M.Dapor, R.C.Masters, I.Ross, D.Lidzey, A.Pearson, I.Abril, R.Garcia-Molina, J.Sharp, M.Unčovský, T.Vystavel, C.Rodenburg

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1 Comparison between Experimental Measurement and Monte Carlo Simulation of the Secondary Electron Energy Spectrum of Poly methylmethacrylate (PMMA) and Poly(3- hexylthiophene-2,5-diyl) M.Dapor, R.C.Masters, I.Ross, D.Lidzey, A.Pearson, I.Abril, R.Garcia-Molina, J.Sharp, M.Unčovský, T.Vystavel, C.Rodenburg VIII Taller de colisiones inelásticas en la materia Playa del Carmen, Quintana Roo, December 2, 206

2 Outline Introduction Monte Carlo Code Monte Carlo Ingredients Spectra of PMMA Spectra of P3HT 2

3 Introduction Poly methylmethacrylate (PMMA) is considered as a water-equivalent material, having density and electronic properties quite similar to those of liquid water, hence being frequently used as a solid water or tissue phantom in order to facilitate dosimetry measurements. It is employed as well in microelectronics, since it is a common resist in nanolitographic techniques. Poly(3-hexylthiophene-2,5-diyl) (P3HT) is a polymer widely used in organic electronics. 3

Letting the particles carry out an artificial, random walk taking into account the effect of the single collisions it is possible to

4 Monte Carlo Method It is used for evaluating the many physical quantities necessary to the study of the interactions of particle-beams with solid targets. Letting the particles carry out an artificial, random walk taking into account the effect of the single collisions it is possible to accurately evaluate the diffusion process. 8 kev electrons striking a Si3N4 layer with a SiO2 substrate (Chris Walker, Mohamed El Gomati) 5 kev electrons in fayalite (Fe2SiO4). Casino software ( 4

5 * ) Monte Carlo Method Reflection electron energy loss spectra (MC, silicon dioxide, 2 kev) 0.04 Applications Secondary electron spectra (MC, silicon, kev) * 0.08 Energy loss of Auger electrons (ab-initio+mc, O K-LL Auger line in silicon dioxide) ).0 Intensity-(a.u.) 0.02 dn/de *(arb.*units) Intensity)(a.u.) Energy-loss-(eV) E*(eV) Information from different depths Auger electrons: ~ 0-20 Å Secondary electrons: ~ 50 Å Energy)(eV) Reflected electrons: depth depends on the primary electron energy M. Filippi, L. Calliari, M. Dapor, Phys. Rev. B 75 (2007) M. Dapor, B. J. Inkson, C. Rodenburg, J. M. Rodenburg. EPL 82 (2008) S. Taioli, S. Simonucci, L. Calliari, and M. Dapor. Phys. Rep., 493 (200) 237 5

Monte Carlo Method Applications Doping contrast.

and Energy Critical Dimension Scanning Electron Selective

Dapor, M. Ciappa, and W. Fichtner. M. Dapor, B. J.

6 Monte Carlo Method Applications Doping contrast. Image contrast Linewidth measurement in studies in pn-junctions and Energy Critical Dimension Scanning Electron Selective Scanning Electron Microscopy (CD SEM) Microscopy (ES SEM) M. Dapor, M. Ciappa, and W. Fichtner. M. Dapor, B. J. Inkson, C. J. Micro/Nanolith., MEMS, MOEMS, Rodenburg, J. M. Rodenburg. EPL 9 (200) (2008)

7 ' Monte Carlo Method Energy Selective Scanning Electron Microscopy (ESSEM) Image contrast in p-n junctions, obtained considering only the low energy electrons, is significantly higher than that obtained under standard conditions. Applications E 0 'dn/de ' Energy'(eV) ''' Å ''5' Å ''0 Å ''20'Å Monte Carlo calculated contributions of secondary electrons originating from different depths to secondary electron spectrum in silicon (E 0 = 000 ev) Selecting secondary electrons in a low energy window increases the doping contrast C. Rodenburg, M.A.E. Jepson, E.G.T. Bosch, M. Dapor, Ultramicroscopy, 0 (200) 85 7

Monte Carlo Method Applications The shower of secondary electrons can produce damage in the biomolecules by dissociative electron attachment.

8 Monte Carlo Method Applications The shower of secondary electrons can produce damage in the biomolecules by dissociative electron attachment. Dose-Energy of protons in PMMA Radial deposition of energy of protons in PMMA C. Udalagama, A. A. Bettiol, F. Watt, SEICS code (Abril et al.) Phys. Rev. B 80 (2009) P. de Vera, R. Garcia-Molina, I. Abril I, A.V. Solov yov, Phys. Rev. Lett. 0 (203)

9 Monte Carlo Ingredients A. Electron-atom interaction: elastic scattering cross-section Screened Rutherford cross-section Mott cross-section (relativistic partial wave expansion method) B. Electron-plasmon interaction: inelastic scattering cross-section Dielectric Ritchie s theory C. Electron-phonon interaction: inelastic scattering cross-section Fröhlich s theory D. Trapping phenomena Ganachaud and Mokrani semi-empiric model 9

10 Mott Cross-Section d el d = f(#) 2 + g(#) 2 where and f(#) g(#) are the direct and spin-flip scattering amplitudes, respectively 0

11 Mott Cross-Section l± = phase shifts X f (#) = {(l + )[exp(2i l ) 2iK ] + l[exp(2i l+ ) ]}Pl (cos #) l=0 X g(#) = [ exp(2i l ) + exp(2i l+ )] Pl (cos #) 2iK l= where K2 = E2 m2 c4 ~2 c 2 Pl = Legendres s polynomials Pl (x) 2 /2 dpl (x) = ( x ) dx

12 Cu 000 ev Cu 3000 ev 0 Rutherford " Mott 0.0 Rutherford DESCS ( /sr) " DESCS ( /sr) 0 Mott E Au 000 ev Au 3000 ev Mott Rutherford " DESCS ( /sr) Rutherford " DESCS ( /sr) 00 Scattering angle (deg) Scattering angle (deg) E Mott E-3 80 Scattering angle (deg) Scattering angle (deg) 2

13 Dielectric Theory f (k, ) = Im "(k, ) inel d = d~ E a0 ~ k± = p 2mE ± 3 Z k+ k p dk f (k, ) k 2 m (E ~)

14 Energy Loss Function apple Im = " 2 "(k, ) " 2 + "2 2 "(k, ) =" (k, )+i" 2 (k, ) 4

15 Monte Carlo Method The step-length s= ln(µ ) Elastic and inelastic collisions pin = in in + pel = = el in pin If a random number µ2 is less than or equal to pin, then the collision will be inelastic; otherwise, it will be elastic. 5

16 Monte Carlo Method The polar scattering angle µ3 = Pel (, E) = el Z 0 d el 2 sin # d# d The energy loss µ4 = Pinel (W, E) = 6 inel Z W 0 d inel dw dw

17 Monte Carlo Method 7

18 Fröhlich Cross-Section phonon "0 " ~ n(t ) + = ln a 0 "0 " E 2 + p p ~/E ~/E ~ is the electron energy loss (in the order of 0. ev) "0 is the static dielectric constant " is the high frequency dielectric constant n(t ) = e~/kb T is the occupation number H. Froehlich, Adv. Phys. 3 (954) 325 8

19 Trapping Phenomena Impurities, structural defects, grain boundaries and, in insulating materials, polarization fields have a stabilizing effect on the moving electron: pol = Ce E C and are constant depending on the material. J.P. Ganachaud and A. Mokrani, Surf. Sci. 334(995) 329 9

20 Condition for Transmission The interface with the vacuum represents a potential barrier, and not all the electrons that reach the surface can go beyond it. When a very slow electron reaches the target surface, it can emerge from the surface only if this condition is satisfied: E cos 2 e e is the (effective) electron affinity, i.e. the difference between the vacuum level and the bottom of the conduction band. 20

21 PMMA Energy Loss Function Im[-/ε(E,0)] 0.5 IMFP ( ) 00 S (ev/ ) E (ev) from Ritsko et al. optical data T (ev) T (ev) to IMFP and stopping power J. J. Ritsko, L. J. Brillson, R. W. Bigelow, T. J. Fabish, J. Chem. Phys. 69 (978) 393 M. Dapor, I. Abril, P. de Vera, R. Garcia-Molina, Eur. Phys. J. D 69 (205) 65 M. Dapor, Nucl. Instrum. Methods Phys. Res. B 352 (205) 90 M. Dapor, Frontiers in Materials 2 (205) 27 2

22 PMMA Spectra 200 ev (a), 400 ev (b), 600 ev (c), and 800 ev (d) primary electron energy M. Dapor, Appl. Surf. Sci. 39 (207) 3 22

23 PMMA Spectra 200 ev (a), 400 ev (b), 600 ev (c), and 800 ev (d) primary electron energy M. Dapor, Appl. Surf. Sci. 39 (207) 3 23

24 PMMA Spectra 200 ev (a), 400 ev (b), 600 ev (c), and 800 ev (d) primary electron energy M. Dapor, Appl. Surf. Sci. 39 (207) 3 24

25 PMMA Secondary Electron Yield Poly methylmethacrylate (PMMA) Experimental data: Reimer et al 992, Boubaya and Blaise (2007), Rau et al. (2008), Yasuda et al. (2008) M. Dapor, Appl. Surf. Sci. 39 (207) 3 25

26 P3HT Energy Loss Function ELF of the low-order P3HT as a function of the energy loss W. Black line: experimental data. Red line: Sum of Drude- Lorentz functions. 26

27 P3HT Inelastic Mean Free Path C a l c u l a t e d I M F P o f electrons in low-order P3HT (solid line) compared with the measured IMFP of electrons in Poly(3- octylthiophene) (POT), a polymer structurally very similar to P3HT (filled circles) Experimental data (IMFP of POT): B. Lesiak et al., Applied Surface Science 74(200) 70 27

28 P3HT Spectrum Monte Carlo electron spectrum of low-order P3HT 28

29 P3HT Spectrum S e c o n d a r y e l e c t r o n spectrum (filtering depth =2.5nm) of low-order P3HT, for an incident electron energy E 0 =200eV. The Monte Carlo results (red line) are compared with the experimental data of the un-annealed sample (black line) 29

30 P3HT Spectrum The Monte Carlo simulated SES shows a peak at very low energy followed by a smooth decrease of the spectrum and a second very broad shoulder very similar to that experimentally observed. The reason of this shape is that electrons with very low energy are not effective in exciting target electrons from the valence band to the conduction band. 30

31 P3HT Spectrum Secondary electron spectra of low-order P3HT for different values of the filtering depth, for an incident electron energy E 0 =200eV 3

32 Conclusion We have described the Monte Carlo code We have shown Monte Carlo simulated spectra of electrons emerging from PMMA and P3HT We have compared our simulations with the available experimental data 32

33 Thank you for your kind attention 33

Supplementary Figure 1: Comparison of SE spectra from annealed and unannealed P3HT samples. See Supplementary Note 1 for discussion.

Supplementary Figure 1: Comparison of SE spectra from annealed and unannealed P3HT samples. See Supplementary Note 1 for discussion. Supplementary Figure 2: SE spectra from blend films. a) and b) compare