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

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)())((

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)(