Basics of Plasma Spectroscopy
Hands(-)on Spectroscopy
Volker Schulz-von der Gathen
Institute for Experimental Physics II Chair of Physics of Reactive Plasmas Ruhr-Universität Bochum, Germany
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 1 Disclaimer
Astrophysical plasmas Atmospheric pressure plasmas
He/O2 rf discharge 10 W
Technical plasmas (low pressure) We confine ourselves to low-temperature plasmas. We neglect continuum radiation. We only present a very limited set of diagnostics
What can we learn from the light coming out of the discharge for free?
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 2 Outline
Introduction neutrals Basics radicals atoms Emission and absorption ions plasma Atoms and molecules metastables h Detectors and spectrometers molecules electrons Equipment
(Collisional radiative) models Analysis Diagnostic methods Applications: Examples Summary and conclusions
Powerful diagnostic tool
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 3 Radiation of a low temperature plasma
Colors of plasmas Neutrals atoms and molecules Ions single charged
Electrons ne << nn drive processes
Collisions and spontaneous emission a+ e → a*+ e → a+ h ν+ e Gas discharge f s s
Emission of light from the IR to the UV
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 4 Components of a spectrum
Spectral lines Continuum
26
24
22
20
18 Continuum
16 ionization limit Ar I radiation
14 2p 1 2p 2p 2p 2 3 4 2p5 2p 2p 6 7 2p8 2p9 2p10 728738 772 750795826841 696706715 764852772751801810842 12 802811 912 Lines 1s 1s2 Energy [eV] Energy 1s 3 1s5 4 10
8 104.822 6 106.666
4
2
0 3 P2,1,0 groundground level level Transitions between bound states Free-bound transitions, of atoms, ions, molecules Bremsstrahlung, … Thermal radiation
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 5 Lines – Transitions between atomic states
Spectroscopic notation
w 2S+1 nl LL+S LS coupling electron Multiplicity J=L+S (fine structure) Spin S=SSi Angular momentum L= SL 706 nm i
2p 3P 2,1,0 Selection rules
Metastable optically forbidden state Large ground state energy Resonant optically allowed gap transitions HELIUM Transition probability A : Einstein coefficient for ground state ik spontaneous emission
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 6 Atoms and molecules Annotations
Paschen notation Spectroscopic notation not convenient for every situation J = 2 1 0 1 1 3 2 1 2 0 1 2 1 0 JJ coupling, mixed states s5 s4 s3 s2 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1
Paschen notation 2p (for heavy noble gases) 13 Simple, empirical Numbering of levels from Argon highest to lowest energy 12 Argon
1s5-1s2, 2p10-2p1,... 3P => s ; 3P => s 5 5 0 3 2 5 11 3p (n+3)s 3p (n+2)p 1 3 P1 & P1 => s2, s4 (mixed states) 1 Racah notation 1p2 2s2 2p6 3s2 3p6
0
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 7 Sources of information: NIST
www.nist.gov/pml/data/asd.cfm
Convenient unit: 1 ν̃ [cm− ]: wavenumber
1 1 1 ν̃ [cm− ]= ∝ ν[ s− ]∝[eV ] λ [cm]
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 8 Atoms and molecules Sources of information: Web
Web pages (Cross sections) www.lxcat.laplace.univ-tlse.fr ELECTRON SCATTERING DATABASE www.icecat.laplace.univ-tlse.fr ION SCATTERING DATABASE www.hitrans.com Molecular data Books K.P. Huber and G. Herzberg: Constants of diatomic molecules R.W.B. Pearse; A.G. Gaydon: The identification of molecular spectra H. Okabe: Photochemistry of Small Molecules
YOU are responsible for the selection of data, cross sections etc.! Select carefully! Check for the applicability of the data!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 9 Information included in line emission
I Wavelength species max n(p) Apk Wavelength shift particle velocity Line profile broadening mechanism
Intensity plasma parameters P l density and temperature of neutrals, ions, electrons insight in plasma processes Tgas
Line emission coefficient: Emissivity
1 ε = n( p) A h ν pk pk pk 4π = d ∫line εν ν photons×energy l0 [time×solid angle ] Element
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 10 Basic questions
Plasma emission yields information on plasma state
F T F T F,G,R,E
Plasma Optics Spectrometer Detector Analysis
Technical questions How to collect the light most efficiently? How to do it quantitatively? … 1 Measured 'Intensity'/ Signal: I ∝ n h ν A T ( ν )E ( ν )GR [V , A ,cts] F i ik ik ik ik
F: Area; T: Transmission; G: Gain; R: Measuring Resistance; E: Spectral sensitivity [electrons/photon @ ]
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 11 Transfer of light
Lens systems Imaging optics Solid angle (Aperture)
VIS – VUV (MgF2) Plasma Optics
Fibers Very flexible VIS: Glass, Quarz, UV enhanced
Plasma
Fiber (bundle)
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 12 That's a spectrograph!
PGS-2 2 m plane grating spectrograph ~ 500 kg Real resolution with ICCD:
~ 4 pm
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 13 5 basic components of EACH spectrograph
1) Entrance slit ES 2) Collimator (mirror) FL 3) Dispersing element Prism Grating
Etalon C DE
… S 4) Focusing lens (mirror) ES 5) Focal plane C
Exit slit (Monochromator) DE Screen (Spectrograph) Detector S Eye, Photomultiplier, ... FL (Intensified) CCD chip
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 14 Miniature USB spectrograph
Very handy
Light fiber coupled (F) Fixed entrance slit (ES) Fixed grating (G) Spectroscopy grade CCD arrays (D) NO moveable parts M/BF USB interface to computer USB M What can we do with these devices? G D What are the limits? ES What to take care of? F Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 15 Entrance slit
Entrance slit defines a clear-cut object for the optical bench. Typically 2 sharp, parallel wedged metal edges 5 -200 µm apart Don't touch it!
Size of the entrance slit affects the throughput of the spectrograph. Lower width limit determined by diffraction (onto first lens) Has to be fitted to the detector and optics (height, geometry)!
The entrance slit is imaged (~1:1) onto the detector (spectral lines!).
ES Entrance Exit FL
Intensity in plane of C DE Screen plane pixel line detector S Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 16 Grating
KEY FACTOR! influences optical resolution Dispersion of a grating d β m Angular dispersion ⇒ Angular dispersion = d λ c cosβ Groove distance c (mm)
Grating constant 1/c (lines/mm) dx m ⇒ Linear dispersion =f⋅ d λ c cosβ
Resolution of 2 lines is defined by the Optimum resolution R requires „Rayleigh“-Criterion complete illumination of dispersing element
Δ λR R=λ Δ λ R R2m=150.000 R=m⋅N
N: Number of illuminated grooves
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 17 Spectroscopic systems Detectors
PMT I(ntensified) CCD (Photomultiplier tube) (Charge coupled device)
Gateable Gateable Extremely sensitive Sensitive (~1/10 PMT) Spatially integrating Imaging VUV to near Infrared VUV to near infrared (cathode material dependent) (cathode material dependent)
Choose carefully: Wavelength, response time, sensitivity, amplification!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 18 Detector
HR 4000 high resolution spectrometer Chip Toshiba linear CCD array TCD1304AP Pixel Number: 3648 Pixel Size: 8 μm × 200 μm Photo Sensing Region (~ exit slit) Total width: ~22 mm Detector range: 200 -1100 nm Sensitivity: 130 photons/count at 400 nm; 60 photons/count at 600 nm
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 19 Exit slit width and resolution
Change the slit width for a given imaged line
small wide Move line across slit slit slit (Rotate grating)
Collected Intensity
If slit is to wide you don't gain intensity but loose resolution! If slit is to small you loose intensity but you don't gain resolution!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 20 Correct selection of grating
High resolution requires: Large grating (N), high groove density (c), long focal length (f), small slits (d) Dimensions of USB spectrometers limit possible resolution
Typical: f= 10 cm, dslit= 10 µm, width of detector= 25 mm
Groove density and width of detector determine the total observable spectral width. Set angle of incidence and blaze angle determine the actual position of the spectral range projected on the detector.
Resolution: 900 nm / 2048 pixel → Ropt~ 0,5 nm / Pixel → Reff~ 1500
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 21 Optimization of gratings
Special groove profile improves efficiency for a specific wavelength range. Wavelength and orientation specific (marked by arrow) blaze angle
η 2 3 η= bei ⋅λ und ⋅λ η≈10 bei 0,5⋅λ 2 3 B 2 B b
Efficiency range
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 22 Select your instrument
Example „Entrance slits are rectangular apertures, 1-mm tall and various widths from 5 μm to 200 μm, with the width determining the amount of light entering the bench. A slit is fixed in place. Note that the smallest slit achieves the best optical resolution.“
Cross talk
5 x intensity, only 1.7 x resolution
So, yes but … Throughput and resolution of the system should be balanced by selecting a proper entrance slit width and pixel width.
Reducing the width of the entrance slit below the pixel width
won’t improve the resolution of the system but Reduces the throughput
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 23 USB spectrometers: Interface
Interface
Dark spectrum
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 24 Basic corrections
Reference Spectra Identification of lines used to divide each pixel in a processed spectrum (normalization, changes)
Dark spectra is subtracted from the raw data spectrum removes e.g. Background light (lamps, etc.) Noise / dark current has to be adjusted for every change (integration time, setup,..)
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 25 Basic corrections
Electrical dark spectrum Electrical dark appears to be a bias correction. First 24 (uniluminated )pixels are used to estimate the mean dark level As the dark current varies from pixel to pixel this only provides a first order correction.
! Takes some time at long Ne I spectrum: integration times dark corrected, averaged ! Important! Do it!
How do we read a line intensity?
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 26 Calibration of spectroscopic systems
Wavelength: pixel nm Radiance – intensity counts W/m2/sr, ph/m2/s Spectral lamps, plasma, tables Example: HgCd lamp Tungsten ribbon lamp
Deuterium lamp
Ulbricht sphere
Branching ratios
Resolution – line broadening – second order Limited lifetime of calibrated lamps relative – absolute calibration
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 27 Calibration of spectroscopic systems Radiance – intensity Solid angle Ulbricht sphere counts W/m2/sr, ph/m2/s d [sr]
spectral radiance [W/m2/sr/nm]
Measurement intensity [cts/s]
d =dA/r2 Conversion factor: spectral sensitivity
W 4 πλ photons x = [ m2 sr nm(cts /s)] hc [ m2 s nm(cts/ s) ]
Exposure time
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 28 Optical thickness / radiation transport
Radiation transport Special cases
lens plasma Optically thick κ '⋅L≫1 I (x) e , k I (0) ν v v εν → I ν (L)= κν ' detector εν =B ν (T ) in LTE: Kirchhoff's law x=L L x=0 κν ' for a homogeneous plasma → I ν (L)=B ν(T ) Blackbody radiation from outer border of plasma dI ν=εν dx−I ν κν 'dx Δ E εν= Optically thin Δ t Δ V Δ Ω Δ ν
κν '⋅L≪1 −κ 'L −κ 'L ν εν ν − κ ν'⋅L I ν(L)=I ν(0)e + [ 1−e ] →e ≈1− κν '⋅L κν ' →I ν(L)=εν L(+I ν (0)) Radiation transport equation Emissivity is integrated over Line of Sight ! κν '=Absorption coefficient Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 29 Abel inversion: overcome ''line of sight'' problem
Plasmas are not homogeneous For radially symmetric plasmas Line of Sight (LOS) Division into (onion) rings of constant emissivity
x 2+ y 2=r 2 x I (y)=2 ϵ(x )dx Observed transversal (y) ∫0 Line of Sight Transformation:2 x dx=2r dr measurement
y =R rdr I y 2 r → ( )= ∫y r ϵ( ) = √r 2− y2
Abel- Inversion Important: I(R)= 0 ! 1 y =R dI(y ) dy →ϵ(r )=− Sensitive due to differentiation π ∫y =r dy 2 2 √r −y Fit of analytical functions (cos) We measure an intensity and transform into emissivity.
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 30 So let's start to investigate spectra!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 31 Information included in line emission
Wavelength species Wavelength shift particle velocity Line profile broadening mechanism
Intensity plasma parameters P l density and temperature of neutrals, ions, electrons insight in plasma processes
l0
Element
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 32 Identification of species (Wavelenght)
What do we learn? UV: resonance lines, VIS, IR
Dissociation products radicals, neutrals, ions Impurities water (→ O, OH),
air (→ N2, NO), surface (Cu, C, …)
Courtesy U. Fantz Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 33 Identification of species ?
What the heck is this?
FIRST: Ask NIST lines and levels database (www.nist.org)
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 34 Identification of species
Compare as many lines as possible in your spectra to be sure!
Shown are the Argon neutral lines with relative intensities from NIST.
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 35 Identification of species
Agreement in many lines allows unambiguous identification
?
Displacement – Line shift Velocity of species (Doppler shift) Calibration of the spectrograph Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 36 Correction
USB spectrometers are robust and wavelength stable but…
Polynomial fit
Can be stored to the system
Check the settings from time to time!
You don't want to analyse the wrong line!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 37 Monitoring of processes
Follow the timely development of spectral lines – simultaneously! Easy with an USB spectrometer
Argon µJet
But how to interpret this behavior? Molecules and dissociated products become visible Generated AND excited!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 38 Plasma parameters from line shapes
Wavelength species Wavelength shift particle velocity Line profile broadening mechanism
Intensity plasma parameters P l density and temperature of neutrals, ions, electrons insight in plasma processes T, n
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 39 Natural line width
Basic idea From uncertainty relation
Disturbance of an infinite wave train ℏ E i 1 Ai (decaying amplitude, wavelength Δ E i= Δ νi =Δ = = τi h 2 π τ 2π spread) i Energy loss can be inerpreted as damping Overlay of monochromatic, damped components
1 I ( ω−ω0 ) =I 0 (ω−ω0)²+(γ/ 2)² ! Both levels contribute Lorentz profile Energy uncertainties sum up Typical values? <=1 pm
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 40 Species temperatures; translational temperature
Description of line shape ε(ν)=g(ν)⋅εL mit ∫g(ν)d ν=1 L
Line broadening mechanism: Doppler shift due to velocity distribution of heavy species
M 2 − v dn M z v z = e 2 kT dv add (Doppler effect) Δ λ = ⇒ n √ 2π kT z λ c 2 2 M 2 M 2 v = Δ λ c ≡ Δ λ 2kT z 2 kT 2 2 λ0 Δ λD I0
2 kT Δ λ = λ D √ Mc2 0 FWHM I0/2 Doppler profile: Gauss
2 − Δ λ 1 ( Δ λ D ) g(Δ λ)= e √π Δ λD Full width half 0 maximum FWHM 8ln2kT Δ λ =2√ln2 Δ λD= λ 0 →Choose large λ0 , small M √ Mc2 Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 41 Species temperatures; translational temperature
Convolution by other line broadening mechanisms Apparatus profile: Gaussian
Example: Δ λFWHM = (Δ λFWHM )2+(Δ λ FWHM)2 √ D A T = 500 K → ∆λ(H ) = 0.01 nm = 10 pm FWHM 2 n α M c Δ λ D if ∆λ = 10 pm then ∆λ = 14 pm mit T= A meas 8ln2k λ 0 b [ ]
Line overlap
Ha; = 656,2 nm Contribution of 5 (out of 7) fine structure components Best fit of convoluted line profiles
at TH= 1250 K
Spectral overlap can deform the expected lineshape! Be aware of your resolution!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 42 Electron density: Stark broadening
Degenerated levels Line broadening mechanism: Pressure broadening Separation and displacement of degenerated levels by electric fields
Prominent: Atomic hydrogen Transitions Linear Stark effect Undisplaced term n-times degenerated Term separation ~ n (n-1) equidistant levels
∆E~|EF|nk with nk= ±n(n-1),n(n-2),...;0
H and H show no central component
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 43 Electron density: Pressure broadening: Stark
Separation and displacement of degenerated levels by electric fields
Atomic hydrogen: Linear Stark effect ↑ N (β) Most simple theories Electrons: collisional theory (Coulomb interaction of electrons passing by) E β → e β= E 0=0,206 n Ions: quasi-static approximation E0 c (surrounding ions generate a statistical field; Holtsmark micro field, ~ n 2/3 ) i + + e + + + EH + P b + + P + + b: collision parameter + + electron collisions quasi-static ions Overlay of multitude of processes yields broadening of individual components!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 44 Electron density: Pressure broadening: Stark
Variety of theories
Simplified analysis from FWHM
Δ λ [Å ]=α ⋅2.5⋅10−9⋅(n [cm− 3])2/3 FWHM 1/2 e ^
with tabulated /2(ne,T) e.g. for H Rule of thumb
Δ λ [nm]∼2⋅10−11⋅(n [cm−3])2/3 FWHM , Hβ e Values of Stark-broadening parameter α for the H line of 1/2 β hydrogen (486.1 nm) for various temperatures and electron densities
-3 15 16 17 18 T [K] Ne [cm ] 10 10 10 10 5000 0.0787 0.0808 0.0765 ...
10000 0.0803 0.0840 0.0851 0.0781 Overlap of Doppler and Stark broadening! 20000 0.0815 0.0860 0.0902 0.0896 30000 0.0814 0.0860 0.0919 0.0946 Stark dominant for relatively high ne!
Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 45 Summary of broadening mechanisms
Various components can overlapp
Natural linewidth Very small ( Apparatus profile Should be very small Shape ? Check! Doppler-Broadening Gaussian profile ( 10 pm) Collisional broadening (Interaction via collisions, ~ Lorentz-profile) Stark-broadening E- field; complex (often approximated by Lorentz-profiles) (80 pm @ 1016cm-3) Van der Waal- broadening Neutrals Pressure broadening massive collisions Weighting and deconvolution often difficult! Try to get an estimate in advance? No chances with USB spectrometers!!!! Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 46 Overlapp of broadening mechanisms Lorentz-, Gauss- and Voigt-Profiles of identical full width half maximum and same integral intensity (area under curves) Voigt-Profile: Convolution of a Lorentz profile with a Gauss profile of the same FWHM 1/2 Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 47 Intensity information I Wavelength species max n(p) Apk Wavelength shift particle velocity Line profile broadening mechanism Intensity plasma parameters Pl (Emissivity) density and temperature of neutrals, ions, electrons insight in plasma processes εpk =n( p) Apk h νpk Photon ε pk =n( p) Apk 'Photon flow' Absolute calibrated intensities Complicated calibration Species densities (for known ne) Relative intensities Simplified calibration Temperatures, densities (models!) Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 48 Population densities of atoms and molecules Ionization Emission (absorption) spectroscopy E → population density of excited states Excited state electronic, vibrational, rotational n(p), v’, J’ v ' ,v ' ' ,J ' . J ' ' v ' ,v ' ' , J ' . J ' ' hv ε pk , photons =n(p ,v ' , J ') Apk depends on plasma parameters Lower state n(k), v'', J'' Te, ne, TA, nA, n(v), n(J), D, I, ... Population? depend on plasma processes Population models Electron collisions Heavy particle collisions Dissociation Radiation Ground state … n(0), v, J Insight into plasma processes and parameters! Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 49 Population models Equilibrium models LTE (local thermodynamic equilibrium) or PLTE Ek − n(k) g(k) k T Describe state population, velocity distribution, = e B N Z(T) ionisation by equilibrium equations as the Boltzmann equation Collisional radiative models For most low pressure, low temperature discharges Describes population and depopulation of states by rate equations incl. Electron collision excitation and deexcitation Radiative population and depopulation Ionisation out of states, …. Corona model exc n1 ne X 1p (T e)=n(p)∑ Apk k Simplest case Electron collision excitation from the ground state 1 Spontaneous radiative deexcitation of excited state p Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 50 Thermodynamic equilibrium ONE temperature T, EVERYWHERE Population of bound states: Boltzmann equation Models Basic models Thermodynamic equilibrium ONE temperature T, EVERYWHERE Population of bound states: Boltzmann equation −E k n0 k T n(k)= e B Z (T ) Distribution of velocities: Maxwell equation mv2 3/2 − m 2 k bT 2 f (v )dv= e ( )4 πv dv 2 k T ( π B ) Distribution of ionized states: Saha-Eggert equation E ' 2 3/2 − i n 2 g 2 m k T k T e ⋅ i π B ( B ) = e =S (T ) n Z T 2 0 0 ( )( h ) Distribution of radiation: Planck's equation 2hν3 1 Bν(T )d ν= 2 h ν d ν c k T ( e B −1 ) Detailed equilibrium Process⇔Counter process A+ e⇔A++ e+ e Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 51 Collisional radiative model Rate equation balances excitation and de-excitation processes for each state d n(p) =∑ n(k )ne X kp+ ∑ n(r)ne X rp − ∑ n(p)ne X pk − ∑ n(p)ne X pr dt k < p r> p k < p r > p electron impact excitation and de-excitation with rate coefficient X [m3/s] − ∑ n(p)Apk+ ∑ n(r )Arp k< p p< r spontaneous emission with transition probability A [1/s] − n(p)ne S p+ ne ne ni βp+ ne ni αp+ …−… Ionization S[m3/s] radiative recombination α [m3/s] rad. 3-body rec. β [m6/s] =0 Steady state Set of coupled equations solved with dependence on ground state and ion density n(p) = R1(p)n1ne + Ri(p)ni ne R(p) = population coefficients Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 52 Connection to measurement photons Photon flux εpk =n(p)Apk Measurement n(p)= species in state (level) p CR model n(p) = f(Te, ne, nn, Tn, .…) Emission is determined by electron excitation collisions from the ground state → dependence on electron- and ground state density 1 Lifetime of the excited state τp= ∑ Apk k photons exc εpk =n0 ne Apk τp X pk (E e ,ne ,...) Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 53 Cross sections and rate coefficients ∞ ∞ Electron impact excitation X exc (T e)=∫ σ (E)√ 2E / me f (E)dE with ∫f (E )dE=1 Ethr 0 Rate coefficient cross section electron energy threshold energy distribution function EEDF High quality of σ close to Ethr required Emission is determined by ● Electron- and Ground state density and also by ● Electron collision excitation cross section and the ● (space-and time dependent) electron energy distribution function (EEDF) Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 54 Cross sections Quality of a CR model depends on the start data. Optically allowed E 1 σ ∝f ln ;E ≫E jk jk E E E jk ( kj ) kj Optically forbidden (Monopol) 1 σ ∝ ;E ≫E jk E jk Optically forbidden (Spin exchange) 1 σ ∝ ;E ≫E jk E 3 jk Although electronic processes, there are (Charastic for excitation into the similarities to the optical selection rules Triplet-States) Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 55 Electron temperature Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 56 Electron temperature: Line ratio method Lines with different Ethr or different shape of σ (E) Find suitable gases and diagnostic lines line ratio ratio of rate coefficients n1, n2 inert gases (or n1=n2) 1 1 εpk n1 ne X pk (T e) ε undisturbed lines pk 2 ∝ 2 Ground state excitation εpk n2 ne X pk (T e) Xpk ratio depends on Te (Maxwellian!?) Example: He and Ar lines MW discharge, pressure variation 3.5eV 2.8eV 2.5eV Intensity[a.u.] wavelength Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 57 A simple practical example: Excitation temperature DC hydrogen discharge Observation of 4 “Balmer” lines Ha to Hd Basic assumptions Model: (P)LTE ! Population relation between two levels described by Bolzmann distribution with Tk Intensity of a single emission line g E I =K h ν A n k exp − k kj k kj kj 0 Z (T ) k T { B k } Relative(!) comparison of two lines I ij K i νij Aij gi Ei −Ek = ν exp − I K kj A g k T kj k kj k { B ik } Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 58 Excitation temperature = Electron temperature? Calibrate your system relatively Look for all the constants (NIST) Measure the spectrum Calculate the excitation temperature E i −E k T ik= I ν A g k ln ij kj kj k B I νij A g { kj ij i } Edels & Gambling Proc. Royal Soc. 1959, A 249, 225 Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 59 Gas temperature from rotational lines Molecules Much more complicated spectra Additional degrees of freedom Electronic excitation Vibrational excitation Rotational excitation Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 60 Atoms and molecules Energy level diagram – potential curves + - Hydrogen H2, H2 , H2 Designation: Potential curves of H 2S+1 +,- 2 + g,u multiplet symmetry of wave function Letter rises with electronic energy (A, B, C....) X: ground state upper case letters Repulsive state (same multiplicity as ground state) H + H (Designations partialy historic!) ➢Rotation and vibration of molecules Zoom Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 61 Energy level diagram – potential curves Excitation and radiation Total energy of a ro-vibrational state Rotational energy: E =B h J (J +1) Franck-Condon principle rot e Vibrational energy: E ν=(v +1/2)ω E = Eelec + Evib + Erot Electronic ro-vibrational transition Fulcher transition h νv ', J ',v '' ,J'=Δ E elek .+Δ E vib,v ',v ''+Δ E rot , J ',J '' Emissivity k 4 Electron impact excitation ' εν J ' ν ''J ''∝nν' , J ' gJ ' ν S ν' J ' ν ''J '' k gJ '= Nuclear spin depending degree of degeneration Transition moment S = |D⃗ (R )|2 ⋅ FC(v ',v '') ⋅HL(J ',J '') ν' J ' ν'' J'' ⏟ik e ⏟ ⏟ Electronic Transition Moment Frank Condon Factor Hönl London Factor R2 q H = ⏟e⋅ v ', v ''⋅ J' , J '' tabelled for molecules and transitions Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 62 Atoms and molecules Selection rules for optical transitions Atoms Molecules (diatomic) 2S+1 2S +1 +,- nl LL+S + g,u Energy L=0,±1; 00 =0 J=0,±1; 00 u g S=0 J'-J''=J=0,±1 P, Q, R branch Electronic ro-vibrational transitions in VIS 2nd pos. band system Actual shape depends on spectral resolution Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 63 Species temperatures: gas temperature Rotational population of molecules in excited state Excitation mechanism from ground state n(p,v’,J’) accessible by spectroscopy v’+1 J’ T (p,v’) n(p), v’ rot rotational quantum number is preserved (∆J= 0, ±1) by electron impact excitation e rotational population in the ground state due to heavy particle collisions Trot(ground state) = Tn J ∆EJ → J+1 << Tn → Boltzmann distribution TGas n(1), v=0 E (J ') Emissivity of a − rot ν H kT ro-vibrational transition J ', J'' J' ,J '' gas ε =εν ', ν'' e J ',J '' ( νν ', ν'' ) k (for constant upper v ) gJ ' Z J '(T ) Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 64 Boltzmann Plot: Fulcher Q-branch (v=2, J=0) Assumptions: H2 Ground state: Boltzmann Excitation without change of J k ε J' ,J '' gJ ' 1 ⇒ ln = −B J '(J '+1) +const . ν H ν' kT ( J' ,J '' J,J '' ) rot Slope gives Trot Trot is often assumed to correspond to Tgas Boltzmann-Plot 3 3 - H2 3d u(v=2) 2a g (v=2) Q(J'') Also often used for excited states of atoms! Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 65 Gas temperature from rotational population of molecules 3 3 Computer simulation of molecular bands Measurements of N2 C Πu – B Πu, v’=0 – v’’=2 Trot as fit parameter Shape is sensitive on Trot N Þ T = T 2 rot gas ✔ Excitation transfer: Ar* to N Þ T ≠ T ✔ BUT! 2 rot gas Dissociative excitation: CH* from CH and CH4 Þ Trot ≠ Tgas Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 66 Electron dynamics Electrons are fast and can follow changes of the applied electric field e.g. in RF discharges operated at 13.56 MHz Excitation is time-dependent photons εpk =n0 ne Apk X pk (f (E e(t)),...) ∞ X exc (E )=∫ σ (E)√2E /me f (E e (t))dE E thr Fluorescence lifetimes are short Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 67 Phase Resolved Optical Emission Spectroscopy (PROES) Time dependent excitation (e.g. RF discharges) High repetition rate ICCD camera - gateable @13.56 MHz - photons from every cycle rf- voltage time Delay Gate width (3 ns) trigger Periode length (74 ns) time Phase resolved emission images Analysis of phase resolved emission allows insight in electron dynamics V. Schulz-von der Gathen, et al Contrib. Plasma Phys. 47, 508 (2007) ➔ Phase-space diagrams Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 68 Discharge dynamics: a– modes Phase (1 period) - space (electrode gap) graphs 30W Pos: 0.25 0.5 0.5 6.75E4 -- 7.5E4 6E4 -- 6.75E4 0,4 5.25E4 -- 6E4 Field 4.5E4 -- 5.25E4 3.75E4 -- 4.5E4 3E4 -- 3.75E4 reversal/ 0.25 2.25E4 -- 3E40.25 0,2 1.5E4 -- 2.25E4 Sheath 0 0,0 0 collaps Low power -0,2 electrode position [mm] -0.25 α-mode -0.25 Sheath -0,4 expansion -0.5 -0.5 0 10 20 30 40 50 60 70 Power_Sheath_Pos360_300107 T [ns] 0.5 0.5 0.25 0.25 0 0 High power -0.25 Electron Interelectrode[mm] position -0.25 -mode amplification -0.5 -0.5 (so-called) 0 25 50 74 0 25 50 74 Time [ns] Time [ns] V. Schulz- von der Gathen, et al., J. Waskoenig, T. Gans, QUB J Phys D: Appl Phys, 41 (2008) 194004 Reduced electron mobility yields field reversal Model description shows good agreement with observations Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 69 Analysis of the excitation function RF excited plasma with asymmetric electrodes Field sheath reversal Heavy expansion particles secondary electrons bulk 1 n˙ Ph ,i (t) Time dependent excitation function E i (t)= + Ai n˙ Ph ,i (t ) no Aik { dt } Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 70 Species densities Particlularly important in reactive plasmas How many radicals have been generated? Whta is the degree of dissociation? Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 71 Actinometry Task: Measure ground state densities of dissociated atoms by emission Problematics: We only can observe excited states Connection to unknown ground state by (unknown) electron excitation EEDF and time dependencies not known! Phase resolved emission of a 13.56 MHz discharge Spatial emission structures change on ns scale driven by electron collision excitation Camera images with 1 ns gate width in 75 ns excitation period Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 72 Actinometry Idea of actinometry Compare to emission from a known (density) reference species that responses to the electrons „identically“ Remember: Response is determined by cross sections and EEDF photons εpk =n0 ne Apk X pk (f (E e(t)),...) ∞ X exc (E )=∫ σ (E)√2E /me f (E e (t))dE E thr Select two species with states that σ 2 (λ)=C⋅σ 1(λ) show excitation cross sections of identical (similar) shape threshold energy Inert (noble gas) Undisturbed lines For H use Kr (and Ne) Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 73 Actinometry Prepare relative measurements Xpk ratio gets independent of f(E,t) or Te ∞ σ (E) 2E /m f (E ,t)dE X E ∫ 1 √ e 1 ( ) E thr 1 = ∞ = X 2 (E) C ∫ C σ1(E )√2E /me f (E ,t)dE E thr Electron density exciting from the ground states is identical and cancels 1 1 1 εpk n1 ne X pk (f (E )) εpk 2 ∝ 2 n1 ∝ 2 n2 C εpk n2 ne X pk (f (E )) εpk For well known and given actinometer gas density n2 we can calculate the unknown density of the dissociated species n1 J. W. Coburn and M. Chen, Journal of Applied Physics, 51, 3134-3136 (1980) Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 74 Problem in actinometry Same excited atomic level can be populate from atom and molecule Direct and dissociative excitation * Direct: H2 + es(4 eV) → 2H + evs → H + ef (11 eV) → H (n=3) + es * Dissociative: H2 + ef (15 eV) → H + H (n=3) + evs H , eff H , eff ε ∝n n X (T ,n ,...)+n n X 2 (T ,n ,...) H γ H e H γ e e H2 e H γ e e Two densities ~ 100 · , but n ~ 100 · n ! dir diss mol atom Solution: Add a second actinometer gas Knowledge of dominant excitation mechanism is essential! Requires measurements of several lines and check of consistency! For each species you have to select the optimum actinometer gas! Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 75 Example: Atmospheric Pressure Plasma Jet µAPPJ with 0.5% oxygen added to 1 slm flow of helium Capacitively coupled, 1mm electrode gap driven at 13.56 MHz ~ 1 W Actinometer gas: Argon Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 76 Example: Microjet Oxygen in 1 atmosphere of helium Actinometer gas: Argon Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 77 Typical applications of plasma spectroscopy Identification of species radicals from dissociation impurities Plasma stability time traces of inert gases Plasma monitoring Plasma process time traces of process gases Particle densities degree of dissociation Plasma parameter n , T active variation e e Quantitative analysis Plasma chemistry, processes insight in complex systems Excitation processes plasma dynamics Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 78 Summary Optical emission spectroscopy is a powerful diagnostic tool requires only 'simple' equipment is in-situ and non-invasive is line-of-sight integrated Analysis is based on atomic and molecular physics ranges from simple to quite complex based on collisional radiative models Some more details will follow today : Nikita, Felix, Marc Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 79 Some rules / advices / tips The optical system is not as simple as it might seem Imaging, sensitivities, polarities, ... Be aware of what you are assuming Can we really assume some equilibrium? Double check your basic data (cross sections, ...) Are they valid for your application? General literature U. Fantz, Basics of plasma spectroscopy, Plasma Sources Sci. Technol. 15 p. 137 V.N. Ochkin, Spectroscopy of Low Temperature Plasma, Wiley-VCH I.H. Hutchinson, Principles of plasma diagnostics, Cambridge University Press Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 80 Finis Thank you! WWW.EP2.RUB.DE [email protected] ….. Everything will be fine! Basics of Plasma Spectroscopy | V. Schulz-von der Gathen | Int. Plasma School 2016 | Bad Honnef, October 2 2016 | 81