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Modeling of LASER
Micromachining Process
Debkalpa GoswamiDepartment of Production
Engineering Jadapur !niersit"
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Light
Amplification by
Stimulated
Emission of
Radiation
•Population
Inversion
•Stimulated
Emission
• Amplification
Albert Einstein
T. H. Maiman
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Population Inversion
Boltzmann Distribution Law
(Thermal Equilibrium)
2 1
2 1
E E
kT N N e
− − ÷ =
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Stimulated Emission
2 1h E E ν = −
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Amplification
( )21 1 2 0
k L I r r I e
γ −=
( )21 2 1
thk Lr r e γ − =
1 2
1 1
ln2thk L r r γ
= + ÷
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Properties of Laser Radiation
• Monochromaticity
• Collimation
• Beam Coherence
• Temporal Modes
• Frequency
Multiplication
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Types of Industrial Lasers
•
Solid-state Lasers
• Gas Lasers
• Semiconductor Lasers
• Liquid dye Lasers
Nd:YAG (1064 nm)
Ruby (694 nm)
Nd:glass (1062 nm)
HeNe (632.8 nm)
CO2 (10,600 nm)
Argon (488, 514.5 nm)
InGaAs (980 nm)
Rhodamine 6G (570-640 nm)
Coumarin 102 (460-515 nm)
Stilbene (403-428 nm)
Kumar Patel
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Laser Materials Interactions
Laser Parameters Material Parameters
• intensity
• wavelength
• spatial and
temporal coherence
•angle of incidence
• polarization
• illumination time
• absorptivity
• thermal
conductivity
• specific heat
•density
• latent heat
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Thermal Effects
; for( ) ( )
2
2, ,T z t T z t
t z α ∂ ∂=∂ ∂ ( )
0,0T z T = 0 z ≤ ≤ ∞
( )0,T t k H
z δ
∂− =
∂
1 0
0
p
p
t t
t t
δ ≤ ≤
= >
( )
( )( )
( ) ( ) ( )( )
1 2
1 2
1 21 2
1 2
1 2 1 2
4 ierfc 0 heating4
,
2
ierfc ierfc cooling4 4
p
p p
p
H z t t t
k t
T z t
H z z
t t t t t k t t t
α α
α
α α
≤ ≤ ÷
÷ ∆ = ÷− − > ÷ ÷ ÷ ÷−
( ) ( ) ( )( ){ }
( )
2
2
0
1ierfc exp 1 erf
2
where erf .
x
x x x x
x e d
ξ
π
ξ π
−
= − − −
= ∫
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a
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b b
Hz T
kT T π π
= ÷ ÷
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Important Practical Considerations
• Beam Shapes
( )2
0 2
2exp
r I r I
w
−=
( ) ( ) ( ) ( )2 2 2
2 2 2
, , , , , , , , , , , ,T x y z t T x y z t T x y z t T x y z t
t x y z α
∂ ∂ ∂ ∂= + + ∂ ∂ ∂ ∂
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• Pulse Shapes
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• Moving Source of Heat
(quasi-stationary heat flow)
(trial function)
x vt ξ = −
( ) ( ) ( ) ( ) ( )2 2 2
2 2 2
, , , , , , , , , , , , , , ,T y z t T y z t T y z t T y z t T y z t v
t y z
ξ ξ ξ ξ ξ α
ξ ξ
∂ ∂ ∂ ∂ ∂− + = + +
∂ ∂ ∂ ∂ ∂
( ), , ,0
T y z t
t
ξ ∂=
∂
( )0 , ,vT T e y z λ ξ ϕ ξ −= +
( ) ( ) ( ) ( )
2 2 2 2
2 2 2
, , , , , ,, ,
2
y z y z y z v y z
y z
ϕ ξ ϕ ξ ϕ ξ ϕ ξ
α ξ
∂ ∂ ∂ − = + + ÷ ∂ ∂ ∂
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• Temperature dependent properties
• Thermal conductivity
•
Thermal diffusivity
• Absorptivity
Etc.
f(T)
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Laser Micromachining Mechanisms
• Laser Ablation • Laser AssistedChemical Etching
material removal processes
by photo-thermal or photo-
chemical interactions.
multiphoton
mechanism: even
though the energy
associated with each
photon is less than thedissociation energy of
bond, the bond breaking
is achieved by
simultaneous absorption
of two or photons.
carried out by using
suitable etchant
(precursors).
gaseous precursors:
Cl2 and Br2(dry etching)
liquid precursors: HCl,
HNO3, H2SO4, NaCl,
and K2SO4(wet
etching)
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Laser Micromachining Applications
•
MicroviaDrilling
• Drilling of
Inkjet
NozzleHoles
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• Fuel
Injector
Drillin
g
• Laser
Scribing
Bio-medical applications:
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Relevant Research and Recent Trends
•
ExperimentalModels
• Semi-analytical
Models
• Numerical or
Computer Models
Kuar et. al (2006)
Gospavic et. al(2004)
Ding et. al (2012)
Kuar, A. S., B. Doloi and B. Bhattacharyya (2006). "Modelling and analysis of pulsed Nd:YAG laser machining
characteristics during micro-drilling of zirconia (ZrO2)." International Journal of Machine Tools and Manufacture46(12-
13): 1301-1310.
Gospavic, R., M. Sreckovic and V. Popov (2004). "Modelling of laser-material interaction using semi-analytical approach."
Mathematics and Computers in Simulation65(3): 211-219.
Ding, H., N. Shen and Y. C. Shin (2012). "Thermal and mechanical modeling analysis of laser-assisted micro-milling ofdifficult-to-machine alloys." Journal of Materials Processing Technology212(3): 601-613.
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• Kuar et. al
(2006)
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• Gospavic et.
al (2004)
Semi-analytical model
Particular cases with
cylindrical geometry
Laplace Transform and
Fourier Method of
Variable Separation
PDE ODE
Alternative
method
Differential
Transform
Mukherjee, S.,D. Goswami and B. Roy (2012). "Solution of Higher-Order
Abel Equations by Differential Transform Method." International Journal ofModern Physics C23(09): 1250056.
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• Ding et. al
(2012)
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Laser Thermal Lab, UC Berkeley
Laser-Assisted Nano-wire Growth and Harvest
Nanoplasians harvesting their nanowires selectively grown on a field by a laser-
assisted method. (SEM image)
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Thank You