Laser based plasma diagnostic techniques:Velocity distribution by Laser Induced

Fluorescence (LIF) technique

Nader SADEGHI

LaboratoireInterdisciplinairede Physique (LIPhy, ex LSP) et LaboratoireInterdisciplinairede Physique (LIPhy, ex LSP) et Laboratoire des Technologies de la Microélectronique(LTM),

Université Joseph Fourier & CNRS Grenoble, B.P. 87, 38 402 St Martin d ’Hères (France)E-mail: Nader.Sadeghi@ujf-grenoble.fr

Principle of Laser Spectroscopy

Laser frequency is tuned to a specific transition of interest

1

2

Intensity

I 0(ν)

∼

LaserAbs.

νν0

I (ν)

Either in Laser Absorption or in Laser Induced Fluorescence techniques, spectral information comes from the first step:

absorption of photons

LIF

LaserAbs.

Principle of Laser Spectroscopy

Intensity

νν0

I 0(ν)

I (ν)

ν0

−= )()(

4)( 2

2

11

12 ννλγ

να ng

gn

hBAbsorption Coefficient

)(.))(

)(( 0 να

νν

lI

ILn =-From absorption signal

-From LIF signal )().()( ναν LaserLIF PI Φ≈

transition probability

α(ν) = Ν k Φ(ν)

Densitytraces Detection

Line profile Analysis

What can we learn by measuring α(ν) ?

probabilitytraces Detection Analysis

Φ(ν)

ν

Units used in spectroscopy

1 eV = 1.6 x 10-19 J = 8065 cm-1

300 kT = 207 cm-1

1 cm-1 = 30 GHz

c * λ∆c

Wavenumber

λν c=

2

*

λλν ∆=∆ c

Linewidth:At 563 nm, ∆λ =1 nm → ∆ν = 1000 GHz

Photon energy:λ = 500 nm 1/λ = 20000 cm-1

Different type of LasersFrequency fixed: (often used as pump laser)

- Ar +, Kr +, Nd-Yag, Excimer (XeCl), Cu, HeNe ….. ∆νL≅ 10 GHz

Tunable lasers:- Pumped by a laser: Dye, Ti:Sa, OPO (tuning range 10 to 100 nm)

Lasers available from 400 nm to µm (+ frequency doubling)

* Pulsed lasers: P up to 10 mJ, ∆ t ≈ 3 to 30 ns, ∆νL≥ 1 GHz* Pulsed lasers: P up to 10 mJ, ∆ t ≈ 3 to 30 ns, ∆νL≥ 1 GHzConvenient for frequency doubling and n photon transitions

* CW lasers: P= up to a few W, ∆νL ≈ 0.001 GHzConvenient for high resolution spectroscopy

- Diode laser: lasers available from 400 nm to 10 µm with

* tuning range up to 10 nm

* P= up to a few 10 mW, ∆νL ≈ 0.001 GHz(if single mode) They are more compact, easier to run and cheaper

How the line profile is related to the velocity distribution function?

Doppler shift: )/.1(0 cVkL

rr+=νν

c

Vkr

//

00

0 =∆=−ν

νν

νν

The frequency shift is related to only velocity along the laser propagation direction

zV V yx dVdVVfVfy z∫ ∫= .).()(

r

The measured velocity distribution function is an integral over the other two directions

)(.)( 0xVf

cf

νν =

Laser Absorption Spectroscopy

- provides sight of line averaged quantities

Laser Induced fluorescence

-has very high space resolution

LAS vsLIF

quantities

-has limited sensitivity

- Provides absolute density of absorbing species

- is very high sensitivity (a single atom can be excited many many times); photon counting

- But cannot provide absolute densities without a calibration method

Origin of optical saturation

• 1- Laser beam transfers a significant number of atoms from the lower to the upper state and

−= )()(

4)( 2

2

11

12 ννλγ

να ng

gn

hB α becomes no more proportional to n1

atoms from the lower to the upper state and n2 becomes no more negligible compared to n1.(short pulse lasers)

• 2- Atoms in the upper state are lost by radiation, or collisional transfers, to a 3rd state and atoms in the lower state are not renewed fast enough: the lower state becomes depleted.(cw lasers)

Rate equations governing the population densities N1 and N2 of states |1⟩ and |2⟩ are:

1

2

11,1112221211 )/1()(/ CNMkBNABdtdNq

qq +++−+= ∑τρρ

22,22321211122/ CNMkAABNBdtdNq

qq +

+++−= ∑ρρ

is is the Einstein coefficient for stimulated emission

we assume g1 = g2 , ρ is the energy density of the beam,

Ci accounts for the repopulation of state |i⟩ from different paths, including diffusion transport into the laser volume and radiative cascades

and

are the total relaxation rates of the states

21

30

122

121 8

Ah

Bg

gB

πλ==

∑∑ +=ℜ= q

qqloweri

i NkA ,222∑+=ℜq

qqNk ,111 1τ

in steady state, (dNi/dt=0) the density difference of states |1⟩ and |2⟩ is:

Where is in the absence of laser beam (ρ=0),

and*

12 /ℜ= ρBS is The saturation parameter

related to the mean relaxation rate:

)/( 2121* ℜ+ℜℜℜ=ℜ

)/( 1212

2

1

102

01

0 ℜ−ℜ−ℜ=−=∆ AgCC

gNNN

)1(21

1212021 ℜ+ℜ

ℜ+−ℜ+∆=−=∆ gASNgNNN

:2121

Larger S is, lower the measured population will be

The resulting population density in the lower state is:

When ρ → 0, For ρ → ∞1

11 ℜ

= CN

2212

211

)(ℜ+−ℜ

+=gA

CCgN

)(][)/()/(

211212

*212

*21

1 RRgRARSAgSCRgSC

N +++−ℜ++ℜ+= When

C2 0 )(][)/(

211212

*21

1 RRgRARSRgSC

N +++−ℜ+=

Intensity of Laser Induced Fluorescence signal

1

2

LIF signal is proportional to N2 density given by:

221

1223123223 ),,(

ℜ+∝∝

ρρ

B

BARVElNANI

When LIF is used to determine the relative populations of two different species, m and n:populations of two different species, m and n:

At low laser power limit, the LIF signal ratio is:

2,

2,

23

23

12

12

1

1

23

23

)(

)(

)32;(

)32;(

n

m

n

m

n

m

n

m

A

A

B

B

nN

mN

nI

mI

ττ

=→→

At high laser power limit, the LIF signal ratio is:

n

m

n

n

m

m

n

m

A

A

g

g

g

g

nN

mN

nI

mI

23

23

,2

,1

,1

,2

1

1

23

23

)(

)(

)32;(

)32;(

=

→→

τ could be p and T dependent

Calculation of the saturation parameter S1- Pulsed laser:

λ= 589 nm ; τ2=16 ns ; A21=6 106 s-1 ; R2=1/τ2=6.25 107 s-1;

R1=(1/transit time inside a beam of φ=2 mm)=(0.5 km.s-1)/(2 mm)=2.5 105 s-1 g2= g1

Laser pulse: P=1 mJ; ∆L= 4 ns pulse duration; ∆νL= 0.2 cm-1= 6 GHz; φ=2 mm

∆L< τ2

J.s/m3

m3/J/s2 s-119639

213

10*3.710*6*)10*589( ===

−λ AB

898239

3

10*410*6*10*3*)10(**10*4

10

***−

−−

−

==∆∆

=πν

ρLL cs

P

521 10*5.2=== RRR

Rm3/J/s2 s-1

B12*ρ= 3* 1012 s-1 >> R2 Very Big

Then immediately during the laser pulse N2 = N1 = 0.5* N10

GHz Broader than the laser line

If : τ2=5 ns; A21=2 107 s-1 ; R2=1/τ2=2 108 s-1; P=1 mJ; ∆L= 40 ns > τ2

B12*ρ= 1* 1012 s-1 >> R2 Very Big

Then in the end of the laser pulse

1934

2112 10*3.7

10*6.6**8

10*6*)10*589(

8=== −ππ

λh

AB

51

21

21 10*5.2==+

= RRR

RRR

35*35001* ==+= δνδνδν SS

6

1

12 10*4* ==

R

BS

ρ

01

012

0112 *018.0)4()2/( NExpNRExpNNN L =−=∆−==

7

1

12 10*2.1* ==

R

BS

ρ

Calculation of the saturation parameter Scw laser:

λ= 589 nm; τ2=16 ns ; A21=6 106 s-1 ; R2=1/τ2=6.25 107 s-1;R1=(1/transit time inside a beam of φ=2 mm)=(0.5 km.s-1)/(2 mm)=2.5 105 s-1 g2= g1

Laser power: P=10 mW; ∆νL= 1 MHz <<1/(2πτ2) ; φ=2 mm

220

2

0 )2/()(

)2/()(

δνννδνρνρ

+−=

πτπδν

*2**2

1 2

2

R==

Then:

J.s/m3

m3/J/s2

Large saturation: MHzBut much smaller than the Doppler width at 300 K (≅ 1000 MHz)

0 πτπ *2**2 2

cs

Pd

*2)( 0 ==∫

πδνρννρ

137823

2

20 10*7.6

10*25.6*10*3*)10(*

10*1*4

**

*4 −−

−

===π

ρRcs

P

1934

63921

3

12 10*3.710*6.6**8

10*6*)10*589(

8=== −

−

ππλ

h

AB 200

*1

12 ==R

BS

ρ

140*141* ==+= δνδνδν SS

- Velocity distribution function of Ar* metastable atoms in a helicon reactor

- Velocity distribution function of Ar* atoms in an expanding arc jet

- Velocity of Ar+ ions in ECR reactor

Examples of LIF experiments

- Velocity of Ar ions in ECR reactor

- Velocity distribution function of Xe+ in a Hall thruster

- Velocity of sputtered Al atoms under Ar+ ion bombardment

Velocity distribution function of Ar* metastable atoms in a Helicon reactor

0

-20

-40

N o6

N o5

Antenna between 4 and 5I1 to 6 =3,3,3,3,3,-4.5 A

Dis

tanc

e fr

om th

e ce

nter

of a

nten

na (

cm)

Quartz tube

Antenna

80

60

40

20

0

-50 0 50 100 150 200 250 300

N o5N o4

N o3

N o2

N o1

B fie ld ( G auss )

Dis

tanc

e fr

om th

e ce

nter

of a

nten

na (

cm)

Antenna

Laser beam

Recorded signals when the laser frequency is scanned

0.4

0.5

0.6

0.7

0.8

discharges on

discharges off

LASER ON

Sig

nal [

arb.

u.]

Laser IntensityLIF Signal

0 1000 2000 3000 4000 5000

0.0

0.1

0.2

0.3Fabry-Perot

discharges off

Sig

nal [

arb.

u.]

channel number

discharges onLASER OFF

For frequency calibration

Determination of the Doppler width

-0.015

-0.010

-0.005

0.000

-0.3

-0.2

-0.1

0.0

Ln

(I/I

0)

Ln

(I/I

0)

Cl2 + 10% Ar at 5 mTorr

-2 -1 0 1 2-0.035

-0.030

-0.025

-0.020

-2 -1 0 1 2-0.7

-0.6

-0.5

-0.4 Ln

(I/I

P=100 WT=404 K

Ln

(I/I

Frequency shift (GHz)

P=700 WT=572 K

MTc

MRTcGHzD /1016.7)/(2ln2)/2()(0

160 λ

νδν −⋅==

Line profile in presence of strong magnetic field

B=0

+1 0−1

B≠0

2p7

MB=0

+1 0−1

B≠0

2p2

M

Zeeman components of the absorbing lines of Argon

772.38 nm; 2p7 ← 3P2 line 772.42 nm; 2p2 ← 3P0 line

+2+1 0−1−2

1s5

σ+ σ−

π

01s3

σ+ σ−

π

Bkrr

⊥ if only σ+ and σ- lines existBErr

⊥if only π line (s) existBk

rr⊥ BE

rr//

then only σ+ and σ- lines existBkrr

//

helicon, 20W, 3,7sccmB strong

absorption between B2-B3772,38nm

B=146gauss0,2

0,25

0,3polarizationperpendicular to B

polarization parallel to B

σ, ∆ Μ = + 1

Experimental profiles of the 722.38 nm line with two different polarization fitted with Gaussians

B=146gaussT=248K

0

0,05

0,1

0,15

6 6,5 7 7,5 8 8,5frequency (GHz)

ln(I0

/I)

σ, ∆ Μ = − 1

π , ∆ Μ = 0

Reflexion of Ar* atoms on Pyrex surface

LIF signal near the surface fromlaser beam to the surface

R=0.28 ± 0.05

Velocity mapping of argon atoms (metastable) in an expanding cascaded arc jet

By Laser Induced Fluorescence technique & by absorptionby absorption

Experimental determination of argon atoms vdf in an expanding arc jet by LIF (Eindhoven)

cathode anode

gas

stationaryshock

M>>1 M<1

P = 5 kWTe = 1 eVne = 1022 m-3

psource = 5.104 Papbg = 10…100 Pa

Expected density and velocity distribution along the jet axis

Velocity

z

stationaryshock

Density

M>1 M<1

Laser Doppler-Shift setup

1.0

Argon lamp

inte

nsity

(a.

u.)

BSBS

chopperdiode laser

ArgonFabry

z-axis

1 2 3 4 5 6 7 8 9 10 11

0.0

0.5 Fabry Perot

LIF signal

inte

nsity

(a.

u.)

piezo voltage (a.u.)Lock in

amplifier

Argonlamp

FabryPerot

diodes

PMT

filter

reference

trigger

inte

nsity

(a.

u.)

0.5z=59 mm

0.0

0.5 z=46 mm

012

z=26 mm

Ar* velocity distribution functions

0.2

0.3

(axial v at axis center)

(radial v at z = 50 mm)

-1 0 1 2 3 4 5 60.00.51.01.5 z=174 mm

velocity (km/s)

inte

nsity

(a.

u.)

0.0

0.5

1.0 z=100 mm

0.0

0.5z=59 mm

-3 -2 -1 0 1 2 30.0

0.5

1.0

0.0

0.1

0.2

velocity (km/s)

inte

nsity

(a.u

.)

r=25 mm

r=0 mm

Velocity distribution of Ar + metastable ions in an ECR reactor

Electron Cyclotron Resonance reactor

In 1990th, the goal for µ-electronics industry is to separate the generation of the plasma from the energy of ions impinging on the substrate

- Electron Cyclotron Resonance ( ECR)- Helicon- Inductively coupled plasmas (ICP)

Pulsed versus CW laser for the LIF

Pulsed laser∆νL≅1 GHz

CW laser∆νL<0.1 GHz

Acceleration of Ar+ ions leaving the ECR zone

Azimuthal velocity of Ar+ ions due to the ExB Lorentz force

Velocity distribution function of Xe+

metastable ions in a Hall effect thruster

The 5 kW-class PPS®X000 thruster in the Pivoine facility

High power Hall Effect Thruster150 mm outer channel diameter40 mm channel lengthP = 2 – 6 kWUd = 200-1000 VΦa = 3 – 20 mg/s

Experimental arrangement

Energy diagram and LIF scheme for metastable Xe + ions

6p 2D

o5/2

air = 834.7233 nm

= 541 915 nm

113512.36 cm-1rad = 9.3 ns)

LIF bench: high-power tunable single-mode laser diode

5d 2F7/2

6s 2P3/2

air = 541.915 nm

BR = 0.9

101535.67 cm-1

95064.38 cm-1

Xe+

metastable level

9 stable istopes→ istopic shifts and HF structure

→ 19 components

Hypothesis: fluorescence profile = VDF

Detection branch

The fluorescence collectionlens housing and holder areat floating potential

1:1 imaging systemf = 40 mm lens200 µm core optical fiber

x-y high-precision long range translation stages

Trouble: optics pollution and wear

Example of the Steady-state on-axis development of the IVDF

0.5

1.0 x = 0 mm

x = -5 mm

x = -10 mm

Nor

mal

ized

ion

VD

F (

arb.

units

)

x = -15 mm

0.0

0.5

1.0

0.0

0.5

1.0

0.0

0.5

1.0

0 5000 10000 15000 20000 25000 300000.0

0.5

1.0

Axial velocity (m/s)

0.0

0.5

1.0

0.0

0.5

1.0

0.0

0.5

1.0

0.0

x = 40 mm

x = 30 mm

x = 20 mm

x = 6 mm

Nor

mal

ized

ion

VD

F (

arb.

units

)

Macroscopic quantities

- mean velocity

- max velocity (10%)

- dispersion

σ×= )( 222 Lnp

20000

25000

30000

Ion

axia

l vel

ocity

(m

/s)

Comparison between hybrid model outcome and experim ental result

PPS®X000 thruster, 500V and 6 mg/s

The electron mobility through the magnetic barrier is inferred from

-20 -10 0 10 20 30 400

5000

10000

15000

20000

Ion

axia

l vel

ocity

(m

/s)

Axial position (mm)

hybrid modelling experiment

outcome of PIC simulations

IVD Characteristics of the HET in the oscillating regime The best performance

Anode discharge currentpower shutdown

τc = 10 µs

f = 2500 Hz

PPS100-LM Hall thrusterBN-SiO2 wallsUd = 250 VΦa = 4.5 mg/s xenon gasIc = 5 A forcedIc = 5 APback = 2×10-5 mbar-Xe

Discharge propertiesId = 4.1 Af = 21 kHz

PerformancesT = 69 mN (wo line cut)T = 67 mN (w line cut)

Id: ensemble averaged over 128 cycles

forcedoscillations

quasi-normaloscillations

linecut

restarting

Detection of LIF by Photon-counting technique

Requirements

to monitor the time evolution of the Xe+ VDF during a breathing oscillation time period (~20 kHz)

LIF tool with a time resolution < 1 µsnb of fluorescence photons during 1 µs ≈ 10-2 (with Plaser = 1 mW)nb of background photons during 1 µs ≈ 1

a) Photon-counting technique → high time resolutionb) Real time add and subtract operation with chopped laser beam → high S/N

Remote discharge current breakdischarge stability (quasi-periodic regime vs non-stationary regime)trigger for all devicesforced as well as natural oscillations

Temporal traces at different Ion velocities11 measurement locations along the channel axis

Time-averaged electric field on-axis distribution.The electric field is inferred from the mean ion velocity.

Extracted Time series for various velocity groups

Number of on/offcycles ~ 1M

Width of a velocitygroup:δv = 10 m/s

Between 10-15 points to reconstruct the local ion VDF

Validity of the measurement technique: Checkout

At each location, comparison between

Time-averaged IVDF measured by means of a lock-in detector ( τ = 1s; power cut)

Combining time-resolved IVDFs recorded with the photon counting technique

x = -2 mm x = 4 mm

Contour map of the IVDF(t)

anode dischargecurrent break restarting

Combining all velocity group time-series at a given measurement location

Velocity distribution of sputtered Aluminum atoms under Ar+ Bombardment

By Laser Induced Fluorescence technique

Sticking coefficient of sputtered Al atoms on trench side walls and on different surfaces strongly depends on their velocity (energy)

distribution.

Diode

LaserLIF

B.S.optical fiber LIF

Laser absorption and (LIF) with a Diode Laser

2S1/2

PD1

Diode Laser

Controler

PD2

Mono+ PMT

Lock-InOscilloscopesynchro

C.M.

xz

reference

substrat Al

-15 -10 -5 0 5 10 15

0,0

0,2

0,4

0,6

0,8

1,0

0.98 GHz

Inte

nsité

(u.

a.)

∆ν = ν − ν0 (GHz)

2S1/2

2P1/2

394.40 nmLIF

396.15 nmLASER

2P3/2

LIF

Energy diagram ofAl

Hyperfine structure of the 396.15 nm transition of Al atoms

2S1/2F=3

F=2 Total line

Hyperfine components:

4 to 3 3 to 3 3 to 2

2P3/22P1/2

394.40 nm

396.15 nm

F=4F=3F=2F=1

0.014 eV

-3 0 3ν - ν

0 (GHz)

3 to 2 2 to 3 2 to 2 1 to 2

-20 -15 -10 -5 0 5 10 15 20

-0.06

-0.03

0.00

ln (

I / I

0 )∆ν (GHz)

1 mTorr

-20 -15 -10 -5 0 5 10 15 20-0.12

-0.08

-0.04

0.00

ln (

I / I

0 )

∆ν (GHz)

2 mTorrFrom zero collision to thermalization

-20 -10 0 10 20

-0.04

-0.02

0.00

0.5 mTorr

ln (

I / I

0 )

∆ν (GHz)

Absorption line profile

∆ν (GHz)

-15 -10 -5 0 5 10 15

-0.2

-0.1

0.0

ln

( I

/ I0 )

5 mTorr

∆ν (GHz)-15 -10 -5 0 5 10 15

-0.8

-0.6

-0.4

-0.2

0.0

ln (

I / I

0 )

∆ν (GHz)

20 mTorr∆ν (GHz)

-15 -10 -5 0 5 10 15

-0.6

-0.4

-0.2

0.0

ln (

I / I

0 )

∆ν (GHz)

84 mTorr

Gas pressure (mTorr) 0.5 1 2

Collision mean free path (cm) 25 12 6

5 20 84

2.5 0.6 0.1

( ) dEdE

EE

EE

EdEdEf b

b

Ω

Λ+−

+×∝Ω

13 1cos),( θθ

Velocity distribution function of sputtered Atoms

Comparison with Thompson theoryof velocity distributions recorded at very low

argon pressure (0.4 mTorr)

LIF: distribution de Vangular distribution

-8 -6 -4 -2 0 2 4 6

0,00

0,01

0,02

0,03

velocity (km/s)

ln (

Io /

I )

Vz distribution (b)

Vx distribution (a)

Cosine(dashed

)Harte(solid)

LIF: Vz distribution

Eb surface binding energy

Under low energy bombardment (ICP), the angular distribution of sputtered Al atoms is much closer to a “Hart shape" than to a cosine distribution

θ (°C)

LIF: distribution de Vz

absorption: distribution de Vx

30

60

90-90

-60

-30

0 2 4 6 8 10

0,00

0,25

0,50

0,75

1,00

velocity (km/s)

Vz distribution (b)

LIF

inte

nsity

(a.

u)

LIF: Vz distribution

Absorption: V x distribution

Cosine(dashed)

Harte(solid)

Few References to consult- W. Demtröder, Laser Spectroscopy, 2nd Ed. (Springer, Berlin, 1996).

-N. Sadeghi, Molecular Spectroscopy Techniques Applied for Processing Plasma Diagnostics,J. Plasma & Fusion Research,

80 (2004) 767.- T. Nakano, N. Sadeghi, and R.A. Gottscho, Ion and neutral temperatures in electron cyclotron resonance plasma Reactors,Appl. Phys. Lett. 58 (1991) 458

- N. Sadeghi, T. Nakano, D.J. Trevor, and R.A. Gottscho, Ion transport in an electron cyclotron resonance plasma,J. Appl. Phys. 70 (1991) 2552- R Engeln, S Mazouffre, P Vankan, D C Schram and N Sadeghi, Flow dynamics and invasion by background gas of a supersonically expanding thermal plasma,Plasma Sources Sci. Technol. 10 (2001) 1.-P. Macko and N. Sadeghi, Determination of the non-relaxation (reflection) probability of metastable Ar(3P2) atoms on aPyrex surface, Plasma Sources Sci. Technol. 13 (2004) 303- G. Cunge, R. Ramos, D. Vempaire, M. Touzeau, M. Neijbauer, and N. Sadeghi, Gas temperature measurement in CF4, SF6, O2, Cl2, and HBr inductively coupled plasmas, JVST A 27 (2009) 471- R Ramos, G Cunge, M Touzeau and N Sadeghi, Measured velocity distribution of sputtered Al atoms perpendicular and- R Ramos, G Cunge, M Touzeau and N Sadeghi, Measured velocity distribution of sputtered Al atoms perpendicular andparallel to the target, J. Phys. D: Appl. Phys. 41 (2008) 152003- E. Despiau-Pujoa, P. Chabert, R. Ramos, G. Cunge, and N. Sadeghi, Velocity distribution function of sputtered gallium atoms during inductively coupled argon plasma treatment of a GaAs surface, JVST A 27 (2009) 356

- G. Cunge, D. Vempaire, and N. Sadeghi, Gas convection caused by electron pressure drop in the afterglow of a pulsed inductively coupled plasma discharge, App. Phys. Lett. 96 (2010) 131501

- D. Gawron, S. Mazouffre, N. Sadeghi and A. Héron, Influence of magnetic field and discharge voltage on the acceleration layer features in a Hall effect thruster, Plasma Sources Sci. Technol. 17 (2008) 025001

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- G. Bourgeois, S. Mazouffre and N. Sadeghi, Unexpected transverse velocity component of Xe+ ions near the exit plane of a Hall thruster, Physics of Plasmas 17 (2010) 113502

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