Laser Plasma and Laser-Matter Interactions Laboratory
http://aries.ucsd.edu/LASERLAB
The effect of ionization on
condensation in ablation plumes
M. S. Tillack, D. Blair, S. S. Harilal
Center for Energy Research
and Mechanical and Aerospace Engineering Department
Jacobs School of Engineering
ARIES Town Meeting on Liquid Wall Chamber Dynamics
Livermore, CA
5-6 May 2003
We are investigating late-stage laser
ablation plume phenomena at UCSD
1. Experimental studies of the
expansion dynamics of
plumes interpenetrating into
ambient gases (with and
without magnetic fields)
2. Modeling and experiments
on homogeneous nucleation
and growth of clusters
Surface absorption
Thermal conduction
0
Surface melting
Vaporization
Multiphoton ionization
Plasma ignition
Explosive phase change
Plasma absorption
Self-regulating heat transfer
Adiabatic expansion
Collisional acceleration
Ambient interpenetration
8 ns
Adiabatic cooling
Rapid condensation
Plume stagnation
3. Spinodal decomposition and
liquid droplet ejection
1000 ns
Lasers used in the UCSD Laser Plasma and
Laser-Matter Interactions Laboratory
Spectra Physics 2-J, 8 ns
Nd:YAG with harmonics
1064, 532, 355, 266 nm
QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture.
Lambda Physik 420 mJ, 20 ns
multi-gas excimer laser
(248
nm with KrF)
Similarities and differences in ablation
plume parameters
Parameter
X-rays from HI
target explosion
Laser simulation
(107-1010 W/cm2)
pulse length
~2 ns
8 ns
1Š5 µm (Pb/Flibe)
10 nm
1Š10 µm
1Š2 µm (thermal)
background gas
density
0Š50 mTorr
0Š1 atm
background gas
temperature
>1000ūC
room temperature
spot size
1000 m2
1 mm2
geometry
quasi-1D
quasi-1D
attenuation length
ablation depth
initial plume: temp.
density
Zeff
plume @1 µs: temp.
plasma density
Zeff
* uncertainties in
Ablator ionization
Theory
Classical theory of aerosol nucleation and
growth
∂n
[ ]
v
v
+
∇
• (nv ) − ∇ • (D∇n) + ∇ • c n = ∂n
∂t
∂t
growth,
homo
[ ]
+ ∂n ∂t
growth ,
hetero
[ ]
+ ∂n ∂ t
coag
Particle Growth Rates
Transport and Rate of Change
Homogeneous Nucleation (Becker-Doring model)
∂n/∂t = C β Z
p
DW
C = kT exp e- kT k o
Z = DWk / 3r kTN k2
r* = 2v
nDn
Condensation Growth
J = m/ 2r k f C
v c pg v e p
p
Tg
Tf
sat
ps = po exp[Qv/(kTb) – Qv/(kTs)]
Coagulation
[ ∂t]
∂n
coag
V
∞
1
= ∫ β (V*,V − V *)n(V*)n(V − V*)dV * − ∫ β (V,V *)n(V)n(V*)dV *
20
0
(
)
where the coagulation kernel is given by β (V,V *) = 2π ( D + D *) d p + d p Fcoag
*
Dependence of homogeneous nucleation rate
and critical radius on saturation ratio
4π r3
2
(µ L − µv ) + 4πσr
∆G =
3Vm
Si, n=1020 cm–3, T=2000 K
•
High saturation ratios result from rapid cooling due to plume expansion and
heat transfer to background gas
•
•
Extremely high nucleation rate and small critical radius result
Reduction in S due to condensation shuts down HNR quickly; competition
between homogeneous and heterogeneous condensation determines final size
and density distribution
Effect of ionization on cluster nucleation rate
•
•
Ion jacketing produces seed sites
Dielectric constant of vapor
Si, n=1020 cm–3, T=2000 K, Zeff=0.01
reduces free energy
e2
4π 3 3
−1
−1
2
−1
2
(r − ra )(µ L − µv ) + 4πσ (r − ra ) + (1 − ε )(r − ra )
∆G =
2
3Vm
Modeling
A 1-D multi-physics scoping tool was developed
to help interpret plume condensation results
Ablation plumes provide a highly dynamic,
nonlinear, spatially inhomogeneous
environment for condensation, where strong
coupling of physics led us to a combined
experimental and modeling approach.
¾ Laser absorption
¾ Thermal response
¾ Evaporation flux
Ioe–αx, inverse bremsstrahlung
cond., convection, heat of evaporation
p 
p
M
 Γσ c v − σ e sat 
j=
RTf 
RTv
2π 
¾ Transient gasdynamics
2-fluid Navier-Stokes
¾ Radiation transport
Stefan-Boltzmann model
¾ Condensation
ion-modified Becker-Doring model
¾ Ionization/recombination
high-n Saha, 3-body recombination
Model prediction of expansion dynamics
Target
: Si
Laser Intensity : 5x109 W cm-2 (peak of Gaussian)
Ambient
: 500 mTorr He
High ambient pressure prevents interpenetration
(note, the 2-fluid model lacks single-particle effects)
The plume front is accelerated to hypersonic
velocities
Thermal energy is
converted into kinetic
energy; collisions also
appear to transfer energy
from the bulk of the plume
to the plume front
~62 eV
Model prediction of cluster birth and growth
•
•
Clusters are born at the contact surface and grow behind it
Nucleation shuts down rapidly as the plume expands
µs
Spatial distribution of nucleation (*) and
growth (o) rates at 500 ns
Time-dependence of
growth rate/birth rate
Experiments
Experimental setup for studies of ablation
plume dynamics
Target
: Al, Si
Laser Intensity : 107–5x109 W/cm2
Ambient
: 10-8 Torr – 100 Torr air
Expansion of interpenetrating plumes depends
strongly on the background pressure
0.01 Torr
Free expansion (collisionless)
0.1 Torr
Weakly collisional transition flow
1 Torr
Collisional transition flow
10 Torr
100 Torr
Fully collisional plume
Confined plume
Example: plume behavior in weakly
collisional transition regime (150 mTorr)
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Plume behavior in weakly collisional
transition regime (150 mTorr)
•
Strong interpenetration of
the laser plasma and the
ambient low density gas
•
Plume splitting and
sharpening observed
•
This pressure range falls in
the region of transition from
collisionless to collisional
interaction of the plume
species with the gas
•
Enhanced emission from all
species
Plasma parameters are measured using
spectroscopic techniques
Electron Density:
Measured using Stark broadening
Initial ~ 1019cm-3
Falls very rapidly within 200 ns
Follows ~1/t – Adiabatic
Temperature:
Measured from line intensity ratios
Initial ~8 eV
falls very rapidly
(Experiment Parameters: 5 GW cm-2, 150 mTorr air)
Besides spectroscopy, witness plates served as a
primary diagnostic
Witness plate preparation technique:
• Start with single crystal Si
• HF acid dip to strip native
oxide
• Spin, rinse, dry
• Controlled thermal oxide
growth at 1350 K to ~1µm, 4
Å roughness
• Ta/Au sputter coat for SEM
• Locate witness plate near
plume stagnation point
Witness plate prior to exposure,
showing a single defect in the
native crystal structure
Measurement of final condensate size
500 mTorr He
5x108 W/cm2
5x109 W/cm2
Cluster size distribution – comparison of theory &
experiment
• Good correlation between laser intensity and cluster size is observed.
• Is it due to increasing saturation ratio or charge state?
note: the discrepancy at low irradiance is believed to be caused by
anomolously high charge state induced by free electrons
Saturation ratio and charge state derived from
experimental measurements
• Saturation ratio is inversely related to laser intensity!
Saturation ratio derived from
spectroscopy, assuming LTE
Maximum ionization state derived
from spectroscopy, assuming LTE
Summary
•
We have obtained a better understanding of the mechanisms which
form particulate in laser plasma, through both modeling and
experiments
•
We have shown that ionization has a dominant effect on cluster
formation in laser ablation plumes, even at low laser intensity
•
•
•
The cluster sizes obtained are very small – of the order of 10 nm
•
IFE relevance of experiments would be improved greatly with control
of the background gas temperature
•
Other applications include nanocluster formation, laser
micromachining quality, thin film deposition by PLD
Model improvements are needed: 2-D, kinetic treatment, ...
In-situ particle measurements (scattering, cluster spectroscopy)
would be very useful to further validate the mechanisms