1. 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
2. • Introduction
• Biological and artificial neural
networks
• RBS data analysis with ANNs
• Application to real time RBS
• Outlook and prospects
3. 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
6. Multilayer perceptron (MLP) 1
outputs
outputs
Second hidden
layer
Hidden nodes First hidden
layer
inputs inputs
7. 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
8. Neural Networks are
Advanced Learning Machines
They can learn higher order correlations.
FRUSTATION
Age
Money
9. 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?
11. 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
12. 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
14. 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
15. 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.
16. 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)
17. 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
18. 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
19. 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
22. 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
23. 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
30. 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%).
32. 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
33. 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
35. 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.
36. 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
37. 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
39. 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!
40. Systems tested so far
• CoSi
• NiErSi
• NiPtSi
• For each layer we want to evaluate:
• Thickness
• Concentrations
• Roughness (?)
41. 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
44. (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.
46. 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)
50. The Ni Pt Si system
• layer 1: Ni (Pt)
• layer 2: Pt Six
• layer 3: Ni2 Si (Pt)
• layer 4: Ni Si (Pt)
• layer 5: Ni Si (Pt)
• layer 6: Ni Si (Pt)
• 12 parameters (6 thickness + 6 concentrations)