Tutorial "Ion Implantation and Irradiation" - SPIRIT

Tutorial "Ion Implantation and Irradiation" 

Dresden, Germany, December 13-14, 2010 

Tel. +49 351 2602245 

E-mail w.moeller@fzd.de 

Internet http://www.fzd.de/FWI 

Fundamentals of Ion-Solid Interaction 

III: Computer Simulation 

Wolfhard Möller 

Forschungszentrum Dresden-Rossendorf, Dresden, Germany 

Institute of Ion Beam Physics and Materials Research 

Institute of Ion Beam Physics and Materials Research Prof. Wolfhard Möller

Computer Simulation of Ion-Solid Interaction 

V(R) 

Binary Collision 

Approximation 

(BCA) 

R 

Classical Molecular 

Dynamics (MD) 

V(R) 

Lattice Kinetic 

Monte Carlo (KMC) 

Institute of Ion Beam Physics and Materials Research Prof. Wolfhard Möller 

R 

E 

Coord. # 

T = 0, t < 10 -13 s T > 0, t < 10 -9 s T > 0, 10 -13 s < t < ∞

TRIM BCA Computer Simulation 

Trajectories of incident ions and all 

recoil atoms as sequence of binary 

collisions (BCA = Binary Collision 

Approximation) 

“Linear” cascade regime: Only 

collisions with target atoms at rest 

Validity: above E 10..30 eV 

(“Collisional phase” of the 

cascade) 

Collisional Transformation 

E E Tn 

nSes 

 

r r s 

, 

Tr 

, 

, 

TRIM = TRansport of Ions in Matter 

S e Electronic Stopping 

Cross Section 

n Atomic Density 

T n Nuclear Energy Loss 

(from ) 

Tr Angular Transformation 


E 

r 

, 

s 

, 

“State” of moving atom 

Energy E 

Coordinates r 

Flight Direction , 

Collisional Variables 

Free Pathlength s 

Polar Deflection 

Azimuthal Deflection 

Energy Loss E el


Amorphous Substance 

Position of target atoms and 

thereby impact parameter are 

randomly chosen 

Path is random 

Random Generator r 0 

, 1 

p 

Impact Parameter p 

Azimuthal Angle 

p 

max r 

2r 

Conservation of atomic density, 

one collision per target atom 

Constant free pathlength 

equal to mean atomic distance 

 

 

Fast algorithm for classical scattering 

integral (p) (“Magic Formula”) 

Multiatomic target materials 

Static target: No modification 

s 

p 


p 

2 

max 

 

n 

s 

 

1 

/ 

3 

n 

1 

 

p 

p max 

Biersack and Haggmark 

1978 

Eckstein and Biersack 

1982 (Sputter Version) 

Ziegler ~1980 ... 2010 

http://www.srim.org 

s


Classical Scattering Integral (CMS System) 

2 p 

V ( R ) 

R 

1 

min 

 

0 

1 

d 

R 

V 

1 

E 

2 

Z1Z 

2e 

 

 

4 

R 

0 

 

 

 

R c 

 

R 

 

a 

p 

R 

Screened Coulomb Potential 

Asymptotic Path Approximation 

Approximate Time Integral 

(Hard Sphere Approximation) 

 

t p tan R 0 

2 

t 

2 

2 

0 10 20 30 

x = R/a 


1 

f U(x) 

10 -2 

10 -4 

p 

Bohr 

R 

t 

 

t R 

HFS atomic calculations with 

linear superposition of atomic 

electron densities for 522 

projectile-target 

combinations 

“Universal” 

Fit 

Function 

R 

Thomas-Fermi

TRIM Energy Parameters 

Sputtering 

BCA Parameters 

Radiation 

Damage 

Ion 

Slowing 

Down 

Cutoff energy at which particle histories 

are terminated (~ 3 eV) 


Eco 

Bulk binding energy subtracted from 

nuclear energy transfer (often set to 0) Eb 

Surface binding energy for sputtering 

(enthalpy of sublimation for monoatomic 

materials: 2...8 eV; from thermodynamic 

data for multicomponent materials) 

Threshold energy of Frenkel pair 

formation for damage calculation 

(25...80 eV) 

Electronic stopping model (nonlocal, 

local) and data 

Es 

Ed 

Se

TRIM: Ion Trajectories 

Ions only 

Ions and recoil atoms 

4 ions 

100 ions 


TRIM: Range, Energy Deposition, Damage Profiles 

Projected Range 

Distribution (nm-1 ) 

Vacancy Distribution (nm -1 ) 

0.2 1 keV 

Ar + Si 

0 

5 

0 

0 

Depth (nm) 

10 

0 10 

Depth (nm) 


Energy Deposition (eV/nm) 

200 

0 

50 

0 

nuclear 

electronic

TRIM Results: Doping Profiles 


TRIDYN – Including Dynamic Alteration 

Collision cascade simulation as in TRIM 

Initially equidistant depth slabs 

(i=1,...,N) with thickness x 0 and 

fractional compositions c ik (k=1,...,M) 

for M different elements (including 

projectile) 

Each pseudoparticle (deposited, 

relocated or sputtered atom) in the 

computer simulation corresponds to 

an increment in areal density 

 

 

 

N 

tot 

pp 

tot Total Ion Fluence 

N pp Total Number of 

Pseudoprojectiles 

Only compositional information is 

provided. BCA is unable to treat 

sructure or morphology. 

For each incident pseudoprojectile, 

simulation in two steps: 

Slowing down and cascade formation, 

implantation, sputtering and 

relocation 

Relaxation of depth intervals 

according to fixed atomic volumes 

Möller, Eckstein and Biersack 1984 


TRIDYN Dynamic Relaxation 

After termination of pseudoprojectile and recoil 

histories, new areal densities ik are calculated 

all components and depth intervals. From these 

Fractional 

Compositions 

Total 

Atomic 

Densities 

Slab 

Thicknesses 

Limitation 

of Slab 

Thicknesses 

cik 

1 

n 

tot 

i 

x 

0. 

5 

i 

 

ik 

 

j 

 

j 

 

1 

n 

tot 

i 

ij 

c 

n 

ij 

0 

j 

 

j 

n j 0 Pure Element 

Atomic Densities 

ij 

xi 

1. 

5 

x 

Otherwise Splitting 

or Combination 

0 

For reasonable statistics 

and precision, the relative 

change per slab has to be 

kept sufficiently small, by 

choosing Δν small enough. 

From experience, 

0. 

05 


max 

i 

 

i 

 

 

 

 

i 

 

per pseudoprojectile

TRIDYN - Artificial Add-ons 

Local Saturation 

e.g., stoichiometric limitation 

Feeding excess into vacuum ("reemission") 

or to flanks of profile ("diffusion") 

Molecular Release 

e.g., by local saturation or by bond breaking 

Release 

R 

2 

fc 

c concentration of 

excess or free atoms 

Matrix Effects in Sputtering: Simple Model 

Sputter yield of a specified component depends 

linearly on surface concentration of another 

component 

Molecular Sputtering: Simple Model 

Diatomic "molecular" yield is assumed to be 

proportional to product of monomer yields 

Y 


Implant Concentration 

M 

i 

f 

i 

M 

, j 

c 

s, 

j 

f predefined factor 

Y 

mol 

i, 

j 

f 

f Predefined 

Factor 

Depth 

mol 

i, 

j 

YY 

i 

j 

C max

TRIDYN Applications 

Implant Concentration 

Partial Sputtering Yields 

High-Fluence Implantation 

Fluence 

Depth 

Preferential Sputtering 

A 

B 

Time or Fluence 

A xB y 

Ion Mixing 

A B 

Depth 


Atomic Fractions 

Atomic Fractions 

Ion-Assisted Deposition 

B 

A 

Depth 

A o 

B + 

A B 

C 

C


Ion-Beam Assisted Deposition 

of Boron Nitride 

0 

0 0.4 0.8 1.2 1.6 20 


N/B Bulk Ratio 

3.0 

2.4 

1.8 

1.2 

0.6 

500 eV N + 

N + 

Expt. 

w/o 

N/B Flux Ratio 

Ag 

TRIDYN 

with 

molecular 

reemissio 

n 

W. Möller and D. Bouchier, SCT 45(1991)73 

B


Target Poisoning during 

Reactive Magnetron Sputtering 

Ion (Ar + ,N 2 + ,N + ) and radical (N 0 ) fluxes 

from simple 0D plasma model 

Sticking 0 

N 2 addition (mol%) 

TRIDYN 

Ar+N 2 

→ Ti 

Sticking 1 

W. Möller and D. Güttler, JAP 45(2007)094501 


3D Lattice Kinetic Monte Carlo Simulation 

Precipitate 

Detachment 

Monomer 

Attachment 

Diffusion 

Empty 

Site 

"Ising" Model: Configurational energy 

of each atom depends only on 

occupied 

number of 

lattice 

nearest 

site 

neighbours 

selected Probability for of jump attempt from 

initial site i to final site f 

empty lattice site 

diffusion jump 

detachment jump 

attachment 0 jump 

{ 

1 if Ni 

N f 

E p 

N i N 

f 

kT e else 


w 

Ed Ep Ni,f if 

 

 

0 

e 

Ed 

 

kT 

Attempt frequency 

Activation energy of diffusion 

Energy gain per nearest neighbour 

Initial and final number of nearest 

neighbours

Ostwald Ripening by LKMC Simulation 

GT Equation Reproduced 


Inverse Ostwald Ripening by LKMC Simulation 

Start 

Conventional OR Inverse OR

Tutorial "Ion Implantation and Irradiation" - SPIRIT

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