A Joule of Light: Laser-Matter Inter-actions Near the Ablation Threshold

Mark S. Tillack

Mechanical and Aerospace Engineering Department and the

Center for Energy Research

Jacobs School of Engineering

13 May 2002

108 1010 1012 1014 1016 1018

1 MeV

100 eV

1000 K

100 Kmechanicsof materials

10000 K(1 eV)

10 eV

Power Density, W/cm2

Temperatureablation,

cluster formation(materials processing)

10 keV

1JKrF

1JNd:YAG

50 mJCPA

air breakdown

sheath fields,ponderomotive forces,

x-ray generation,

relativistic plasmas,nuclear reactions

ultra-fast phenomena(e.g., Coulomb explosions)

Regimes of Short-Pulse Laser-Matter Interactions

E[V/cm]=27.5 √I [W/cm2]

108 W/cm2: Laser-induced damage to grazing-incidence metal mirrors

85˚

Goal is 5 J/cm2 normal to the beam for 108 shots

=532 nm

Surface damage leads to roughening, loss of beam quality and increased absorption

Single Shot Effects:

Laser heating generates defects (or melting)

Coupling between diffusion and elastic fields lead to permanent deformation

Progressive Damage in Multiple Shots:

Thermoelastic stress cycles shear atomic planes relative to one another (slip by dislocations)

Extrusions & intrusions are formed when dislocations emerge to the surface, or by grain boundary sliding.

Operation beyond the normal incidence damage threshold raises new concerns

Experiments are performed at the UCSD laser plasma & laser-matter interactions lab

Spectra Physics YAG laser:2J, 10 ns @1064 nm;800, 500, 300 mJ @532, 355, 266

nmInjection seededPeak power density ~1014 W/cm2

1 cmfluence is quoted normal to the beam

Mirrors are fabricated by diamond turning or substrate coating

E-Beam Al (<2 m)

CVD-SiC (100 m)

SiC Foam (3 mm)

Composite face (1 mm)

SiC Foam (3 mm)

MER composite mirror

MER composite mirrorDiamond-turned Al

fabricated at GA micromachining lab

Impurities dominate the damage threshold in Al 6061 & Al 1100

Fe MgSi

1000x

Several shots in Al 6061 at 80˚, 1 J/cm2 1000 shots in Al 1100 at 85˚, 1 J/cm2

1000x

Exposure of Al 1100 to 1000 shots at 85˚ exhibited no damage up to 18 J/cm2

Occlusions preferentially absorb light, causing explosive ejection and melting; Fe impurities appear unaffected

Design window for Al-1100

Exposure of Al 1100 to 104 shots at 85˚ exhibits catastrophic damage at fluence >18 J/cm2

10000 shots in Al 1100 at 85˚, 20 J/cm2

4000x

Goal =5 J/cm2 for 108 shots

Design window for 99.999% pure Al

Design window

Estimate of energy required to melt:T - To = (2q”/k) sqrt(tt/)e = q”t/[(1-R) cos]

T-To = 640˚Ct = 10 ns, =85˚e = 143 J/cm2

180 J/cm2

Multipulse damage morphology in pure aluminum, 104 shots

I

II III

IV

Region I

I. Unaffected zoneII. Slipped zoneIII. Damage haloIV. Catastrophic damage

Mechanical damage in pure Al exhibits both slip channels and oriented “ripples”

Mesoscopic modeling of surface deformation

x1 y1

1

0

1

eg1

tg2

bbg =3

Q

)(in

)(is

)(in

)(is)(in

)(is

)(in

)(is)(* in

)(* is

⊥

*

C

(1) Surface Deforms by Slip Lines (Dislocations) within each grain.

(2) Each line is represented by a 3-D space curve that moves and produces its own stress field (like a crack).

(3) Slip on atomic planes in one grain results in relative grain rotation and surface misorientation.

~100 atom diameters~10000 atom diameters

Interaction between dislocations and dipolar loops during laser pulses

I

II

Region IQuickTime™ and aBMP decompressor

are needed to see this picture.

The slip of dislocations pushes the dipolar loops closer to the surface, causing its deformation. This condition is very important in metal fatigue by laser pulses, and is known as "Persistent Slip Bands (PSB's)"

Regimes of Laser-Matter Interactions

108 1010 1012 1014 1016 1018

1 MeV

100 eV

1000 K

100 Kmechanicsof materials

10000 K(1 eV)

10 eV

Power Density, W/cm2

Temperatureablation,

cluster formation(materials processing)

10 keV

1JKrF

1JNd:YAG

50 mJCPA

air breakdown

sheath fields,ponderomotive forces,

x-ray generation,

relativistic plasmas,nuclear reactions

ultra-fast phenomena(e.g., Coulomb explosions)

1010 W/cm2: Ablation plume dynamics

Applications: Process improvements for laser micromachining, cluster production,

thin film deposition

Ion source for laser-IFE blast simulations

Physical processes: Laser absorption Thermal response Evaporation Transient gasdynamics Radiation transport Condensation Ionization/recombination

Laser absorption processes

• Initial absorption creates high-pressure vapor

• Large E-field (30√ I V/cm) ionizes the vapor

• Electron density cascades as high as pe=laser

(n=4x1021/cm3 ~150 atm for =532 nm)

• =(ei/c)(pe/)2(1/n) n = no+ik = (1–p2/2)1/2

• Self-regulating evaporation during pulse

initial energy deposition

critical surface

absorption in expanding plasma plume

Inverse bremsstrahlung (collisional wave damping) in underdense plasma

Estimates of parameters

• Temperature estimate from flux limit:

fa I ~ F n Te ve

• Density in the plume

n ~ 1020/cm3, ne ~ 1018/cm3

solid density ~ 6x1022/cm3

ncr = 4x1021/cm3

1 atm (0˚C) ~3x1019/cm3

I (W/cm2) Te (eV)109 0.251010 1.161011 5.41012 251013 1161014 538

at n=ncr

Experimental set-up

Ablation plume evolution strongly depends on background pressure

Above ~10 Torr, the plume stalls and is “slammed” back into the target

100 Torr

Visible emission measured by 2-ns gated iCCD camera

Al target,

0.6 mm spot

Ablation plume behavior in the low pressure regime

10–6 Torr

Below ~1 mTorr, the plume expands freely

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

0.15 Torr

In the intermediate pressure regime, the plume detaches but continues to interact with the background gas

Ablation plume behavior in the intermediate pressure regime

Plume edge position vs. pressure

Fitting Curves:Free expansion:

R ~ tShock expansion:

R ~ (Eo/o)1/5 t2/5

Drag: R = Ro(1–exp-bt)

Note:mfp of Al ~1/n~3.5mm@150 mTorr

Plume velocity is measured using time-of-flight analysis of emission lines

“Plume splitting” is observed:• slower peak~56 eV

(2.0x106 cm/s)• faster peak~600eV

(6.6x106 cm/s)(nearly free expansion)

Al-I line emission:

Although the ion kinetic energy is up to 1 keV, the temperature in the plume is only a few eV

Line ratio measurement:

kTe=(E1–E2)/ln(I22g1A1/I11g2A2)

Observations of fast ions were made soon after Q-switching was invented

D. W. Gregg and S. J. Thomas, J. Appl. Phys. 37, 4313 (1966).

v2max

v2avg

Comparison of Al-I, Al+ and Al++ time-of-flight spectra suggests presence of electric fields

Estimated expansion velocities:Al 2.3x106 cm/s

(75 eV)Al+ 4x106 cm/s

(224 eV)Al++ 6.6x106 cm/s

(610 eV)

Estimates of electric fields near the wall

“Double layer” (or sheath) potential is ~3/2 kT

Estimates of electric fields near the wall

Ponderomotive force = P•E = (n2-1)/82En2=1–p

2/2

Condensation of aerosol creates problems in several laser (and IFE) applications

Melt zone

Knudsen layer

Vapor

Condensate

A 1D multi-physics model is being developed to explore process improvements for laser micromachining

Physical processes: Laser absorption Thermal response Evaporation

Transient gasdynamics

Radiation transport Condensation Ionization/recombination

Simple absorption coefficient, I=Ioe–x

1D conduction&convection

1D, 2-fluid Navier Stokes fluid equations

(with Knudsen layer jump conditions)

TBD

See below...

Modified Saha, 3-body recombination

j =M2π

Γσ c

pv

RTv

−σ e

psat

RTf

⎛

⎝ ⎜

⎞

⎠ ⎟

Initial estimates of plume parameters

109 W/cm2, 10 ns Gaussian pulse, Si target, 1 Torr airat 10 ns,

n=1020/cm3 T=6000 K (~0.5 eV)vi = 106 cm/sne/n ~ 1%r*=2/(RTlnS) < 0.1 nm

(no barrier to cluster formation)at 100 ns

S ~ 20–40J ~ 1030–1040/m3/s

Classical aerosol generation and transport

Homogeneous Nucleation (Becker-Doring model)

∂n∂t[ ]growth,

homo=

Psat

kT

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2 2σmπ

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1/ 2 S2

ρl

exp−πσdcrit

2

3kT

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥ δ Vcrit( ),

#

m3s

1

m3

⎡ ⎣ ⎢

⎤ ⎦ ⎥ dcrit =

4σmρlkTlnS

, and Vcrit =π6dcrit

3

∂n∂t[ ]growth,

hetero=−∂I

∂ V( ) =−∂∂ V( ) n∂

∂t V( )( ), #

m3s

1

m3

⎡ ⎣ ⎢

⎤ ⎦ ⎥ ∂

∂t V( ) =2π π6( )

1/ 3 S−K( )PsatDdp

kTVmolF,

m3

s

⎡

⎣ ⎢

⎤

⎦ ⎥

Condensation Growth

Coagulation

∂n∂t[ ]coag

=12

β V*,V−V *( )n(V*)n(V−V*)dV*0

V

∫ − β V,V*( )n(V)n(V*)dV*0

∞

∫

β V,V*( ) =2π D+D*( ) dp +dp*

( )Fcoagwhere the coagulation kernel is given by

Convective Diffusionand Transport

∂n

∂t+∇ • nv v ( ) −∇ • D∇n( ) +∇ •

v c n= ∂n

∂t[ ]growth,homo

+ ∂n∂t[ ]growth,

hetero+ ∂n

∂t[ ]coag

Particle Growth Rates

Homogeneous nucleation rate depends very strongly on saturation ratio (S=pvap/psat )

10 14

10 16

10 18

10 20

10 22

10 24

10 26

10 28

10 30

10 32

10 34

10 36

10 38

0.01

0.1

1

10

1 10 100

Critical Radius (nm)(dashed curves)HMG Nucleation Rate (#/m

3/s)

(solid curves)

Saturation Ratio

1500 K

2000 K

2500 K

3000 K

1000 K

1500 K

2000 K2500 K

3000 K

3500 K

3500 K

Formation Rate and Size of Pb droplets in an IFE System

• High saturation ratios result from rapid cooling from adiabatic plume expansion

• Extremely small critical radius results

• Competition between homogeneous and heterogeneous condensation determines final size and density distribution; Reduction in S due to condensation shuts down HNR quickly

ΔG =4πr3

3Vm

(μL −μv)+4πσr2

Modification of homogeneous nucleation rate equation due to small critical radius

• Surface of tension is not accurately described by “4r2 ”

• n=/(1+/R)2, where (~0.1 nm) is the difference between the geometric surface and the “surface of tension”

• Js=A e–W*/kT, where A=zNo: z is a barrier shape parameter, No is the gas density and is the attachment frequency)

• Stark broadening is the dominant broadening mechanisms for many laser-produced plasmas

• Electric microfields produced by nearby charged particles modify the excitation energy of emitters

• ~ne

• High pressure depresses ionization energy:

• ne~0.01 n

Ionization in the ablation plume can affect condensation

NeNz

Nz−1

=2Uz(T)

Uz−1(T)2πmeKBT

h2⎛ ⎝

⎞ ⎠

3/2

exp −Ez−1 −ΔEz−1

kT⎛ ⎝

⎞ ⎠

ΔEz−1 =7×10−7 ne3 Z2/3

Mechanisms of enhanced cluster formation

ΔG =4π3Vm

(r3 −ra3)(μL −μv)+4πσ(r2 −ra

2)+e2

2(1−ε−1)(r−1 −ra

−1)

Gib

bs f

ree

ener

gy

Cluster radius

• Ion jacketing results in an offset in free energy (toward larger r*)

• Dielectric constant of liquid reduces free energy

Ionization has a major impact!

Cluster birthrate vs. saturation ratio(Si, 109 W/cm2, 1% ionization)

Regimes of Laser-Matter Interactions

108 1010 1012 1014 1016 1018

1 MeV

100 eV

1000 K

100 Kmechanicsof materials

10000 K(1 eV)

10 eV

Power Density, W/cm2

Temperatureablation,

cluster formation(materials processing)

10 keV

1JKrF

1JNd:YAG

50 mJCPA

air breakdown

sheath fields,ponderomotive forces,

x-ray generation,

relativistic plasmas,nuclear reactions

ultra-fast phenomena(e.g., Coulomb explosions)

CPA enables table-top ultra-high (TW) intensity research at a “modest” price

CPA = Chirped pulse amplification

1018 W/cm2 Effects of ultra-high field

Electrons become relativistic when:eE(=mec2=5x105 eVrecall E=30I1/2, so [m]I1/2=

for =1 m, I = 1018 W/cm2

Effects include:distortion of electron orbits (in vacuum)reduction in plasma frequency (higher me)self-focusing (due to spatial profile of intensity)ponderomotive channelingfast (MeV) ion generation

A proposal to generate and study fast ions

incident laser

interactionregion sheath

return current

fast electroncurrent

laser absorption mechanisms

electron transport physics

ion acceleration physics

Laser-matter interactions touch upon many fields of engineering science, and offer numerous opportunities for student research

• Mechanics of materials• Ablation plume dynamics• Laser plasmas• Cluster formation• Laser propagation• Relativistic plasma physics

http://aries.ucsd.edu

EXTRAS

Crystallization of amorphous coatings

I

II

Region I

75 nm Al on superpolished flat: ±2Å roughness, 10Å flatness

111

101

001

diamond turned surface

Dependence of plume behavior on laser intensity

2x1012 W/cm21x1011 W/cm23x1010 W/cm2

8x109 W/cm24x109 W/cm22x109 W/cm2

1x109 W/cm29x108 W/cm24x108 W/cm2

Ion energies deviate from a shifted Maxwellian

f (v)≈v3exp−m(v−vo)2 /2kT[ ]

Absorptioncoefficient

=(ei/c)(pe/)2(1/n)

n = no+ik = sqrt[1–p2/2(1+i/)]

Z = 1, =1 m

Inverse bremsstrahlung absorption