LASER IRRADIATION OF MONOCRYSTALLINE CVD DIAMOND: A QUANTUM-KINETIC MODEL BASED ON
BOLTZMANN EQUATION
T. Apostolova1, Stefano Lagomarsino2,3,
Silvio Sciortino2,3, Chiara Corsi4,5, Marco Bellini6
1Institute for Nuclear Research and Nuclear Energy
2Istituto Nazionale di Fisica Nucleare3 Dipartimento di Fisica, Università di Firenze4 Dipartimento di Fisica, Università di Firenze
5LENS Florence6INO-CNR Florence
Motivation• Laser engineering of diamond for writing conductive paths is an
important subject of research for its application in radiation detection (3D detectors)[1,2].
[1] S. Lagomarsino et al Appl. Phys. Lett. 103, 233507 (2013)
[2] S. Lagomarsino , et al Diamond & Related Materials 43 (2014) 23–28
• A deep insight of the process of laser graphitization of diamond is critical to tune at best the laser parameters and obtain low resistivity channels with minimum damage of the surrounding diamond lattice.
• Simulate ultra-short laser-induced electronic excitation, absorption, and the subsequent relaxation processes in CVD monocrystalline diamond and compare to the results of experiment.
+ + +
- - -- - -
+ + +
Lowering charge trapping probability in the bulk
Thus: increasing collection efficiency
Since their very introduction (1997), 3D achitectures for silicon was intended to solve problems of radiation hardness in silicon detectors.
Why a 3D architecture for diamond trackers?
(Nucl. Instr. and Meth. A 395 pp 328-343 (1997) )
Since 2009, a simple 3D pulsed laser technique has been made avalilable for microfabrication of 3D graphitic structures in the bulk Diamond
T.V. Kononenko et al., Femtosecond laser microstructuring in the bulk of diamond, Diamond and Relat. Mater. 18 (2009) 196–199
How it is made
This technique has been used to make conductive electrodes for 3D detectors.
ms
mA
500 V
Experimental approach: The transient current technique (TCT) is used to measure laser induced
current transients.
Our theoretical approach:
Theoretical modeling (Quantum kinetic formalism based on a
Boltzmann-type equation including photo-excitation, free-carrier
absorption, impact ionization, Auger recombination of electron-hole
plasma, thermal exchange with the lattice is performed.
The transient conduction electron distribution functions, electron
densities photo-generated and the average electron energies during the
pumping fs-laser pulses are evaluated and damage criteria are given.
Original picture by S.K. Sundaram, Nature Materials 1 (4) 217-224 (2002) and edited for additional relevant processes
Timescales of various electron and lattice processes in laser-excited solids.
Free carrier absorption (e-phn-pht)
Exciton formation/ non-radiative exciton decay
Mechanisms of absorption and deposition of energy and response of the material.
PIe-phn-pht
II
E-E E-PHN
XD AR
Original picture by S.K. Sundaram, Nature Materials 1 (4) 217-224 (2002) eddited for the relevant processes
XF
Laser radiation
electron
hole
Conduction band
Valence band
Forbidden band
nm800
210 cmTWI
fsL 30
CVD diamond
• Laser -PI, MPI
E-PHN-PHT, II, E-E
AR, XF, XD,E-PHN
Coupling to lattice
• QM – Power density
• Rate equations
PI
JEp 41.0
Boltzmann type scattering equation
)(),(),(),(),( arimpeephephtphne
220
2
0
2 11
2 s
LOq Qq
e
VC
Lqqkk
phqqk
Lqqkk
phqqk
m
tqe
MMq
qphtphnein
k
MEENn
MEENn
JCWL
1
2 2
2
.22
,
))((2*
ek
extk
e
k
PI
k
e
k
outk
e
k
ink
ek nWnGnWnWt
n )())(())(( 11
Huang, Apostolova… PRB 71, 045204, 2005
VQq
eqV
sr
c22
0
2)( )(
3132
22
*
0
22 3 D
rs n
meQ
qkqkkkqkqkk
qk
inimpimpink EEEEnnnqVW
1)(
2 2
,
)())((
21
**220
221
0
)( 11~)(
VBCBsr
inimp
mmVQq
qe
IqV
qkqkkkqkqkk
qk
ccink EEEEnnnqVW
1)(
2 2
,
)())((
Apostolova et al… NIMA, 2014
22
*
3
*
2
EEMm
mE
E
EmWG
Gr
PIk
STEel E
EE
2
1exp
2
2
2Dam
Ec
STE
Apostolova et al… NIMA, 2014
𝜕𝑛𝜕𝑡
=𝛻 ∙𝐷𝑎𝛻𝑛−𝑛−𝑛0𝜏 𝐴
−𝑛−𝑛0𝜏𝑟
𝜕𝐸𝜕𝑡
=𝛻 ∙(𝑘 h𝑡 ,𝑒𝛻𝐸
3𝐾 𝐵𝑛 )+𝛻 ∙(𝐷𝑎𝐸𝑛𝛻𝑛)− 𝐸−3𝑘𝐵𝑇
𝜏 𝑒− h𝑝
+𝐸𝑔
𝑛−𝑛0𝜏 𝐴
A - auger recombination time (inversely proportional to n2)
r- recombination time for processes in which energy is directly released to the lattice
e-ph - electron-phonon energy relaxation time
kth,e - plasma thermal conductivity
Da- ambipolar diffusivity, dependent both on the plasma temperature
- E/(3kBn) and on the lattice temperature T
Da -
Previous results for SiO2
0 2000 4000 6000 80000.00
0.02
0.04
0.06
0.08
0.10
0.12
E-field=105 kV/cmPhoton energy 2.5 eVPulse duration 50 fs
PI PI+IB PI+IB+XF
D
istrib
utio
n fu
nctio
n
Electron energy (meV)
0 1000 2000 3000 4000 5000 6000 7000 8000
1E-4
1E-3
0.01
0.1
Dis
trib
utio
n fu
nctio
n
Electron energy (meV)
Apostolova et al NIMA 2014
Previous results for SiO2
0 10 20 30 40 500
1
2
3
4
5
6
E-field=105 kV/cmPhoton energy 2.5 eVPulse duration 50 fs
PI PI+IB PI+IB+XF
E
lect
ron
dens
ity (10
25 m
-3)
Time (fs)
Apostolova et al NIMA 2014
Results for CVD diamond
Results for CVD diamond
Results for CVD diamond
Results for CVD diamond
Log
Qm
ea
s.
(a.u
.)Log n
calc. (a.u.)
measurements
model
J
• Optical damage
LLth IdttIF )(
• Electrical damage
electcI nN
Tk
ENNN
B
GvcI 2exp
• Structural damage
317107.8 cmn electc
KTm 1512for GaAs
BGkkkkkk EEdEfdEfEE
00
Classification of laser damage to semiconductors
22pL
232*,, )2(2 TkmN Bhevc
*0
2
er
ep m
ne
Conclusions
• Quantum Boltzmann Equation used to describe electronic excitation
below the graphitization threshold - accounts for relevant processes:– PI, E-PHN-PHT, (II, AR, E-E, E-PHN)
• The charge collected as a function of the laser pulse energy predicted by calculation and measured found in good agreement
• Graphitization threshold-connection to density of electrons created by pulsed laser in focusing spot-further investigation
THANK YOU!
Results for CVD diamond
Results for CVD diamond
n (c
m-3)
E (J)
Our experimental approach: The transient current technique (TCT) is used to measure laser induced
current transients.
A.Haug, Phys Stat Sol 108, 443, 1981
dosm
kE
2
22
• Indirect band-gap semiconductors-many valley conduction band with elliptical energy surfaces and a degenerate valence band with heavy and light holes
• Can be reduced to a two-band model with spherical energy surfaces by introducing effective conductivity mass and a density of states masses
312tledos mmm
311111
3
1 ttlc mmmm
E
mED
edos3
23
2
2
2
1)(
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