Artificial neural networks for ion beam analysis

Artificial neural networks for
ion beam analysis

Nuno Barradas1 and Armando Vieira2
1
Instituto Tecnológico e Nuclear, Sacavém
2
Instituto Superior Engenharia, Porto

Armandosvieira.wordpress.com

• Introduction
• Biological and artificial neural
networks
• RBS data analysis with ANNs
• Application to real time RBS
• Outlook and prospects

Neurons – some characteristics
• Inputs: many, coming from many afferent
neurons. Take continuous values
• Outputs: only one, to many neurons. Yes/no
• Synaptic connections: where the output of one
neuron leads to the input in another one, with
efficiency depending on the connection
• Each neuron has a reduced, but non-linear,
processing ability
• The overall processing ability is distributed
amongst the connected set of neurons
• Learning is done through experience, coded in
changes in connection strength

Artificial neuron

inputs
weights
x0
w0
x1 w1
w2 output
x2 sum transmission

wn
xn

Transmission function: sigmoid, allows continuous output

Sigmóide

Multilayer perceptron (MLP) 1

outputs
outputs
Second hidden
layer

Hidden nodes First hidden
layer

inputs inputs

MLP 2

A feedforward ANN based on TLUs may generate
arbitrarily complex decision hipersurfaces

In principle, a MLP with a single hidden layer and sigmoidal
activation functions can approximate wiht any required
precision any functional relationship between two sets of
vectors of finite dimension

Neural Networks are
Advanced Learning Machines
They can learn higher order correlations.
FRUSTATION

Age

Money

Where is the “knowledge” about the
function?
In the weights (for a given architecture)

How does the ANN know what
are “good” weights for a given
problem?

Natural born talent and years of training

Learning - backpropagation
hidden layers

inputs

outputs

• Each connection has a given weight, initially random;
• A known set of inputs with corresponding known outputs is given;
• The weights are adjusted to minimise the diference between the
calculated and known outputs

Generalisation and overtraining
generalisation consists in building a statistical
model of the process that generates the data

error
An independent set of data, the Train set
test set, is used to control the Test set
amount of training required
Noise in the training data also
helps generalisation

Training epoch

Overfitting in action
Simpler hypothesis has lower error rate

Characteristics of ANNs
Characteristic Traditional methods Artificial neural networks
(Von Neumann)
logics Deductive Inductive
Processing principle Logical Gestalt
Processing style Sequential Distributed (parallel)
Functions realised concepts, rules, calculations Concepts, images, categories,
through maps
Connections between Programmed a priori Dynamic, evolving
concepts
Programming Through a limited set of Self-programmable (given an
rigid rules appropriate architecture)
Learning By rules By examples (analogies)
Self-learning Through internal algorithmic Continuously adaptable
parameters
Tolerance to errors Mostly none Inerent

ANNs – some properties
• The mean square error of an ANN decreases with the number of
parameters much faster than in a series expansion, particularly in
high dimensional spaces. The price to pay is the non-linearity in
relation to the parameters to optimise.
• Minising the mean square error of an ANN leads to the fact that the
outputs can be interpreted as probabilities.
• Pre- and post-processing normally increase the effciency of ANNS,
by reducing dimensionality, incorporating previous knowledge, and
making up for incomplete data.
• The role of the hidden layers is to reorganise the results of previous
layers into a more separable or classifiable form, and to establish
relevant characteristics
• Nodes may be added or eliminated during training, providing a
degree of flexibility to the architecture.

ANNs and Ion Beam Analysis
• Objective: automated data analysis
- Simulated annealing: IBA DataFurnace
general (RBS, EBS, ERDA, NRA, NDP)
not optimised for specific systems
- ANNs: (Ge)Si, (Er)Al2O3, Si/NiTC
for specific systems
instantaneous
• Objective: automated optimisation of experiments
- For automated control
• Integrated set of ANNs (and other code)

ANNs and Ion Beam Analysis
• ANNs recognize recurring patterns in the
input data, without knowledge of the
causes. ANNs are then an ideal candidate
to do automatically what RBS analysts
have long done:
to relate specific features of the data to
specific properties of the sample.
• …because RBS spectra can be treated as
just pictures

Rutherford backscattering: where is the pattern?
25Å Ge δ-layer under 400 nm Si
1500

(c)
1000
o
Angle of incidence
50

500
o
25 o
0
0

(b)
Yield (arb. units)

1000 o
120

500 o
Scattering angle
140
o
180

0

1.2 MeV (a)
1000

500
1.6 MeV Beam energy
2 MeV

0
0 100 200 300 400
Channel

Patterns in RBS: Ge δ-layers in Si
1500

1000
(b) 25, 50, 75 Å, under 200 nm Si

500 75
50
Yield (arb. units)

25
0

(a)
1000
25 Å, under 20, 100, 300, 600,
5 Ge 1000 nm Si
5 Si
4 Si 1 Si
500 3 Si 2 Si
4 Ge 3 Ge 2 Ge
1 Ge
0
0 100 200 300 400
Channel
…similar with other parameters

Ge implanted in Si: training data set
200
400
(a) 300
(b)
Number of cases

150 (c)
300
200
100 200
50 100 100

0 0 0
0,1 1 10 100 1000 10 100 1000 10000 10 100 1000
15 2 15 2 15 2
Dose (10 Ge/cm ) Depth (10 at/cm ) Width (10 at/cm )
300 1250
125 (d)
(e) 1000
Number of cases

100 (f)
200 750
75
50 500
100
25 250
0 0 0
1000 1250 1500 1750 2000 10 15 20 25 30 35 40 -30 -20 -10 0 10 20 30
Beam energy (keV) Detector FWHM (keV) θ inc (degree)
500
250 125 (i)
(g) 400 (h)
Number of cases

200 100
150 300
75
100 200 50
50 100 25
0 0 0
130 140 150 160 170 180 0 100 200 300 400 10
-6 -5
10
αscatt (degree) Charge x Ω (µC msr) Pileup factor

Ge in Si: ANN architecture
architecture train set error test set error
(I, 100, O) 6.3 11.7
(I, 250, O) 5.2 10.1
(I, 100, 80, O) 3.6 5.3
(I, 100, 50, 20, O) 4.2 5.1
(I, 100, 80, 50, O) 3.0 4.1
(I, 100, 80, 80, O) 2.8 4.7
(I, 100, 50, 100, O) 3.0 4.2
(I, 100, 80, 80, 50, O) 3.2 4.1
(I, 100, 80, 50, 30, 20, O) 3.8 5.3

Ge in Si: training

0,8
train set
Mean square error

0,6 test set

0,4

0,2

0,0
0 25 50 75 100 125 150
Training iteration

Performance: test set
3000
a) data
at/cm

ANN
Depth (10 )
2

2000
15

1000

0

b)
at/cm

data
Dose (10 )

ANN
2

100
15

10

1

0.1
0 10 20 30 40 50 60
Test case number

Ge in Si training: eliminated cases
5
10
(a)
4
10
Yield (counts)

10
3
Ge
2
10 10
3

Depth (10 at/cm )
2
1
10

15
0
10 2
0 25 50 75 100 125 10

50
(b)
Yield (10 counts)

40
Ge 10
1

30
3

-1 0 1 2 3
10 10 10 10 10
20 15 2
Dose (10 Ge/cm )
10

0
0 20 40 60
Channel

Ge in Si results: real data

8000

6000
Yield (counts)

4000

2000

0
0 20 40 60 80 100 120
Channel

Ge in Si results: real data
Values derived with NDF Values obtained with the ANN

sample Ge (1015 at/cm2) depth (1015 at/cm2) Ge (1015 at/cm2) depth (1015 at/cm2)
1 16.7 332.8 16.3 267.4
2 14.4 302.3 12.4 223.7
3 13.6 318.2 15.3 307.2
4 14.7 334.5 12.4 236.8
5 15.7 378.0 10.6 245.7
6 9.3 250.7 12.2 308.7
7 26.8 246.3 27.9 214.3
8 9.8 349.1 12.7 359.4
9 9.6 356.8 12.6 384.7
10 9.7 316.3 11.9 329.4

Data analysis: (Er)Al2O3
o 15 2
setup II, αscatt=180 , 4x10 Er/cm
10000

7500
Yield (counts)

5000

2500 Er peak

0 20 40 60 80 100
Channel

Anything in Al2O3: test set
4000

DepthANN (10 at/cm )
2
3000 b)

15 2000

1000

0
0 1000 2000 3000 4000
15 2
Depthdata (10 at/cm )

100
DoseANN (10 at/cm )

a)
2

10
15

1

0,1

0,1 1 10 100
15 2
Dosedata (10 at/cm )

Anything in Al2O3
nominal implant beam setup / angle solid dose depth
dose energy energy scattering of angle (1015 at/cm2) (1015 at/cm2)
(at/cm2) (keV) (MeV) angle Incidence -charge
(µC msr) ANN NDF ANN NDF

28 Ti 1×1015 100 1.6 II/160º 6º 18.0 0.26 1.34 1307 742
32 1×1015 100 1.6 II/180º 6º 104.4 0.65 1.08 1561 706
35 1×1017 100 1.6 II/180º 5º 57.6 75.7 92.4 756 632
36 Fe 1×1016 160 1.6 II/160º 4º 17.55 10.0 10.6 1384 1222
40 1×1016 160 1.6 II/180º 4º 99.0 9.49 10.3 1320 904
43 5×1017 160 1.6 II/180º 4º 55.7 365 407 832 487
21 Co 1×1015 150 2 I/180º 7º 99.2 0.68 0.96 1161 680
22 5×1016 150 2 I/180º 3º 94.8 40.9 48.4 1119 729
24 5×1017 150 2 I/180º 2º 64.3 385 448 632 622
8 Er 8×1013 200 1.6 II/160º 0º 5.83 0.03 0.07 650 770
11 4×1015 200 1.6 II/160º 0º 6.87 3.39 3.75 922 726
15 4×1015 200 1.6 II/180º 0º 20.48 4.89 3.83 861 736
26 Au 6×1016 160 2 II/180º 2º 52.0 69.6 59.3 278 394

Architecture as in Ge in Si

Anything in anything
• Any element, with Z between 18 and 83, into any
target composed of one or two lighter elements .

• Same architecture as before led to very large errors
• Extremely large networks were necessary to obtain
train errors around 20%: complexity of ANN
expands to meet complexity of problem.

• Pre-processing: reduce complexity of problem.
• Peak recognition routine determines automatically
the peak position and area. It fails ocasionally (5-
10%).

Anything in anything – inputs and outputs
• Experimental conditions
E0 1 : 2.1 MeV
αscatt 135º : 180º
θinc -20º : 20º (IBM geometry)
Q.Ω 1 : 200 µC msr
(FWHM: 10 : 40 keV)
• Sample
Z 18 : 83
M (redundant)
Z1, Z2 6 : 82
f1, f2 0:1
• Pre-processing: P (peak position), A (area)
• Outputs
Dose 1 : 100 ×1015 at/cm2
Depth 100 : 3700 × 1015 at/cm2

Anything in anything
Network Train error Test error # eliminated cases
Topology (%) (%) (%)
(12:30:10:2) 3.15 3.37 19.7
(12:30:20:2) 3.12 3.70 20.7
(12:40:10:2) 3.20 3.25 19.8
(12:40:20:2) 2.98 3.22 20.5

ANN DoseANN/DoseNDF |DepthANN - DepthNDF|
(1015 at/cm2)
Ge in Si 1.11 53
Er in Al2O3 1.17 106
all in Al2O3 1.02 235
all in all 0.96 83

Data analysis: Si/NiTaC
150

125 a)
100
1.75 MeV protons:
75
EBS
Ta
co 50
un 25 C Si
3ts)
Yi Ni Simulated RBS spectrum
el 0 (solid line) for two samples,
d 80
(1 calculated for the outputs
b)
0 60 given by the ANN. The
dashed lines corresponds
40 to the contribution from
Si Ta each element, squares are
Ni
20
the collected data
C
0
60 80 100 120
Channel

Data analysis: Si/NiTaC
NDF ANN
sample t C (at.%) Ni (at.%) Ta (at.%) t C (at.%) Ni (at.%) Ta (at.%)
(10 at/cm2)
15
(10 at/cm2)
15

1 6890 7.2 79.4 13.4 6918 7.2 78.2 14.6
2 7286 7.6 78.4 14.0 7387 7.5 77.0 15.5
3 6437 10.7 72.4 16.9 6593 10.8 72.3 16.9
4 7516 7.7 72.1 20.2 7752 8.3 72.0 19.7
5 5975 13.7 62.5 23.8 5858 13.1 64.0 22.9
6 6898 12.5 64.4 23.1 7111 13.0 63.1 23.9
7 5774 16.2 57.6 26.3 5719 17.7 56.0 26.3
8 5984 19.1 50.1 30.8 5993 19.8 49.1 31.1
9 7198 22.6 42.8 34.6 7205 22.9 42.1 35.0
10 8352 18.0 44.4 37.6 8419 20.2 41.4 38.4
11 6866 22.4 36.4 41.2 6904 24.2 33.8 42.0
12 7769 24.2 34.1 41.7 7691 25.3 30.6 44.1
13 7662 14.9 61.7 23.4 7858 14.8 61.4 23.8
14 6868 13.9 64.6 21.5 7025 14.5 64.2 21.3
15 5449 16.3 60.6 23.1 5490 16.6 60.4 23.0
16 4809 15.0 63.3 21.7 5208 16.2 62.3 21.5

Ultra thin films of AlNxOy
• Thin films of AlNxOy are being used as
insulating barriers between the metallic
layers of spin-tunnel junctions for
advanced read and recording devices
• RBS analysis of these films is an hard task
• Relevant signals from N and O are small
and superimposed to a large background
of Si signal. Al signal is also partially
superimposed to the Si background.

40

35 (a) Raw Data Sample 3 AlNxOy t
ANN Result
30 Sample 4
25
ANN Result
E = 1 - 2 MeV
Yield (x10 )
3

20 angle of incidence = -40º - +40º
15 Q.Ω = 52.4 - 393 µC msr
10 t = 150 - 850×1015 at/cm2.
5

0 (unintentional channelling)
50 75 100 125 150 175 200
Channel

40

35 (b) Smoothed Data Sample 3
Sample 4
30

25
Yield (x10 )
3

20

15

10

5

0
50 75 100 125 150 175 200
Channel

AlNxOy t - training
1

Mean square error 0,1

Test set

Training set

0,01
0 50 1000 2000 3000 4000 5000 6000 7000
Training iteration

Network Train set MSE (%) Test set MSE (%)
ANN-Raw 2,2 2,8
ANN-Smooth 2,9 3,7
ANN-Differentiated 2,4 3,4
ANN-No Exp. Param 3,1 4,3

Sample ANN Thickness [Al] [N] [O]
1 Raw 0.92 (0.12) 0.87 (0.08) 1.17 (0.08) 0.75 (0.5)
Smoothed 0.92 (0.12) 0.85 (0.08) 1.2 (0.08) 0.78 (0.5)
Differentiated 0.94 (0.16) 0.94 (0.1) 1.07 (0.1) 1.1 (0.3)
No exp. Param. 0.84 (0.19) 0.83 (0.08) 1.14 (0.09) 1.66 (0.78)
2 Raw 1.14 (0.18) 0.76 (0.17) 1.19 (0.09) 1.5 (1.31)
Smoothed 1.4 (0.18) 0.77 (0.2) 1.17 (0.07) 1.59 (1.24)
Differentiated 1.06 (0.08) 1.01 (0.08) 1.02 (0.08) 0.79 (0.34)
No exp. Param. 1.09 (0.15) 0.98 (0.11) 1.04 (0.11) 0.79 (0.26)
3 Raw 0.91 (0.17) 0.95 (0.13) 1.12 (0.13) 0.51 (0.88)
Smoothed 0.9 (0.15) 0.93 (0.11) 1.1 (0.15) 0.85 (0.86)
Differentiated 0.88 (0.15) 0.99 (0.12) 1.04 (0.1) 0.86 (0.3)
No exp. Param. 0.86 (0.12) 0.93 (0.14) 1.09 (0.11) 0.92 (0.51)
4 Raw 1.14 (0.21) 0.83 (0.09) 7.16 (0.64) 0.75 (0.15)
Smoothed 1.1 (0.2) 0.89 (0.1) 6.91 (0.63) 0.73 (0.16)
Differentiated 0.82 (0.17) 1.13 (0.1) 1 (0.27) 0.98 (0.07)
No exp. Param. 0.82 (0.16) 0.95 (0.09) 1.3 (0.31) 1.09 (0.08)
5 Raw 0.08 (0.03) 1.27 (0.12) 16.82 (1.72) 0.01 (0.04)
Smoothed 0.11 (0.07) 1.09 (0.1) 19.1 (1.83) 0.01 (0.05)
Differentiated 0.1 (0.03) 1.38 (0.11) 15.21 (1.64) 0.04 (0.01)
No exp. Param. 0.1 (0.01) 1.7 (0.19) 10.29 (4.59) 0.09 (0.02)

Real time RBS
• Composition and depth profile of thin films
treated through annealing

• Objective: Determine diffusion coefficients

• Hundreds of spectra analysed per sample,
meaning that each sample can take weeks
to analyse!

Systems tested so far
• CoSi
• NiErSi
• NiPtSi
• For each layer we want to evaluate:
• Thickness
• Concentrations
• Roughness (?)

How to define the problem:
The CoSi system

• layer 1: Si
• layer 2: Co2 Si
• layer 3: Co Si2
• layer 4: CoSi
• layer 5: Co

CoSi annealing at 3°C/min (200°C -600°C)

annealing two T-steps; 430°C and 565°C

(left) Comparison between ANN and RUMP at low temperature.
(right) Results after using NDF to optimise the fit, the ANN results
are used as in input for NDF.

The Ni Er Si system
• layer 1: Si
• layer 2: Six Ni1-x
• layer 3: Ni
• layer 4: Six Niy Er 1-x-y
• layer 5: Six Ni1-x

• 9 parameters (5 thickness + layer 2 x,
layer 4 x, layer 4 y,layer 5 x)

0.00, 139.42, 395.48, 95.32, 309.08
2500

2000

1500

1000

500

0
100 150 200 250 300 350

The Ni Pt Si system
• layer 1: Ni (Pt)
• layer 2: Pt Six
• layer 3: Ni2 Si (Pt)
• layer 4: Ni Si (Pt)

• 12 parameters (6 thickness + 6 concentrations)

Layer 4
Concentration Thickness
0.08 800

600
0.06

400
ANN

0.04

200

0.02
0

0 -200
0 200 400 600 800
0 0.02 0.04 0.06 0.08 0.10

Target

Layer 2
Concentration Thickness

0.5 80

60

0.3
40
ANN

20
0.1

0

-0.1 -20
0 0.2 0.4 0.6 0 20 40 60

Target

Conclusion
• Experimental data collection … 2 weeks

• Traditional analysis … 6 months

• ANN Analysis … 1 week - for beginners
• … 2 days - for experts!

Artificial neural networks for ion beam analysis

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