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Initial kinetics of material excitation and relaxation in swift
heavy ion tracks
Alexander Volkov
Russian Research Centre KurchatovInstitute
Swift Heavy Ions
Eion > 1 MeV/uMion > 20 mp
Se > 1 keV/nm
100 – 300 MeVXe+
1 – 2 GeVU+
>20 MeVO+
100
5
10
15
20
25
dE/d
x, k
eV/n
mEion, keV
ElectronicNuclear
Au in SiO2
Sn / Se< 0.01
102 104 106 108
The electronic energy losses are more than two orders larger than the elastic losses
Why SHI are interesting ?
Rd 2Re
~ 100 µm
I. A new tool for nanostructuring
Initial excitation: Re < 5 ÅStructure transformations: Rd~10nm
The energy losses due to elastic collisions are too small to produce detected damage
Why SHI are interesting ?
II. Fundamentals
Nanometric spatial andFemto-picosecond
temporal scalesExtremely high levels of
initial excitations
Unusual kinetics pathways of track
relaxation Which can not be
described by macroscopic models
Models are necessary
which form the basis for controlling the technological processes based on SHI irradiations
Marek Skupinski (Uppsala)
1. Initial electronic excitations 10-17 s
2. Plasmon screening 10-16 s
3. Thermalization of electrons 10-15 s
4. Cooling down of electrons 10-14 s
5. Energy transfer to lattice up to 10-11 s
6. Track cooling down 10-9 s
7. Stress relaxation > 10-9 s
Time Scales
Why the Thermal Spike is popular?
Easier description of structure and phase transformations
Temperature
Macroscopic models with local equilibrium
Thermo activated mechanisms
Heat DiffusionDiffusion
Phase transformations
How to produce Two Temperatures Thermal Spike1. Thermalization of both subsystem of a target (electronic and ionic)
at different temperatures. Local equilibrium
2. A difference between electronic and ionic temperatures forms thedriving force for energy transfer
3. Parabolic equations of heat diffusion
( )
( )
ee e ei
ii i ei
T div T qt
T div T qt
χ
χ
∂= ∇ +
∂∂
= ∇ −∂
( )20 4ci i it R χ= Lattice
cooling down
( )20 4ce e et R χ= Electronic
cooling down
Electrons to ions energy transfer
1Eei ei it q T−=
lattice is not heatedce
t < tEei
ce
t tEei> lattice is heated
Te0
Electron – phonon couplingtos = 10-13 se i e ph− ≡ −
tec < 10-14 s << t Ee-ph
No heating
∆Ti = 10 to 100 K
χe > 10 cm 2s -1Ginzburg et al (1956)
Toulemonde et al. (1992)q = gTe
room temperature experiments in Fe
g = 3.6 s-1 q
eTFTRT
egT2000iT K∆ >
Above the melting point
χe = 1 cm 2s -1when
Te = 1 to 10 εf
Martynenko and Yavlinskii (1983)
tec < tE
e-ph
∆Ti = a few handreds K
12 1110 10Ee pht s− −− = −
Electron-lattice interaction in a SHI trackCooling down time of electrons is much shorter that the
atomic vibration time.
Lattice dynamic can not be ascribed by phonons
< 10-14 s << tos = 10-13 stce = (R0
e)2 4χe
Frozen ionic structure with the ideal gas dynamics(L. van Hove 1952)
Dynamically isolated atoms : ε(k) ~ k2
Phonons ε(k) ~ k, (k<<π/a)
Electron – phonon coupling mechanism can not be applied before 10-13s in SHI tracks
Electron-to-Lattice heat transfer rate
[ ]4 2
3
41 exp( / ) 1 exp( / )
ie
e e
LZne m Tq TM T Tπ µ µ
⎧ ⎫= −⎨ ⎬+ − +⎩ ⎭
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10
0,1
0,2
0,3
0,4
0,5
0,6
Thermal conductivity, KE
nerg
y ex
ch. r
ate,
q
Te /εf
0 1 2 3 4 5 6 7 8
200
400
600
800
1000
33
2
21
Ion
tem
pera
ture
incr
ease
, K
Distance from the track axis, nm
Classical limit at high energies : electron – ion interaction in two
component plasma
Dash lines - e-ph coupling.The maximum initial electronic temperatures:
(1) 10εf , (2) 5εf and (3) εf
No large heating
“Thermometer” and “tool” for defect kinetics investigations
Alkali – Halides ( LiF, NaCl )
a = 0.404 nm
Examination of different temperature-based models of track excitation needs a natural “thermometer” – a system where :a) Relaxation of electronic excitations results in well
detected changesb) Temperature considerably affects to these changes
that also must be easy detected
Defects in alkali – halidesF Li 4.03 Å
- ++ - ++-
++ -++- ++
-++ ++ - ++
- ++ - ++ ++ -++- ++ - ++ - ++ ++
- ++ ++ - ++ -++- ++
-++ - ++ ++
- ++ - ++ ++ -++- ++ - ++ - ++ - ++
e-e-
e-
V
fcc lattice, (100) plane
Electro-neutrality. Vacancies and interstitials must
capture charge carriers
New electronic levels due to localization of carriers
Color Centers
Electron centers
F-center ( stable at RT )+
e
+
++ av e+ −
Hole centers
H-center (T<80K)+
+
++e
2 /X X− −
2 / 2X X− − VK- self-trapped hole (T<140K)+
+ -
1. Well separated by Spectroscopy
2. Different temperatures of stability
F 1000K
Vk 140K
H 80K
I 10-25K
Energy loss, eV54 56 58 60 62 64 66
e0c
Energy, eV10 15 20 25 30 35 40
Cou
ntin
g ra
teplasmon
e0a
LiFLiF
Plasmons 25 eV
Cation exciton 62 eVC
Anion exciton 13.6 eVA
A
C
Li (2s)
F (2p6)
Li (1s2)
Eg= 14.6 eV
Excitons in LiFR. T. Poole et al., PRB 11 (1975) 5179; J. R. Fields et al. PRL 38 (1977) 430
Exciton mechanism of defect creation
In-situ spectroscopy at UNILAC GSI
1. LiF and NaCl
2. The ion energies 11 Mev/u (50 - 2600 MeV)
3. Ions a) Light C, Ti, Nib) Kr, Smc) Heavy Au, Pb, U
4. The electronic energy losses 0.7 - 26 keV/nm
5. Fluences from 108 to 1012 ions/cm2
Prof. Kurt Schwartz
6. Irradiation temperatures 8 K and 300 K
Detection of defects having low thermal stability
200 300 400 500 600 700 8000.0
0.5
1.0
1.5
2.0
Abs
orba
nce
F
HF2
8 K
200 300 400 500 600 700 8000
1
2
Wavelength, nm
Abos
rban
ce 300 KF
V3F2
H centers are not stable at T > 70 K
238U in LiF
«Low temperature» defects
0 20 40 60
10 -7
10 -6
10 -5
12 K
29 K37 K 57 K
109 U5.1010 C
0 20 40 6010 -7
10 -6
10 -5
20 K
Tem perature, K
b)
10K12K
15 K
26 K35 K
53 K
109 U 5x1010 C
LiF
NaCl
I centers are stable onlybefore 10 – 25 K
No dependence on the electronic energy loss
Hillocks in LiF 1400 Pb ions at 8 K and 300 K
1. Core damage2. Threshold dE/dx ~ 6 keV/nm
3. No dependence on Tirr
0.8 ± 0.20.9 ± 0.2h, nm
18.3 ± 319.5 ± 3d, nm
300 K8 K
Athermic process ??
Different spatial scales of the thermal spike and damage creation region
Low heating < 75 – 250 K,
20 - 40 nm
No heating at the periphery of the defect halo
200 300 400 500 600 700 800
0.5
1.0
1.5
2.0
F
H8 K
Abso
rban
ce
nm
0 10 20 30 40 50 60
5000
10000
15000
20000
25000
Lum
ines
cenc
e, I
Temeperature, K
x 20
10K
16K
20K
26 K
35 K
50 K
H centers “10 K” defectsIonization, MC by S. Bouffard
Heating or Athermic ???? < 1 nm
Irradiation temperature effects on fluence dependences of F- center production for light and heavy ions
Increase of defect production rate at 8 K for heavy ions
Decrease of defect production rate at 8 K for light ions
0.0 3.0x1010 6.0x10100
1x1016
2x1016
n F, cm
-2
nF, c
m-2
50Ti 300 K
8 K
0.0 5.0x109 1.0x10100
2x1015
4x1015
6x1015
8x1015
nF, c
m-2
Fluence
300 K
8 K238U
Formation of stable Frenkel pairs (F and H centers)Two lengths govern defect separation and recombination
- -
-
-
- ++ -
++++
++ -++ - ++
++
++-
++-++-++-++
-
-
-
-
++
++
++
++-
++ --++
++ ++ -- ++ ++++ - ++ -
++++ ++ -
++-
++ --++ - ++
++ ++ -- ++ ++++ - ++ -- ++ ++++ ++ -
-
++ -
++++
++ -- ++++ -
++ --
-
-
--
++-++-++-++
- -
-
-
- ++ -
++++ ++
++ -++ - ++
++++
-++ -
-
-
-
--
e- F
- H
- H
e- F
L FF ≈ L HHl HF
l HF
min 5 1.4HF HFl l a nm≥ = =Good separation in a pair:
Separation of F and H centers in Frenkel pairs depends on the local temporal temperature increase
Local heating and the defect production rate
Separation at hot stage and recombination after track cooling down
∆T from heavy ions provides good separation and a similar number of stable pairs at 8 K and 300 K
Recombination of H and F centers is suppressed at 8 K
For light ions a local temperature is too week for effective separation of defects at 8K
lHF [ T(r,τ) ] = lHF [ ∆T(r,τ) + Tirr ]
0.0 3.0x1010 6.0x10100
1x1016
2x1016
n F, cm
-2
nF,
cm-2
50Ti 300 K
8 K
0.0 5.0x109 1.0x10100
2x1015
4x1015
6x1015
8x1015
nF,
cm-2
Fluence
300 K
8 K238U
Estimations of the temperature increase in the defect halo
lHF [ T(r,τ) ] = lHF [ ∆T(r,τ) + Tirr ]
Tirr = 8K
lHF6D0 exp( - UH / T) ti
c ≈ l2HF
D0 = 10 -2 cm2/s , UH = 0.05 – 0.1 eV tic = 10 – 100 ps
Separation due to Diffusion
∆T ≈ 100 K – 250 KHeavy IonsGood sep.
lHF ≈ 2 nm
∆T ≈ 50 K – 100 KLight IonsWeak sep.
lHF ≈ 1 nm
Difficulties of the classical model of heat diffusion
20 40 60 80 1000
30
60
90
120
150
t, ps
r, nm
15.0050.0075.00100.0150.0200.0300.0500.0800.0
1T K Trt C r r rρ
∂ ∂ ∂⎛ ⎞= ⎜ ⎟∂ ∂ ∂⎝ ⎠FJ K T r= − ∂ ∂
Origin : An infinite velocity of heat propagation assumed by the model
Extremely fast cooling down at cryogenic temperatures
χ=K/ρC ~ 102 cm2/s 2 1210ir sχ −<<
No enough time for good defect separation in the defect halo
Cattaneo equation
CC
J TJ Kt r
τ ∂ ∂+ = −
∂ ∂011
2
2
=⎟⎠⎞
⎜⎝⎛
∂∂
∂∂−
∂∂+
∂∂
rTr
rrCK
tT
tT
τρτ
2v
v2 = K/(τρC )= vs2/ 3
For spatial and temporal scales of track relaxation we have to take into account the finite velocity of heat propagation.
For the phonon mechanism - the velocity of sound
10 20 30 40 500
255075
100125150175200
t, ps
r, nm
15.0050.0075.00100.0150.0200.0300.0500.0800.0
Heat front
νs ~105 cm/s
A finite velocity the wave equation
Enough time for defect separation
MD Investigations of the lattice kinetics
Crystal argon with fcc lattice and L - J pair potential
Temperatures
Temperature based approach is questionable till
1 - 4 psFront of Excitation
t = 10-17 s – 10-14 s
Spatial and temporal distributions of
- delta-electrons- electronic vacancies at different shells- excess energy of electronic subsystem- excess energy of lattice
Monte-Carlo simulations of the initial electronic kinetics
-40 -20 0 20 40
-40
-20
0
20
40nm
nm
25
e- e-
e-e-e-
e-e-
e- e-
e-
e-e-
e-e-
1. Creation of 1st generation of delta-electrons and holes by SHI
2. Propagation of primarily electrons. Creation of secondary electrons and holes
3. Auger decays of holes creating free electrons
Experiments which are able to touch the shortest times of of electronic relaxations in a track (t < 10-14s)
Dr. Olga Rosmej et al.
X-rays spectroscopy. Spatially resolved measurements of the K-shell projectile and target radiation along the ion trajectory
x
SiO2 Aerogel Targets3-D network:3 nm - solid beads20 - 50 nm - pore
Ca+19 (E = 5 - 11.4 MeV/u)
27
Disadvantage of the first attempt to fit
0 200 400 600 800 10000
200
400
600
Eion, [MeV]
Theory (Bethe-Bloch) CasP 3.1 SRIM 2006 Presented MC-calculations
Only Ionizations
1. Quantitative agreementIon energy losses/
deposited dose
2. No success with fitting of KαLn (n) spectra
O.Rosmej ey al.
Decay of holes
L or VB
K or L
(a) radiative decay
(b) Auger process
(c) Due to solid-like density - Inter-atomic Augerprocesses
holee- e-
L-shellSi
O(2s)
VB
M.L. Knotek and P.J. Feibelman, Surface Science 90 (1979) 78-90
28
0 1 2 3 4 5 6 70,0
0,1
0,2
0,3
0,4
0 1 2 3 4 5 6 70,0
0,1
0,2
0,3
0,4
0 1 2 3 4 5 6 70,0
0,1
0,2
0,3
0,45 MeV/u MC-calculations Experiment
Num
ber o
f ato
ms
with
diff
eren
t num
ber o
f vac
anci
es, [
a.u.
]
Number of holes in L-shell, n
8 MeV/u MC-calculations Experiment
Num
ber o
f ato
ms
with
diff
eren
t num
ber o
f vac
anci
es, [
a.u.
]
Number of holes in L-shell, n
11.4 MeV/u
Number of holes in L-shell, n
Num
ber o
f ato
ms
with
diff
eren
t num
ber o
f vac
anci
es, [
a.u.
] MC-calculations Experiment
X-ray KαLn Si-spectra can be described for different ion energies by using
only the one (!) free parameter:the time of the inter-atomic Auger process
which fills holes in L-shells of silicon atoms
Verification of the MC model
29
Excess energy
1 10 100 100010-8
10-6
10-4
10-2
100
102
104
1,7x10-6
1,7x10-4
1,7x10-2
1,7x100
1,7x102
1,7x104
1,7x106
E, K
/at
R, nm
E, e
V/nm
3
Electronic vacancies Delta-electrons Lattice atoms
t = 10-15 c
The excess energy densities of δ-electrons, electronic vacancies and lattice atoms.
10-17 10-16 10-15 10-1440
50
60
70
80
E e, [%
]
t, [s]
Decrease of the energy of δ-electrons due to secondary ionization.
1. The energy of vacancies can not be neglected (55%)2. Lattice excitation at times < 10-14 s (before phonons)
Ballistic propagation of the excess energy
Can not be described by heat diffusion
0,1 1 10 100 100010-1010-910-810-710-610-510-410-310-210-1
1,7x10-8
1,7x10-7
1,7x10-6
1,7x10-5
1,7x10-4
1,7x10-3
1,7x10-2
1,7x10-1
1,7x100
1,7x101
E at [e
V/at
om]
E at [e
V/nm
3 ]
R, [nm]
10-14 s 10-15 s 10-16 s 10-17 s
Lattice atoms
0,1 1 10 100 100010-7
10-5
10-3
10-1
101
103
105
1x10-7
1x10-5
1x10-3
1x10-1
1x101
1x103
1x105
E e, [e
V/at
om]
E e, [e
V/nm
3 ]
R, [nm]
t = 0 s t = 10-17 s t = 10-16 s t = 10-15 s t = 10-14 s
δ- electrons
1 10 100 1000 1000010-12
10-10
10-8
10-6
10-4
10-2
100
Si L-shell
Nva
c,[1/
atom
]
R, [nm]
t = 0 s t = 10-17 s t = 10-16 s t = 10-15 s t = 10-14 s
Electronic vacancies
Delocalized electrons
0,1 1 10 100 1000100
101
102
103
104
1,2x104
1,2x105
1,2x106
1,2x107
1,2x108
E spec
, [o K]
E spec
, [eV]
R, [nm]
t = 0 s t = 10-17 s t = 10-16 s t = 10-15 s t = 10-14 s
Energetic and spatial separations.
Ballistic propagation
0,1 1 10 100 10001010
1013
1016
1019
1022
1,4x10-13
1,4x10-10
1,4x10-7
1,4x10-4
1,4x10-1
Ne, [
1/at
om]
Ne,
[1/c
m3 ]
R, [nm]
t = 0 s t = 10-17 s t = 10-16 s t = 10-15 s t = 10-14 s
Thermalization only
2 % of the excess energy in R < 1 nm at 10-15s
6 % of the excess energy in R < 6 nm at 10-14s
0,1 1 10 100 100010-1710-1510-1310-1110-910-710-510-310-1
t e-e, [
s]
R, [nm]
at t=10-17 s at t=10-16 s at t=10-15 s at t=10-14 s
Application of the local temperature approach and heat diffusion model (thermal spike) is questinable
“fragments of a grenade”
Col
or c
ente
rs, c
m-2
Fluence, ions/cm2
Track overlapping results in deviation from the linear
growth of the concentration
Rd = (π Φd )-0.5 =10 – 30 nm
Number of defects produced per a single track
∆NF = dnFlinear ⁄ dΦ
Ro
L~ 100 µm
Average defect concentration in a track
< CF > = ∆NF ⁄ (πR20 L)
Track parameters
Diffusion coefficient of valence holes in SHI tracks
100 200 300 400 500 600 700 800 900 10001017
1018
1019
1020
1021
1022
1023
Den
sity
of v
alen
ce h
oles
, [1/
cm3 ]
R, [A]
Pb (1600 MeV) Pb (2300 MeV) U (1100 MeV) Ti (555 MeV)
<CF> Spatial redistribution of valence holes is necessary before self-trapping (10-12s)
Ch0
<CF>
Ion / energy (MeV)
Dhcm2s-1
Ion / energy (MeV)
Dhcm2s-1
Pb 1600 MeV 9.4 Ti 555 MeV 3.4
Pb 2300 MeV 11.4 C 57.6 MeV 0.3
U 1100 MeV 16.3 C 133 MeV 0.4
Dh =Ch
o Rh2
4τh <CF>
ConclusionsTe
0Thermal Spike Model
0 2 4 60
500
1000
1500
2000
T(r=
0,t)
t, ps
2004 1994
15K
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10
0,1
0,2
0,3
0,4
0,5
0,6
Thermal conductivity, KE
nerg
y lo
ss ra
te,
Q
Te /εf
0 1 2 3 4 5 6 7 8
200
400
600
800
1000
33
2
21
Ion
tem
pera
ture
incr
ease
, K
Distance from the track axis, nm
Electron to ion coupling . No large heating
0 1 0 2 0 3 0 40 50 600
5 00 0
10 00 0
15 00 0
20 00 0
25 00 0
Lum
ines
cenc
e, I
T em e p eratu re, K
x 20
10 K
16 K
20 K
2 6 K
35 K
5 0 K
20 0 3 00 4 00 5 00 60 0 70 0 80 00.0
0.5
1.0
1.5
2.0
Abs
orba
nce
F
HF 2
8 K
Spectroscopy experiments. Low temperatures in the defect halo
200 300 400 500 600 700 800
0.5
1.0
1.5
2.0
F
H8 K
Abso
rban
ce
nm
0 10 20 30 40 50 60
5000
10000
15000
20000
25000
Lum
ines
cenc
e, I
Temeperature, K
x 20
10K
16K
20K
26 K
35 K
50 K
10 20 30 40 500
255075
100125150175200
t, ps
r, nm
0 1x1010 2x1010 3x1010
2x1015
4x1015
6x1015
8x1015
1x1016
F ce
nter
con
cent
ratio
n, n
F (cm
-2)
Fluence (ion/cm2)
197Au
8 K
300 K
0 5x1011 1x1012 2x1012
1x1015
2x1015
3x1015
4x1015 300 K
F ce
nter
con
cent
ratio
n, n
F (cm
-2)
Fluence (ion/cm2)
12C8 K
MD of lattice excitation. Problems with thermalization. Excitation front
Monte-Carlo of electronic excitations. Ballistic front. No thermalization. Interatomic Auger
0,1 1 10 100 100010-7
10-5
10-3
10-1
101
103
105
1x10-7
1x10-5
1x10-3
1x10-1
1x101
1x103
1x105
E e, [eV
/ato
m]
E e, [eV
/nm
3 ]
R, [nm]
t = 0 s t = 10-17 s t = 10-16 s t = 10-15 s t = 10-14 s
x
100 200 300 400 500 600 700 800 900 10001017
1018
1019
1020
1021
1022
1023
Den
sity
of v
alen
ce h
oles
, [1/
cm3 ]
R, [A]
Pb (1600 MeV) Pb (2300 MeV) U (1100 MeV) Ti (555 MeV)
<CF>
Considerable spatial redistributions of valence holes is necessary before sel-ftrapping. Diffusion coefficient of holes
Conceptions of temperature, local equilibrium, heat diffusion, phonons etc. are applied hardly for the most important
stages of track kinetics
Acknowledgements
A.E.Volkov - the Russian Foundation for Basic Research under Contracts No. 08-08-00603-a, 09-08-12196-ofi-m, and
10-08-90024-Bel-a.
K. Schwartz M. Sorokin
N. Medvedev O. Rosmej
V. Lipp N. Scheblanov
B. Rethfeld C. Trautmann