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