )
2
i
Initial guess of wave function & electron density
Set up Hamiltonian
Energy, forces on atoms
New electron density
no
DE < Ebreak
yes
end
Accuracy of DFT
•
•
•
•
•
Structures (bond lengths, bond angles, lattice constants) predicted to within 1 % of
experiments
Material
Expt.
DFT
error
type
Ag (FCC)
4.09
4.11
0.6%
Metal
V (BCC)
3.03
3.02
0.3%
Metal
LaBi
6.57
6.65
1.2%
Alloy
Si
5.43
5.43
0.0%
Semicon
GaAs
5.65
5.66
0.2%
Semicon
HfO2
5.08
5.06
0.4%
Oxide
NbO
4.21
4.23
0.6%
Oxide
CoSi2
5.36
5.30
-1.1%
Silicide
ZrN
4.62
4.63
0.3%
Nitride
CaF2
5.46
5.50
0.6%
Halide
Elastic properties (bulk & shear modulus, etc.) accurate to within 5% of experiments
Bond energies, cohesive energies within 10% of experiments
Relative energies (energy difference between FCC & BCC, for example) are accurate
to within 2%
Band gaps are off by about 50% !!!
Si:HfO2 heterostructure models
Tetragonal HfO2-based
Monoclinic HfO2 -based
Mater
ial
k
E_gap
DEc
SiO2
3.9
8.9
3.2
amor
Si3N4
7
5.1
2
amor
Al2O3
9
8.7
2.1
amor
Y2O3
15
5.6
2.3
cubic
ZrO2
25
5.8
1.2
m, t, c
25
5.7
1.5
m, t, c
La2O3
30
4.3
2.3
Hex, cubic
Ta2O5
26
4.5
0.5
orthorhombic
unstable
TiO2
80
3.5
1.2
t, rutile,
anatase
unstable
E_gap
DEc
HfO2
Tc
400500
Doped
Tc
k
HfTaO
1000
-
HfSiO
1050
?
HfSiO
(N)
> 5
4.6
(~8)
HfYO
NA
HfAlO
> 900
HfLaO
> 900
Structure
Structure
unstable (&
hygroscopic)
Comments
2.1(2.4VBO)
JAP-87-484
data source
thinner IL
apl-85-2893
amor
sharp interface
JAP-87-484
various Eg, CBO
reported
app.surf.sci.253-2770
cubic
5.6
(RPP, 69, 327, Robertson)
amor
amor
1823
data source
Wallace & Wilk 2003
0.5-1.5
(3.0VBO)
27
Comments
amor
apl-86-102906
reduce mobility
IEEE-ele. Dev. Lett-24-556
apl-89-032903 & 85-3205 &
88-202903
Why HfO2
Source: R. M. Wallace and G. D. Wilk, Crit. Rev. Solid State Mater. Sci. 28, 231
Influence of defects on performance
• Charges are trapped in defects, shifting
threshold voltage and making operation
unstable.
• Trapped charges scatter carriers in the
channel  lower carrier mobility
• Cause unreliability (oxide breakdown)
Effect of F
• (APL 90, 112911)
– Remove midgap states from Hf dangling
bonds at HfO2/SiO2 interface;
– Excessive F increase leakage current.
• (APL 89, 142914)
– Defect passivation