Fundamentals of Ion-Solid Interaction - 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 

II: Damage, Sputtering, Mixing, Synthesis 

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

Effects of Collision Cascade 

Sputtering 

Surface 

Erosion 

Ion 

Scattering 

Atomic Displacement 

Radiation Damage 

Atomic Mixing 

Recoil Implantation 

Ion 

Implantation 

TRIM Binary Collision Computer Simulation 

Ion Trajectories 

100 incident ions 

Recoil Distribution 

1000 incident ions 

1 keV 

Ar + Si 

0 Depth (nm) 10 


Cascade Regimes 

Linear Cascade Thermal Spike 

Low energy density 

No interaction between moving particles 

Sequence of binary collisions 

High energy density 

Interaction between moving particles 

Many-body interactions 

Thermal spike regime may be entered in the early phase 

of the cascade at sufficiently high energy density 

(e.g., heavy ion incidence at energy ~100 keV) 

Thermal spike regime is always entered in the 

thermalization phase of the cascade 

(at mean energies of the cascade atoms lower than solid-state 

binding energies - typically a few eV) 


Spatial Structure of Cascades 

E 0 

Light ions, high energies Heavy ions, low energies 

T 

T Nuclear Energy Transfer 

E 0 

T 

Spatial deposition of energy in cascade is often described by a Gaussian rotational ellipsoid 

E 0 

R D 

x,y 

z 

E0 

3 2 2 

z - R 

2 2 2 

D x y 

Dr 

exp - 

2 

2 

2 z 2 

z x 

x 

 

 

 

 

 

 

 

 

 

F 2 

(E 0) total energy deposited into nuclear collisions 

R D mean depth of nuclear energy deposition 

(exact values for R D, x and z best from collisional 

computer simulation) 

Similar average topology 

for multiple ion incidence 


Collisional Damage 

F 

T 

N 

T 

2U 

Cascade atom receives 

sufficient energy to 

become displaced 

Analytical hard-sphere approximation for number of 

resulting I-V pairs (or Frenkel pairs) (Kinchin and Pease) 

d 

T initial energy of recoil atom 

U d damage threshold energy 

(15 ... 80 eV depending on 

material) 

For dense cascades with >> U d, K-P formula holds for 

the total number of FP's generated by one incident ion 

E 

E 

0 

N F 0 Eo incident ion energy 

2Ud 

In dense cascades, I-V recombination might occur during the slowing-down 

phase. Further, corrections arise as part of the energy is dissipated into 

electronic collisions (about 10%), and from a more realistic interaction potential. 

eff 

E 

NF 0 x 

U 

0 

E 

0. 

35 m , m , E 

d 

1 

2 

0 

x "cascade efficiency" (between ~0.3 – heavy 

ions at high energy – and 1 – light ions) 


Collisional Damage – High Fluence 

At increasing fluence, newly generated Frenkel pairs may 

annihilate with previously generated ones (typical for metals) 

c 

(assuming that affected depth is ~2·R p) 

In materials with covalent binding (e.g., semiconductors), lattice damage might increase 

until amorphization. A simple formal estimate for the fluence required for amorphization is 

obtained when each atom in the irradiated volume has been displaced once in average, 

i.e. the FP concentration becomes equal to the atomic density of the irradiated material 

 

 

dpa 

dpa 

eff 

E0 , NF 

E0 

1 cF 

a 

d 

2R 

E 

F V 

am 

2nR 

 

N 

cF 

 

n 

p 

eff 

F 

 

E0 

E 

0 

p 

eff 

NF 

2nR 

 

 

E0 

E 

p 

0 

n atomic density 

0 

ion fluence 

V a annihilation volume (for metals, 

typically 20…50 atomic volumes) 

R p mean projected ion range 

Correspondingly, in radiation damage studies the fluence is often given in units of 

dpa = displacements per atom 

Ion Fluence 

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

Frenkel Pair Concentration 

V a -1 

0

Amorphization and Epitaxial Regrowth 

Ion channeling measurements of damage profiles 

200 keV Ge + 6H- SiC @ R.T. 

Amorphization 

300 keV Si + @ 480 °C 

Ion-Induced Epitaxial 

Regrowth 


Collisional Sputtering 

14 

4.2 10 cm m 

Ys i 

 

U 

s m 

i 

E 

t S E 

Y s sputter yield 

U s surface binding energy 

(3 ... 8 eV depending on 

material) 

S n nuclear stopping power 

momentum reversal 

factor 

m t target atomic mass 

Cascade atom overcomes 

surface binding energy 

nr. 

of sputtered atoms 

Ys Sputtering yield 

nr. 

of incident ions 

Analytical transport theory by Sigmund 

2 

 

0.8 0.8 

0.6 

0.4 

( z) 

0.4 

0.2 

0 

0 

n 

i 

0.1 1 10 

0 1 10 

x( z) 

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

Sputtering Yield 

Ion Energy (eV) 

Read line: Sigmund formula 

Blue line: Corrected for threshold effects 

Dots: From computer simulation (TRIM, 

TRIDYN)

Sputtering Yield – Experiment and Theory 

Thermal Spike ? 


Sputtering – Energy and Angle Distributions 

Thompson energy distribution of sputtered atoms 

f 

s 

E 

s 

~ 

3 E U 

s 

E 

s 

s 

Mean energy of sputtered atoms 

E0 

E 2 ln 3 

U 

, 

s 

Dependence on angles of incidence 

and emission (amorphous substance) 

f 

 

cos 

~ 

cos 

10-3 1 103 0 


f s(E s) (arb. Units) 

1 

 

0.5 

 

E s / U s

Sputtering – Angular Distributions from Crystals 

Angular distribution of sputtered particles may be strongly influenced by crystallinity 

100 eV Hg + → Ag s.cr. 

"Wehner" spots 

G.K. Wehner, JAP 26(1955)1056 

5 keV Ar + → Rh[111] 

oxidized 

1..10 eV 

10..20 eV 

20..30 eV 

J.P. Baxter et al., JVSTA 4(1986)1218 


Preferential Sputtering 

Partial sputtering yields 

Y 

p 

k 

Y 

 

Y 

p 

A 

p 

B 

c 

c 

c 

s 

k 

s 

A 

s 

B 

Y 

c 

k 

are generally different 

Preferential sputtering if 

Irradiation of two-component 

substance A nB m 

k = A,B 

Y k c "component" sputter 

yields 

c k s surface atomic fractions 

Mass conservation requires 

Y 

Y 

p 

A 

p 

B 

t 

cA 

 

t 

cB 

c(x) 

c A 

c B 

0 

Example: B is preferentially sputtered 

A 

B 


Y p (t) 

t 0 

0 

x 

A 

c(x) 

B 

c A 

c B 

0 

t 

A 

B 

t 

x

Preferential Sputtering 

4 He TaC 

TRIDYN 


Expt. 

1 keV 

W. Eckstein and W. Möller, Nucl. Instr. Meth. B 7/8(1985)727

Sputter-Controlled Implantation Profiles 

Deposition 

Profile 

Sputtered 

Flux 

Q( x ) j0 

fR 

j Y j n 

Surface x x st 

Recession 

Concentration 

at Time t 

x, t 


c 

 

s 

c 

s 

0 

x s 

j 0 Ion Flux 

t 

x , t 

Qx 

tdt 

 

Gaussian range distribution 

Surface 

Concentration 

n x st 

erf 

 

 

Ys 

 

 

0 

 

R 

p 

f R Range Distribution 

s 

v s 

 

x’ 

x R 

 

erf 

 

 

 

n 1 x R 

erf 

 

 

Ys 

 

2 

 

t 

p 

c 

x 0, 

t 

n 

 

1 

Ys 

x 

p 

 

 

 

 

 

 

 

 

R 

 

p

2 

 

Ion Beam Mixing 

Analytical transport theory only for 

cascade mixing (Sigmund and Gras-Marti) 

m 

2 

S 2 

 

n 

E 

2 REc 

 

E 

E c min. recoil energy for relocation 

R(E c) Recoil range at E c 

Ion fluence 

c 

Intermixing of layered 

materials by ion-induced 

atomic relocation 

Recoil Mixing Cascade Mixing 

 

4m 

m 

2 m m 

1 

1 

2 

2 

Fluence dependence of recoil implantation 

and mixing difficult to describe analytically 


Ion Beam Mixing: Thermal and Chemical Effects 

Radiation-enhanced 

interdiffusion 

275 keV Si 

→ 144 nm Nb/Si[100] 

radiationenhanced 

interdiffusion 

purely 

collisional 

S. Matteson et al., Rad. Eff. 42(1979)217 

Chemical driving forces: Enthalpy 

of mixing and cohesive energy 

d 

d 

 

 

3 

2 

S 

n E Hmix 

 

1 

K 

2 

2 

H 

H 

2 

1 

m n 

K1, K2 K1 

Constants 

 

coh 

coh 


 

T.W. Workman et al., Appl. Phys. Lett. 50(1987)1485

Ion Implantation and Ion Beam Synthesis 


Nucleation of Precipitates 

Supersaturated Solution of Monomers 

Change in Gibb’s Free Energy 

i G 

 

i 

 

 

Volume Gain 

2 1 3 

36V 

at 

i Monomers / 

Nanocluster 

2 

3 i 

Creation of 

Interface 

V at Atomic Volume 

Surface Tension 

Nucleation Threshold 

Size i 

3 

* 2 

i 

3 

 

 

 


G(i) 

0 

1 

i * 

i * 

< 0: No Supersaturation 

> 0 

* i 

G 

27 

4 

Nucleation by Fluctuations! 

3 

2

Ostwald Ripening 

Monomer Concentration 

around Precipitate 

(Gibbs-Thomson Equation) 

c 

 

R 

 

c 

c 

R c 

exp 

c 

1 

R R 

“Capillary” Length 

R 

c 

 

2V 

kT 

at 

 

c Solubility 

R 

Surface Tension 

V at Atomic Volume 

 

Monomer Concentration 

Diffusive 

Flux 

Position 


R

Ion mixing at precipitates 

R 

 

Atomic relocation 

probability per 

incident ion 

(Assumed to be 

isotropic) 

w r 

 

 

 

exp 

 

 

= (E ion,m ion,m target) 

Characteristic Relocation Length 

R 

Angular and spatial 

integration yields radial 

relocation field 

W r 

r 

r Atomic relocation is 

counteracted by diffusion. 

In local equilibrium 

K.-H. Heinig et al., Mat.Res.Soc.Proc. vol. 650 (2001) 


r D 2 c 

 

- r jW 

2 r 

r r 

r 

 

D Diffusion Coefficient 

r j Ion Flux 

After minor approximations (e.g., r-R > ) 

 

R 

 

 

R 

~ 

c 1 ~ 

c c R 

(Linearized) Gibbs-Thomson 

equation holds for ion mixing ! 

with 

c ~ 

 

c 

1 

R 5 

/ 

R 

1 

~ c 

c 

 

 

Dc 

q 2 

 

4 

q Nr. of displacements per 

Atom and Unit of Time

Inverse Ostwald Ripening 

Conventional Ostwald ripening 

c 

s 

c 

R c 1 

 

R 

c 

Under irradiation 

c 

irr 

s 

R 5 

/ 

R 

1 

~ c 

c 

 

4 

R 

 

 

 

 

 

 

 

c 1 

~ 

c 

R 

irr 

c 

 

R ~ 

R 

Capillary length may become 

negative ! 

Growth of smaller precipitates 

Towards homogeneous size 

distribution 

 

R c 

1 

kT 

increasing 

R 

K.-H. Heinig et al., Mat.Res.Soc.Proc. vol. 650 (2001) 


Nanocluster Evolution under Ion Irradiation

Fundamentals of Ion-Solid Interaction - SPIRIT

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