Artificial neural networks for ion beam analysis

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Artificial neural networks for ion beam analysis

  1. 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. 2. • Introduction• Biological and artificial neural networks• RBS data analysis with ANNs• Application to real time RBS• Outlook and prospects
  3. 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
  4. 4. Artificial neuroninputs weights x0 w0 x1 w1 w2 outputx2 sum transmission wn xn
  5. 5. Transmission function: sigmoid, allows continuous output Sigmóide
  6. 6. Multilayer perceptron (MLP) 1 outputs outputs Second hidden layer Hidden nodes First hidden layer inputs inputs
  7. 7. MLP 2 A feedforward ANN based on TLUs may generate arbitrarily complex decision hipersurfacesIn principle, a MLP with a single hidden layer and sigmoidalactivation functions can approximate wiht any requiredprecision any functional relationship between two sets ofvectors of finite dimension
  8. 8. Neural Networks are Advanced Learning MachinesThey can learn higher order correlations. FRUSTATION Age Money
  9. 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?
  10. 10. Natural born talent and years of training
  11. 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. 12. Generalisation and overtraining generalisation consists in building a statistical model of the process that generates the data errorAn independent set of data, the Train settest set, is used to control the Test setamount of training requiredNoise in the training data alsohelps generalisation Training epoch
  13. 13. Overfitting in actionSimpler hypothesis has lower error rate
  14. 14. Characteristics of ANNsCharacteristic Traditional methods Artificial neural networks (Von Neumann)logics Deductive InductiveProcessing principle Logical GestaltProcessing style Sequential Distributed (parallel)Functions realised concepts, rules, calculations Concepts, images, categories, through mapsConnections between Programmed a priori Dynamic, evolving conceptsProgramming 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 parametersTolerance to errors Mostly none Inerent
  15. 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. 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. 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. 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. 19. Patterns in RBS: Ge δ-layers in Si 1500 1000 (b) 25, 50, 75 Å, under 200 nm Si 500 75 50Yield (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
  20. 20. 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) 1000Number 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
  21. 21. 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
  22. 22. Ge in Si: training 0,8 train setMean square error 0,6 test set 0,4 0,2 0,0 0 25 50 75 100 125 150 Training iteration
  23. 23. Performance: test set 3000 a) data at/cm ANN Depth (10 )2 200015 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
  24. 24. Ge in Si training: eliminated cases 5 10 (a) 4 10Yield (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 1 303 -1 0 1 2 3 10 10 10 10 10 20 15 2 Dose (10 Ge/cm ) 10 0 0 20 40 60 Channel
  25. 25. Ge in Si results: real data 8000 6000Yield (counts) 4000 2000 0 0 20 40 60 80 100 120 Channel
  26. 26. Ge in Si results: real data Values derived with NDF Values obtained with the ANNsample 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
  27. 27. Data analysis: (Er)Al2O3 o 15 2 setup II, αscatt=180 , 4x10 Er/cm 10000 7500Yield (counts) 5000 2500 Er peak 0 20 40 60 80 100 Channel
  28. 28. Anything in Al2O3: test set 4000DepthANN (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 )
  29. 29. 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 NDF28 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 63236 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 48721 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 6228 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 73626 Au 6×1016 160 2 II/180º 2º 52.0 69.6 59.3 278 394Architecture as in Ge in Si
  30. 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%).
  31. 31. 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
  32. 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 106all in Al2O3 1.02 235 all in all 0.96 83
  33. 33. Data analysis: Si/NiTaC 150 125 a) 100 1.75 MeV protons: 75 EBS Ta co 50 un 25 C Si3ts) 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
  34. 34. Data analysis: Si/NiTaC NDF ANNsample 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
  35. 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. 36. 40 35 (a) Raw Data Sample 3 AlNxOy t ANN Result 30 Sample 4 25 ANN Result E = 1 - 2 MeVYield (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. 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 2,8ANN-Smooth 2,9 3,7ANN-Differentiated 2,4 3,4ANN-No Exp. Param 3,1 4,3
  38. 38. 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)
  39. 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. 40. Systems tested so far• CoSi• NiErSi• NiPtSi• For each layer we want to evaluate: • Thickness • Concentrations • Roughness (?)
  41. 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
  42. 42. CoSi annealing at 3°C/min (200°C -600°C)
  43. 43. annealing two T-steps; 430°C and 565°C
  44. 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.
  45. 45. NFD fit to data # 94.
  46. 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)
  47. 47. 0.00, 139.42, 395.48, 95.32, 309.082500200015001000500 0 100 150 200 250 300 350
  48. 48. Example: thickness
  49. 49. Example: concentration
  50. 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)
  51. 51. Thickness
  52. 52. Concentration
  53. 53. Layer 4 Concentration Thickness 0.08 800 600 0.06 400ANN 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
  54. 54. Layer 2 Concentration Thickness 0.5 80 60 0.3 40ANN 20 0.1 0 -0.1 -20 0 0.2 0.4 0.6 0 20 40 60 Target
  55. 55. Conclusion• Experimental data collection … 2 weeks• Traditional analysis … 6 months• ANN Analysis … 1 week - for beginners• … 2 days - for experts!

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