MagDot Participant No.6 MagDot Participant No.6 Institute of - - PowerPoint PPT Presentation

Principal Investigator: Principal Investigator: Miroslav Kotrla Theoretical Department, IPASCR kotrla (at) fzu.cz

MagDot MagDot Participant No.6 Participant No.6

http:// http://www.fzu.cz www.fzu.cz Institute of Physics, Academy of Sciences of the Czech Republic Na Slovance 2, Prague 8, Czech Republic

12.5.2009 Third MagDot Workshop - Napa 2

• IPASCR &

IPASCR & MagDot MagDot

• subm

submo

• nolayer growth

nolayer growth, , MBE MBE and and PLD PLD

mode mode

– – Fe Fe/Mo(110) /Mo(110): experiments and model for : experiments and model for KMC KMC simulations simulations – – results for results for island density vs. temperature island density vs. temperature – – comparison comparison: : MBE MBE vs. vs. PLD PLD

• morfology

morfology

• f islands grown
• f islands grown on BCC(
• n BCC(110

110): MBE ): MBE – – realistic realistic model model of Fe

• f Fe/Mo(110) system

/Mo(110) system – – dependence of dependence of island shapes island shapes

• n T and interactions
• n T and interactions
• conclusion

conclusion

Early Stage

• f

MBE and PLD Growth in Fe/Mo System

Participation of IPASCR in Participation of IPASCR in MagDot MagDot

• Miroslav Kotrla

Miroslav Kotrla – – Principal Investigator Principal Investigator

• Martin

Martin Ma Maší šín n

• researcher

researcher

• postdoc

postdoc (D. (D. Goykolov Goykolov) since ) since Oc Oct to

• ber

ber 2007 2007

• Ond

Ondř řej ej Mar Maršá šálek lek

• graduate student

graduate student

• f
• f Mathematical & Physical

Mathematical & Physical Faculty of Charles University, Prague Faculty of Charles University, Prague

Currently involved people: Currently involved people: External: External:

Sebastian Weber - University of Wuezburg

growth of strained alloys

info on SimNANO Wiki http://simnano.fzu.cz/

Project MetHet

• S. Weber et al., J. Phys.: Cond. Matt. 20, 265004 (2008)

Participation of IPASCR in Participation of IPASCR in MagDot MagDot

kinetic Monte Carlo (KMC) kinetic Monte Carlo (KMC) wo workpackage rkpackage 2 – – real ealist stic Kinet ic Kinetic Monte Car c Monte Carlo Task: Task: Method: Method: Formally: Formally: atomistic modeling of initial stages atomistic modeling of initial stages

• f growth –
• f growth –

submonolayer submonolayer growth rowth

Early stage of MBE and PLD growth in Fe/ Mo system

This workshop: This workshop:

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Submonolayer Submonolayer growth growth

• nucleation

nucleation

• aggregation

aggregation

• coalescence

coalescence

Observed quantity:

Density of islands N

Coverage: Succession of regimes:

ML 1 Θ 

Importance: Importance: (i) the formation of surface features (ii) measurements of surface diffusion

Methods of study

experimental: STM, AFM thery: KMC, rate equations

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Evolution of island density Evolution of island density Ag/ Pt(111) Ag/ Pt(111)

H.Brune H.Brune et al. PRL et al. PRL 73 73, (1994) 1955 , (1994) 1955 a) a) 0.0024 ML 0.0024 ML b) b) 0.006 ML 0.006 ML c) c) 0.03 ML 0.03 ML d) d) 0.06 ML 0.06 ML

There is an interval

• f coverage with

saturated island density

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Arrhenius plot for saturated Arrhenius plot for saturated island density island density

H.

• H. Brune

Brune et al. PRB. et al. PRB. 52 52 (1995) R 14380 (1995) R 14380.

Ag/Pt(111) Ag/Ag/Pt(111) Ag/Ag(111)

 

S D B

N exp -E /k T ฀

E ED

D

can be estimated from can be estimated from an experimental data an experimental data

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Two modes of growth:

some references on PLD: some references on PLD:

MBE – Molecular beam epitaxy PLD – Pulsed laser deposition

• H. Hinnenmann

et al. PRL. 87 (2001) 135701.

MBE MBE -

• extensively studied in the past

extensively studied in the past

P.O Jubert, O. Fruchart, and C. Meyer Surface Science 522 (2003) 8.

MagDot MagDot

Unusual Scaling for PLD Unusual Scaling for PLD

PLD PLD – – new additional parameters new additional parameters pulse repetition rate pulse repetition rate f

f, etc. , etc.

nucleation density nucleation density in PLD depends on in PLD depends on intensity I of pulses intensity I of pulses

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Pulsed laser deposition of Fe on Mo(110)

nucleation density N nucleation density Nx

x

vs vs. . temperature temperature

P.O Jubert, O. Fruchart, and C. Meyer Surface Science 522 (2003) 8.

experiment experiment

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Shape

• f

Fe islands in Fe/Mo(110) grown by MBE

• J. Prokop
• J. Prokop

et al. et al. PRB PRB 73 73 ( (2006 2006) ) 014428 014428. M

• M. B

. Bod

• de et al.

e et al. PR PRL L 9 92 2 ( (2004 2004) ) 067201 067201.

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Microscopic KMC model Microscopic KMC model

• a solid

a solid-

• on
• n-
• solid model

solid model

• random deposition with flux F

random deposition with flux F

• diffusion: jump to

diffusion: jump to n.n n.n. position with . position with the rate the rate

 

b d D B D

nE E E , T /k E

• exp

k R   

Material parameters:

b d

k , E , E

T F,

Control parameters:

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Microscopic KMC model Microscopic KMC model

• a solid

a solid-

• on
• n-
• solid model

solid model

• random deposition with flux F

random deposition with flux F

• diffusion: jump to

diffusion: jump to n.n n.n. position with . position with the rate the rate

 

b d D B D

nE E E , T /k E

• exp

k R   

Material parameters:

b d

k , E , E

T F,

Control parameters:

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How How to to get get material material parameters parameters? ?

a) a)

fitting fitting experimental experimental data data

b) b)

f first irst principle principle calculation calculation

P.O Jubert, O. Fruchart, and C. Meyer Surface Science 522 (2003) 8.

Parameters for KMC simulations of Fe/Mo(110)

kinetic analysis of experiment performed but special character

• pulsed laser

deposition (PLD) considered DFT calculation

• f Mark Asta

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Parameters for Parameters for KMC KMC simulations of Fe/Mo(110) simulations of Fe/Mo(110)

a) a)

Jubert Jubert et al. et al.

b) b)

Mark Mark Asta Asta

varied and

E E

Y b X b

? k ? E ? E ? E

Y b X b d

   

Hz eV

11 d

10 8 k , 05 . 1 . E      Hz

12

10 4 k   eV eV 33 . E , 41 . E

b d

 

two sets used:

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Configurations of islands for different temperatures in MBE mode

T = 200 K T = 200 K T = 300 K T = 300 K T = 400 K T = 400 K

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Configurations of islands for different temperatures in MBE mode

T = 200 K T = 200 K T = 300 K T = 300 K T = 400 K T = 400 K

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Configurations for MBE and PLD (

(θ θ = 0.1 = 0.1) )

T = 400 K T = 400 K T = 500 K T = 500 K T = 400 K T = 400 K

MBE MBE,

, E E

b b

= 0.60 = 0.60 eV eV

PLD PLD,

, E E

b b

= 0.60 = 0.60 eV eV

PLD PLD,

, E E

b b

= 0. = 0.33 33 eV eV

T = 400 K T = 400 K T = 500 K T = 500 K T = 500 K T = 500 K

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Island density Nx as function of the inverse temperature

P.-O. Jubert, O. Fruchart, and C. Meyer Surface Sci. 522 (2003), 8

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Island density Nx as function of the inverse temperature

P.-O. Jubert, O. Fruchart, and C. Meyer Surface Sci. 522 (2003), 8

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Pulsed laser deposition vs. MBE

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Pulsed laser deposition vs. MBE continued

MBEvsPLD.png

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• IPASCR &

IPASCR & MagDot MagDot

• subm

submo

• nolayer growth

nolayer growth, , MBE MBE and and PLD PLD

mode mode

– – Fe Fe/Mo(110) /Mo(110): experiments and model for : experiments and model for KMC KMC simulations simulations – – results for results for island density vs. temperature island density vs. temperature – – comparison comparison: : MBE MBE vs. vs. PLD PLD

  morfology

morfology

• f islands grown
• f islands grown on BCC(
• n BCC(110

110): MBE ): MBE – – realistic realistic model model of Fe

• f Fe/Mo(110) system

/Mo(110) system – – dependence of dependence of island shapes island shapes

• n T and interactions
• n T and interactions
• conclusion

conclusion

Early stage

• f

MBE and PLD Growth in Fe/Mo System

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In In the the previous previous part: part:

ad i) ad i) Mark Mark Asta Asta group group calculated calculated binding binding energy energy for for Fe Fe-

• Fe

Fe dimer on dimer on Mo Mo(110) (110) up up to to sixth sixth neighbor neighbor

 

b

neighbor : nearest second third fouth fifth sixth : 0.3389 0.0717 0.07885 0.01005 0.004125 0.007475

E eV

   

12

k 4 10 Hz  

d b

E 0.41 , E 0.33 eV eV  

i) i)

more complex interaction more complex interaction

ii) ii)

true bcc(110) geometry true bcc(110) geometry

More realistic More realistic model model of Fe

• f Fe/Mo(110) system

/Mo(110) system

Two additional aspects needed Two additional aspects needed: :

simple cubic simple cubic

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ad ii) Computer realization of the bcc(110) lattice

Regular square lattice Representation of the bcc(110) lattice by square array - adding two next-nearest neighbors and allow jumps to their location. a a

1 2

b2 b1 To produce picture of the regular triangular lattice one need to perform coordinate system transformation: tilt the lattice. Coordinates transformation:

y' x'+b b = x

2x 1x

y' x'+b b = y

2y 1y

b , b , b , b - correspondent projections of the unit vectors in the bcc(110) coordinate system to the

• rthogonal axes.

x', y' – coordinates in the bcc(110) lattice coordinate system

1x 2x 1y 2y

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Snapshot of the lattice before and after transformation

b2 b1 Square lattice before the transformation bcc(110) lattice after the transformation a a

1 2

Coordinate system before the transformation Coordinate system after the transformation Due to this kind of transformation boundary islands are getting distorted. In the following simulation pictures they are deleted. For Molibdenium tilting angle is α=19.47º. α Coordinates transformation (for molibdenum):

' + x' = x 0.5774y 0.8165 ' = y 0.8165y

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Model with interactions up to third neighbor

Lattice geometry Adatom Nearest neighbors that interact with adatom (I – first, II – second, III – third nearest neighbors Arrows – allowed directions of adatom hop En - with the first nearest neighbor (0.14 .. 0.329 eV) E2n - with the second nearest neighbor (0 .. 0.15 eV) E3n - with the third nearest neighbor (0 .. 0.1 eV) Interaction energies: Es - with the substrate (0.2 .. 0.4 eV) Other model parameters: Fvib – vibrational frequency (2x1012 .. 4x1012 Hz) ( Lattice size in the range 300x300 .. 1000x1000

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T=350K T=360K T=370K T=400K T=390K T=380K

Transition from the fat-fractal to compact island shape

Shown are fragments of the 300x300 lattices: En=0.329 eV, Enn=0.072 eV, Flux=0.01 ML/s, Θ=0.05 ML, ν=4x10 Hz

12

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En=0.33 eV En=0.36 eV En=0.4 eV En=0.55 eV En=0.5 eV En=0.45 eV

Dependence of the island shape on the NN binding energy

Shown are fragments of the 300x300 lattices: Enn=0 eV, T=400K, Flux=0.01 ML/s, Θ=0.1 ML, ν=4x10 Hz

12

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Change of Island Shape with Temperature

T=325K T=350K T=400K T=500K T=450K T=425K Conditions of simulations: 300x300 lattice (T=325..450K) 1000x1000 lattice (T=500K) Flux = 0.01 ML/s θ = 0.05 ML Fvib = 4x1012 Hz Es = 0.4 eV En = 0.329 eV E2n = 0.072 eV E3n = 0.079 eV Shape evolution with coverage Scale: θ=0.01 ML θ=0.05 ML Coverage step = 0.01 ML

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Island Shape for Scaled Energies and Higher Temperature

We have used scaled energies and temperature to reduce computation time. Since simultaneous scaling does not change the hopping rates, we may claim, that the results for scaling factor 0.5 are the same as for the factor equal to 1. Scale: θ=0.01 ML θ=0.05 ML Coverage step = 0.01 ML Conditions of simulations: 300x300 lattice Flux = 0.01 ML/s θ = 0.05 ML T = 350K Fvib = 4x1012 Hz Es = 0.2 eV En = 0.1645 eV E2n = 0.036 eV E3n = 0.0395 eV scaling factor = 0.5 The same result may be obtained for calculated energies and T=700K, which is observed in

• J. Prokop, A. Kukunin, and H. J. Elmers, Phys. Rev. B 73, 014428 (2006).

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Change of Island Shape with Temperature

Insets: examples of the island shape at the particular temperatures

Quantitative parameter to study island shape: average aspect ratio. Average aspect ratio is defined as average ratio of transversal and longitudinal dimensions of the islands. Conditions of simulations: 300x300 lattice (T=180..200K) 600x600 lattice (T=210..230K) 1000x1000 lattice (T=240K) Flux = 0.01 ML/s θ = 0.1 ML Fvib = 2x1012 Hz Es = 0.2 eV En = 0.14 eV E2n = 0 E3n = 0.06 eV Data points for 300x300 lattice are averaged over 10 runs. Data points for 600x600 and 1000x1000 lattice are averaged

• ver 5 runs.

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Average Aspect Ratio vs E2n

(E2n = 0.14 eV) Insets: examples of the island shape at the particular values of E2n

Conditions of simulations: 300x300 lattice Flux = 0.01 ML/s θ = 0.1 ML T = 230K Fvib = 2x1012 Hz Es = 0.2 eV En = 0.14 eV E3n = 0.03 eV Data points are averagd

• ver 10 independent runs.

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Average Aspect Ratio vs E3n

Insets: examples of the island shape at the particular values of E3n

Conditions of simulations: 300x300 lattice Flux = 0.01 ML/s θ=0.1 ML T=250K Fvib = 2x1012 Hz Es = 0.2 eV En =0.14 eV E2n =0.04 eV Data points are averagd

• ver 10 independent runs.

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Special Case: Islands with Extra Facet

We get the shape that resemble hexagons under the special condition: when interaction energies with the first and second nearest neighbors are approximately the same. Conditions of simulations: 300x300 lattice Flux = 0.01 ML/s θ=0.1 ML; T=400K Fvib = 4x1012 Hz Es = 0.4 eV; En =0.15 eV E2n =0.13 eV; E3n =0 Conditions of simulations: 300x300 lattice Flux = 0.01 ML/s θ=0.1 ML; T=480K Fvib = 4x1012 Hz Es = 0.4 eV; En =0.15 eV E2n =0.15 eV; E3n =0 Scale: θ=0.01 ML θ=0.05 ML Coverage step = 0.01 ML

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Conclusions Conclusions

 

subm submo

• nolayer

nolayer growth growth & & lattice lattice KMC KMC

• choice
• f

parameterts for KMC simulation

• f

Fe/Mo(110) discussed

• results
• f

lattice KMC simulations:

• Arrhenius

plot for island density were calculated and compared with the PLD experiment,

• PLD vs. MBE
• anomaly

in PLD (more M. Mašín)

  island island morphology morphology

• n BCC(110)
• n BCC(110) surface

surface

• island shape

– morfological transition with the temperature and binding interactions

• averaged

aspect ratio measured

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Presentations Presentations

• the

17th Int. Vacuum Congress (IVC-17), 13th Int. Conference on Surface Science (ICSS-13), Int. Conference on Nanoscience and Technology (ICN+T 2007) Stockholm, Sweden (July 2-6, 2007) Nano-pattern formation in strained 2D metallic alloys: comparison of simple cubic(100) and fcc(111) surfaces by M. Kotrla, S. Weber, M. Biehl (talk)

• the

CCP2007 - International Conference

• n Computational

Physics, Brussels (Sep. 5-8, 2007) Pulsed depositions vs. continuous growth: Monte-Carlo study of sub-- monolayer regime by M. Masin, and M. Kotrla (poster)

• the
• Int. conference NANO'07,

Brno, October, 8-10, 2007 Self-assembled nano-patterns in strained 2D metalic alloys: stripes vs. islands by M. Kotrla, S. Weber, F. Much, M. Biehl, W. Kinzel (talk)

12.5.2009 Third MagDot Workshop - Napa 37

Presentations Presentations cont.

• nt.
• Self-assembled nanopatterns

in strained 2D alloys on fcc(111) surface: equilibrium Monte Carlo simulation

• the

17th Int. Vacuum Congress (IVC-17), 13th Int. Conference on Surface Science (ICSS- 13), Int. Conference on Nanoscience and Technology (ICN+T 2007) Stockholm, Sweden (July 2-6, 2007) Nano-pattern formation in strained 2D metallic alloys: comparison of simple cubic(100) and fcc(111) surfaces by M. Kotrla, S. Weber, M. Biehl (talk)

• the

CCP2007 - International Conference

• n Computational

Physics, Brussels (Sep. 5-8, 2007) Pulsed depositions vs. continuous growth: Monte-Carlo study of sub--monolayer regime by M. Masin, and M. Kotrla (poster)

• ECOSS ,

Brno, October, 8-10, 2007 Self-assembled nano-patterns in strained 2D metalic alloys: stripes vs. islands by M. Kotrla, S. Weber, F. Much, M. Biehl, W. Kinzel (talk)

Work in Progress

The modified model:

• 1. Hopping rate that depends on the atomic configuration before and after the jump

Atoms involved in one hopping event I, II and III – first, second and third nearest neighbors. Indexes i, f labels neighbors at the initial and final positions of the hopping atom.

Eif = Es + (Nn – μMn )En + (N2n – μM2n )E2n + (N3n – μM3n )E3n

Energy barrier is now calculated as follows:

Eif – diffusion barrier for jump from initial to final position Es – diffusion barrier of the free adatom Nn , N2n , N3n – number of first, second and third nearest neighbors before the jump Mn , M2n , M3n

• number of first, second and third nearest

neighbors after the jump En , E2n , E3n – interaction energies of the adatom with first, second and third nearest neighbors μ – influence of the atomic configuration after the jump

• 2. Hopping rate now depends on the direction of jump: allows to select and treat separately

some special jumps (edge diffusion, detachment, etc.)

Results of the new code Comparison of the lattice configurations obtained under the same conditions: Conditions: 300x300 lattice Flux = 0.01 ML/s θ = 0.1 ML T = 300 K Fvib = 4x1012 Hz Es = 0.4 eV En = 0.329 eV E2n = 0.072 E3n = 0.079 eV Old code New code. μ = 0.05

Shape of the compact islands Old code conditions: 1000x1000 lattice Flux = 0.01 ML/s θ = 0.05 ML T = 500 K Fvib = 4x1012 Hz Es = 0.4 eV En = 0.329 eV E2n = 0.072 E3n = 0.079 eV New code conditions: 300x300 lattice Flux = 0.01 ML/s θ = 0.1 ML T = 300 K Fvib = 4x1012 Hz Es = 0.4 eV En = 0.329 eV E2n = 0.072 E3n = 0.079 eV μ = 0.05