Artificial neural networks for ion beam analysis

Artificial neural networks for ion beam analysis Nuno Barradas 1 and Armando Vieira 2 1 Instituto Tecnológico e Nuclear, Sacavém 2 Instituto Superior Engenharia, Porto www.defi.isep.ipp.pt/~asv [email_address]

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

Introduction
Simple problems:
“ What is the emission of a black body?”
“ How do two charged particles interact?”
“ How do two massive particles interact?”
“ How does a system composed of 10 23 similar particles evolve?”
“ What are things made of?”
Complex problems:
“ What happens when a butterfly flies?”
“ Why life is so diverse?”
“ Will it rain tomorrow? And in 10 years’ time?”
“ How the brain builds models?”
An emergent paradigm of problem solving?
Artificial neural networks: conectionism
Genetic algorithms: search schematas
Simulated annealing: energy minimization

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 x 0 x 1 x 2 x n w 0 w 1 w 2 w n output inputs su m transmis sion weights

TLU (threshold logic unit)
activation a = x  w
output y(a) = 1 if a   , 0 if a < 
Hardware implementation: 1 0.8 0.8 0.8 1 0.8 1 1 1 1 1 1 0 0.2 0.2 0.8 0 0.2 0 1 0 0 0 1 1 0.8 0.8 0.2 1 0.8 1 0 1 1 1 0 0 0.2 0.2 0.2 0 0.2 0 0 0 0 0 0 output a x 2 x 1 output a x 2 x 1 output a x 2 x 1 Degraded inputs Degraded weights w = (0.2,0.8),  =0.5 w = (0.2,0.8),  =0.5 w = (0,1),  =0.5

Decision hiperplanes
a=  leads to w  x =  , which, for fixed w and  , defines an hiperplane normal to the weight vector w , with position defined by the threshold  .
Let e.g. w =(1,1) and  =1.5 1 2 1 1 0 1 0 1 0 1 1 0 0 0 0 0 output a x 2 x 1 w = (1,1),  =1.5

Decision hiperplanes 3 – non linearly separable classes

Transmission function: sigmoid, allows continuous output

Multilayer perceptron (MLP) 1

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.
Money Age FRUSTATION

How does the ANN know what are “good” weights for a given problem? Where is the “knowledge” about the function? In the weights (for a given architecture)

Natural born talent and years of training

Learning - backpropagation
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
An independent set of data, the test set, is used to control the amount of training required Noise in the training data also helps generalisation

Overfitting in action Simpler hypothesis has lower error rate

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

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) Al 2 O 3 , Si/NiTC
for specific systems
instantaneous
 Objective: automated optimisation of experiments
- For automated control
 Integrated set of ANNs (and other code)

RUTHERFORD BACK SCATTERING Basic Principles

ELASTIC COULOMB SCATTERING Consider an ion of charge z, mass m and initial kinetic energy E o being scattered elastically from a stationary nucleus of charge Z and mass M purely by the Coulomb force. The final energy E of the scattered ion is a function of the angle of scatter  from the initial direction and the ratio M/m.  m, E o m, E M, 0 M , ( E o – E ) Recoiling nucleus Scattered ion

Ion beam analysis

Rutherford backscattering K=E/E 0 =   2 1 2 2 2 2 / sin cos M m m M m                                                    2 2 4 4 4 2 1 2 1 2 2 1 2 1 2 2 m Z M Z e E m M m M sin / / sin cos / / sin  E/  t = K . dE dt E 0 + dE dt E' 0 /|cos  |  E 0 E Energy E E 0 E 1 E 2 Energy E 2 E 1 E 0 E 1 E 2 E 3 E 3 E 1 Energy E 2 What? Where? How much?

KINEMATIC FACTOR E can be derived from the principle of conservation of energy and momentum, and is given by (in laboratory frame of reference): The multiplication factor of E o on the right hand side of the equation is often referred to as the kinematic factor and is denoted by k . For M/m > 1, k is a slow-varying function of  , having the maximum value of 1 at  = 0 and the minimum value at  = 180 o . For M/m = 1, the value of k is zero beyond 90 o .

M/m = 1 M/m = 4 M/m = 20 Plots of k vs  for M/m = 0, 4, 20

Plots of k vs M/m for  = 180 o The small gradient at large M/m ratios implies that mass separation is poor for higher M/m ratios.

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  -layer under 400 nm Si
Angle of incidence
Scattering angle
Beam energy

Patterns in RBS: Ge  -layers in Si
25, 50, 75 Å, under 200 nm Si
25 Å, under 20, 100, 300, 600, 1000 nm Si
… similar with other parameters

Ge implanted in Si: training data set

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

Ge in Si: training

Performance: test set

Ge in Si training: eliminated cases

Ge in Si results: real data

Ge in Si results: real data 329.4 11.9 316.3 9.7 10 384.7 12.6 356.8 9.6 9 359.4 12.7 349.1 9.8 8 214.3 27.9 246.3 26.8 7 308.7 12.2 250.7 9.3 6 245.7 10.6 378.0 15.7 5 236.8 12.4 334.5 14.7 4 307.2 15.3 318.2 13.6 3 223.7 12.4 302.3 14.4 2 267.4 16.3 332.8 16.7 1 depth (10 15 at/cm 2 ) Ge (10 15 at/cm 2 ) depth (10 15 at/cm 2 ) Ge (10 15 at/cm 2 ) sample Values obtained with the ANN Values derived with NDF

Data analysis: (Er) Al 2 O 3

Anything in Al 2 O 3 : test set

Anything in Al2O3 Architecture as in Ge in Si 394 278 59.3 69.6 52.0 2º II/180º 2 160 6  10 16 26 Au 736 861 3.83 4.89 20.48 0º II/180º 1.6 200 4  10 15 15 726 922 3.75 3.39 6.87 0º II/160º 1.6 200 4  10 15 11 770 650 0.07 0.03 5.83 0º II/160º 1.6 200 8  10 13 8 Er 622 632 448 385 64.3 2º I/180º 2 150 5  10 17 24 729 1119 48.4 40.9 94.8 3º I/180º 2 150 5  10 16 22 680 1161 0.96 0.68 99.2 7º I/180º 2 150 1  10 15 21 Co 487 832 407 365 55.7 4º II/180º 1.6 160 5  10 17 43 904 1320 10.3 9.49 99.0 4º II/180º 1.6 160 1  10 16 40 1222 1384 10.6 10.0 17.55 4º II/160º 1.6 160 1  10 16 36 Fe 632 756 92.4 75.7 57.6 5º II/180º 1.6 100 1  10 17 35 706 1561 1.08 0.65 104.4 6º II/180º 1.6 100 1  10 15 32 742 1307 1.34 0.26 18.0 6º II/160º 1.6 100 1  10 15 28 Ti depth (10 15 at/cm 2 ) ANN NDF dose (10 15 at/cm 2 ) ANN NDF solid angle -charge (  C msr) angle of Incidence setup / scattering angle beam energy (MeV) implant energy (keV) nominal dose (at/cm 2 )

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
 scatt 135º : 180º
 inc -20º : 20º (IBM geometry)
Q.  1 : 200  C 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  10 15 at/cm 2
Depth 100 : 3700  10 15 at/cm 2

Anything in anything 20.5 3.22 2.98 (12:40:20:2) 19.8 3.25 3.20 (12:40:10:2) 20.7 3.70 3.12 (12:30:20:2) 19.7 3.37 3.15 (12:30:10:2) # eliminated cases (%) Test error (%) Train error (%) Network Topology 83 0.96 all in all 235 1.02 all in Al 2 O 3 106 1.17 Er in Al 2 O 3 53 1.11 Ge in Si |Depth ANN - Depth NDF | (10 15 at/cm 2 ) Dose ANN /Dose NDF ANN

Data analysis: Si/NiTaC
1.75 MeV protons: EBS
Simulated RBS spectrum (solid line) for two samples, calculated for the outputs given by the ANN. The dashed lines corresponds to the contribution from each element, squares are the collected data

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

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.

AlN x O y t E = 1 - 2 MeV angle of incidence = -40º - +40º Q.  = 52.4 - 393  C msr t = 150 - 850×10 15 at/cm 2 . (unintentional channelling)

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

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

RBS without humans
N. P. Barradas a,b,* , A. Vieira a,c , R. Patrício a,d
a Instituto Tecnológico e Nuclear, Sacavém, Portugal
b Centro de Física Nuclear da Universidade de Lisboa, Portugal
c Instituto Superior de Engenharia do Porto, Portugal
d Instituto Superior Técnico, Lisboa, Portugal
* e-mail: [email_address]
Presented at IBA15 - Cairns

Data classification: (Ge) Si
Three classes:
(1) clean spectra
(2) superimposed signals
(3) separated signals, small doses
There may be class mixing:
(1)+(2): partial superposition
(1)+(3): intermediate doses
(2)+(3): superimposed signals, small doses
(1)+(2)+(3): partial superposition, small doses

Code required for automation
ANNC: for classification. Output is membership probability
ANNi: for class (i). Output is Ge dose and depth
Feed i: feedback algorithm for class (i):
4× F old - - 1.1×E min_no_superp if C > 300  C msr F3 - 180º (2 nd step) 0º (1 st step) 2 MeV (3 rd step) F2 2.25× F old if low Statistics - 0º if partial superposition - F1 C  scatt  inc E

Integrated feedback system ANNC ANN 1 ANN 2 ANN 3 <O> Feed 1 Feed 2 Feed 3 <E> D ANN =O D E 1 E 2 E 3 E O 1 O 2 O 3 w i w i w i 1 st or E changed? no yes begin end

Results: experimental conditions class (1)

Results: Classes (2) and (3)
a) Initial classif: correct Initial class (3) in both
b) Initial classif: (3) a) Final class: (1)
Final class (1) in both b) Final class: (3)

Results of the classification ANN for the spectra before and (after) optimisation of the experimental conditions
65.3 (29.9) 33.1 (7.5) 1.6 (62.6) 3 7.3 (4.0) 90.0 (65.2) 2.7 (30.8) 2 2.4 (0) 5.9 (1.1) 91.7 (98.9) 1 3 2 1 ANNC real

1.03(51) 2.67(3.00) 0.94(25) 1.27(82) NDF 7.64(9.55) 4.41(5.06) 3.57(4.75) 2.10(1.91) ANN f 33.2(21.0) 8.94(8.21) 2.47(1.34) 1.37(71) ANN i 2 or 3 0.94(18) 1.05(25) 0.93(24) 1.05(31) NDF 1.39(47) 1.35(80) 1.08(46) 1.08(54) ANN f 17.1(15.1) 5.80(5.69) 1.56(71) 1.27(65) ANN i 1 3 0.88(24) 0.96(13) 0.96(15) 0.97(3) NDF 0.94(99) 0.73(33) 1.22(51) 0.98(06) ANN f 0.14(17) 0.37(14) 1.08(56) 0.98(11) ANN i 2 or 3 0.93(17) 1.00(5) 0.98(3) 1.00(1) NDF 0.55(35) 0.72(36) 0.87(11) 0.98(3) ANN f 0.53(47) 0.66(35) 1.17(38) 1.08(13) ANN i 1 2 1.00(1) 1.00(1) 0.99(2) 1.00(2) NDF 0.81(10) 0.98(4) 0.85(14) 1.01(12) ANN f 1.08(12) 1.07(11) 0.87(14) 1.03(13) ANN i 1 1 dose depth dose depth analysis final class real class ANNC i : wrong ANNC i : correct

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: Co 2 Si
layer 3: Co Si 2
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.

NFD fit to data # 94
.

The Ni Er Si system
layer 1: Si
layer 2: Si x Ni 1-x
layer 3: Ni
layer 4: Si x Ni y Er 1-x-y
layer 5: Si x Ni 1-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

Example: thickness

Example: concentration

The Ni Pt Si system
layer 1: Ni (Pt)
layer 2: Pt Si x
layer 3: Ni 2 Si (Pt)
layer 4: Ni Si (Pt)
layer 5: Ni Si (Pt)
layer 6: Ni Si (Pt)
12 parameters (6 thickness + 6 concentrations)

Thickness

Concentration

Layer 4 Concentration Thickness

Layer 2 Concentration Thickness

Conclusion
Experimental data collection … 2 weeks
Traditional analysis … 6 months
ANN Analysis … 1 week - for beginners
… 2 days - for experts!

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Artificial neural networks for ion beam analysis

by Armando Vieira on Jun 14, 2010

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Artificial neural networks for ion beam analysis — Presentation Transcript