a3mht-EVJAS2016-P8-RBS

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Tabacniks, MH. XIX EVJAS - 2016
University of São Paulo
Institute of Physics
A3 - Rutherford Backscattering Spectrometry - RBS
Manfredo H. Tabacniks
2016
TTéécnicas de Caracterizacnicas de Caracterizaçção de Materiais ão de Materiais 
IFUSP 4302504IFUSP 4302504
Feixes iônicos para modificaFeixes iônicos para modificaçção e ão e 
caracterizacaracterizaçção de materiaisão de materiais
Tabacniks, MH. XIX EVJAS - 2016
BREMSTRAHLUNG
SECONDARY ELECTRON 
Ee>100eV
SECUNDARY 
TRACK
Ep>5000eV
PROJECTILE
SECUNDARY 
TRACK
Ep< 5keV
IONIZED COLUMN 
PRIMARY TRACK
RECOIL 
ATOM 
pair e-ion
E* ~30eV
~2 nm
Secondary electrons
10-100eV 
A
da
pt
ed
 fr
om
 C
ho
pp
in
, L
ilj
en
zi
n
e 
R
yd
be
rg
, R
ad
io
ch
em
is
tr
y 
an
d 
N
uc
le
ar
 C
he
m
is
tr
y,
 2
00
2.
When an energetic ion (~MeV) penetrates a solid...
M >> me
Tabacniks, MH. XIX EVJAS - 2016
RADIAÇÃO DE FREAMENTO
ELÉTRON 
SECUNDÁRIO Ee>100eV
TRAÇO 
SECUNDÁRIO
Ep>5000eV
PROJÉTIL
IÔNICO
TRAÇO
SECUNDÁRIO
Ep< 5keV
COLUNA IONIZADA 
TRAÇO PRIMÁRIO
ÁTOMO
de RECUO 
Par e-íon
E* ~30eV
~10 nm
elétrons secundários
(Delat Rays) 10-100eV
Adaptado de Choppin, Liljenzin e Rydberg, 
Radiochemistry and Nuclear Chemistry, 2002.
RBS
PIXE
BREMSTRAHLUNG
NRA
FRS ou ERDA
Particle 
Induced 
X-ray 
Emission
Nuclear 
Reaction
Analysis
Rutherford 
Backscattering 
Spectrometry
Forward 
Recoil 
Spectrometry
... the interactions can be used for material analysis
Tabacniks, MH. XIX EVJAS - 2016
RBS
• Kinematic factor
• Stopping power
• Cross section
• Examples
2
Tabacniks, MH. XIX EVJAS - 2016
Ion scattering by matter
The speed (or energy) of the 
scattered ion identifies the 
target atom. 
θ
M1 a line 
of 
atoms
Tabacniks, MH. XIX EVJAS - 2016
θ
M2 at rest
001 vEM
r
111 vEM
r
222 vEM
r
φ
Tabacniks, MH. XIX EVJAS - 2016
The mean free path between 
collisions is much greater than 
the interatomic spacing (a rare 
event) 
Correlation effects, due to 
neighboring atoms, are 
negligible. 
The momentum transferred 
to the recoiling atom is part 
of the ion energy-loss 
process.
Two-body elastic collision
θ
M2 at rest
001 vEM
r
111 vEM
r
222 vEM
r
φ
Tabacniks, MH. XIX EVJAS - 2016
Kinematics of Elastic Collisions 
θ
M2 at rest
001 vEM
r
111 vEM
r
222 vEM
r
φ
φθ
φθ
sinsin0
coscos
2
1
2
1
2
1
2211
221101
2
21
2
11
2
010
vMvM
vMvMvM
vMvMvME
−=
+=
+==
( ) φ
2
2
21
21
0,2 cos
4
MM
MM
EE LAB
+
=
normalized reduced mass
3
Tabacniks, MH. XIX EVJAS - 2016
Maximum Energy Transferred to the target atom
( ) φ
2
2
21
21
0,2 cos
4
MM
MM
EE LAB
+
=
( ) 0221
21
M2,
4
E
MM
MM
E
+
=
The maximum energy transferred is a head-on collision (φ = 0)
M1 = M2, all the energy is 
transferred. 
For M1 # M2 only a fraction 
of the energy can be 
transferred.
500
~
cos
4
0
,2
2
2
1
0,2
E
E
M
M
EE
M
M φ=
M1 << M2
electrons
For M1>> M2 φ2
1
2
0,2 cos
4
M
M
EE M =
Tabacniks, MH. XIX EVJAS - 2016
Kinematic factor
( )( ) ( ) 2
21
21
2/122
211
2,1 )(1
cossen1 


+
⋅+⋅−=≡
MM
MMMM
E
E
K
o
θθ
E1=KEo determines M2.
E0
E1=K.E0
θ
ϕ
α
01 EM
12 'EM( )
LABLABLAB
LAB
EEE
MM
MM
EE
,2,0,1
2
2
21
21
0,2 cos
4
−=
+
= φ
Tabacniks, MH. XIX EVJAS - 2016
( )( ) ( ) 2
21
21
2/122
211
1 )(1
cossen1




+
⋅+⋅−=≡
MM
MMMM
E
E
K
o
θθ
C
h
u
, M
ay
er
 &
 N
ic
ol
et
, 
1
9
78
θ
K1
Ma
xim
um
 sl
op
e
21 MM =
MAX
M
M
K =


∆
∆
1
2
Kinematic factor
Tabacniks, MH. XIX EVJAS - 2016
The incident ion looses energy 
along its path. The energy of 
the scattered ion does not 
identifies the target atom 
anymore.
001 vEM
r 11 EM
Stopping power
4
Tabacniks, MH. XIX EVJAS - 2016
Photons in matter
xe
N
N ∆−
=
.
0
µ
cteE =ν
Ions in matter
∆x
cteN =0
x
dx
dE
EE ∆

−= 01
Stopping power
Tabacniks, MH. XIX EVJAS - 2016
Stopping Power
dx
dE
S −= 


Å
eV
dx
dE
s
ρ
1
−= 


2μg/cm
eV ρ is the mass 
density of the 
material
dx
dE
N
1
ε −= [ ]22 cmeVat/cmeV = N is the atomic density of the 
material
Tabacniks, MH. XIX EVJAS - 2016
Halo
surfaceIncident ion
Secondary
electrons
• Molecular Scisoring
• Radical recombination
• Gas release
Electronic Electronic 
stoppingstopping
E > 1 MeV Track
Core
Nuclear Nuclear 
stoppingstopping
E ~ keV
• Ion implant
• atoms dislocations
Ions (MeV) in matter (10 -14 a 10-10s)
At stopping the ion 
captures electrons 
and “grows”.
Ion is totally 
stripped
Tabacniks, MH. XIX EVJAS - 2016
Effective charge (swift ions loose electrons)
250 keV
β ≡ v/c = 0,023
A
da
pta
do d
e
Z
ie
gler, 1980
N
a
sta
sietal., 199
6
5
Tabacniks, MH. XIX EVJAS - 2016
•Lattice disorder and radiation-damage effects are produced in the substrate by 
the incident ion. 
•As an implanted ion slows down and comes to rest, it has many violent 
collisions with lattice atoms, displacing them from their lattice sites. 
•These displaced atoms can in turn displace others, and the net result is the 
production of a highly disordered region around the path of the ion 
Lattice Disorder and Radiation-Damage
Normal atom
Interstitial atom
Incident ion
Sputtering
Implantation
Cascade
Solid
Depth
Cascade
Sputtering
Solid
Implantation
Normal atom
Interstitial atom
Incident ion
Sputtering
Implantation
Cascade
Solid
Depth
Cascade
Sputtering
Solid
Implantation
Low Dose:
Individual Regions
High Dose:
Amorphous Layer
N
as
ta
si
, M
. X
V
 J
or
ge
 A
nd
ré
S
w
ie
ca
S
um
m
er
 S
ch
oo
l, 
18
 F
eb
ru
ar
y 
20
08
Tabacniks, MH. XIX EVJAS - 2016
Stopping power
Nuclear stopping
Binary collisions in screened and 
repulsive Coulomb fields.
Ion implantation MeV PIXE / RBS
keV/u.m.a.
ht
tp
://
w
w
w
.s
rim
.o
rg
/S
R
IM
/S
R
IM
P
IC
S
/S
T
O
P
02
/S
T
O
P
02
14
.g
if
Bethe-Bloch
Andersen-Ziegler
Lindhard, Scharff
& Schiöt (LSS)
Electronic stopping (RBS region) 
Ions passing through an electron gas. Theory is 
well known and uncertainties are ~few %
Tabacniks, MH. XIX EVJAS - 2016
SRIM: http://www.srim.org/
Tabacniks, MH. XIX EVJAS - 2016
Stopping factor
x
Eo
KEo
E1
E
KE
θ1
θ2
detector can only measure
KE0 and
E1
6
Tabacniks, MH. XIX EVJAS - 2016
dx
dE
N
1
−=ε
dx
dE
S −=
x
Eo
KEo
E1
E
KE
θ1
θ2
e
o dx
dEx
EE
1cosθ
−=
sdx
dEx
KEE
2
1 cosθ
−=
[ ]xSEKEE od .1 =−=∆
[ ] 

 +−=
se dx
dE
dx
dEK
S
21 cos
1
cos θθ
[ ] 

 +=
21 cos
)(
cos
)(
θθ
oo KESESKS
stopping power factor
[ ] 

 +=
21 cos
)(
cos
)(
θ
ε
θ
εε oo KEEK
stopping cross section factor
linear relation ∆E and xe
s
Stopping factor (surface approximation)
Tabacniks, MH. XIX EVJAS - 2016
Beam stopping
The incident ion looses energy 
along its path. The energy of 
the scattered ion does not 
identifies the target atom 
anymore.
001 vEM
r 11 EM
...but, knowing the sample 
composition it is possible to 
calculate [S] and solve the 
ambiguity introduced by the 
ion stopping. 
[ ]xSEKEE od =−=∆ 2
[ ] 

 +−=
se dx
dE
dx
dEK
S
21 cos
1
cos θθ
?SIMULATION
Tabacniks, MH. XIX EVJAS - 2016
The incident ion looses energy 
along its path. The energy of 
the scattered ion does not 
identifies the target atom 
anymore.
001 vEM
r 11 EM
...but, knowing the sample 
composition it is possible to 
calculate [S] and solve the 
ambiguity introduced by the 
ion stopping. 
[ ]xSEKEE od =−=∆ 2
[ ] 

 +−=
se dx
dE
dx
dEK
S
21 cos
1
cos θθ
SIMULATION…and you gain elemental
depth profiles.
Beam stopping
Tabacniks, MH. XIX EVJAS - 2016
Rutherford scattering – Cross section
θ
x
E0
E1
E2
KE1
KE0
θ
ϕ
α
Rutherford 
cross section (CM)
( )
)2(
1
44
1
,
4
22
21
2
0 cc
cc senE
eZZ
E
d
d
θπε
θσ 



⋅⋅
⋅⋅



=Ω
hitsevents Nd
d
N 

 ∆ΩΩ=
σ
yprobabilitevent 
∆Ω
Ω
ΩΩ
= ∫
Ω
d
d
d
.
1 σ
σ tNQA ....Ω= σ
7
Tabacniks, MH. XIX EVJAS - 2016
( )
)2(
1
4
,
4
22
21
θ
θσ
senE
eZZ
E
d
d
c



⋅⋅
⋅⋅=Ω
CM
( ) ( ) 

 +



⋅⋅
⋅⋅=Ω a
a
senE
eZZ
E
d
d 2
4
22
21 cos4
4
,
θ
θ
θσ
Laboratory
E1, Z1, M1
E2, Z2, M2
θ
2
2
1
2
1
2/1
2
2
2
1
1
1
1
cossen1













+
⋅


+


 ⋅


−
=≡
M
M
M
M
M
M
E
E
K
o
θθ
Rutherford Cross Section 
2
1
2
2
11 






−= θsen
M
M
a
Tabacniks, MH. XIX EVJAS - 2016
Rutherford Cross Section
Chu, Mayer & Nicolet, 1978
( )
)2(
1
4
,
4
22
21
θ
θσ
senE
eZZ
E
d
d
c




⋅⋅
⋅⋅=Ω
Tabacniks, MH. XIX EVJAS - 2016
from Nastasi
Tabacniks, MH. XIX EVJAS - 2016
0 100 200 300 400 500
Channel
0
1
2
3
4
5
6
7
Y
ie
ld
(#
/u
C
/k
e
V
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0
Energy (MeV)
Li73
C126
O168
Ne2010
Si2814
Ca4020
Fe5626
Mo9542
U23892
ϕ
ρ
π cos4 2
2
2
2
1 li
i E
ZZ
QcteN
Ω=
½ of the periodic table
2.0MeV alphas on a monoatomic layer 
8
Tabacniks, MH. XIX EVJAS - 2016
100%O
RBS – Stoichiometry
0 100 200 300 400 500 600 700
Channel
0
2
4
6
8
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
Tabacniks, MH. XIX EVJAS - 2016
0 100 200 300 400 500 600 700
Channel
0
2
4
6
8
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
100%Cu
RBS – Stoichiometry
Tabacniks, MH. XIX EVJAS - 2016
0 100 200 300 400 500 600 700
Channel
0
2
4
6
8
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
CuO
0 100 200 300 400 500 600 700
Channel
0
2
4
6
8
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
Cu2O 
0 100 200 300 400 500 600 700
Channel
0
2
4
6
8
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
Cu
0 100 200 300 400 500 600 700
Channel
0
2
4
6
8
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
100%O
67% Cu
100% Cu
50% Cu
100%
RBS – Stoichiometry
Tabacniks, MH. XIX EVJAS - 2016
50 nm
200 nm
1 µm
5 µm
Fe (1%)
Ti (1)
O (2)
superfície Ti
superfície O
0 100 200 300 400 500
Channel
0
1
2
3
4
5
Y
ie
ld
(#
/u
C
/k
eV
/ m
sr
)1/
2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
2.0MeV alphas on a TiO 2 film 
9
Tabacniks, MH. XIX EVJAS - 2016
Choosing the right substrate (2 MeV alphas on a CuO f ilm)
100nm CuO
Si
0 100 200 300 400 500 600 700
Channel
0
2
4
6
8
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
Si
Cu
O
0 100 200 300 400 500 600 700
Channel
0
2
4
6
8
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
C
100nm CuO
C
Tabacniks, MH. XIX EVJAS - 2016
Energia
Y
 (
#/
µC
/m
sr
/k
eV
)
C
substrato
O Si
SiO2
C
Eo
KEo
E1
EoKSiEo
E1(Si)E1(O)
KOEoE1(C)
1/E2
HO
HSi
θE
∆EO
∆ESi
t
[ ] tSE meioOO .=∆
[ ] tSE meioSiSi .=∆
E1(C) = KCEo - [S].t
E1(O) = KOEo - [S].t 
E1(Si) = KSiEo - [S].t
RBS – Compound analysis
Tabacniks, MH. XIX EVJAS - 2016
Peak and plateau heights
( ) 


Ω=
1cos
....
θ
σ iikik
x
NQEH
( ) [ ] 


Ω=
1cos
....
θε
δσ
meio
io
ikik nQEH
Hk
0 100 200 300 400 500
Channel
0
10
20
30
40
50
N
or
m
al
iz
ed
Y
ie
ld
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
xi
θ1
at the surface
( ) [ ] 


Ω=
1
00
cos
....
θε
δσ
meio
io
ii nQEH
( )
( )
[ ]
[ ]meioAo
meio
Bo
B
A
oB
oA
Bo
Ao
n
n
E
E
H
H
ε
ε
σ
σ
=
δ
Tabacniks, MH. XIX EVJAS - 2016
Peak areas
0 100 200 300 400 500
Channel
0
10
20
30
40
50
N
or
m
a
liz
ed
Y
ie
ld
0.0 0.5 1.0 1.5 2.0 2.5
Energy (MeV)
( ) 


Ω=
1cos
....
θ
σ tNQEA ioio
( )
( ) B
A
B
A
B
A
oiB
oiA
Bo
Ao
N
N
Z
Z
N
N
E
E
A
A
2
. 


==
σ
σ
10
Tabacniks, MH. XIX EVJAS - 2016
δ
√t
Initial condition
TAmb, t=0s
Annealing
T = 180 °C, ∆t= 2, 4, 16 h
Atmosphere: O2
RBS – surface contaminants (oxidation)
Tabacniks, MH. XIX EVJAS - 2016
Initial condition
Tamb, t=0
Annealed
∆t = 2,4,16h
T=500°
Atmosfera
W
Si
WSi2
RBS – Reactions at the interface
Tabacniks, MH. XIX EVJAS - 2016
0 100 200 300 400 500 600
Channel
0
5
10
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0
Energy (MeV)
0 100 200 300 400 500 600
Channel
0
5
10
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0
Energy (MeV)
40nm
W
Cu
Si
40nmW
Cu
Si
0 100 200 300 400 500 600
Channel
0
5
10
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0
Energy (MeV)
0 100 200 300 400 500 600
Channel
0
5
10
Y
ie
ld
(#
/u
C
/k
eV
/m
sr
)1/2
0.0 0.5 1.0 1.5 2.0
Energy (MeV)
W
CuSi
W
CuSi
Roughness
Tabacniks, MH. XIX EVJAS - 2016
Martins, et al International Workshop 
on Surface Engineering. Rio de Janeiro, 
RJ, Jul. 28-30. (1993).
NiO/C
thin film 
simulationsubstrate 
diffused in 
the sample
NiO film 
diffused in 
the substrate
Roughness
equivalent situations
11
Tabacniks, MH. XIX EVJAS - 2016
12C(p,p0)12C for Carbon profiling 16O(α,α0)16O for oxygen profiling
ρ
d
Resonaces
Tabacniks, MH. XIX EVJAS - 2016
Tabacniks, MH. XIX EVJAS - 2016 Tabacniks, MH. XIX EVJAS - 2016
PIXE
RBS ERDA
Resonant RBS
MODEL
RESULT
Self-consistent analysis – Multi-SIMNRA T F Silva et al. NIMB 2016
12
Tabacniks, MH. XIX EVJAS - 2016
Self-consistent analysis – Multi-SIMNRA T F Silva et al. NIMB 2016
Tabacniks, MH. XIX EVJAS - 2016
Self-consistent analysis – Multi-SIMNRA
Non Rutherford 
Cross Sections
T F Silva et al. NIMB 2016
Tabacniks, MH. XIX EVJAS - 2016
Self-consistent analysis – Multi-SIMNRA T F Silva et al. NIMB 2016
Tabacniks, MH. XIX EVJAS - 2016
Acelerador
Fontes de íons
Console
Laboratório para Análise de Materiais com Feixes Iônicos - LAMFI
13
Tabacniks, MH. XIX EVJAS - 2016
RBS @ LAMFIRBS @ LAMFI
Dois detetores, 
aumentam a 
precisão da
análise
Blindagem eletrostática
(para evitar elétrons 
espúrios). Garante σQ<1%
Colimador de feixe
intercambiável
0.1 – 3.0 mm
Detetor móvel
170° - 30° (ERDA)
Porta
amostras de 
alta precisão
Goniômetro
xyz 0.1 mm
Tabacniks, MH. XIX EVJAS - 2016
• Chu, Mayer & Nicolet, Backscattering Spectrometry, Ac. Press., 1978. 
• Feldman, L.C. & Mayer, J.W. Fundamentals of surface and thin film analysis. North-Holland, 
(1986) 
• M. Mayer, SIMNRA User's Guide 6.0, Max-Planck-Institut für Plasmaphysik, Garching, 
Germany, 2006. http://www.rzg.mpg.de/~mam/MANUAL.pdf(2649 kB).
• Tabacniks, M.H. Análise de filmes finos por PIXE e RBS. www.if.usp.br/lamfi/tutoriais.htm.
• RBS tutorial:http://www.eaglabs.com/training/tutorials/
References
Simulation programs
• Multi-SIMNRA: http://deuterio.if.usp.br/multisimnra
• SIMNRA 6.03(fev 2008) http://www.rzg.mpg.de/~mam/index.html
• RMP/GENPLOT http://www.genplot.com/
• Tabacniks, M.H. Análise de espectros RBS com programa de computador RUMP "um breviário" versão 2 / 
2000 http://www.if.usp.br/lamfi/guia-rump-v2.pdf
• IBANDL (non Rutherford cross sections) http://www-nds.iaea.org/ibandl/