Transition from periodic lattice to solid plasma in ultrashort pulse irradiation of metals Dimitri...
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Transcript of Transition from periodic lattice to solid plasma in ultrashort pulse irradiation of metals Dimitri...
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).
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?!