Optická emisní spektroskopie atomů Diagnostické metody 1 Zdeněk Navrátil Ustav fyzikální elektroniky Přírodovědecké fakulty Masarykovy univerzity, Brno OE R modelling CRM neon Examples ooo Self-absorptio Outline O OES 0 CR modelling Q CR model for neon discharge Q Examples • DC • RF • MW Q Measurement of densities by self-absorption methods OES R modelling CRM neon Examples ooo Self-absorptio ■ Instrumentation • typically grating spectrometer of Czerny-Turner mounting equipped with CCD/ICCD detector • typical spectral range 190-1100 nm • sensitivity of detectors (silicon CCD, photocathode of PMT), grating efficiency 9 resolution: number of illuminated grating grooves, slit width, pixel size R = A/AA = mN OES R modelling CRM neon Sensitivities Examples ooo Self-absorptior PMC-150: Cathode Quantum Efficiency 100 c ai E 4-1 c a « 10 0,1 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 XI nm • grating efficacy, fibre efficacy, windows 200 300 400 500 600 700 800 900 1000 1100 1200 Wavelength (nm) OES R modelling CRM neon Examples ooo Self-absorptio Technique overview - how we measure • collecting the light emitted by plasma (optical emission spectroscopy, OES): • non-intrusive • sensing the light at the plasma boundary • optical probes • sending the light through the plasma (optical absorption spectroscopy): • based on Lambert-Beer law • can disturb the plasma, two ports • white light, hollow cathode lamps, lasers • collecting the light emitted and reabsorbed by the plasma (self-absorption methods of OES) OES R modelling CRM neon Examples ooo Self-absorptio Technique overview - how we measure • collecting the light emitted by plasma (optical emission spectroscopy, OES): • non-intrusive • sensing the light at the plasma boundary —> self-absorption can play a role • optical probes • sending the light through the plasma (optical absorption spectroscopy): • based on Lambert-Beer law • can disturb the plasma, two ports • white light, hollow cathode lamps, lasers • collecting the light emitted and reabsorbed by the plasma (self-absorption methods of OES) OES R modelling CRM neon Examples ooo Self-absorptio Technique overview - what we look at • line positions = wavelengths: electric, magnetic fields, atom velocities (Stark, Zeeman, Doppler effect) • lineshapes and linewidths: electron density, gas pressure, density, temperatures (Stark, van der Waals, resonance, Doppler line broadening) • line intensities:... all OES R modelling CRM neon Examples ooo Self-absorptio Technique overview - what we look at • line positions = wavelengths: electric, magnetic fields, atom velocities (Stark, Zeeman, Doppler effect) • lineshapes and linewidths: electron density, gas pressure, density, temperatures (Stark, van der Waals, resonance, Doppler line broadening) • line intensities:... all • relative - instrument spectral sensitivity is taken into account, no absolute intensity calibration is performed output: relative populations of excited states, excitation temperatures etc. • absolute - access to absolute densities of excited states, electron density etc. OES R modelling CRM neon Examples ooo Absolute intensity measurement radiant flux/zarivy tok - energy emitted/incident on surface per unit irradiance - flux density (per unit surface) / = áS ~ átአWm • specified during calibratrion of calibrated light sources (spectral irradiance) • optical fibre is not a detector of irradiance (acceptance angle) • radiometric irradiance probes, cosine correction diffusers, integrating spheres,... OES R modelling CRM neon Examples ooo Self-absorptior Absolute intensity measurement 2 radiance (zář) - radiant flux per unit perpendicular surface and unit solid angle L = d20 á3ď dScosfldft dtdScosfldft Wm 2sr 1 (3) radiance x irradiance / = J L(0) cosfldft ft For constant L (Lambert) radiators / = 7iL. for description of radiating solid surfaces (4) OES R modelling CRM neon Examples ooo Self-absorptio ■ Absolute intensity measurement 3 • emission coefficient - radiant power emited by unit volume into unit solid angle d3 1.6-10 V^AE)3 (cm"3) OE CR modelling CRM neon Example ooo Collisional-radiative modelling coupled DE for densities of excited states drij dt d n; ~dt c,r population and depopulation processes are very fast d tij ( d tij dt dt = 0 c,r not valid for ground-state atoms, ions, metastables, high pressure 0,0 2,0x10"' 4,0x10"' gas ^ 1,0x10* 2,0x10* 3,0x10* CR modelling CRM neon Level balance drip + VÍ^O^O) = -ScrA7eA7o + acrA7eA7 ion dn ion dt + VisionViin) = +ScrA7eA70 - acrA?eA? ion classification of models (plasma state) • ionizing plasma Scr/7e^o — ^cr^e^ion > 0 • plasma conducting current, ionizing waves • recombining plasma ScrneA?o — Ofcr/7e/7ion < 0 • afterglows, outer regions of flames • equilibrium plasma ScrA7e^o — ^cr^e^ion = 0 (ioniozation-recombination equilibrium) Example ooo Self-absorpti Wn/2řiJ V.(n0w0l -t-i-0 ionizing plasma . <7.(njW,) V.(n0wa) recombining plasma A equilibrium plasma OE CR modelling CRM neon Examples ooo Excitation phases: corona phase population by electron impact excitation, radiative deexcitation j>i j TT ii 0 • saturation of the excited state densities with increased nQ • no Saha equilibrium, S//7/ ^> a;/7ion OE< CR modelling CRM neon Examples ooo Self-absorptio Excitation phases: excitation saturation phase 2 • stepwise excitation —>• ladder-like excitation flow • coefficients of upward processes are larger (closer upper levels, higher statistical weights of upper levels) /c/_i}/nen/_i - /c/7/_iA7eA7/ = /c/7/+iA7eA7/ /c/+i}/A7eA7/+i S/A7eA7/ OE CR modelling CRM neon Examples ooo Excitation phases: partial local thermodynamic equilibrium 9 2 equilibria: excited state x ion state, neighbouring excited states • ionization ~ recombination ^> excitation flow /c/_l,/nen/_i - /c/,/_lA7eA7/ = /c/7/+lA7eA7/ /c/+i}/A7eA7/+i S/A7eA7/ + a/A7eA7 ion n ± 0 CR modelling CRM neon Role of dominant electron collisions Examples ooo Self-absorpti 1016 m'3 10' 10l 10 11 12 13 tV Í4 He =1016 m-3 1016 fO4- _L_ 10 -1-1_I I 11 12 13 tV n Hp =1018 m 3 Cr1 10' vŕ -J-1_1 10 11 12 13 sV 1i He =1020 rrT3 1016 -3 m 70' 70' Í04 Soňa line j_r i_I_r 10 11 12 " 13 eV 14 nP =1022 rrT3 Boltzmann n Saha n deviation from B & S n B _ S _ nogi/goe Ei/kTe nenion^(h2/27imekTQf/2cEion,i/^ gegion rfnf + r}nf OE CR modelling CRM neon Examples ooo Self-absorptio n Excitation phases argon van der Sijde B 1984. Beitr. Plasmaphys. 24 447 OES CR modelling CRM neon Examples ooo Self-absorptio Collisional-radiative mode cross sections EDF Ť rate coefficients for electron excitation 7e, ne E/N, oj/N line broadening I Einstein coefficients escape factors system of rate equations I emission spectrum rate coefficients OE CR modelling CRM neon Examples ooo Electron distribution function Self-absorptio ■ • Maxwellian EDF o solution of Boltzmann kinetic equation • normalization of the EDF f* oo / f(e)e1/2de = 1 (13) Jo • mean electron energy f* oo (e) = / f(e)e3/2de, (14) Jo • rate coefficients k, /qnv of electron collision with cross section o and of inverse process k = 2e mc Jo a(e)fo(e)ede 2egj »00 L. — Ainv — \/ / ^K^J'UK^ <-// ™e gi Jeu -± / O(£)fo(£-£ij)£d£ OE CR modelling CRM neon Examples ooo Self-absorptio Approaches of OES data processing • line ratio methods • selection of convenient line pair (sensitivity, model simplicity, ease of measurement) • no control of model validity • ,,many line fitting"methods OES CR modelling CRM neon Examples ooo Self-absorptio Line ratio method - ideal case Electron energy (eV) OES CR modelling CRM neon Examples ooo Electron temperature and EDF measurement by OES+CR Self-absorptior E 00 CD E o CM I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I N n /nn metastable fraction m 0 ........1x10"4 -5x10"' ---2x10: 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 T n (eV) S 4 (a)CCP. 10 Pa. 100 W. Ar/Kr = 2/1 JyC I Inn I o Z 6 (b) KT. 5 Pa. 66 W. Ar/Kr = 3/1 □ OES x0.5 □ OGS I I cniuäd ifi SjÍ rí t' O Electron induced excitation transfer among 2p53s states Ne(/) + e" -^Ne(y)+e", /'J = 2,...5 O Spontaneous emission and absorption of radiation Ne(/) Ne(y) + hv, i = 2,... 29, /' >> ► < a OE R modelling CRM neon Examples ooo Self-absorptior Considered elementary processes 2 O Two-body collision induced deactivation and excitation transfer among 2p53p states ki Ne(/) + Ne(l) 4 Ne(y) +Ne(l), i J = 6,... 15 O Chemoionization kmet Ne(2 - 5) + Ne(2 - 5) ~4 Ne( 1) + Ne+ + e O Two-body collision induced deactivation Ne(2-5) + Ne(l)^2Ne(l) O Penning ionization of impurities Ne(2-5) + H2 4' H2++Ne(l)+e~ Ne(2-5) + H2 NeH+ + H + e Ne(2-5)+N2 4 N2++Ne(l)+e~ NeN2 + Ne(2-5)+N2 'h?' NeN2++e OE< '.R modelling CRM neon Examples ooo Self-absorptio Considered elementary processes 3 © Electron impact ionization of the ground-state and metastable atoms Q Three-body production of dimers Ne(2,4) + Ne(l) + Ne(l) ^ Ne£ + Ne(l) Ne(3) + Ne(l) + Ne(l) ^3Ne51 + Ne(l) Ne(5) + Ne(l) + Ne(l) %5 Ne51 + Ne(l) OE R modelling Spontaneous emission CRM neon Examples ooo Self-absorptior absent 2 4 6 8 10 12 14 16 18 9 s Lower state no transition Einstein coefficient A, An = An = ^ 16tt3v3 S 3e0hc3 gi gj 2ne2v2 f gi £omo effective levels Li gi ^— relative differences of two data source -NIST and Seaton 1998 < r3> ► •< ► < ► OE R modelling CRM neon Examples ooo Self-absorptior Absorption of radiation Number of absorption transitions between states /, j (j is lower) in unit volume is njBjip(cOo) What is p(ft)o)? The spatial distribution of population of excited state due to the radiation propagation can be described by Holstein equation dn{r) dt = -An(r) + A J n(r')G(r/, ?)dr': (15) G{f,r) = - 1 dT f-r Anp2 dp ' Solution of Holstein equation has a form n(r,t) = £c/nj(?)e-A^t T(p) = j f{co)e-kf^pdco. (16) in which gj are trapping factors attached to eigenfunctions nj. Escape ^ctor_A =J./gQ. Parameters of solution: • discharge geometry • opacity koR • spectral line profile OE< '.R modelling CRM neon Examples ooo Solution of rate-equations Initial conditions n/(t = 0) = KbTn ' /' = 1 0. / > 1 Runge-Kutta methods stationary state solution: all excited states reach stationary state Non-linear dependence of some rate equations d ri2 = -4/cmetA72 - 2/cmetA72A74 - ... - (/cH + + /cNeH+) [H2] A72 met D2 -(^N2+ + %eN2+)[N2]^2 - ^o2+[°2]A72 ~ ~J2 n2 ~ Monmetl OE R modelling CRM neon Examples ooo Self-absorptio ■ Spectrum calculation and comparison • measured spectral line intensities, integrated over lineshapes [hJkXP]i k = 1, = 30 • calculated total emission coefficients of transitions ICY _ njAjjAjjhVy Sum S 0.030 comparison of spectra by least squares method 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Scaling factor F (a. u.) ^ /exp /c=l 'k OE R modelling CRM neon Examples ooo Self-absorptio ■ Role of metastables simplified OD scheme is not valid dři; (dři; dt dt c,r longer computational times increased sensitivity at low electron energies 1.7 eV 16.6 eV .. ^ / stepwise direct / r neon ground state (18) (a) 811.53 nm 2p ->1s, weighted metastable level (2/m/5 2™(£) m £°'5x [b. / n] ground state 10 15 20 Electron energy (eV) 1 1 1 1 I 1 1 1 1 I 1 1 1 ■ (b) 750.39 nm 2p1 ->1s2 i i i i i i i i i i i i i i i weighted ,''\ . metastable level / \ ground state I weighted \ I resonance level \ \ - i- . . . . i . . . ~7-i—.----- . argon Boffard J B, Jung R 0,*Lm *C C'fnd We^dt Á §Í010 Plasma Sources Sci. Technol. 19(6) 065001 7 = 2.8 eV, nm/ng =3 x 10 4, nr/ng =1 x 10 4 OE R modelling Direct and stepwise excitation CRM neon Examples ooo Self-absorptior in 25 " 20 " 15 -10 - 5 - 0 total- direct X 1.0eV 1 -Á—H IM6K 580 600 620 640 660 680 700 720 740 wavelength (nm) in 580 600 620 640 660 680 700 720 740 wavelength (nm) in 580 600 620 640 660 680 700 720 740 wavelength (nm) 7000 Hi*—i-1-1-1-1-1-1-1— in 6000 " 5000 " 4000 " 3000 " 2000 -1000 - 0 ÚJm total - direct X 1 4.0eV ft X X L t>:——i 580 600 620 640 660 680 700 720 740 wavelength (nm) Maxwellian EDF, gas temperature 300 K, fixed densities of all Is; levels^ glow discharge in neon • positive column of DC glow discharge at 1.1 Torr • OES in spectral range 300-850 nm • CR model with stationary BKE solver • probe measurement ......—r 4 6 8 10 12 14 0 iu 10 □ qp Number of iteration Discharge current (mA) Navrátil Z, Trunec D, Hrachová V and Kaňka A 2007 J. Phys. D: Appl. Phys. 40(4) 1037 OES '.R modelling CRM neon Radio-frequency discharge in neon Examples otoo Self-absorptior capacitively coupled RF discharge in neon (13.56 MHz) low pressure (10 Pa) reactor R3 "Temelin", inner diameter 33 cm, discharge gap 40mm, electrodes 8 cm in diameter studied by OES/CR, OAS, PIC/MC, Langmuir probe absolute intensity measurement OES OE R modelling CRM neon Examples oc*o RF (13.56 MHz) capacitive discharge in neon at 10 Pa Self-absorptior 20 a) LU 21- -i—i—i—i—i—i—i—i—i—i—i—i—i—i—i— PIC/MC model: 7". * CR model en > 18 , ■ • PIC/MC model: 7"h.gh ♦ Langmuir probe s 16: 3 14 - 2 12- T _i_i_i_i_i_i_i_i_i_i_i_i_i_i_i_ 0 5 10 15 20 25 30 35 40 Axial position (mm) 20 30 40 Power (W) (0 CO E -4—' c a> 'o it a> o o c o "(0 (0 "E LU 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 ZD Measurement: pos. 4 mm, power 50 W ■* Fit with CR model I J 600 620 640 660 680 700 720 740 Wavelength (nm) Power (W) Navrátil Z, Dvořák P, Brzobohatý O and Trunec D 2010 J. Phys. D: Appl. Phys. 43(50) 505203. OES CR modelling CRM neon Examples o»ooooooo elf-absorptio MW surface-wave driven discharge in neon in coaxial configuration 00 O) OES =—— magnetron 2.45 GHz □.O B x 0 <-1 Ne argon • two-cylinder quartz tube with copper rod antenna, length 320 mm, dimensions di = 5 mm, 62 = 7 mm, c/3 = 11 mm, c/4 = 20 mm and d$ = 24 mm • microwave power 60 W • pressure 300-700 Pa of neon with research purity 99.999%, flow rate 6-30seem • OES: Jobin Yvon HR640 spectrometer with CCD detector cooled with LN2 (focal length 640 mm, grating 1200 gr mm-1) "O °\ c* OE CR modelling CRM neon Electron distribution function CO > CD Q LU 10"4t- 10"5 b- 10"6 b- 10"7r 10" 500 Pa ----1.5 eV ----11.9 Td 700 Pa ...... 1.4 eV ......7.7 Td Examples ooo«oooooo 0 8 10 12 14 16 18 20 Electron energy (eV) Ti = 2.1 - 2.5 eV, S < 15eV T2 = 0.33 - 0.43 eV 18eV < g < 20eV 7e = 1.4 - 1.6 eV Maxwellian OE CR modelling Spectra fit 1.2 = 1.0 - d 0.8 - CD ■ 0.6 - "to c 0 0.4 - 0.2 - 0.0 - —1—i—1—r 320 Pa I 1 I I,Liu h CRM neon n—1—r •4 ->—i—1—i—1—i—1—r measured * fitted X ■ 580 600 620 640 660 680 700 720 740 760 Wavelength (nm) Examples oooo^ooooo 1.2 = 1.0 - d 0.8 - CO -i—* 0.6 - "to c 0 0.4 - 0.2 - 0.0 - —1—i—1—r 700 Pa Self-absorptior i 1 i 1 i 1—r T measured ► fitted •« fitted with 2B 3p transfer l 580 600 620 640 660 680 700 720 740 760 Wavelength (nm) • using BKE solver • effect of deactivation by heavy particles on spectra under studied conditions is small OE CR modelling CRM neon Examples ooooo^oooo Self-absorptio n Sensitivity to electron density and metastable density Electron density (cm3) Used / measured metastable density ratio sensitivity to metastables: 0.3 eV or 2Td per order of density OES CR modelling CRM neon Axial dependencies for T = 300 K Examples oooooo«ooo Self-absorptior > CO 0 Q. E 0 -*—> C O 4_ o Q) LU 1.7 1.6 - 1.5 - 1.4 - 1.3 - Maxwellian EDF T-1-r 320 Pa 500 Pa 700 Pa 0 2 4 6 8 10 12 14 Axial position (cm) o CD "D CD Ü "D CD 12 - CD ü= 10 I- 8 - 6 - 1 A. I 1 0 solution BKE T T I 1 _l_ I 1 I 1 1 1 1 _1_ 300 K ■ 320 Pa • 500 Pa a 700 Pa I i 8 10 12 Axial position (cm) í i í i l i i * í i 14 OE< CR modelling CRM neon Examples ooooooo^oo Self-absorptio N2 rotational temperature in C Uu state 376 377 378 379 380 381 382 300 350 400 450 500 550 600 Wavelength (nm) N2 rotational temperature (K) Program Specair. Laux C O 2002. In Fletcher D, Charbonnier J M, Sarma GSR and Magin T, eds., von Karman Institute Lecture Series 2002—07, Physico-Chemical Modeling of High Enthalpy and Plasma Flows Rhode-Saint-Gencse, Belgium. OES CR modelling CRM neon Examples 00000000*0 Self-absorptio N2 rotational temperature in C Uu state ^ 550 \- Q) "CO 500 h Q) Q_ E 450 k 400 k O ^ 350 h 0 ■ 320 Pa • 500 Pa A 700 Pa 4 6 8 10 12 14 16 Axial position (cm) OE CR modelling Effect of gas temperature 300 K CRM neon Examples 000000000« Self-absorptior N2 rotational temperature 12 - T3 CD = 10 - o 0 CD "O CD Ü "D CD 8 - 6 - ->-1-1-1-1-1-1-r T-1-1-1-r 0 + ■ 1 300 K ■ 320 Pa • 500 Pa a 700 Pa í { i i l i i * í i i i l i t i i i i i _i_i_i_i_i_i_i_i_i_i_i___ 8 10 12 14 T3 CD 18 - 16 - 14 - Ü 12 CD § 4 I "O © ß L ->-1->-r T->-1-1-1-1-1->-r 1 0 i 1 ! } 1 f } I 1 I 1 1 1 I 1 ■ 320 Pa • 500 Pa A 700 Pa i 1 ± ■ 1. 8 10 12 14 Axial position (cm) Axial position (cm) heating by oscillating field is governed by E/N and co/N, elastic collisions inhance heating co/N is not constant along the column in effective field approximation OE R modelling CRM neon Examples ooo Self-absorption 3 CO 1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2- 570 n 1 i 1 i 1 i 1 -Azimuthal direction, axial position 2.5cm -Axial direction 590 610 630 650 670 690 710 730 750 Wavelength (nm) OES '.R modelling CRM neon Examples ooo Self-absorption Effective branching fractions V u isolated atom plasma absorption coefficient • measured r,= A> Li An reff= eitfWi k?:= ^ mo g, IJ 8nV2\2kbTgJ |-exp _ hj/hVij &l A -Aijnj Li hi/hvi OE R modelling CRM neon Escape factor Examples ooo Self-absorption Mewe approximate expression 2_e-k?jL/1000 1 + ^ assumption of homogeneous distribution of atoms e.g. Ar 2p6 —> IS5 (763.5 nm), p = 10 cm -i—i 1111111—i—i 1111111—i—i 1111111—i—i 1111111—i—i 1111111—i i i inii|"'~F~PlÍ7Íi 1E13 1E14 1E15 1E16 1E17 1E18 1E19 1E20 1s metastable density (nf3) >ES CR modelling CRM neon Examples ooo Example - density of Ti and Ti+ in magnetron discharge (a) y3D° J 3 J = 2 J = 3/2 Figure 1. Energy levels and selected transitions for density measurement of (a) Ti neutral atom and (b) Ti ion. Vašina P 2015 Plasma Sources Sci. Technol. 24 065022 '.R modelling CRM neon Examples ooo Self-absorption xample - density of Ti and Ti+ in magnetron discharge Li_ 02 LU l.U 0.8- 0.6- 0.4- 0.2- X rexp frea _ 0.0 — I X _ V a) i .u 0.8- Ll CD LU 392 394 396 398 400 402 392 394 396 398 400 402 Wavelength (nm) Wavelength (nm) OES '.R modelling CRM neon Examples ooo Example - density of Ti and Ti+ in magnetron discharge Self-absorption 2.0x10 -8 1.5x1018H 1.0x1018H 5.0x1017H 0.0 0 [Ti] [Ti+] [Ti]+[Ti+] Discharge current 400 - 300 c 200 g CD s— cc o - 100 Q 250 Time (us) Figure 7. Measurements of the Ti atom and ion density for 200 fis milsp in HiPTMS mnrip Thp nrpssnrp was spr rn S Pa rhp rpnphrinn