Laser based plasma diagnostic techniques: Velocity distribution by Laser Induced Fluorescence (LIF) technique Nader SADEGHI Laboratoire Interdisciplinaire de Physique (LIPhy , ex LSP) et Laboratoire Interdisciplinaire de 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: [email protected]
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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: [email protected]
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:
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).
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
- S. Mazouffre, D. Gawron and N. Sadeghi, A time-resolved laser induced fluorescence study on the ion velocity distribution function in a Hall thruster after a fast current disruption, Physics of Plasmas 16 (2009) 043504
- 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
- S. Mazouffre, C. Foissac, P. Supiot, R. Engeln, D.C. Schram and N. Sadeghi, Density and temperature of N atoms in the afterglow of a microwave discharge by two-photon laser induced fluorescence technique, Plasma Source, Sci. Technol., 10(2001) 168.