Plasma diagnostics using spectroscopic techniques

Timo Gans

York Plasma Institute

YPI – Low temperature plasma

activities• Plasma dynamics

& chemical kinetics• Advanced plasma diagnostics• Special emphasis on optical

diagnostics & laser spectroscopy

• Modelling & numerical simulations

• Technological exploitations

• Special emphasis on plasma medicine, plasma

etching, plasma deposition

Plasmas & other disciplines

• Optics• Atomic & Molecular Physics• Laser Physics• Surface Science• Electro Dynamics• Statistics• Numerical Simulations

• Electrical Engineering• Chemistry• Bio-medical Sciences

What is a plasma? ionised gas with variety of particles electrons positive and negative ions neutral particles

(atoms, molecules, radicals) excited species dust particles

What do we like to measure? densities distribution functions (temperatures) electric and magnetic fields

electrons

ionsradicals

neutralsbulkplasma

sheath

chemistry

synergisms

physics

po

we

r

electrons

ionsradicals

neutralsbulkplasma

sheath

chemistry

synergisms

physics

electrons

ionsradicals

neutralsbulkplasma

electrons

ionsradicals

neutralsbulkplasma

sheath

chemistry

synergisms

physics

po

we

rp

ow

er

Plasma – Complex Multi-Particle System

Multiphase interfaces:

Plasma – gas – liquid – surface (solid)

Multispecies:

Electrons, pos. ions, neg. ions, neutrals, radicals, excited species, photons

Multiscale problem – time:

Electron dynamics: ps – ns

Ion dynamics: 100 ns – μs

Plasma chemistry: 100 μs – ms

Surface chemistry: s – min

Multiscale problem – space:

Surface structures: nm – μm

Charged particle gradients: μm – m

Neutral particle gradients: 10 μm – m

Challenges & opportunities

Electrical diagnostics charged particles and fields

external current and voltage measurements+ simple+ non-intrusive– indirect– model based– global information only

probe measurements+ simple+ local information+ direct– model based– reactive environment (gases)– intrusive

How do we measure plasma quantities?

Mass spectrometry

neutral particles and ions

energy distribution functions

+ non-intrusive

+ direct

How do we measure plasma quantities?

– complicated in detail

– external measurement

– reactive gases

Optical diagnostics

in principle all plasma parameters+ non-intrusive

+ high temporal and spatial resolution

Plasma physics

Atomic & molecular physics

Optical diagnostics

How do we measure plasma quantities?

Emission spectroscopy+ passive+ simple+ robust– indirect– model based– data needed

Laser spectroscopy

+ direct+ highly reliable– active– involving– expensive

Combination of passive and active methods

Optical Diagnostics

Typical OES set-up

line emission which emission lines (qualitative)

® species absolute intensities (calibration difficult)

® density of excited species line ratios

® robust model based analysis (this lecture!) line shapes (high experimental requirements)

® temperatures, fields, densities temporal variations

® plasma dynamics

continuum radiation spectral distributions absolute intensities

Optical Emission Spectroscopy (OES)

Complete thermodynamic equilibrium (CTE) homogeneity

unique temperature (Te = Ti = Tgas)

black body radiation

Maxwell – Boltzmann distribution

1

2 :Planck

3

2

Tkh

Bec

hI

Plasma concepts - CTE

Maxwell – Boltzmann distribution

population distributions

Tk

EE

g

g

n

n

B

jk

i

k

j

k exp

:Boltzmann

® Spectroscopy: line intensities and ratios

velocity distribution

Tk

mv

m

Tk

vn

dv

vdn

BB2

exp2

4)(

:Maxwell2

23

2

® Spectroscopy: line shape, e.g. Doppler effect

Plasma concepts - CTE

Main constraints and limitations

inhomogeneities

Planck

® Local thermodynamic equilibrium?

Plasma concepts - CTE

Local thermodynamic equilibrium (LTE) local parameters collision dominated

® equilibrium of collisions® no equilibrium of radiation

requirement

example (hydrogen arc)

ne = 1016 cm-3, Te 104 K

® (Ek - Ei)LTE 4 eV

® Partial LTE

312106.1 ikee EETn

Plasma concepts - LTE

Partial local thermodynamic equilibrium (PLTE)

over population of the ground state

LTE for excited states

constraints and limitations low electron densities

® Corona model

® collisional radiative models

Plasma concepts - PLTE

Corona model

model for plasmas with "low" electron densities (ne < 1013 cm-3)

applicable to most technological plasmas

far from thermodynamic equilibrium

most particles are in the ground state

electron impact excitation=

relaxation by radiation

(spontaneous emission)

Plasma concepts - Corona

iiki,Ph nAn

ni : population density of state i

Aik : spontaneous emission rate

nPh,i : photons per unit volume and time

Plasma concepts - Corona

Electron impactexcitation

Ground state n0

i

k

ik

Corona model

electron impact excitation=

relaxation by radiation

(spontaneous emission)

k

ikieeii AnTnEndt

dn,0

n0 : ground state density

Ei : electron impact excitation rate of state i,

(depending on ne and Te)

ikikA

1

i : radiative lifetime

Plasma concepts - Corona

dEEfm

EEnvnE

eieiei

2

0

i : electron impact excitation cross-section of state i

f(E): normalised EEDF

kik

ikik

i0iki0

kik

ikiiki,Ph

A

Aa

EnaEnA

AnAn

aik : branching ratio

RF - discharges

iRFT

1

(later) OES Resolved Phase 0 dt

dni

steady state of excited states

kik

ii

i

A

Enn

dt

dn 0 0

Plasma concepts - Corona

Additional excitation and de-excitation processes

Þ applicable to most technological plasmas

cascades from higher electronic states

one dominating or effective cascade state

ccii

ii0

i nAn

Endt

dn

Aci : transition rate from the cascade state c

nc : population densities of the cascade state c

nc = ?

Corona: cascade transitions

Electron impactexcitation

Ground state n0

i

k

ik

neglecting second order cascades:

ccii0iii

i

icc0cii0

i

cc0cc

c

cc0

c

EaEnn0dt

dn

nEnAEn

dt

dn

Enn0dt

dn

nEn

dt

dn

Determination of Ec is difficult(reabsorption!)

Corona: cascade transitions

Electron impactexcitation

Ground state n0

i

k

ik

excitation out of metastable states

?

,0

m

mimi

iccii

i

n

Enn

nAEndt

dn

long lifetimes of metastable states transport problem plasma wall interaction

Þ complex® avoid through proper choice of state i with small cross-

sections for excitation out of metastable states (small Ei,m)

® turn into diagnostics of metastable states by comparing with states excited out of metastable levels

Corona: stepwise excitation

collisional de-excitation (quenching)

A* + Q ?

especially important at high pressures!

qq

qik

ikimimcciii knnAnEnnAEndt

dn ,0

qq

qk

iki nkAA

kq : quenching coefficient with species Q

nq : density of species Q

Corona: collisional de-excitation

q : quenching cross-section, Tgas indepedent

Tgas : gas temperature

<v> : mean velocity

: reduced mass

gasBqqgasq

TkvTk

8

® Importance of Tgas

® Which quenching partners are present?

® What are the densities?

Corona: collisional de-excitation

selection rules for emission lines good quality of electron impact excitation cross-sections

(same source!) negligible excitation out of metastables small cascade contribution short lifetimes

competition with quenching high intensities high temporal resolution

known quenching coefficient (better small) no excitation transfer with other species no spectral overlap with other emission

Which emission line should I analyse?

Actinometry & Limitations

Direct excitation:

Dissociative excitation:

Influence of the EEDF

Time & space dependence of the EEDF

N Knake, et al., APL, 93 (2008) 131503

Comparison with laser spectroscopy

K NIEMI, et al., Appl. Phys. Lett. 95 (2009) 151504

Thank you!

York Plasma Institute