center for laser micro-fabrication school of mechanical engineering purdue university large scale...

Center for Laser Micro-Fabrication School of Mechanical Engineering Purdue University

Large Scale Numerical Modeling of Laser Ablation


Background

• Goal: to understand ultrafast laser (pulsewidth < 10-12 s) – material interaction (application: laser micro-machining)

• The process of ultrafast laser-matter interaction is highly non-equilibrium. The heating rate can reach 1014 K/s, and the material can be superheated above the thermo-dynamic critical point.


Fundamental Processes and Time Scales Involved in Ultrafast (fs) Pulsed

Laser Ablation of Metal

– Heating of electrons (before lattice being heated) ~ fs– Transfer of energy from electrons to the lattice and heating of

the lattice to temperatures above the melting point ~ 1 - 10 ps – the temperature of elections could be much higher than the lattice temperature

– Liquid – vapor phase change, phase explosion ~ 10 – 100 ps– Melting duration ~ 100 ps – 1 ns– Cooling of the lattice ~ s


Mechanism for material removal

1.2

0.8

0.4

0.00.4 0.6 0.8 1.0 1.2

Red

uce

d p

ress

ure

, p

/pc

Reduced temperature, T/Tc

Equilibrium vaporization, binode

Normal heating

Spinode

Tc

pV

T

0

Superheating

• Phase explosion versus spinal decomposition?


Continuum (the Two Step Energy Transfer) Model and Its Limitation

•

For Tl = 5,000 K,

For Te = 10 eV,

For Te = 50 eV,

In laser heating, the electron temperature Te can exceed50 eV (500,000 K!).


The Two Step Energy Transfer Model - cont.

• Kinetic relation at the solid-liquid interface

• Energy balance at the solid-liquid interface

mslb

sloslsl TTk

TLVTV exp1)(

slslsliq

liqs

s LVx

T

x

T


The Two Step Energy Transfer Model - cont.

• Kinetic relation at the liquid-vapor interface

where

• Energy balance at the liquid-vapor interface

lvuliq

lvTMR

AMpV

2

c

b

c

lv

cuc

b

bc

lv

lvu T

T

T

T

TR

L

T

T

TT

T

TR

Lpp 110

22

00 sinsin1

11

1exp

lvlvliqliq

liq LVx

T


Procedure of the Finite Difference (Enthalpy) Method

• The electron temperature field is solved for by using the semi-implicit Crank-Nicholson scheme.

• The lattice temperature field and related phase changes are solved for by using an enthalpy formulation.

),( txQx

T

xt

Ha

lvliqvslliqliq

T

T

l LfLfdTcH 0


Numerical Results

Thickness of gold film (nm)

Mel

ting

thre

shol

dfl

uenc

e(m

J/cm

2 )

0 500 1000 150020

40

60

80

100

120

Experimentb = 200 nmb = 0


Numerical Results – Cont.

Time (ps)

Sur

face

latti

cete

mpe

ratu

re(K

)

0 5000 10000 15000500

1000

1500

2000

2500

3000

3500

4000

4500

5000

55000.5 J/cm2

0.4 J/cm2

0.3 J/cm2

0.2 J/cm2

(a)

Time (ps)

Mel

tdep

th(n

m)

0 5000 10000 150000

100

200

300

400

500

600

7000.5 J/cm2

0.4 J/cm2

0.3 J/cm2

0.2 J/cm2

(b)

Time (ps)

Sol

id-l

iqui

din

terf

ace

tem

pera

ture

(K)

0 500 1000 1500 2000 25001000

1500

2000

2500

3000

3500

4000

45000.5 J/cm2

0.4 J/cm2

0.3 J/cm2

0.2 J/cm2

(c)

Time (ps)

Sol

id-l

iqui

din

terf

ace

velo

city

(m/s

)

0 500 1000 1500 2000 2500-200

0

200

400

600

800

1000

1200

1400

16000.5 J/cm2

0.4 J/cm2

0.3 J/cm2

0.2 J/cm2

(d)

- Evaporation rate is very small (< 0.1 nm per pulse)- Unable to compute phase explosion


Governing Equations:

rc

1

2 5

78

MD Simulation of Laser Melting and Ablation of an Argon Solid


Snapshots of Atomic Positions(laser irradiates from the right hand side)

(a) t=5 ps (b) t=10 ps (c) t=15 ps (d) t=20 ps (e) t=25ps (f) t=30 ps

0

4

8

12

x (n

m)

(a)

0

4

8

12

x (n

m)

(b)

0

4

8

12

3 5 7 9 11 13 15 17

x (n

m)

(c)

z (nm)

0

4

8

12

x (n

m)

(d)

0

4

8

12

x (n

m)

(e)

0

4

8

12

3 5 7 9 11 13 15 17

x (n

m)

z (nm)

(f)


MD Simulation – Phase Explosion


Future Work

Simulating laser ablation of ‘engineering materials’Morse potential for fcc metals

Stillinger-Weber potential for Si

Large scale simulation: increase the number of molecules from the current 2,000,000 to 500,000,000.

Combined MD and continuum approach.

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