rbs - rutherford backscattering...

© Matej Mayer 2003

1

RBS - Rutherford Backscattering SpectrometryM. Mayer

Max-Planck-Institut für Plasmaphysik, EURATOM Association, 85748 Garching, Germany

• History• Scattering geometry and kinematics• Rutherford cross section and limitations• RBS spectra from thin and thick films• Stopping power and energy loss• Detector resolution• Energy loss straggling• Cross sections from selected light elements

- incident 1H- incident 4He

© Matej Mayer 2003

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Introduction

RBS - Rutherford Backscattering Spectrometry• Widely used for near-surface layer analysis of solids• Elemental composition and depth profiling of individual elements• Quantitative without reference samples (≠ SIMS, sputter-XPS,...)• Non-destructive (≠ SIMS, sputter-XPS,...)• Analysed depth: 2 µm (He-ions); 20 µm (protons)• Very sensitive for heavy elements: ≈ ppm• Less sensitive for light elements ⇒ NRA

Sample

E0 ≈ MeV

EEnergy

sensitivedetector

© Matej Mayer 2003

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Introduction (2)

Rutherford Backscattering (RBS) is• Elastic scattering of protons, 4He, 6,7Li, ...

≠ Nuclear Reaction Analysis (NRA): Inelastic scattering, nuclear reactions≠ Detection of recoils: Elastic Recoil Detection Analysis (ERD) ≠ Particle Induced X-ray Emission (PIXE)≠ Particle Induced γ-ray Emission (PIGE)

• RBS is a badly selected name, as it includes:- Scattering with non-Rutherford cross sections- Back- and forward scattering

• Sometimes called Particle Elastic scattering Spectrometry (PES)• Ion beam Analysis (IBA) acronyms: G. Amsel, Nucl. Instr. Meth. B118 (1996) 52

© Matej Mayer 2003

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History

Sir Ernest Rutherford (1871 - 1937)• 1911: Rutherford’s scattering experiments: 4He on Au

⇒ Atomic nucleus, nature of the atom

RBS as materials analysis method• 1957: S. Rubin, T.O. Passell, E. Bailey, “Chemical Analysis of

Surfaces by Nuclear Methods”, Analytical Chemistry 29 (1957) 736

“Nuclear scattering and nuclear reactions induced by high energy protons and deuteronshave been applied to the analysis of solid surfaces. The theory of the scattering method, anddetermination of O, Al, Si, S, Ca, Fe, Cu, Ag, Ba, and Pb by scattering method are described.C, N, O, F, and Na were also determined by nuclear reactions other than scattering. The methods are applicable to the detection of all elements to a depth of several µm, withsensitivities in the range of 10-8 to 10-6 g/cm2.”

© Matej Mayer 2003

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History (2)

• 1970’s: RBS becomes a popular method due to invention of silicon solid state detectors

• 1977: H.H. Andersen and J.F. ZieglerStopping Powers of H, He in All Elements

• 1977: J.W. Mayer and E. RiminiIon Beam Handbook for Materials Analysis

• 1979: R.A. JarjisNuclear Cross Section Data for Surface Analysis

• 1985: M. ThompsonComputer code RUMP for analysis of RBS spectra

• 1995: J.R. Tesmer and M. NastasiHandbook of Modern Ion Beam Materials Analysis

• 1997: M. MayerComputer code SIMNRA for analysis of RBS, NRA spectra

© Matej Mayer 2003

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Index

© Matej Mayer 2003

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Scattering Geometry

αβ

θ

α: incident angleβ: exit angleθ: scattering angle

Often (but not exclusive): 160° ≤ θ ≤ 170°⇒ optimised mass resolution

αβ

θ

IBM geometryIncident beam, exit beam,surface normal in one plane⇒ α + β + θ = 180°Advantage: Simple

Cornell geometryIncident beam, exit beam,rotation axis in one plane⇒ cos(β) = − cos(α) cos(θ)

Advantage:large scattering angle andgrazing incident + exit anglesgood mass and depthresolution simultaneously

General geometryα, β, θ not related

© Matej Mayer 2003

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Scattering Kinematics

Elastic scattering: E0 = E1 + E2

Kinematic factor: E1 = K E0

( ) 2

21

12/122

122 cossin

++−

=MM

MMMK θθ

0 20 40 60 80 100 120 140 160 180 2000.0

0.2

0.4

0.6

0.8

1.0θ = 165°

K

M2

1H 4He 7Li

22

01 MdMdKEE ∆=∆

∆E1: Energy separation∆M2: Mass difference

© Matej Mayer 2003

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Channel2,0001,8001,6001,4001,2001,0008006004002000

Cou

nts

12,000

11,000

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Energy [keV]

Scattering Kinematics: Example (1)

Au: 197

Mo: 96

Fe: 56

O: 16C: 12 Si: 28

2000 keV 4He, θ = 165°

backscattered fromC, O, Fe, Mo, Au3×1016 Atoms/cm2 each

on Si substrate

⇒ light elements may overlapwith thick layers of heavierelements

© Matej Mayer 2003

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Scattering Kinematics: Example (2)

Channel2,0001,8001,6001,4001,2001,0008006004002000

Cou

nts

20,000

19,000

18,000

17,000

16,000

15,000

14,000

13,000

12,000

11,000

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Energy [keV]

800

C12

O16

Cr52

Fe56

Cr52

Fe56

Au197

Hg201

Au197

Hg201

⇒ Decreased mass resolution for heavier elements

2000 keV 4He, θ = 165°

© Matej Mayer 2003

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Mass Resolution

22

01 MdMdKEE ∆=∆

1

202

−

=

dMdK

EEM δδ δM2: Resolvable mass difference

δE: Energy resolution of the system⇒

⇒ Improved mass resolution with increasing M1

But: For surface barrier detectorsδE = δE(M1)

δE(1): 12 keVδE(4): 15 keVδE(12): 50 keV⇒ optimum mass resolution

for M1 = 4 – 7

Heavier M1 only useful with magnetic analysers,time-of-flight detectorsJ.R. Tesmer and M. Nastasi,

Handbook of Modern Ion Beam Materials Analysis,MRS, 1995

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Index

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Rutherford Cross Section

• Neglect shielding by electron clouds• Distance of closest approach large enough

that nuclear force is negligible⇒ Rutherford scattering cross section

2

22

21

EZZ

R ∝σNote that:

Sensitivity increases with• increasing Z1• increasing Z2• decreasing E

© Matej Mayer 2003

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Channel2,0001,8001,6001,4001,2001,0008006004002000

Cou

nts

12,000

11,000

10,000

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Energy [keV]

Au: 79

Mo: 42

Fe: 26

O: 8C: 6Si

Rutherford Cross Section: Example

2000 keV 4He, θ = 165°

backscattered fromC, O, Fe, Mo, Au3×1016 Atoms/cm2 each

on Si substrate

⇒ Increased sensitivity for heavier elements ∝ Z2

2

⇒ Good for heavier elementson lighter substrate⇒ Less good for lighterelements on heavier substrate

© Matej Mayer 2003

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Shielded Rutherford Cross Section

Shielding by electron clouds gets important at• low energies• low scattering angles• high Z2

Shielding is taken into account by a shielding factor F(E, θ)

),( ),(),( θσθθσ EEFE R= F(E, θ) close to unity

F(E, θ) is obtained by solving the scattering equationsfor a shielded interatomic potential:

)/()(2

21 arr

eZZrV ϕ=

ϕ: Screening functionUse Thomas-Fermi or Lenz-Jenssen screening function

a: Screening radius

a0: Bohr radius

( ) 2/13/22

3/210885.0 −

+= ZZaa

© Matej Mayer 2003

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CMR EZZ 3/4

21 049.01−=σσ

CMR EZZ 2/7

21 0326.01−=σσ

For 90° ≤ θ ≤ 180°:

L’Ecuyer et al. (1979) Wenzel and Whaling (1952)

For all θ: Andersen et al. (1980)

Shielded Rutherford Cross Section (2)

0 30 60 90 120 150 1800.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.002000 keV1000 keV500 keV

250 keV

F(E,

θ)

θ (degree)

L’Ecuyer 1979

Andersen 1980

4He backscattered from Au

© Matej Mayer 2003

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Non-Rutherford Cross Section

Cross section becomes non-Rutherford if nuclear forces get important • high energies• high scattering angles• low Z2

Energy at which the cross section deviatesby > 4% from Rutherford at 160° ≤ θ ≤ 180°Bozoian (1991)1H: ENR

Lab = 0.12 Z2 - 0.5 [MeV]4He: ENR

Lab = 0.25 Z2 + 0.4 [MeV]

Linear Fit to experimental values (1H, 4He)or optical model calculations (7Li)

Accurate within ± 0.5 MeVJ.R. Tesmer and M. Nastasi,Handbook of Modern Ion Beam Materials Analysis,MRS, 1995

© Matej Mayer 2003

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Index

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RBS-Spectrum of a thin layer

αβ

θ

A layer is thin, if:• Energy loss in layer < experimental energy resolution• Negligible change of cross section in the layer

ασ

cos)(0

xENQ ∆Ω=

Q: Number of counts in detectorN0: Number of incident particlesΩ: Detector solid angleσ(E): Differential scattering cross section (Barns/sr)∆x: Layer thickness (Atoms/cm2)α: Angle of incidence

Energy E of backscattered particles:E = K E0

Number Q of backscattered particles:

500 1000 1500 20000

50

100

150

200

250

300

Coun

ts/c

hann

el

Energy

Q

© Matej Mayer 2003

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RBS-Spectrum of a thin layer (2)

Convolution with experimental energy resolutionAssume Gaussian energy resolution function f(x) with standard deviation w

2

20

2)(

21)( w

xx

ew

xf−

−=

π

2

20

2) (

2)( w

EKE

ew

QEn−

−=

π

500 1000 1500 20000

50

100

150

200

250

300

Coun

ts/c

hann

el

Energy

Count density function

∫=Highi

Lowi

E

Ei dEEnN )(Counts Ni in channel i

© Matej Mayer 2003

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RBS-Spectrum of a thick layer

• Target is divided into thin sublayers (“slabs”)

• Calculate backscattering from front and backside of each sublayer taking energy loss into account

Energy at front side E1 = E0 - ∆Ein

Starting energy from front side E1’ = K E1

Energy at surface E1out = E1’ - ∆E1

out

Energy at back side E2 = E1 - ∆EStarting energy from back side E2’ = K E2

Energy at surface E2out = E2’ - ∆E2

out

• For each isotope of each element in sublayer⇒ “Brick”

E1

E2

E1outE2

out

© Matej Mayer 2003

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ασ

cos)(0

xENQ ∆Ω=

Q: Number of countsN0: Number of incident particlesΩ: Detector solid angleσ(E): Differential scattering cross section∆x: Thickness of sublayer (in Atoms/cm2)α: Angle of incidence

E1

E2

E1outE2

out

How to determine σ(E)?

• Mean energy approximation:Use σ(<E>), with <E> = E1 - ∆E/2

• Mean cross section <σ>:

Area Q of the brick:

21

1

2

)(

EE

dEEE

E

−>=<

∫σσ ⇒ More accurate, but time consuming

RBS-Spectrum of a thick layer (2)

© Matej Mayer 2003

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E1

E2

E1outE2

out

Shape of the brick:• Height of high energy side ∝ σ(E1)• Height of low energy side ∝ σ(E2)• use linear interpolation

Better approximations:• Height of high energy side ∝ σ(E1)/Seff(E1)• Height of low energy side ∝ σ(E2)/Seff(E2)• Seff: Effective stopping power, taking stopping

on incident and exit path into account• use quadratic interpolation with additional

point <E>


© Matej Mayer 2003

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E1

E2

E1outE2

out

Convolution of brick with energy broadening• Detector resolution• Energy straggling• Depth dependent

⇒


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0 500 1000 1500 20000

10000

20000

30000

40000Au-thickness[x1017 at/cm2]

1 4 8 12 16 20

Coun

ts

Energy [keV]

RBS-Spectrum of a thick layer: Example

2000 keV 4He, θ = 165° backscattered from Au on Si substrate

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RBS-Spectra: Example (1)

0

200

400

600

800

Experiment SIMNRA

Co

Nb

2.2 MeV 6Li

Coun

ts

1200 1400 1600 18000

200

400

600

Co

Nb2.0 MeV 4He

Coun

ts

Energy [keV]

NbCoNb

NbCo

Nb: 1.0×1017 at/cm2

Co: 2.2×1017 at/cm2

M. Mayer et al., Nucl. Instr. Meth. B190 (2002) 405

© Matej Mayer 2003

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400 6000

500

1000

1500

2000 Initial 550°C 650°C Simulation

Coun

ts

Channel

Ag 1.2x1018

TiN 1.0x1017

Si substrate


3980 keV 4He, θ = 165°

Si

Ti

Ag

M. Balden, unpublished

© Matej Mayer 2003

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1.9 MeV 4He, 170° backscattered from ceramic glass

200 400 600 8000

2000

4000

6000

8000

Co

unts

Channel

O64Na11Si22K2Zn2Cd0.04

CdZnK

Si

Na

O

© Matej Mayer 2003

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Index

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Stopping Power

• Electronic stopping power:- Andersen, Ziegler (1977):

H, He in all elements- Ziegler, Biersack, Littmarck (1985):

All ions in all elements- Several SRIM-versions since then- Additional work by Kalbitzer, Paul, ...- Accuracy: 5% for H, He

10% for heavy ions• Nuclear stopping power:

- Only important for heavy ionsor low energies

- Ziegler, Biersack, Littmarck (1985):All ions in all elements using ZBL potential

4He in Ni

J.F. Ziegler, Helium - Stopping Powers and Ranges in All Elements,Vol. 4, Pergamon Press, 1977

© Matej Mayer 2003

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Stopping Power (2)

Stopping in compounds:consider compound AmBn, with m + n = 1SA is stopping power in element ASB is stopping power in element BWhat is stopping power SAB in compound?

Bragg’s rule (Bragg and Kleeman, 1905):SAB = m SA + n SB

Bragg’s rule is accurate in:• Metal alloys

Bragg’s rule is inaccurate (up to 20%) in:• Hydrocarbons• Oxides• Nitrides• ...

Other models for compounds

• Hydrocarbons:Cores-and-Bonds (CAB) modelZiegler, Manoyan (1988)Contributions of atomic coresand chemical bonds between atoms

• Large number of experimental data,especially for hydrocarbons, plastics, ...

© Matej Mayer 2003

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Evaluation of Energy Loss

Question: Energy E(x) in depth x?⇒ Taylor expansion of E(x) at x = 0:

0 x

E...61

21)0()(

03

33

02

22

0

++++==== xxx dx

Edxdx

EdxdxdExExE

SdxdE

−= S: Stopping power

( ) SSdxdE

dEdSS

dxd

dxEd ′=−=−=2

2

( ) SSSSdxdSSS

dxSdSS

dxd

dxEdx

223

′−′′−=′+′

=′=

( ) ...61

21)( 2232

0 +′+′′−′+−= SSSSxSSxxSExE S, S’, S’’ evaluated at x = 0⇒

© Matej Mayer 2003

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Evaluation of Energy Loss (2)

3 MeV 4He in Pt

L.R. Doolittle, Nucl. Instr. Meth. B9 (1985) 344

© Matej Mayer 2003

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Index

© Matej Mayer 2003

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Silicon Detector Resolution

V

+++

- - -

Principle of operation:• Creation of electron-hole pairs by charged particles• Separation of electron-hole pairs by high voltage V

⇒ Number of electron-hole pairs ∝ Particle energy⇒ Charge pulse ∝ Particle energy

Limited energy resolution due to:• Statistical fluctuations in energy transfer to electrons and phonons• Statistical fluctuations in annihilation of electron-hole pairs

Additional energy broadening due to:• Preamplifier noise• Other electronic noise

© Matej Mayer 2003

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Silicon Detector Resolution (2)

H

HeLiBCNe

Typical values (FWHM):• H 2 MeV: 10 keV• He 2 MeV: 12 keV• Li 5 MeV: 20 keV

J.F. Ziegler, Nucl. Instr. Meth. B136-138 (1998) 141

Ad-hoc fit to experimental data:

Better energy resolution for heavy ions can be obtained by:• Electrostatic analyser (Disadvantage: large)• Magnetic analyser (Disadvantage: large)• Time-of-flight (Disadvantage: length, small solid angle)

© Matej Mayer 2003

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Index

© Matej Mayer 2003

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Energy Straggling

Slowing down of ions in matter is accompanied by a spread of beam energy

⇒ energy straggling

• Electronic energy loss straggling due to statistical fluctuations in the transferof energy to electrons

• Nuclear energy loss straggling due to statistical fluctuations in the nuclear energy loss

• Geometrical straggling due to finite detector solid angle and finite beam spot size

• Multiple small angle scattering

• Surface and interlayer roughness

© Matej Mayer 2003

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Electronic Energy Loss Straggling

Due to statistical fluctuations in the transfer of energy to electrons⇒ statistical fluctuations in energy loss

Energy after penetrating a layer ∆x: <E> = E0 - S ∆x<E> mean energy

S stopping power

⇒ only applicable for mean energy of many particles

© Matej Mayer 2003

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Shape of the energy distribution?∆E/E0

< 10% Vavilov theory Low number of ion-electron collisionsNon-Gaussian

10% – 20% Bohr theory Large number of ion-electron collisionsGaussian

20% – 50% Symon theory Non-stochastic broadening due to stoppingAlmost Gaussian

50% – 90% Payne, Tschalär Energy below stopping power maximumtheory Non stochastic squeezing due to stopping

Non-Gaussian

Electronic Energy Loss Straggling (2)

Vavilov

Gaussian

© Matej Mayer 2003

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Vavilov Theory

Vavilov 1957P.V. Vavilov, Soviet Physics J.E.T.P. 5 (1957) 749

Valid for small energy losses⇒ Low number of ion-electron collisions⇒ Non-Gaussian energy distribution with tail towards low energies

Mostly replaced by Bohr’s theory and approximated by Gaussian distribution⇒ Total energy resolution near the surface usually dominated by detector resolution

due to small energy loss straggling

⇒ Only necessary in high resolution experiments

© Matej Mayer 2003

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Bohr Theory

Bohr 1948N. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 18 (1948)

Valid for intermediate energy losses⇒ Large number of ion-electron collisions⇒ Gaussian energy distribution

Approximations in Bohr’s theory:• Ions penetrating a gas of free electrons• Ions are fully ionised• Ion velocity >> electron velocity ⇒ stationary electrons• Stopping power effects are neglected

xZZBohr ∆= 26.0 22

12σ

σ2Bohr variance of the Gaussian distribution [keV2]

∆x depth [1018 atoms/cm2]Z1 atomic number of incident ionsZ2 atomic number of target atoms

© Matej Mayer 2003

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Bohr Theory: Example

0 1 2 3 40

20

40

60

80

Max50%20%10%

2.5 MeV 4He in Si

Stra

gglin

g (k

eV F

WHM

)

Depth (1019 atoms/cm2)Vavilov

x∝

© Matej Mayer 2003

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Improvements to Bohr Theory

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

E/M[keV/amu]

1050

100200300500750

1500

3000

1000

2000

H(E

/M, Z

2)

Z2

5000

Chu 1977J.W. Mayer, E. Rimini, Ion Beam Handbook for Material Analysis, 1977

Approximations in Chu’s theory:• Binding of electrons is taken into account• Hartree-Fock electron distribution• Stopping power effects are neglected

22

1

2 , BohrChu ZMEH σσ

=

⇒ Smaller straggling than Bohr

© Matej Mayer 2003

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Straggling in Compounds

Additive rule proposed by Chu 1977J.W. Mayer, E. Rimini, Ion Beam Handbook for Material Analysis, 1977

consider compound AmBn, with m + n = 1σA

2 is variance of straggling in element AσB

2 is variance of straggling in element B

σAB2 = σA

2 + σB2

σA2 Straggling in element A in a layer m ∆x

σB2 Straggling in element B in a layer n ∆x

© Matej Mayer 2003

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Propagation of Straggling in Thick Layers

0 1000 2000 3000 4000 50000

20

40

60

80

Stop

ping

Pow

erEnergy [keV]

E

Consider particles with energy distribution

• Energy above stopping power maximumhigher energetic particles ⇒ smaller stopping⇒ non-stochastic broadening

• Energy below stopping power maximumhigher energetic particles ⇒ larger stopping⇒ non-stochastic squeezing

C. Tschalär, Nucl. Instr. Meth. 61 (1968) 141M.G. Payne, Phys. Rev. 185 (1969) 611

© Matej Mayer 2003

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Propagation of Straggling in Thick Layers (2)

EEE δ+= 12

∫ ∫−

−

−−=xx x

xx

dyyESdyyESEEδ

δ01

*1 ))(( ))((

0 x

E2E1

δE

E2*E1*

δE*

δx x−δx

∫

∫ ∫

−=

−−=

x

x

x x

x

dyyESE

dyyESdyyESEE

δ

δ

δ

))((

))(( ))((

1

02

*2

iSEx δδ ≈ Select δx so, that

E2 decreases to E1

xS

dyyES

EEE

f

x

xx

δ

δ

δ

))((

*1

*2

*

≈

=

−=

∫−

ESS

Ei

f δδ =*⇒ Sf Final stopping powerSi Initial stopping power

Si Sf

© Matej Mayer 2003

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Propagation of Straggling in Thick Layers (3)

0 1000 2000 3000 4000 50000

20

40

60

80

Stop

ping

Pow

er

Energy [keV]

1>i

f

SS

Broadening

1<i

f

SS

Squeezing

Smax

222

2Chui

i

ff S

Sσσσ +

=

Adding stochastic and non-stochastic effects:• Statistically independent

Si Sf

σi σf

© Matej Mayer 2003

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Propagation of Straggling: Examples

0 1 2 3 40

20

40

60

80

Max50%20%10%

2.5 MeV 4He in Si

Chu + Propagation Bohr

Stra

gglin

g (k

eV F

WHM

)

Depth (1019 atoms/cm2)

0 2 4 6 8 100

20

40

60

80

90%50%Max 20%

1.0 MeV 4He in Au

Chu + Propagation Bohr

Stra

gglin

g (k

eV F

WHM

)

Depth (1018 atoms/cm2)

222

2Chui

i

ff S

Sσσσ +

=

© Matej Mayer 2003

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Multiple and Plural Scattering

Multiple small angle deflections

• Path length differences on ingoing and outgoing paths⇒ energy spread

• Spread in scattering angle⇒ energy spread of starting particles

P. Sigmund and K. Winterbon, Nucl. Instr. Meth. 119 (1974) 541E. Szilagy et al., Nucl. Instr. Meth. B100 (1995) 103

Large angle deflections (Plural scattering)

• For example: Background below high-Z layers

W. Eckstein and M. Mayer, Nucl. Instr. Meth. B153 (1999) 337

etc. 100 200 3000

2000

4000

6000

8000

10000

12000

14000

Au

Si

Experimental Dual scattering Single scattering

Coun

ts

Channel

100 200 300 400 500

Energy (keV)500 keV 4He, 100 nm Au on Si, θ = 165°

© Matej Mayer 2003

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J.R. Tesmer and M. Nastasi,Handbook of Modern Ion Beam Materials Analysis,MRS, 1995

Threshold for Non-Rutherford Scattering

Thresholds for non-Rutherford scattering [MeV]

• For 1H: E ≈ 0.12 Z2 - 0.5• For 4He: E ≈ 0.25 Z2 + 0.4

Z2 for Non-Rutherford scattering

1H 4He1 MeV 12 32 MeV 21 6

© Matej Mayer 2003

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Non-Rutherford Scattering: Example

1.5 MeV H, θ = 165°6x1017 at/cm2 Be, C, O on Si

Channel500480460440420400380360340320300280260240220200180160

Cou

nts

3,400

3,200

3,000

2,800

2,600

2,400

2,200

2,000

1,800

1,600

1,400

1,200

1,000

800

600

400

200

0

500 600 700 800 900 1000 1100 1200 1300 1400

Energy [keV]

Be

C

O

Si

Typical problem for light elements:Overlap with thick layers of heavier elements ⇒ High cross sections wishful

M. Mayer, unpublished

© Matej Mayer 2003

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• Many non-Rutherford scattering cross sections weremeasured in the years 1950 - 1970 for nuclear physics research⇒ goal was nuclear physics, not materials analysis⇒ most data published only in graphical form

• Since 1980 - to now non-Rutherford scattering cross sections aremeasured for RBS analysis⇒ some data published in graphical form and tabular form⇒ for typical angles of RBS

• Data compilation by R.A. Jarjis, Nuclear Cross Section Data for Surface Analysis, University of Manchester, UK 19792 volumes, 600 pages → unpublishedstill the most comprehensive compilation of cross section data (RBS + NRA)

Cross Section Data Sources

© Matej Mayer 2003

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• Data compilation by R.P. Cox et al. for J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Analysis, MRS 1995Digitised (or tabulated) data from original publications in RTR file format

• These data are available at SigmaBase:ibaserver.physics.isu.edu/sigmabase/ or www.mfa.kfki.hu/sigmabase/Also included in the computer code SIMNRA

• Data compilation by M. Mayer since 1996Digitised (or tabulated) data from original publications (or authors)in R33 file formatMost of these data are available at SigmaBaseIncluded in the computer code SIMNRA

Cross Section Data Sources (2)

© Matej Mayer 2003

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12C(p,p)12C

500 1000 1500 2000 2500 3000 3500 4000 45000

10

20

30

40

50

60

70

80

90

100

Amirikas 170° Amirikas Fit 170° Mazzoni 170° Liu 170° Rauhala 170° Jackson 168.2 Amirikas Fit 165° Mazzoni 165° Gurbich 165°

C(p,p)C, θ = 165° - 170°

Cro

ss S

ectio

n [R

atio

to R

uthe

rford

]

E [keV]

High to very high cross sectionabove 500 keV

Typical energies for RBS:• 1500 or 2500 keV

⇒ smooth cross section⇒ easy data evaluation, thick layers

• ≈ 1740 keV⇒ maximum sensitivity

SIMNRA Home Page http://www.rzg.mpg.de/~mam

© Matej Mayer 2003

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500 1000 1500 2000 2500 3000 3500 40000

10

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30

40

50

60

70

80

14N(p,p)14N

Ramos 178° Rauhala 170° Guohua 170° Olness 167° Lambert 165°

Cro

ss S

ectio

n [R

atio

to R

uthe

rford

]

E [keV]

14N(p,p)14N

High to very high cross section

but: large scatter of data


© Matej Mayer 2003

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1000 1500 2000 2500 3000 3500 40000

10

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16O(p,p)16O

Ramos 178° Amirikas 170° Gurbich 165°

Cro

ss S

ectio

n [R

atio

to R

uthe

rford

]

E [keV]

High to very high cross section

Typical energies for RBS:• 1500 or 2500 keV

⇒ smooth cross section⇒ together with C

• ≈ 3470 keV⇒ maximum sensitivity

16O(p,p)16O


© Matej Mayer 2003

60

1000 1500 2000 2500 30000

1

2

3

4

27Al(p,p)27Al

Rauhala 170° Chiari 170° Chiari 165°

Cro

ss S

ectio

n [R

atio

to R

uthe

rford

]

E [keV]

27Al(p,p)27Al

Small cross sectionMany resonances⇒ complicated spectrum

Not useful for RBS with protons


© Matej Mayer 2003

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1000 1500 2000 2500 30000

1

2

3

4

Si(p,p)Si

Amirikas 170° Amirikas Fit Rauhala 170° Vorona 167.2° Salomonovic 160° Salomonovic 170° Gurbich 165°

Cro

ss S

ectio

n [R

atio

to R

uthe

rford

]

E [keV]

Si(p,p)Si

Small cross section⇒ advantageous if used as substrate

Typical energies for RBS:

• 1500 - 1600 keV⇒ small background from substrate

• 1670 or 2090 keV⇒ maximum sensitivity


© Matej Mayer 2003

63

12C(α,α)12C

• Small cross section at E < 3000 keV⇒ not suitable for RBS

• High and smooth cross section around 4000 keV• Maximum sensitivity at 4270 keV

J.R. Tesmer and M. Nastasi, Handbook of Modern Ion Beam Materials Analysis, MRS, 1995

© Matej Mayer 2003

64

14N(α,α)14N

• Small cross section at E < 3000 keV⇒ not suitable for RBS

• Several useful resonances at higher energies


© Matej Mayer 2003

67

Computer Simulation Codes

Program Author SinceRUMP M. Thompson 1983

Cornell UniversityUSA

RBX E. Kótai 1985Research Institute forParticle and Nuclear PhysicsHungary

SIMNRA M. Mayer 1996Max-Planck-Institutefor Plasma PhysicsGermany

DEPTH E. Szilágyi 1994Research Institute forParticle and Nuclear PhysicsHungary

WINDF N. Barradas 1997Technological and NuclearInstitute SacavemPortugal

Spectrumsimulator

Depthresolution

Depthprofile

rbs - rutherford backscattering...

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