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Multi-scale modeling of High-k oxides growth: kinetic Monte-Carlo simulation. Guillaume MAZALEYRAT Ph-D supervisors: Alain ESTEVE & Mehdi DJAFARI-ROUHANI. January 4 2006, LAAS-CNRS, Toulouse. Outline. PART 1: Introduction and methodological choices PART 2:

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multi scale modeling of high k oxides growth kinetic monte carlo simulation
Multi-scale modeling of High-k oxides growth: kinetic Monte-Carlo simulation


Ph-D supervisors: Alain ESTEVE & Mehdi DJAFARI-ROUHANI

January 4 2006, LAAS-CNRS, Toulouse.



Introduction and methodological choices


Lattice based kinetic Monte-Carlo algorithm (HfO2)


Exploitation, validation and results


Introduction and methodological choices

  • High-k oxides: Why? How?
  • Methodology: available approaches overview
  • Multi-scale strategy
  • The “Hike” project
  • Our goal: first predictive and generic kMC tool for high-k oxides deposition (ALD first steps, kinetics, process optimization…)

Why high-k oxides ?

  • MOSFET evolution: “scaling”

Intel Corp.

ITRS 2004


Why high-k oxides ?

  • To extend Moore’s Law

Problem: high leakage current through the gate.

A solution: use a gate oxide of greater permittivity than SiO2.

Intel Corp.


High-k oxides implementation into microelectronics

  • Materials properties considerations
  • High permittivity
  • Sufficient band offset (to minimize leakage)
  • Low fix charges density (for reliable threshold voltage)
  • Low interface states density (to keep an acceptable mobility in the channel)
  • Low dopant diffusivity (to keep them in the electrode or the channel)
  • Limitation of SiO2 regrowth (which would reduce the capacitance)
  • Amorphous phase or at least few grain boundaries (to minimize leakage)
  • Process considerations
  • Known solution for the gate electrode
  • High-k oxide deposition process compatibility (with other materials, with industrial needs)
  • High-k oxide (itself) compatibility with other CMOS processes (e.g. crystallization problems, dopant diffusivity)
  • Reproducibility
  • Reliability

The “Hike” project:

  • New simulation tools for High-k oxides growth: Atomic Layer Deposition of HfO2, ZrO2, Al2O3
  • NMRC/Tyndall, Ireland (S. Elliott):


  • Motorola/Freescale, Germany (J. Schmidt):

DFT/mechanisms, molecular dynamics, rate equations

  • University College London, United Kingdom (A. Schluger, J. Gavartin):

interface, defects, dopant diffusivity

  • Infineon, Germany (A. Kersch):

reactor scale and feature scale simulations

  • LAAS-CNRS (G. Mazaleyrat, A. Estève, M. Djafari-Rouhani, L. Jeloaica): DFT/mechanisms, kinetic Monte-Carlo

Phase 1 :

Precursor pulse

Phase 2 :

Precursor purge

Phase 3 :

Water pulse

Phase 4 :

Water purge


High-k oxides implementation into microelectronics

  • Process choice: Atomic Layer Deposition (ALD)

Methodology: available approaches overview

Available experimental data:

IR spectroscopy, X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), low energy ion scattering (LEIS)…


Macroscopic simulations:

feature scale and reactor scale.


Experimentation, Macroscopic simulations

Kinetic Monte-Carlo

ab initio / DFT / MD




About 100 atoms

Time scale: picoseconds

Up to millions of atoms

Time scale: seconds

Multi-scale strategy

  • Microscopic – Mesoscopic - Macroscopic

Lattice based kinetic Monte-Carlo algorithm (HfO2)

  • Preliminary considerations: space and time scales
  • Lattice based model: how the atomistic configuration is described
  • Temporal dynamics: how the atomistic configuration changes
  • Elementary mechanisms: some examples

Preliminary considerations:

  • Space scale: lattice based model


Preliminary considerations:

  • Time scale: simulation algorithm choice


Attainable phenomenon duration: second

Realistic evolution

Monte-Carlo steps have time meaning


Conventional HfO2 cell on substrate

Discrete locating model

Si (layer k=1) Hf (k=2 and even layers)

Ionic oxygen (k + 1/2) Hf (k=3 and odd layers)

2D cell

Lattice based model

  • Merging different structures into one framework

Lattice based model

  • Other aspects: strands, contaminants…

Example: non-crystalline HfCl3 group, bound to the substrate via one oxygen atom.

  • Non-crystalline aspects:
  • Non-crystalline Hf
  • Non-crystalline O
  • OH strands
  • Cl strands
  • HCl contamination
  • H2O

Lattice based model

  • Substrate initialization (example)

Si (100) layer (k=1)


User defined OH and siloxane distributions (random, row, or cross…)


Large variety of available substrates


Lattice based model

  • Zhuravlev model for substrate initialization

From the Monte-Carlo point of view, OH density is the percentage of sites that have an OH


Temporal dynamics

  • Mechanisms and events (definitions)

Mechanism = elementary reaction mechanism with associated activation barrier E≠

Site = one cell within the lattice, located by (i,j,k) indexes and containing occupation fields (can be empty)

Event = Mechanism + Site, (depending on the local occupation, can be possible or not, thus must be “filtered”)


Temporal dynamics

  • Acceptances and occurrence times calculation

Arrhenius law derived acceptance with attempt frequency ν

for all other mechanisms:

Maxwell-Boltzmann statistics derived

acceptance for arrival mechanisms

(1-precursor and 2-water):

Occurrence time of event « mechanism m on site (i,j,k) », if possible :

where Z is a random number between 0 and 1


Events filtering

Occurrence times


and comparison




Temporal dynamics

  • Summary: the kinetic Monte-Carlo cycle

Occurrence of the event of smallest occurrence time


Phase 1 : Precursor Pulse

- duration T1

- temperature Th1

-pressure P1

Phase 4 : Water Purge

- duration T4

- temperature Th4

Phase 2 : Precursor Purge

- duration T2

- temperature Th2

Phase 3 : Water Pulse

- duration T3

- temperature Th3

- pressure P3

Temporal dynamics

  • ALD cycle + kMC cycle

As the kMC cycle works, ALD parameters change periodically:


Mechanisms: complete list

01 MeCl4 adsorption

02 H2O adsorption

03 MeCl4 Desorption

04 HCl Production

05 H2O Desorption

06 Hydrolysis

07 HCl Recombination

08 HCl Desorption

09 Dens. Inter_CI_1N_cOH-iOH (all k)

10 Dens. Inter_CI_1N_cOH-iCl (all k)

11 Dens. Inter_CI_1N_cCl-iOH (all k)

12 Dens. Inter_CI_2N_cOH-iOH (all k not2)

13 Dens. Inter_CI_2N_cOH-iCl (all k not2)

14 Dens. Inter_CI_2N_cCl-iOH (all k not2)

15 Dens. Intra_CI_1N_cOH-iOH (k=2)

16 Dens. Intra_CI_1N_cOH-iCl (k=2)

17 Dens. Intra_CI_1N_cCl-iOH (k=2)

18 Dens. Intra_CC_1N_cOH-cOH (k=2)

19 Dens. Intra_CC_1N_cOH-cCl (k=2)

20 Dens. Intra_CC_2N_cOH-cOH (k=2)

21 Dens. Intra_CC_2N_cOH-cCl (k=2)

22 Dens. Bridge_TI_2N_tOH-iOH (k=2)

23 Dens. Bridge_TI_2N_tOH-iCl (k=2)

24 Dens. Bridge_TI_2N_tCl-iOH (k=2)

25 Dens. Bridge_TI_3N_tOH-iOH (k=2)

26 Dens. Bridge_TI_3N_tOH-iCl (k=2)

27 Dens. Bridge_TI_3N_tCl-iOH (k=2)

28 Dens. Bridge_TC_3N_tOH-cOH (k=2)

29 Dens. Bridge_TC_3N_tOH-cCl (k=2)

30 Dens. Bridge_TC_3N_tCl-cOH (k=2)

31 Dens. Bridge_TC_4N_tOH-cOH

32 Dens. Bridge_TC_4N_tOH-cCl

33 Dens. Bridge_TC_4N_tCl-cOH

34 Dens. Bridge_TT_3N_tOH-tOH (k=2)

35 Dens. Bridge_TT_3N_tOH-tCl (k=2)

36 Dens. Bridge_TT_4N_tOH-tOH

37 Dens. Bridge_TT_4N_tOH-tCl

38 Dens. Bridge_TT_5N_tOH-tOH

39 Dens. Bridge_TT_5N_tOH-tCl

40 Siloxane Bridge Opening

Suggested by…

-DFT studies

-kMC investigation



Mechanisms (some examples)

  • HfCl4 adsorption (from DFT)

Mechanisms (some examples)

  • Dissociative chemisorption (from DFT)

Mechanisms (some examples)

  • Densification mechanisms purpose

Mechanisms (some examples)

  • Densification: interlayer non-cryst./cryst. (from kMC)

Mechanisms (some examples)

  • Densification: multilayer non-cryst./tree (from kMC)

Mechanisms (some examples)

  • Siloxane bridge opening (from experiments)

Exploitation, validation and results

  • Hikad simulation platform
  • ALD first steps
  • Growth kinetics: transient regime
  • Growth kinetics: steady state regime

Hikad simulation platform

  • ‘Hikad’ = simulation application ‘kmc’ + analysis application ‘anl’
  • Written in Fortran90
  • Running on Linux (kernel 2.6)
  • Using ‘AtomEye’, free atomistic configuration viewer: Ref: J. Li, Modelling Simul. Mater. Sci. Eng.11 (2003) 173

Hikad simulation platform

  • Main features
  • ZrO2, HfO2 and Al2O3 ALD
  • ALD thermodynamic parameters (link with experimental data)
  • Start from an existing atomistic configuration file (Recovery option)
  • Initial substrate atomistic configuration customization
  • Feedback options (log file + automatic configuration/graphic files export)
  • Back up option
  • Evolutivity
  • Steric restriction switch (for big precursors)
  • Mechanisms activation energies
  • Performance
  • Huge substrates compared to ab initio or DFT
  • Up to 1015 events
  • Improved events filtering (SmartFilter option)
  • Shortcuts method preventing fast flip back events (SmartEvents option)
  • Computation effectiveness analysis
  • Analysis
  • Simulation data analysis, even during simulation job
  • Easy and fast browsing through events using bookmarks (find event, ALD phase, ALD cycle...)
  • Atomistic configuration visualisation using AtomEye
  • Snapshots (jpeg, ps or png formats)
  • Configuration analysis (substrate, coverage, coordination...)
  • Batch processing

ALD first steps

  • Coverage vs. substrate initialization

ALD first steps

  • Coverage vs. substrate initialization

One precursor pulse phase:

100ms, 1.33mbar, 300°C

-Best start substrates: 50% and Random on dimers

-Crystallinity seems too high (because of 0.5eV barrier)


ALD first steps

  • Early densifications barrier fit

One precursor pulse phase:

90% OH, 200ms, 1.33mbar, 300°C

Criteria: 90% OH => 80% coverage (exp.)

=> Densifications barriers: 1.5 eV


ALD first steps

  • Coverage vs. Deposition temperature

Precursor pulse phase:

50ms, 1.33mbar + purge

-Low temperatures: chemisorptions can’t occur

-High temperatures: poor OH density

=> Optimal temperature: 300°C


ALD first steps

  • Surface saturation

One precursor pulse phase:

1.33mbar, 300°C

Saturation: 48% coverage for a 90ms long pulse


Growth kinetics: transient regime

  • Coverage for 10 ALD cycles

Pulse phases: 1.33mbar, 300°C

+ purges

Fast first cycle, then slow growth…

73% coverage saturation = simulation artefact


Growth kinetics: transient regime

  • Siloxane bridge opening barrier fit

800ms water pre-treatment

then: 50ms precursor pulse

1.33mbar, 300°C

OH density increase => higher coverage after precursor pulse

Experimental fit => siloxane bridge opening barrier = 1.3eV


Growth kinetics: transient regime

  • End configuration

-Poor crystallinity for first layer

-High cristalinity above

-Poor crystallinity and filling on top because of “blocking states” (simulation artefact)

-First layer will never be full nor dense: bridge densifications needed

-Hard to achieve 100% substrate coverage, “waiting” for SiOSi openings

-“Blocking states” are visible (“trees”)


Growth kinetics: steady state regime

  • Start configuration for steady state regime



Growth kinetics: steady state regime

  • End configuration

-Very high crystallinity for most of layers

-Again: poor crystallinity and filling on top because of “blocking states” (simulation artefact)

-Growth works better (no waiting effect)

-“Blocking states” are visible (“trees”)


Growth kinetics: speeds

Hard to obtain a reliable and stable growth speed because of blocking effect

Steady state regime simulations suffer less

Transient regime

Steady state regime

Vt,exp = 7E+13 Hf/cm²/cycle (TXRF)

Vs,exp = 12E+13 Hf/cm²/cycle (TXRF)


1st cycle

Fast initial Si-OH sites saturation

Steady state regime (Vs>Vt)

HfO2 growth onto HfOx(OH)y (more OH)

Amount of deposited Hf atoms

Transient regime (Vt)

“Waiting” for siloxane bridges openings until full SiO2 coverage.

ALD cycle

Growth kinetics: conclusions

  • Original methodology:

- Multi-scale strategy

- First predictive tool at these space and time scales for high-k oxides growth

- Link between atomic scale considerations and industrial needs for process optimisation

  • Lattice based time continuous kinetic Monte-Carlo algorithm:

- Lattice based => millions of atoms

- Time continuous kMC => process duration

- Non-crystalline aspects: strands, contaminant, densification issues…

- Large initial substrates variety

- Each Monte-Carlo step has time meaning (variable duration)

- ALD process parameters (phases, duration, pressure, temperatures)

- Elementary mechanisms (suggested by DFT or kMC or Experiment)

  • Exploitation:

- Hikad simulation platform

- Powerful, flexible and “user friendly” Analysis tool (events browsing, atomistic viewer, batch analysis…)

- Generic method: MeO2 oxides (changing barriers), other precursors (using steric restriction switch)

  • Validation and first encouraging results:

- Substrate preparation dependence

- Optimal growth temperature

- Surface saturation

- Activation barriers calibration (densifications and siloxane bridge opening)

- Growth kinetics: two growth regimes, hard substrate coverage, but “blocking effect”



  • First:

- Reduce blocking effect with new densification mechanisms

- Add migration mechanisms, and lateral growth mechanisms to obtain complete substrate coverage and maybe grain boundaries

- Study coordination evolution and crystallisation

- Optimisation: keep on event smart filtering, add shortcuts procedure for water based mechanisms, maybe Kawasaki generic barriers for future simple mechanisms

  • Next:

- Simulate thermal annealing (migrations, crystallisation…)

- Study interfacial SiO2 regrowth, thanks to another existing kMC tool (Oxcad)

- Dopant migration

- Etching

- Standardisation