Femtosecond laser interactions with semiconductor and dielectric materialsNikita S. Shcheblanov, Thibault J. Y. Derrien, and Tatiana E. Itina Citation: AIP Conf. Proc. 1464, 79 (2012); doi: 10.1063/1.4739862 View online: http://dx.doi.org/10.1063/1.4739862 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1464&Issue=1 Published by the American Institute of Physics. Related ArticlesOptical absorption of silicon nanowires J. Appl. Phys. 112, 033506 (2012) Crystallization of fused silica surfaces by ultra-violet laser irradiation J. Appl. Phys. 112, 023118 (2012) Mechanism for atmosphere dependence of laser damage morphology in HfO2/SiO2 high reflective films J. Appl. Phys. 112, 023111 (2012) Spectral analysis of x-ray emission created by intense laser irradiation of copper materials Rev. Sci. Instrum. 83, 10E114 (2012) Four-domain twisted nematic structure with enhanced liquid crystal alignment stability and fast response time J. Appl. Phys. 112, 014512 (2012) Additional information on AIP Conf. Proc.Journal Homepage: http://proceedings.aip.org/ Journal Information: http://proceedings.aip.org/about/about_the_proceedings Top downloads: http://proceedings.aip.org/dbt/most_downloaded.jsp?KEY=APCPCS Information for Authors: http://proceedings.aip.org/authors/information_for_authors

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Femtosecond Laser Interactions with Semiconductor and Dielectric Materials

Nikita S. Shcheblanova, Thibault J. Y. Derrienb and Tatiana E. Itinaa

a Laboratoire Hubert Curien, CNRS/Université Jeann Monnet, 18 rue du Prof. Benoit Lauras, 42000 Saint-Etienne, France

b Laboratoire Lasers, Plasmas et Procédés Photoniques, CNRS/Université de la Méditerranée, 162 avenue de Luminy, 13288, Marseille, France

Abstract. Electronic excitation-relaxation processes induced by ultra-short laser pulses are studied numerically for semiconductors and dielectric materials (Si, quartz). A detailed kinetic approach is used in the calculations accounting for electron-photon-phonon, electron-phonon and electron-electron scatterings. In addition, both laser field ionization ranging from multi-photon to tunneling one, and electron impact (avalanche) ionization processes are included in the model. Based on the performed calculations we study the relaxation time as a function of laser parameters. It is shown that this time depends on the density of the created free carriers, which in turn is a nonlinear function of laser intensity. In addition, a simple damage criterion is proposed based on the mean electron energy density rather than on critical free electron density. This criterion gives a reasonable agreement with the available experimental data practically without adjustable parameters. Furthermore, the performed modeling provides energy absorbed in the target, conditions for damage of dielectric materials, as well as conditions for surface plasmon excitation and for periodic surface structure formation on the surface of semiconductor materials.

Keywords: Femtosecond laser, damage, Boltzmann equation, surface plasmon, ripples, surface structures. PACS: 78.20.Bh, 72.80.Ey, 72.20.Jv, 52.50.Jm, 42.65.Re, 72.80.Sk.

INTRODUCTION

Interactions of ultra-short laser pulses with wide band gap materials are used in numerous areas such as photonics, micromachining, and medicine [1,2]. In particular, femtosecond lasers have found many promising applications in texturing semiconductor and dielectric materials forsollar cells, in microelectronics and in microfluidics [3,4,5]. However, it is still difficult to control over the quality and the size of laser-treated areas due to the lack of understanding of ultra-short laser interactions. Thus, our knowledge of ionization probabilities defining electronic excitation processes is very limited and is based on numerous assumptions (monochromatic waves, parabolic band structure, etc [6,7]). These probabilities were often limited by extreme regions of the Keldysh parameter (multi-photon or tunneling ionization) [8]. The correct description of the the relaxation processes is even more challenging, since such effects as the formation of self-trapped excitons and

International Symposium on High Power Laser Ablation 2012AIP Conf. Proc. 1464, 79-90 (2012); doi: 10.1063/1.4739862

© 2012 American Institute of Physics 978-0-7354-1068-8/$30.00

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recombination processes remain rather poorly understood. All these processes are, however, important in determining such parameters as laser damage threshold. Therefore, to further develop the applications of femtosecond lasers, it is essential to develop theoretical and numerical models of ultra-short interactions with dielectric and semiconductor materials. In these models, time-dependent electron distribution function should be considered. In fact, the assumption of equilibrium strongly limits the capacities of many simplified models to correctly predict the kinetics of laser excitation processes [9]. As a result of this assumption, many adjustable parameters were used in these models. Because of the adjustable parameters, such as collision frequency and ionization probabilities, even when the results of the modeling agree with the experiments, they do not provide an explanation of the physical processes involved.

Previously, many models were based on a simplified rate equation [10,11] and only several theoretical studies used a detailed quantum-kinetic approach [9]. In fact, these approaches often c disregarded strong deviations from equilibrium that typically occur in the electron sub-system upon femtosecond interactions. A study of the detailed non-equilibrium kinetics was performed by Kaiser [9]. These calculations provided an information about the relaxation time for metal and dielectric materials, as well as about the final electron density of free electrons created in the conduction band due to both photo-ionization and electron-impact ionization processes. In addition, the role of laser pulse duration in the elucidation of the prevailing ionization mechanism was investigated [12]. However, many issues are still puzzling. For instance, it is unclear how the relaxation time depends on laser parameters. In fact, the density of the created carriers and the collision frequency depend strongly on both laser intensity and pulse duration. A more detailed investigation of these parameters is, therefore, required for to better understand ultra-short laser interactions with dielectric and/or semiconductor materials.

In addition, it was demonstrated that if laser intensity is above a certain value, optical breakdown (OB) occurs in dielectric materials [10]. This intensity value was often taken to be equal to the damage threshold. This assumption, however, requires a careful verification. For instance, in several studies the OB-based threshold was found to disagree with the measured damage thresholds. As a result, several modifications of the damage criterion were proposed based on a comparison of the electron energy with melting temperature [13,14]. To calculate laser damage criterion correctly, one should consider the non-equilibrium electron energy distribution, and know the corresponding relaxation times. For this, we develop a model based on the solution of a system of Boltzmann transport equations (BTEs) for electrons and phonons. A series of calculations is performed for quartz. The electron energy distribution is calculated as a function of time. Then, an average electron energy is investigated as a function of laser parameters. In addition, electron relaxation time is examined and a damage criterion is proposed based on the mean electron energy rather than on the fee electron density.

Finally, a similar approach is used for Si. As a result, collision frequency can be obtained, which is then introduced in a traditional rate-diffusion equation. The formation mechanisms of surface periodic structures on Si surface are then considered. The possibility of surface plasmons exitation and their role in formation of periodic

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surface structures is then discussed on the basis of the results for single pulse experiments, and our numerical simulations.

MODELING DETAILS

Our model is based on a system of Boltzmann transport equations (BTEs) for

electrons and phonons [8,9,15]. For dielectric materials, the system can be written as follows

0

,0

,

0 ,

,

0

pi e ph pht e e imp

ph e pht

f f f f ft t t t t

f t f

g gt t

g t g

(1)

where f is free electron distribution function, g is phonon distribution function for -th phonon mode, pi is the photoionization collision integral (CI) [8,9,16], e-ph-pht is electron-phonon-photon CI, which describes pure electron-phonon collisions and absorbing laser energy by free electrons due to electron-phonon collisions [17], imp CI describes the impact ionization process [18,19], e-e is electron-electron CI [19], ph-e-pht is phonon-electron-photon CI [17]. All CIs are written with the assumptions of parabolic electron bands and for the monochromatic wave cost t0E E . We use

a complete Keldysh expression for the photoionization rate in [mpiW -3·sec-1] as follows

3 22 2

2 1

2 , exp9

rpi pi

K EmW Q x lE

(2)

2 2 2

01 1

2, exp

2 2pi

m

l x mK EQ x m

K E K 1 1E, (3)

where x ; vbcbr mmm 111 is the reduced mass; mcb and mvb are conduction

band and valence band electron masses, respectively; 1~pil (here,

[�…] stands for the integer part); 12

2~ E is the effective ionization potential;

is the energy gap; 0eE

mr is the Keldysh parameter; 21

11 ;

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221

; is the Dawson�’s integral; K and E are complete elliptic integrals of

the first and second kinds, respectively. And photoionization�’s CI is given by 2

42

,2

2 M , 1

M ,2 kin

pi v v v v pipi

pipi v

r cb

f f f lt

W

m m

, (4)

where vvf is valence electron distribution function and 1vvf (since maximum of free electron density much less than valence electron density);

kin r cb pim m l . In the calculations, we assume that laser intensity is constant during the pulse (top hat temporal shape). The two significant LO-phonon branches (0.063 and 0.153 eV) have been treated with the usual Fröhlich Hamiltonian formalism [20], the acoustical branch applied as Kaiser [8,9]. In addition to the one-photon processes, many-photon processes were taken into account in e(ph)-ph(e)-pht collisions.

Once equilibrium is established in the electron subsystem, by assuming flux-doubling condition [10], the BTE equation can be replaced by the rate or drift diffusion equation for dielectric target [21]

e

V

eVe

ll

leV

e nn

nnnIInnt

ztn pi

pi

pi )()()(

)(),( , (5)

where ne is the number density of conduction band electrons, nv is the total number of valence band electrons, is laser frequency,

pil is the multi-photon collision cross-section, is the avalanche ionization parameter, and is the relaxation time. In this simplified approach, Drude-Lorentz model is often used to calculate absorption [22]. For the calculations of free-carriers energy absorption in dielectric materials, the dielectric function is typically written as follows

inn

nnn

cr

e

V

ee

1

1111)( , (6)

where is collision frequency, is the dielectric constant of unexcited material, is the critical density of free electrons required for optical breakdown.

crn

For semiconductor materials, one should account for the formation of free carries (electrons and holes), for their recombination and diffusion processes. The corresponding drift diffusion equations can be written as follows [22,23,24]

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hn

h

gap

eff

PE

heA

e

hn

heIIeeeB

e

nnn

ElzI

nnC

nnn

nnIInTket

n

exp21

121

1

0

221

(7)

heA

e

hn

heIIhheB

h

nnC

nnn

nnIInTket

n12

1

0

221 (8)

where and are the mobility of free carriers; eµ hµ 1 , 2 are ionization probability from the multi-photonic regime approximation [24]; II is the impact ionization rate,

0 is the Auger recombination time and is the recombination rate [25], despite that the electron-hole plasma recombination lifetime is driven by carrier diffusion [26]. The other parameters are the same as in [24]. The optical response of the material is considered by using the dielectric function and taking into account the effect of band gap renormalization due to electron photo-excitation. [22]. The collision frequency is matched to the reflectivity measurements for Si [27].

AC

CALCULATION RESULTS AND DISCUSSION

Electronic excitation and relaxation process in dielectric materials

First, we investigate electron energy distribution (electron distribution function, or DF). The calculated DFs are shown in Fig. 1 . One can see in the Figure that right after the photoionization, the distribution is far from the equilibrium Fermi function. It takes from around 30 to 50 fs to reach equilibrium at laser pulse duration of 100 fs and laser intensity of 6.25×1013 W/cm2.

Then, we demonstrate the dependency of the thermalization time on laser pulse duration (Fig. 2). One can see in Fig. 2 that a maximum can be observed at certain pulse duration. This behavior can be explained as follows. When the density of free electrons is small, the collision rate responsible for absorption and photo-ionization is larger than the rate of electron-electron (e-e) collisions, which are responsible for their thermalization. Therefore, until a certain pulse duration, the increase in pulse duration results in the increase in absorption, rather than in the reduction of the e-e relaxation time. Only when laser pulse duration overcomes a certain value (here, 55 fs, keeping the same laser field, or intensity), the electron density increases enough so that the e-e collisions become more frequent than that responsible for absorption. As a result, the thermalization time starts diminishing for pulses longer than this value.

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0 5 10 15 201E-7

1E-6

1E-5

1E-4

1E-3

0,01nm, fs, E0 MV/cm

Elec

tron

dis

trib

utio

n fu

nctio

n f(

)

Electron energy [eV]

10 fs 25 fs 50 fs 55 fs 80 fs 150 fs

Figure 1. Calculated electron energy distributions at different instants of time. The calculation

parameters are laser wavelength = 400 nm, energy gap = 9 eV (SiO2), and laser intensity I0 = 9×1013 W/cm2.

Figure 3 demonstrates that the optimum value of laser intensity can be observed in

our calculations. Here, the laser absorption decays because of the screening effect. In fact, when the electron density exceeds a critical value , . .o b

crn n . . 2 20

o bcr r cbn m e

[28], the laser irradiated dielectric is transformed in an absorbing and reflecting material.

25 50 75 100 12530

35

40

45

50

55

Ther

mal

izat

ion

time

[fs]

[fs]

nm, I0 × W/cm2

Figure 2. Thermalization time as a function of pulse duration. The calculation parameters are the same

as in Fig. 1.

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Figure 3. Calculated average electron kinetic energy for different laser pulse durations. The calculation

parameters are laser wavelength = 800 nm, energy gap = 9 eV.

Laser damage criterion for dielectric materials

A correct definition of laser damage criterion is a challenging task. Previously, the criterion of OB was used based on the critical electron density as follows . Our calculations demonstrate that the critical electron density typically

. .o bcrn n

does not exceed 1-2 % of valence electrons if the criterion is based on the OB concept. In addition, material�’s structure is completely disregarded in such condition. Moreover, one can show thatthe density of free electrons having enough energy to ionize other neutral atoms/molecules can be insufficient by the end of the pulseeven if the critical density is reached [29]. It should be noted that only extensive bond breaking could guarantee laser damage, rather than OB itself. Therefore, a thermal criterion is more relevant. To obtain such a criterion, we propose to compare the total energy of free electrons per atom with the energy of atoms at melting temperature

at B mV Q k T , (9)

where 33

12

totQ k f k d k n is total energy density of free electrons

in eV/m3, tot , and Vat is the mean volume of atom. Thus, we obtain the following condition for the required number of free electrons

thcrn n , th B m

crat tot

k TnV

. (10)

In this equation, material properties are taken into account. For wide band-gap dielectrics and for short pulses when photo-ionized electrons have no time to absorb addition energy, i.e. tot pinl ; and we can rewrite our condition as following

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thcrn n , th B m

crat pi

k TnV l

. (11)

To check the validity of this criterion we perform a comparison with the experiment findings [30] ( Fig. 4). The calculation results agree with experimental data forlaser pulse durations longer than 50-70 fs.

0 50 100 150 200 250 3000

2

4

6

8

10

Fth,

J/c

m2

fs

Optical Breakdown Thermal Sanner

Figure 4. Calculated and measured damage thresholds are shown. The black solid and red dash curves correspond to optical breakdown criterion and thermal criterion, respectively. Here, laser wavelength = 800 nm, energy gap = 9 eV (SiO2). The blue dash-dot curve shows the results of experiments by

Sanner et al. [30]

Surface periodic structure formation on Si surface

In this section, we check conditions that are required for surface plasmon excitation on Si surface. It is well known that surface plasmons (SPs) can be excited at a metal-insulator interface. Thus, the first condition is that the real part of the refractive index of laser-excited target has to be negative, as in the case of the metal-dielectric interface [31]. The second condition is that the absolute value of the real part of �“metallic�” medium has to be larger than the refractive index of the �“insulator�” part of the interface. This condition is required to respect the continuity of fields at the interface. The period of the resulting surface plasmon polaritons (SPP) is given by

11Re2 c at vacuum/Si interface, and thus strongly depends on

collision frequency in the fs ablation regime.

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Figure 5. Period of a surface plasmon polariton wave as a function of electron density for different

collision frequencies. The critical electron density is 1.73×1027 m-3. Figure 5 shows the period of a SPPs as a function of free-electron-density for a wide range of collision frequencies permitted by continuous models available in literature [32]. One can observe that the SPP�’s period is sensitive to collision frequency. Periodic structures can be attributed to the SPPs if the free-carrier density grows above the critical density (OB condition). The calculations show that the plasmon model explains single-shot ripples, for which the period is slightly above the laser wavelength [33].

Figure 6. Conditions on free electron density obtained by using the Drude model to initiate plasmon resonance. Green dashed curve shows the free-electron density needed to reach the metallic condition

(as a function of collision frequency). The red plain curve is the free-electron density necessary to excite surface plasmons.

To clearly examine the conditions of SP excitation, Fig. 6 defines the collision

frequency required to reach the OB condition and the other one , which is needed to reach SP�’s excitation ( 1Re ). By solving the equation 0Re , it is possible to

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extract the free-electron density as a function of collision frequency. The half-space above the curves defines the free electron density, which is required to excite SPs.

The calculation results show that SPs can be exited at the interface between the air/vacuum and the bulk silicon under a femtosecond irradiation. The corresponding conditions have revealed that the free-electron density has to be larger than

m281.7 10en -3. In addition, a phase matching condition was also discussed in [34]

Figure 7. Both calculated and experimentally measured periods of ripples normalized by laser

wavelength as a function of laser fluence. The corresponding period is shown at the right axis. The spots obtained with equal number of pulses have been linked by splines interpolation curves. The

surface plasmon model has provided periods reported by a plain curve. Our single laser pulse experiments are shown by continuous error bars on the top right of the figure, and correspond to the SPP model [33]. The results of Sipe�’s roughness model [35] are shown by using point-dashed curve with error bars. Experimental points with low number of pulses are shown by long-dashed and short-

dashed curves. Figure 7 compares the calculated and the measured [34] periods of laser-induced periodic surface structures in femtosecond regime. The period of SPPs and the results of single pulse experiments are in agreement. The results explain why ripples with period slightly higher than the laser wavelength appear after a single-pulse irradiation.

SUMMARY

In summary, first we have investigated ultra-short laser interactions with quartz by accounting for the absence of equilibrium in the electronic sub-system. The relaxation time has been shown to depend on laser parameters, such as pulse duration and laser fluence. This result has been attributed to the difference in free electron densities that are reached.

In addition, an effect of screening has been revealed in our investigation of laser absorption efficiency as a function of laser parameters. This effect is connected with the OB. Then, we have proposed a new criterion for laser damage that is based on the

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effect of bond breaking rather than on the OB. The calculated damage threshold agrees with the available experimental measurements. The proposed equations are simple enough and can be used in many models.

Finally, based on the dielectric index and phase-matching conditions, we have shown that SPs can be excited on Si during a 100 fs and 800 nm single-pulse irradiation. In particular, the required free-electron density has been reached upon an ultrafast laser irradiation of Si with sufficient fluence. In addition, the period of SPPs has been calculated depending on laser fluence. It has been shown that SPPs can be responsible for certain periodic structures on Si.

ACKNOWLEDGMENTS

The authors acknowledge the help of grant ANR �“Ultra-Sonde�” 0010 BLAN 0943 01. They are also grateful to CINES for computer support (under project c2011085015). NSS and TJYD acknowledge the Ministry of National Education and Research (France) for the support of their PhD research.

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