Transition from periodic lattice to solid plasma in ultrashort pulse irradiation of metals Dimitri Fisher Soreq NRC Israel 25 th Hirschegg PHEDM Workshop.

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!!!