Download Interaction of ultrashort laser pulses with solids

Physics on femtoscale
L. Nánai
Univ. of Szeged, TTIK,
Dept. of Exp. Phys.
H-6720 SZEGED DÓM t 9
Summer School on Optics
June 7-10, 2015 Siófok (H)
1
Fundamentals of laser-matter
interactions
•Classical model
•Optical characteristic of materials
•Linear and nonlinear optics
•Material processing (general)
•Melting, damage, vaporization, surface,
plasma formation
•Heat treatment
•Cleaing
•Laser ablation
•Laser induced surface patterning
•Gas and liquid phase processes
•Role of pulse duration (thermal vs
photoinduced processes)
2
3
General tasks of
laser-matter
interaction
•
•
•
•
•
•
•
•
•
•
•
Surface
modifications
include
oxidation/nitridation of metals, surface
doping, etc.
PLA: pulsed laser ablation
PLD: pulsed laser deposition
LA: laser annealing
LC: laser cleaning
LIS: laser-induced isotope separation/IRlaser photochemistry
MPA (MPI): Multiphoton absorption
(ionization)
LSDW
(LSCW):
laser-supported
detonation (combustion)
LCVD (LCLD): laser-induced chemical
vapour (liquid)-phase deposition
LEC: laser-induced electrochemical
plating/etching
RED/OX: long pulse or cw CO2 laseinduced reduction/oxidation
4
Interaction processes depend on many parameters
The most important ones are:
Laser
Wavelength
Pulse length
Fluence (energy density)
Materials Optical properties
Surface structure
Thermal characteristics
Generally, the most important effect is heating, which can
lead to phase transformation.
5
Light absorption
Absorption in a medium with refraction index
n  n1 + in2
is given by the Beer-Lambert law
I(z) = I0 e- z
where I0 is the light intensity at z = 0 and
I(z) is the intensiy at depth z.
The attenuation coefficient is
 = -(1/I)(dI/dz)=2n2/c=4 n2/
Penetration depth is given by
 -1
For UV radiation:
dielectrics
For metals and semiconductors
  1 cm-1
 = (2-3)x106 cm-1
6
Light absorption
THE PARTITION OF THE ABSORBED ENERGY IS
NOT THERMAL AT FIRST
LASER LIGHT PRODUCES:
• PARTICLE EXCESS ENERGY
• EXCITATION ENERGY OF BOUND ELECTRONS
• KINETIC ENERGY OF FREE ELECTRONS
• EXCESS PHONONS
7
Heat propagation
Heath conduction equation
I a ( x, y, t )V z
T
2
 k T 
e
t
cp
Where
k=KV/cp heat diffusivity
K: thermal conductivity
Ia=(1-R)Io: unreflected part of the
incident irradiance
8
Free carriers
FREE-CARRIER GENERATION IS THE MOST IMPORTANT
SELF-INDUCED COUPLING EFFECT IN NON-METALS.
THE EFFECTS OF FREE CARRIERS IS TO REDUCE THE REAL
PART AND TO INCREASE THE IMAGINARY PART OF n.
THIS INCREASES THE ABSORPTION COEFFICIENT
 = 4 n2/
9
Free carriers
IN SEMICONDUCTORS HOLES AND ELECTRONS ARE IN EQUAL
NUMBERS.
IT IS CONVENIENT TO TREAT THEM TOGETHER AND TO WRITE
=0+Neheh
WHERE
0 is the lattice absorption coefficient
Neh = Ne = Nh
eh = absorpt. cross section of a carrier pair
eh scales with  , making the free-carrier absorption mainly
2
relevant for infrared beams.
10
Evaporation and plasma formation
EVAPORATION USUALLY OCCURS FROM A LIQUID.
PHASE EQUILIBRIUM BETWEEN A MELT AND ITS VAPOR REQUIRES
EQUALITIES OF THE FREE ENERGIES.
SINCE VAPORS ARE COMPRESSIBLE, THE EQUILIBRIUM CONDITIONS
DEPEND ON p TOO.
THE CHANGE OF FREE ENERGY WITH T CAN BE WRITTEN AS
dG G G dp
dp


 S  V
dT T p dT
dT
IT MUST HOLD FOR EACH PHASE INDIVIDUALLY.
AT EQUILIBRIUM THE PRESSURE INSIDE THE LIQUID AND THE
VAPOR MUST BE THE SAME
11
Interaction of ultrashort laser
pulses with solids
• Optical parameters n and k
• Role in excitation of electronic subsystem
• linear and nonlinear response of target
• Energy transfer
– electromagnetic field
e-e „thermalization”
transfer to ionic subsystem
• role of „time scale”
12
Solids in Very Intense Laser Field
Linear optics: validity of the superposition theory
P  E
Nonlinear optics: at high enough intensities
Pi   (1) Ei   ( 2) Ei Ek   (3) Ei Ek E j
Limit (classical):
m 2e5
9
Eat  4

5
.
14

10
_ V / cm
3
 (40 )
I at 
 0 cEat 2
2
(for H)
 3.5 1016 _ W / cm 2
13
Optical properties and ()
n()   () ()
(): electric dipole approximation
 p

p
 ( )  1   xcv 
 i (  cv ) 
 i (  cv ) 
  cv
vc
   cv

while , _ H (t )  (e) xE(t ), _ xcv  c x v
2
e2
 0h
In solids:

b ,k
 ub ,k ( x)ei k x _ Bloch
1 x  2
1 p  2

im12
3
2

d
k
p
e
 ( )  1   m 2 2   3 pcv (k ) 
 i ( Ecv (k )   )
0
8
vc
 Ecv (k )  

2
For semiconductors:
im  ( )  12 J ( )
14
Metals
• Linear optics if I< 1015 W/cm2
• Free carrier absorption (through inverse Bremsstrahlung)
=(5-10)*10-5 cm-1 up to -1=10-20 nm
- role of ballistic transport
(vb~ 106 m/s for 100 fs ~ 100-200 nm)
- role of density of states (DOS)
at Fermi level
• ballistic transport of non-thermalized
electrons and diffusive transport of
thermalized electrons
Heat transport from electronic subsystem to
initially cold lattice
15
Two temperature models (TTM)
Te
e t


z
Tl
l t


z
C
C
k  g (T  T )  S ( z, t )
k  g (T  T )
Te
e z
Tl
l z
e
e
l
l
S ( z, t )  I (t ) A exp( z )
Where Ce, ke and Cl, kl are the lattice and electron capacity and thermal conductivity,
S(z,t) is the laser heating source term.
Nolte model:
 t 
Te ( z, t )  exp  ( z )
 L 
( z )  a exp( z )  b exp(  z )
Tl  Te
Tp- excitation radius
Tl- relaxation radius
16
 t 

Te ( z, t )  Teq  T
exp  
  
 e  l
 eq 
 t 
e

Tl ( z , t )  Teq  T
exp  
  
 e  l
 eq 
 L eq
Fa  l
 2 2
1
1
Teq 
Te ( z,0) 

exp(


z
)


exp(  z )
2
2
 l eff
Cl  e   l   
l

T  Te ( z ,0)  Tl ( z,0)
 eq 
 e l
 e  l
e=Ce/g and l=Cl/g are the electron cooling and lattice heating times
eq
Caracteristic timescale of the thermal equilibration
Teq
final equilibration temperature
17

Temporal distribution of electron Te and lattice Tl surface
temperature for a copper target irradiated by a 120 fs, 800 nm
pulse at a laser intensity I0=5x1012 W/cm2
Comparison between nickel and gold surface temperatures
dynamics, in the same conditions as previous fig.
18
Semiconductors
• One-photon excitation yielding electron-hole pairs
(interband transition)
if hn< Eg
multiphoton abs. ~ IN
• Free carrier absorption
• Impact ionization
Relaxation by several channels:
- radiative
- nonradiative
19
TTM for semiconductors:

U e
 (keTe )   g eo (Te  To )  (1  R)(  n) I ( z, t )  (1  R) 2  2 I 2 ( z, t )
t
U o
 g eo (Te  To )  g ol (To  Ta )
t
U a
 (k a Ta )  g oa (To  Ta )
t

Uo=CoTo and Ua=CaTa are the optical and acoustic phonon energy
g
is the coupling coefficient

is the free carrier absorption coefficient
20
Dielectrics
• multiphoton transition
• avalanche ionization
Two photon absorption
21
Temperature evolution
The temperature, T, at a depth, x, below the surface of a material hit by an
ultrashort laser pulse is governed by the Quantum Heat Transport equation:
1  2T m T  2T

 2
2
2
v t
 t x
v: thermal pulse propagation speed
m: heat carrier mass
Two-part solution:
x

p: laser pulse duration
 t    x
x


v e v H  t   : mv2/2ħ
Ballistic: TB ( x, t )  Sech 2 
 p 
 v  H: Heaviside’s step function




2



2
x
I1   y 
 x t
Diffusive:
v    x 




2  t  y   y
TD ( x, t )    Sech
e
dy  H  t  


2
 v vx
  v
 p 
y2  x
v


 
 
22
Evolution of Carrier Densities
The densities of the electrons and holes created when an
ultrashort laser pulse hits a semiconductor were calculated using the
following equation:
4 ln 2  x  nc t 
2

 
 D 2  I 0e
t
x
2

 p2
 (1  R)e
x


l
I0: peak laser intensity (adjusted to get max carrier density of 1018 1/cm3)
c: speed of light
n: index of refraction
p: FWHM pulse duration (Gaussian pulse)
: absorption constant
R: reflectivity (0.286)
l: electron-hole pair lifetime
D: diffusivity
23
Dember Electric Field
The diffusivity of the electrons is about 20 times larger than for the holes.
The electrons diffuse faster into the material than the holes causing the net
charge density to be positive near the surface and negative deeper into the
material. This produces a strong „Dember” electric field that can be
calculated as follows:
E ( x) 
e
 r 0
x
  ( x' )   ( x' )dx'
h
e
0
e: elementary charge
0: permittivity of free space
r: dielectric constant
h: density of holes
e: density of electrons
24
Solutions to the QHT equation
for a 50 attosecond laser pulse
25
Solutions to the QHT equation
for a 20 femtosecond laser pulse
26
Calculated density of holes (a) and
electrons (b) created by a 50 as
laser pulse
27
Density of holes (dark line) and
electrons (light line) at the
surface (up) and a depth of
500 nm below the surface
(right) for a 20 fs laser pulse
28
Density of holes (dark line) and
electrons (light line) at the
surface (up) and a depth of
250 nm below the surface
(right) for a 50 as laser pulse
29
Dember electric field versus depth
in material for 50 as laser pulses
Dember electric field versus depth
in material for 20 fs laser pulses
30
Summary of temperature Evolution
For a 50-as pulse:
- Ballistic solution dominates
- A short thermal pulse propagates into the medium
For a 20-fs pulse:
- Diffusive solution dominates
- Temperature at the surface is high for a period of
time approximately equal to the laser pulse
duration
31
Structural Changes
- Thermal model:
rapid Equilibration of hot el-ns with lattice
heating up to melting temperature (ns, ps)
- Plasma model:
destabilization of the covalent bonds due
to electronic exitation (slow rate of phonon
emission) (fs)
32
Pump and Probe measurements
Ti:sapphire laser
Output power: 400 mW
Rep.rate: 90 MHz
Energy/pulse: 4.4 nJ
Central wavelength:
820 nm (FWHM: 43 nm)
AOM freq.: 25 kHz
Pump power: 25 mW
Probe power: 2.5 mW
33
Reflectivity at different sample orienteation
normalized
34
Fourier transformations of the scans
FFT
4pstoto10ps
FFT
5ps
FFT
0.5ps
to 8ps
4ps
Amplitude (a.u.)
Amplitude (a.u.)
Amplitude (a.u.)
1,8E-02
1,8E-02
8,E-02
1,6E-02
1,6E-02
7,E-02
1,4E-02
1,4E-02
6,E-02
1,2E-02
1,2E-02
5,E-02 1,0E-02
1,0E-02
4,E-02 8,0E-03
8,0E-03
6,0E-03
3,E-02
6,0E-03
90deg
90deg
90deg
75deg
75deg
75deg
60deg
60deg
45deg
60deg
45deg
30deg
45deg
5x
5x
30deg
30deg
5x
5x
4,0E-03
2,E-02
4,0E-03
2,0E-03
5x
1,E-02
2,0E-03
5x
0,0E+00
0,0E+00
0,E+00
0
100
200
300
400
500
0
100
200
300
400
500
0
100
200
300
400
500
Wavenumber(1/cm)
Wavenumber(1/cm)
Wavenumber(1/cm)
600
600
600
700
700
700
35
75deg FFT
90deg FFT
0.5ps to 4ps
4ps to 8ps
0.5ps to 4ps
5ps to 10ps
4ps to 8ps
5ps to 10ps
2,0E-03
1,4E-02
1,8E-03
5x
1,2E-02
Amplitude (a.u.)
Amplitude (a.u.)
1,6E-03
1,0E-02
8,0E-03
5x
6,0E-03
4,0E-03
1,4E-03
1,2E-03
1,0E-03
8,0E-04
6,0E-04
4,0E-04
2,0E-03
2,0E-04
0,0E+00
0,0E+00
0
100
200
300
400
500
600
700
0
100
200
300
Wavenumber (1/cm)
4ps to 8ps
5ps to 10ps
10X
Amplitude (a.u.)
1,5E-02
10X
1,0E-02
0,0E+00
400
Wavenumber (1/cm)
500
600
700
10X
10X
4,0E-02
0,0E+00
300
700
5ps to 10ps
6,0E-02
2,0E-02
200
4ps to 8ps
8,0E-02
5,0E-03
100
600
1,0E-01
2,0E-02
Amplitude (a.u.)
0.5ps to 4 ps
1,2E-01
2,5E-02
0
500
45deg FFT
60deg FFT
0.5ps to 4ps
400
Wavenumber (1/cm)
0
100
200
300
400
Wavenumber (1/cm)
500
600
700
36
37
Reflectivity at different TeO2 sample orienteation
-12
Amplitude X3
90 deg
5 to 60
8 ps
deg
-12
2x10
2,0x10
Amplitude -4(a.u.)
45 deg
2 to 5 ps
-12
1x10
30 deg
Amplitude X3
0 deg
0,0
Reflectivity (a.u.)
4,0x10
-4
3x10
deg FFTvs.
of time
TeOdelay
Dynamic45
reflectivity
2
0,1 to 3,5 ps
0
50
2000
100
4000
150
200
6000
250
8000
-1
Wavenumber
(cm )
Time delay (fs)
38
Thank You For Your
Attention !
40