Transition from periodic lattice to solid plasma in ultrashort pulse irradiation of metals

Dimitri Fisher

Soreq NRC Israel

25th Hirschegg PHEDM Workshop

Jan 30 – Feb 04 , 2005

Femtosecond laser irradiation of metals - 1

))(,(),()( ieieiei

ii TTTTgTTUtTTC

),(),())(()( txQTTUxTT

xtTTC ie

ee

eee

2),(),(Re

21),( txEtxtxQ

electron subsystem:

ion (phonon) subsystem:

laser energy deposition:

S.I.Anisimov, B.L.Kapeliovich, T.L.Perel'man, JETP 39, 375-377 (1974)

Femtosecond laser irradiation of metals - 2

0 25 50 75 100

103

104

105

dashed line - Ti

solid line - Te

tem

pera

ture

s T

e a

nd

Ti

[K]

I0 [W/cm2]:

1011

1012

1013

1014

near

the

irra

diat

ed t

arge

t su

rfac

e

time t [fs]. Laser pulse peak occurs at t = 50 fs

D.V.Fisher, M. Fraenkel, Z. Henis, E. Moshe, S. Eliezer PRE 65, 16409 (2001).

Femtosecond laser irradiation of metals - 3

Feee TTTC forFeBeee TTkTnC for )(2/3

iBii knC T allfor 3

fs3000foreV,1eV,1001 tTT ie

Typical regime:

Approximations available:

OK

Fe

Fe

TTgTTg

at theory SCP from,at theory band from,

What at

Te~TF???

103 104 1051013

1014

1015

1016independent of T

i

Ti = 1000 K

Ti = 3000 K

Ti = 300 K

e

lect

ron

mo

me

ntu

m r

ela

xatio

n r

ate

[s-1]

electron temperature Te [K]

e,e

,

= e,e

+ e,ph

Longitudinal momentum relaxation rate

electron-ion coupling mismatch

element

gmetal

(any Te ‘Ti)

[erg / cm3 K s]

gplasma

(Te = 10 eV)

[erg / cm3 K s]

gmax

(Te = 10 eV)

[erg / cm3 K s]

Al 3.8×1018 2.8×1019 2.7×1019

Cu 6.1×1017 1.8×1019 2.0×1019

e-i coupling in NFE metal

bVsqkk

qkk

qk

qopt

qkk

kkqkkqq

qqie

qqM

nf

kkm

M

ffnffnddkkn

ndqqVTTU

iTBKq

eTBKeTkE

,min

,,where

2

111cos422

1

42

),(

2,

2

1exp

11exp

1

2222

1

10

23

0

23

2

e-i coupling in SCP

Strongly - Coupled Plasma: Coulomb logarithm = 1

ieBeie

iiie TTK

uMm

neZTTU

3

24312),(

Maximal energy transfer regime:

3/134

max

where

2

2

3),(

iNN

ieBNN

e

i

eeie

na

TTKa

u

M

mnTTU

What are the mechanisms of the gradual transition from

metal to plasma electron behavior?

• Non-isochoric:– surface layer expansion;– (possibly) local breach of charge neutrality?

• Isochoric:– ultrafast melting (thermal or nonthermal);– ionization of localized electron states,

charge-disordered solid regime;– electron localization due to e-e collisions?

Isochoric transition from metal to plasma behavior time scales:

• ultrafast melting: ~ 100-1000 fs

(governed by forces and ion mass);

• charge disorder: ~ 1-10 fs

(governed by electron impact ionization);

• electron localization: ~ 1 fs or shorter

(governed by electron spread and velocity).

ORDEREDSOLID

CHARGE – DISORDERED

SOLID

Z = 2 Z = 2.5 Z = 3

Mg, Ca; Zn, Cd, Sn?, Pb?: charge disorder

by ionization of core states

• No experimental evidence so far!

The predictions are pure theory.

• Zn: localized 3d-states ~8 eV below Fermi level. Should ionize at modest electron temperatures, leading to charge disorder.

• Mg: L-shell ionization by electron impact.

• Must do ultrafast melting experiments!

s-band (2 states)

d-band (10 states)

Cu: outer shell:11 electrons per atom

Fermi level

diagram from: Janak ,Williams, and Moruzzi,

Phys Rev B 11 p. 1522

noble metals: charge disorder by d-band states localization

noble metals: charge disorder by d-band states localization

0 2 4 6 8 10-2

0

2

4

6

Cu

d-band position evaluated using INFERNO code

en

erg

y o

f d

-ba

nd

pe

ak

[ eV

]

electron temperature Te [ eV ]

D.V.Fisher et. al.: proceedings XXVIII ECLIM, Rome, Sept. 2004

0.1 1 10 1000.00

0.01

0.02

0.03

Cu

Interband absorption amplitude at two wavelengths

in

terb

an

d a

bso

rptio

n a

mp

litu

de

arb

itra

ry u

nits

, n

ot

no

rma

lize

d.

electron temperature Te [ eV ]

800 nm 400 nm

0 20 40 60 80 1000.01

0.1

1

10

100

Cu target = 800 nm

ele

ctro

n t

em

pe

ratu

re

Te

[ eV

]

time t [ fs ]

I0 = 1013 W/cm2

I0 = 1014 W/cm2

I0 = 1015 W/cm2

1011 1012 1013 1014 10150.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Cu target50fs FWHM pulse

a

bso

rptio

n c

oe

ffic

ien

t a

vera

ge o

ver

pu

lse

du

ratio

n a

nd

o

ver

spo

t in

ten

sity

dis

trib

utio

n

Intensity [ W/cm2 ] at pulse peak at spot center

800 nm experiment 800 nm theory 400 nm theory

Results: theory vs. experiment

5 10 15 20 25 30 35 40 450.0

0.1

0.2

0.3

0.4

0.5

laser duration: 50 fs FWHM laser wavelength: 400 nm

1 nm deep, proper g 1 nm deep, constant g 10 nm deep, proper g 10 nm deep, constant g

symbol: Ti (t

m ) = 1.5

T

melt

lower error bar: Ti (t

m ) = 1.0

T

melt

upper error bar: Ti (t

m ) = 2.0

T

melt

me

ltin

g t

ime

t m

[ p

s ]

peak laser intensity I0 [ 1013 W/cm2 ]

d-shell localization - 1

• In this model: d-states localize as the d-band peak crosses the bottom of the conductivity band. Can localization occur at lower Te?

Yes it can.

• Band width ~ inverse tunneling time ( ~ 0.2 fs ). This is NOT related to d-shell hole lifetime with

respect to recombination ( ~ 20 - 50 fs ).

• INFERNO model underestimates band width, but we can trust the trend.

d-shell localization - 2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Cu

sc

ale

d 3

d b

an

d w

idth

W

/ W

RT

scaled electron temperature Te / ( - E

peak )

d-shell localization - 3

fs1.0~/ timetunneling

whenlocalizedy essentiall is state band-d

eNNtunn ua

0.5 W/W :)E-( 4.0Tat Cu

:INFERNO

eV 3 W :T roomat Cu

eV 7W widthband toscorrespond This

RTpeak 3de

RT

Experimental evidence:X.Y.Wang, D.M.Riffe, Y.-S.Lee, M.C.Downer, PRB 50, 8016-8019 (1994)

Two-pulse thermionic emission from gold targets shows significant increase in g at Te ~ 1eV

Phonon emission & absorption by d-band holes?

Onset of charge disorder?

Suprathermal electron contribution?

Photon energy is very close to d-shell absorption edge, so direct production of d-shell holes is possible! NB: Holes are short-lived with respect to tunneling between ion wells, but long-lived with respect to recombination.

!!!

CONCLUSIONS:

• Fascinating physics is revealed, pertaining to both fundamental physics (quantum mechanics, electron properties of disordered systems) and to applications.

• Any experimental data are welcome!!!

• What happens at higher photon energies?!

THANKS:

Zeev Zinamon

Zohar Henis

Shalom Eliezer

Moshe Fraenkel

Organizers!!!