First Principles Studies of Defects in HfOFirst Principles Studies of Defects in HfO22 and at Si:HfOSi:HfO22 Heterojunctions Heterojunctions

Chunguang Tang ( 唐春光 )(Bachelor Eng.: Univ. Sci. Tech. Beijing)

(Master. Sci.: NUS)

Chemical, Materials & Biomolecular EngineeringInstitute of Materials Science

University of Connecticut

Principal Advisor: Prof. R. Ramprasad Associate Advisor: Prof. L. Shaw Associate Advisor: Prof. P. S. Alpay

Ph.D. Dissertation Proposal

Introduction: device miniaturization

# of

tr

ansi

stor

s

First transistor radio: 4 transistors.

Quad core processor contains 820 million transistors

high k (dielectric constant) transistor

K ~ 4

K ~ 30

High k issuesHigh k issues• Formation of interface phases (SiOx, silicate, Hf-Si)

– Effects of oxygen point defects*• Point defects migration may contribute to interfacial phase formation • High oxygen pressure favors silica & low pressure favors Hf silicide

Locquet et al, JAP (2006);Stemmer et al

Wong et al, Microelectronic Eng. (2006)

* 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

– Doped HfO2 with alloying elements.• Si, Y, La, F, N• Increase crystallization temperatures• Stabilize higher k phases

amorphous cubic tetragonal monoclinic k ~ 30 k ~ 29 k ~ 70 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 MethodsComputational Methods• Density Functional Theory (DFT)

– Many nuclei-many electron problem one electron problem

– 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.

rrrVm iiieff

2

2

2

0 1 2 3 4

Reaction path Emigr.E

Completed Research• Bulk HfO2 results

E/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)

Table I: relative energies (eV) and lattice constants (Å) of bulk HfO2

Defects in bulk HfO2

Eform + 1 O atom

Eform = Evac+ (EO2)/2 - Eperf

3-fold site 4-fold site

O interstitial 1.7 2.5

O vacancy 6.6 6.5

Hf vacancy 6.1

Table II: Formation energies (eV) of point defects in bulk HfO2

O interstitial Formation and Migration*O interstitial Formation and Migration*

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)

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).

Si HfO2

Hf

O

Experimental Emigr. of O interstitial in bulk Si: 2.44 eV** (2.26 eV, calculated)

O Vacancy Formation and Migration*O Vacancy Formation and Migration*

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)

Si HfO2

Hf

O

Hf Vacancy Formation and Migration*Hf Vacancy Formation and Migration*

• Hf vacancies prefer the interface

• Si strongly prefers to penetrate into HfO2

* C. Tang & R. Ramprasad, Appl. Phys. Lett., 92, 152911 (2008)

Hf vacancies could lead to the formation of Hf silicate

Hf

O

Si penetration

Accumulation of O Point Defects*Accumulation of O Point Defects*

Thermodynamics favors accumulation of point defects at interface, and consequently, the creation of Hf silicide or SiOx

* C. Tang & R. Ramprasad, Appl. Phys. Lett., 92, 182908 (2008)

“Hf-Si” InterfaceAbrupt Interface “SiOx” Interface

Si doped HfO2 (SDH)

c-SDH m-SDH t-SDH

(1-x) HfO2 + xSiO2 + Ef = Hf1-xSixO2

C-SDH

m-SDHt-SDH

1. If Si > 12% t-HfO2 most stable

2. The local chemistry of Si prefers SiO2 configuration

Y doped HfO2 (YDH)

(1-x) HfO2+(x/2)Y2O3+Ef=Hf1-xYxO2-x/2

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.

m-YDH

c-YDH

t-YDH

Charge neutrality 2 Y atoms & 1 O vacancy

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

• 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

Remaining research

Publication list1. 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).

AcknowledgmentAcknowledgment

Group students:

Ning, Luke, Tom, Ghanshyam and Hong

Committee members:

Profs. Rampi Ramprasad, Leon L. Shaw and Pamir S. Alpay

Profs. Puxian Gao and George A. Rossetti

Computational resources:

IMS computation clusters; SGI supercomputer in SoE

Funding:

NSF & ACS-PRF

Backup slides

(P, T) dependence of O defects(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

Jiang et alAppl. Phys. Lett. 87, 141917 (2005)

22

ln2

1 0OOperfectdefect

formationdefect PkTEEE

C. Tang & R. RamprasadAppl. Phys. Lett. 91, 022904 (2007)

Pick up T, find P to make formation energy 0, corresponding to equilibrium condition.

(P, T) dependence of interface morphology(P, T) dependence of interface morphology

• Pressure changes could stabilize silicide or SiOx

• Increase in T makes abrupt Si:HfO2 interface less stable

T = 400 KT = 1200 K

“Hf-Si” Interface Abrupt Interface “SiOx” Interface

22 Oabruptcoverageformation

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Si doped HfO2 (SDH)

c-SDH m-SDH t-SDH

The local chemistry of Si prefers SiO2 configuration

(1-x) HfO2+xSiO2+Ef=Hf1-xSixO2

1

2

Y doped HfO2

Density Functional Theory)()(ˆ rrH iii

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Initial guess of wave function & electron density

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Energy, forces on atoms

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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% !!!

Tetragonal HfO2-based Monoclinic HfO2 -based

Si:HfO2 heterostructure models

Material

Tc kE_ga

pc Structure Comments data source

SiO2   3.9 8.9 3.2 amor   Wallace & Wilk 2003

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    

HfO2400-500

25 5.7 1.5 m, t, c    

La2O3

  30 4.3 2.3 Hex, cubicunstable (& hygroscopic)

 (RPP, 69, 327, Robertson)

Ta2O5

  26 4.5 0.5orthorhombic

unstable JAP-87-484

TiO2   80 3.5 1.2t, rutile, anatase

unstable  

Doped

Tc kE_ga

pc Structure Comments data source

HfTaO

1000

-     amor thinner IL apl-85-2893

HfSiO

1050

? > 5   amor sharp interface JAP-87-484

HfSiO(N)

    4.6 (~8)

0.5-1.5 (3.0VBO)   various Eg, CBO

reportedapp.surf.sci.253-2770

HfYO NA 27     cubic   apl-86-102906

HfAlO

> 900

      amor reduce mobility IEEE-ele. Dev. Lett-24-556

HfLaO

> 900

18-23

5.6 2.1(2.4VBO) amor   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