INVITED PAPER

Confined micro-explosion induced by ultrashort laser pulseat SiO2/Si interface

Ludovic Rapp • Bianca Haberl • Jodie E. Bradby •

Eugene G. Gamaly • Jim S. Williams •

Andrei V. Rode

Received: 11 November 2013 / Accepted: 12 November 2013 / Published online: 30 November 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract Ultrashort laser pulses tightly focused inside a

transparent material present an example of laser interaction

with matter where all the laser-affected material remains

inside the bulk, thus the mass is conserved. In this paper,

we present the case where the high intensity of a laser pulse

is above the threshold for optical breakdown, and the

material is ionised in the focal area. We consider in detail a

special case where a micro-explosion is formed at the

boundary of a silicon surface buried under a 10-micron-

thick oxidised layer, providing the opportunity to affect the

silicon crystal by a strong shock wave and creating new

material phases from the plasma state. We summarise the

main conclusions on ultrafast laser-induced material mod-

ifications in confined geometry and discuss the prospects of

confined micro-explosion for forming new silicon phases.

1 Introduction

Ultrashort laser pulse tightly focused inside the bulk of a

transparent solid can easily generate MJ/cm3 energy den-

sity with the energy per pulse around a lJ within a focal

volume less than a cubic micron. The pressure in the order

of several TPa (1 TPa = 10 Mbar) inside a focal volume

that is higher then the strength of any solid transforms a

material to the plasma state, and then leads to the formation

of a cavity (void) surrounded by a shell of compressed

material. These features of the phenomenon delineate the

areas of potential applications. The first area relates to the

formation of different 3D structures, such as photonic

crystals, waveguides, and gratings, by making use of

multiple voids, separated or interconnected. For these

studies the most important part is the process of void for-

mation. To produce a void one has to generate a pressure in

excess of the strength (the modulus) of a material. The

second area of research relates to the studies of material

transformations under high pressure–temperature condi-

tions in the focal zone created on the laboratory’s tabletop.

The interaction of a laser with matter at an intensity above

the ionisation and ablation threshold proceeds in a similar

way for all the materials. The solid converts into plasma in

a few femtoseconds at the very beginning of the pulse,

changing the interaction to the laser–plasma mode,

increasing the absorption coefficient and reducing the

absorption length, which ensures fast energy release in a

very small volume. A strong shock wave generated in the

interaction region propagates into the surrounding cold

material. The shock wave propagation is accompanied by

the compression of the solid material at the wave front and

decompression behind it, leading to the formation of a void

inside the material. The laser and shock wave-affected

material is confined in the shell that surrounds the void.

This shell is the major object for studies of new phases

formation in the strongly non-equilibrium conditions of

confined micro-explosions. Single pulse action thereby

allows a formation of various three-dimensional structures

inside a transparent solid in a controllable and predictable

way.

The first notion that the extreme conditions produced in

the ultrafast laser-driven confined micro-explosion may

L. Rapp � E. G. Gamaly � A. V. Rode (&)

Laser Physics Centre, Research School of Physics and

Engineering, The Australian National University, Canberra,

ACT 0200, Australia

e-mail: avr111@physics.anu.edu.au

B. Haberl � J. E. Bradby � J. S. Williams

Electronic Materials Engineering, Research School of Physics

and Engineering, The Australian National University, Canberra,

ACT 0200, Australia

123

Appl. Phys. A (2014) 114:33–43

DOI 10.1007/s00339-013-8161-x

serve as a novel microscopic laboratory for high pressure

and temperature studies, well beyond the levels achieved in

diamond anvil cell (DAC), was presented by Glezer and

Mazur in 1997 [1]. Recently, it was experimentally dem-

onstrated that it was possible to create super-high pressure

and temperature conditions in tabletop laboratory experi-

ments with ultrashort laser pulses focused inside transpar-

ent materials to the level significantly above the threshold

for optical breakdown [2–4]. The laser energy absorbed in

a sub-micron volume confined inside a bulk of pristine

solid is fully converted into internal energy. Therefore,

high energy density, several times higher than the strength

of any material, can be achieved with *100 fs, 1 lJ laser

pulses focused down to a 1 lm3 volume inside the solid.

Let us first underline the differences between the intense

laser–matter interaction at the surface of a solid and the

case when an interaction is confined deep inside a solid by

comparing the pressure created in the absorption region at

the same intensity and total absorbed energy. In the case of

laser–surface interactions, the pressure at the ablated

plume–solid interface equals the sum of the thermal pres-

sure of the plasma next to the boundary plus the pressure

from the recoil momentum of the expanding plasma. A

significant part of absorbed energy is spent on the expan-

sion and heating of the plume. Therefore, the ablation

pressure in the case of surface interactions depends on the

absorbed intensity by the power law Pabl / Imabs; m\1. In

the case of confined interactions (no expansion), the

maximum pressure is proportional to the absorbed intensity

Pconf / Iabs and it is almost twice as large as in the surface

interaction mode. Full description of the laser–matter

interaction processes and laser-induced material modifica-

tion from first principles embraces the self-consistent set of

equations that includes Maxwell’s equations for the laser

field coupling with matter, complemented with the equa-

tions describing the evolution of energy distribution func-

tions for electrons and phonons (ions) and the ionisation

state. A resolution of such a system of equations is a for-

midable task even for modern supercomputers. Therefore,

thorough analytical analysis is needed. We split this com-

plicated problem into a sequence of simpler interconnected

problems: the absorption of laser light, the ionisation and

energy transfer from electrons to ions, the heat conduction

and hydrodynamic expansion.

2 Energy density in confined ultrashort laser

interaction with solids

The sequence of processes in the ultrashort laser-induced

micro-explosion is the following. First the energy absorb-

ing plasma layer inside the focal area is formed during the

pulse time (100–200 fs). Then, hydrodynamics develops

with shock/rarefaction waves (*1 ps –100 ps) accompa-

nied by the formation of a void surrounded by a dense shell

(*100 ps –1 ns). In the following section, we consider the

major mechanisms of laser ionisation and absorption fol-

lowed by hydrodynamics in a confined geometry.

2.1 Absorbed energy density

The laser pulse with *100 nJ of energy focused into the

area Sfoc / k2 *10-8 cm2 delivers an energy density in

excess of 10 J/cm2, well above the ionisation and ablation

thresholds for any material [5]. Thus, the pressure level

above the strength of any material can be created in a

plasma layer of a typical thickness from 30 nm to 60 nm.

The absorbed laser energy per unit time and per unit vol-

ume during the pulse reads:

dEabs

dt¼ 2A

labs

I r; z; tð Þ ð1Þ

The electric field exponentially decays inside a plasma

layer, E ¼ E0exp �x=labsð Þ. Here, labs ¼ c=xk, A is the

Fresnel absorption coefficient [6]:

A ¼ 4n

ðnþ 1Þ2 þ k2¼ 2e00

j1þ e1=2j2kð2Þ

where e = ere ? ieim = (n ? ik)2 = (n2 - k2) ? i2nk; e is

the dielectric function, n and k are real and imaginary parts

of the complex refractive index.

The duration of an ultrashort pulse by definition is shorter

than the electron–phonon and electron–ion collision times

(typically *100 fs). We denote the energy per single elec-

tron by ee. Then the electron energy density change reads:

dðne eeÞdt

¼ 2A

labs

IðtÞ: ð3Þ

It has been shown [2–5] that electrons in these

conditions could be treated as ideal gas. Thus the

electron temperature to the end of the pulse is estimated

as the following:

Te �2A

1:5kB ne labs

IðtÞ t: ð4Þ

The electron temperature rises to tens of electron volts at

the very beginning of the pulse. Fast ionisation of a solid

occurs affecting absorption coefficient and absorption length.

We introduce below the optical properties dependent on the

changing electron density and electron energy.

2.2 Ionisation processes

Analytical estimates of the breakdown threshold, ionisation

rates and transient number density of electrons created in the

absorption region, based on previous studies [2–5], allow one

34 L. Rapp et al.

123

to obtain the general picture of the processes in qualitative

and quantitative agreement with computer simulations.

2.2.1 Ionisation thresholds

It was generally accepted that the breakdown of dielectrics

occurs when the number density of electrons in the con-

duction band reaches the critical density, nthe � nc ¼

me x2=4p e2 (x is the laser frequency). Recently, it was

proved that the exact threshold condition occurs at the

transformation of the travelling laser wave into an eva-

nescent wave, which results in nthe � e0nc (e0 is the initial

dielectric permittivity of material). Thus, laser parameters,

(intensity, wavelength, pulse duration) and material

parameters (band-gap width and electron–phonon effective

collision rate) at the breakdown threshold are linked

together by the condition, nthe � e0nc.

We stress that the ionisation threshold is the integral

characteristic dependent on the fluence and not on the

instantaneous maximum value of the intensity. For the

majority of transparent dielectrics, the ionisation threshold

fluence is around 2 J/cm2. It was determined that the ion-

isation threshold in fused silica is reached at the intensity

2 9 1013 W/cm2 at the end of a 100 fs pulse at 800 nm [7,

8]. Similar breakdown thresholds in the range of

(2.8 ± 1) 9 1013 W/cm2 were measured for the interac-

tion of a 120 fs, 620 nm laser with glass, MgF2, sapphire

and fused silica [9]. A weak dependence of the threshold

fluence on pulse duration was established. For example, for

fused silica the following threshold fluencies were deter-

mined: *2 J/cm2 at 1053 nm 300 fs; *1 J/cm2 at 526 nm

200 fs [10]; 1.2 J/cm2 (620 nm; *120 fs) [9]; 2.25 J/cm2

at 780 nm 220 fs [11, 12]; and 3 J/cm2 at 800 nm

10–100 fs [13].

The conduction band electrons gain energy in an intense

short pulse much faster than they transfer energy to the

lattice. Therefore, the actual structural damage (breaking

inter-atomic bonds) occurs after the electron-to-lattice

energy transfer, usually after the end of the pulse.

2.2.2 Multi-photon ionisation rate

Multi-photon ionisation has no intensity threshold and

hence creates the seed electrons at low intensities, n0, which

then multiplies by the electron impact ionisation process. A

reasonable estimate of the multi-photon ionisation proba-

bility (per atom, per second) is the following [14]:

wmpi � x n3=2ph

eosc

2 Dgap

� �nph

; ð5Þ

here nph ¼ Dgap

��hx is the number of photons necessary for

an electron to be transferred from the valence to the

conductivity band. At high intensity, the contribution of

electron impact processes becomes crucially important: at

wmpi–wimp the seed electrons are generated by multi-photon

effect, whilst final growth is due to the avalanche ionisa-

tion. Such an interplay of two mechanisms has been

demonstrated with the direct numerical solution of the

kinetic Fokker–Planck equation [14]. Under the condition

eosc = Dgap, �hx = 1.55 eV, nph ¼ Dgap

��hx * 6.4, and

x ¼ 2:356� 1015s�1, the multi-photon rate comprises

wmpi *5.95 9 1015 s-1. The ionisation time is estimated

as tion � w�1mpi. Thus, the ionisation threshold is reached in a

few femtoseconds at the beginning of a 100-fs pulse. After

that, the interaction proceeds in a laser–plasma interaction

mode.

2.2.3 Electron impact ionisation rates

Few electrons seeded by the multi-photon process oscillate

in the laser electromagnetic field and can be gradually

accelerated to the energy in excess of the band-gap. Elec-

trons with ee [ Dgap collide with electrons in the valence

band and can transfer sufficient energy to excite them into

the conduction band. Thus the number of free electrons

increases, which provokes the effect of avalanche ionisa-

tion. The probability of such an event per unit time (ioni-

sation rate) can be estimated as follows:

wimp �1

Dgap

dee

dt¼ 2eosc

Dgap

x2 meff

ðm2eff þ x2Þ /

I � meff

ðm2eff þ x2Þ : ð6Þ

Analysis shows that in the beginning of the ionisation

process the condition holds, x [ me�ph. The impact

ionisation rate expresses as, wimp � 2me�ph*1014–

1015 s-1. At the intensity maximum, the collision rate

reaches its maximum, x\me�i � xpe, and then the

ionisation rate equals to wimp � 2x2=me�i � 2x2=

xpe *5 9 1014 s-1 competing and exceeding the multi-

photon rate.

The qualitative estimates based on Eq. (6) are in

agreement with the Monte Carlo solutions to the Boltz-

mann kinetic equation for electrons [15].

2.2.4 Ionisation state during the laser pulse

To estimate the electron number density generated by

ionisation during the laser pulse, the recombination pro-

cesses should be taken into account. Electron recombina-

tion proceeds in a dense plasma mainly by three-body

Coulomb collisions with one of the electrons acting as a

third body [16]. The quantitative analysis performed in [4]

shows that in the solid density plasma, three-body recom-

bination leads fast to establishing the ionisation equilib-

rium when the ionisation rate is balanced by

Confined micro-explosion induced by ultrashort laser pulse 35

123

recombination. In these conditions, multiple ionisations

take place producing ions with charge Z [ 1. The electron

number density at the end of the pulse can be estimated in a

stationary approximation as follows: n2e � wion=Zbe (here,

be is the three-body recombination rate from [16]). Taking

wion* 1015 s-1; ee * 30 eV; Z = 5; lnK *2, one obtains

that the number density of electrons at the end of the pulse

becomes comparable to the atomic number density

ne * 1023 cm-3.

2.3 Increase in the absorbed energy density due

to modification of optical properties

Thus, to the end of the pulse, the electron number density

becomes comparable to the atomic number density and the

electron–ion collision rate reaches its maximum equalling

the plasma frequency. The optical properties of this tran-

sient plasma are described by Drude-like dielectric per-

mittivity depending on the electron density and

temperature. Let us estimate the absorption coefficient and

absorption length at the end of the pulse. The dielectric

function and refractive index in the beginning of the laser

pulse when me�i � xpe [ [x are estimated as the

following:

ere �x2

x2pe

; eim �xpe

x; n � k ¼ eim

2

� �1=2

: ð7Þ

For example, after the optical breakdown of fused silica

glass induced by an 800 nm laser (x = 4.7 9 1015 s-1;

xpe = 1.45 9 1016 s-1), the real and imaginary parts of

refractive index are n * k = 1.18, the absorption length of

ls = 54 nm, and the absorption coefficient A = 0.77 [4].

Therefore, the ionisation and heating convert silica into

plasma by reducing the energy deposition volume by up to

two orders of magnitude when compared with the focal

volume, and massively increasing the maximum pressure

in the absorption region. As a first approximation, the

energy absorption volume is taken as the focal area

multiplied by the absorption length. For the interaction

parameters presented above (I = 1014 W/cm2; A = 0.77;

ls = 54 nm; tp = 150 fs), the pressure corresponding to the

absorbed energy density equals to 4.4 TPa, ten times higher

than the Young modulus of sapphire, one of the hardest of

dielectrics. The general approach presented above is

applicable for estimating parameters of any wide band-

gap dielectric affected by a high-intensity short pulse laser.

2.4 Energy transfer from electrons to ions: relaxation

processes after the pulse

The hydrodynamic motion starts after the electrons transfer

the absorbed energy to the ions. The major processes

responsible for the energy transfer from electrons to ions

are electron–ion Coulomb collisions and electronic heat

conduction [4]. Below, the energy transfer times for dif-

ferent processes are presented.

The maximum value for the electron–ion momentum

exchange rate in the non-ideal plasma of confined micro-

explosion approximately equals the plasma frequency,

mei � xpe *3 9 1016 s-1 [8, 17–19]. Hence electrons in

ionised fused silica transfer their energy to ions over a time

of tenei � men

ei

� ��1� Mi=memeið Þ * (1–2) ps [8, 17–19].

The electro energy at the end of the pulse is much higher

then the ionisation potential. Therefore, ionisation by the

electron impact continues after the pulse ends [4, 16].

Losses in ionisation lead to temporary decrease in the

electron temperature and in the total pressure [4]. However,

fast recombination results in an increase in the ionic

pressure.

Energy transfer by non-linear electronic heat conduction

starts immediately after energy absorption. The heat wave

propagates outside of the heated area before the shock

wave emerges. The thermal diffusion coefficient is defined

conventionally as the following, D ¼ le ve=3 ¼ v2e

�3 mei,

where le, ve and nei are the electron mean free path, the

electron velocity and the momentum transfer rate, respec-

tively. The characteristic cooling time is conventionally

defined as tcool ¼ l2s

�D. For the conditions of the experi-

ments [2] nei–xpe *3 9 1016 s-1, ee = 50 eV, and the

cooling time is tcool ¼ 3 xpe me l2abs

�2ee = 14.9 ps.

Summing up, one concludes that the electrons transfer

energy to ions on approximately picosecond timescales.

The thermal ionisation and recombination are in a balance

after the end of the pulse permitting the description of the

plasma state by the Saha equations. The electronic non-

linear heat conduction becomes important in the first

*15 ps after the pulse and dominates the return to the

ambient conditions.

3 Shock wave propagation and void formation

It was shown above that focal volumes as small as 0.2 lm3

can be illuminated by focusing 800 nm laser pulses in the

bulk of fused silica glass (n = 1.453) with a microscope

objective with NA = 1.35 [2, 3]. The original focal volume

shrinks to much smaller energy deposition regions due to a

fast decrease in the absorption length, approximately five

times less than the averaged focal radius. The modified

shape of the absorption region is unknown. We assume for

further calculations that a sphere of effective radius

approximates the absorption volume, the focal area multi-

plied by the absorption length. 100 nJ of laser energy

deposited in the focal volume of 0.2 lm3 creates an energy

36 L. Rapp et al.

123

density of 5 9 105 J/cm3 (the pressure of 0.5 TPa or 5

Mbar). However, this energy absorbs in a much smaller

volume thereby generating a pressure in excess of P = 10

TPa. All absorbed energy is confined to the electron

component at the end of the 150-fs pulse.

3.1 Shock wave generation and propagation

The hydrodynamic motion of atoms and ions starts when

the electrons have transferred their energy to ions. This

process is completed in a few picoseconds; however, one

should note that the energy transfer time by the Coulomb

collisions increases in proportion to the electron tempera-

ture. So, in the solid-state density plasma formed in a

confined micro-explosion, the higher the absorbed energy,

the longer is the time that elapses before hydrodynamic

motion starts. The pressure in a range of several TPa builds

up after electron–ion energy equilibration; this pressure

considerably exceeds the Young modulus for a majority of

materials. For example, the Young modulus for sapphire

equals 0.3–0.4 TPa, and that for silica is *0.07 TPa. The

high pressure generates a shock wave propagating from the

energy absorption region to the surrounding cold material.

The counterpressure of the cold material, Pc, approxi-

mately equal to the modulus, finally decelerates and stops

the shock wave. The strong shock, P � Pc, compresses a

solid to the limit value, which can be estimated under the

assumption that the solid density plasma is treated as a

perfect gas with the adiabatic constant equal to c * 3 [16].

Therefore, the maximum density after the shock front is

expected to be qmax ¼ q0ðcþ 1Þ=ðc� 1Þ � 2q0. The

compression ratio gradually decreases to unity along shock

propagation, deceleration and transformation into a sound

wave.

Thus, the material is compressed and heated behind the

shock wave front. Hence, the conditions for transformation

to another phase might be created and this phase might be

preserved after unloading to the normal pressure. The final

state of matter may possess different properties from those

in the initial state.

3.2 Shock wave dissipation

The shock wave propagating in a cold material loses its

energy due to dissipation. The distance at which the shock

wave effectively stops defines the shock-affected area. The

distance where the shock wave stops can be estimated from

the condition that the internal cold energy in the whole

volume enclosed by the shock front is equal to the absorbed

energy: 4p P0r3stop

.3 � Eabs [4, 16]. The stopping radius

obtained from this condition reads:

rstop �3Eabs

4p P0

� �1=3

� ð8Þ

One can reasonably suggest that the sharp boundary

observed between the amorphous (laser-affected) and

crystalline (pristine) sapphire in the experiments [2, 3]

corresponds to the distance where the shock wave

effectively stopped. The sound wave continues to

propagate at r [ rstop, apparently not affecting the

properties of the material. For 100 nJ of absorbed energy

in sapphire, taking Pc = 0.4 TPa for sapphire, one obtains

from Eq. (8) rstop = 180 nm, which is in qualitative

agreement with the experimental values.

3.3 Rarefaction wave: formation of void

Formation of voids, hollow or low-density regions at the

focal spot, can be qualitatively understood from the ana-

lysis of spherically symmetric explosions. The strong

spherical shock wave propagates outside the centre of

symmetry of the absorbed energy region. Simultaneously, a

rarefaction wave propagates to the centre of symmetry.

Due to mass conservation, the density increase behind the

shock is accompanied by the density decrease in the central

area. This problem qualitatively resembles point spherical

explosions in a homogeneous atmosphere with counter-

pressure taken into account [16].

In point explosions, the whole energy is concentrated in

the central point. The entire mass of the material, initially

uniformly distributed inside a sphere, is concentrated

within a thin shell near the shock front some time after the

explosion. The temperature increases and density decreases

towards the centre of symmetry, while the pressure is

almost constant along the radius [16]. This picture is

qualitatively similar to that observed in the micro-explo-

sion experiments [4] where a void surrounded by a shell of

laser-modified material was formed at the focal spot.

The mass conservation law, under the assumption of

absence of mass losses applicable to confined micro-

explosions, relates the measured size of the void, rv, and

the size of the laser-affected zone, rstop, to the level of

compression of the surrounding shell. The void formation

inside a solid is only possible if the mass initially contained

in the volume of the void of radius rv was pushed out and

compressed in a shell with thickness, (rstop - rv). Thus, the

density of the shell, q ¼ dq0; d [ 1, reads:

4p3

r3stopq0 ¼

4p3

r3stop � r3

void

� �q: ð9Þ

The compression ratio is an explicit function of the

experimentally measured values, rvoid, and, rstop, as

follows:

Confined micro-explosion induced by ultrashort laser pulse 37

123

rvoid ¼ rstop 1� d�1� �1=3

: ð10Þ

It was typically observed that rvoid *0.5rstop in

experiments of [4]. Applying Eqs. (9, 10), the

compressed material in a shell has a density 1.14 times

higher than that of crystalline sapphire. Note that the void

size was measured at room temperature long after the

interaction.

4 Density and temperature in the shock wave- and heat

wave-affected solid

4.1 Two characteristic areas in confined micro-

explosions

There are two distinctive regions in the laser-affected area

confined inside a solid. The first area is the laser energy

absorption zone. The second area is the zone where the

initially strong shock wave propagates outside the

absorption region and finally decelerates into the sound

wave, which does not affect a crystal.

In the first area, a material becomes a solid density

plasma at the temperature of tens of eV (*105 K). Within

picoseconds the energy is transferred to ions and a shock

wave emerges. Conservatively, the heating rate is esti-

mated approximately as 10 eV/ps * 1017 K/s. Then, a part

of the plasma undergoes fast compression by strong shock

to the density of up to *2 times the solid density. Note,

that material in this zone is swiftly transformed from an

ordered solid to a randomised plasma state and is, after fast

isochoric quenching, returned back to ambient conditions.

In the second zone, heated and compressed exclusively

by the shock wave, the maximum temperature reaches

several thousands of Kelvin, approximately ten times less

than in the first zone. The laser-unaffected material might

be transformed into different phase states and then cooled

to the ambient almost isochorically. The energy dissipation

in the shock wave and by the heat conduction takes

nanoseconds. Heating and cooling rates in this zone are of

the order of 10 eV/ns * 1014 K/s.

Phase transformations in quartz, silica and glasses

induced by strong shock waves generated either by high

explosives or kJ-level ns lasers have been studied for

decades in open geometry, see [16, 20] and references

therein. Dense phases usually transform into low-density

phases (2.29–2.14 g/cm3) when the pressure is released

back to the ambient level. Numerous observations exist of

amorphisation upon compression and decompression.

Analysis of experiments shows that the pressure release

and the reverse phase transition follow an isentropic path.

The loading and release time in these experiments are in

the order of *1 to 10 ns [21–24]. The heating rate in the

shock wave experiments is 103 K/ns = 1012 K/s, five

orders of magnitude slower than in the confined micro-

explosion.

In contrast, the peak pressure in confined geometry

reaches the level of several TPa. Note that the upper limit

in the diamond anvil cell set by the Young modulus of

diamond is in the order of TPa. Short heating and cooling

times along with the small size of the area where the phase

transition takes place can affect the rate of the direct and

reverse phase transitions. The discovery of super-dense

bcc-Al is probably the result of non-equilibrium conditions

and fast quenching [25].

There is experimental evidence that the refraction index

changes in the laser-induced micro-explosion in a bulk of

silica [26]. This is an indication of the formation of a

denser phase; however, little is known of the exact nature

of this phase.

4.2 Upper limit for the pressure achievable in confined

interaction

The micro-explosion can be considered as a confined one if

the shock wave-affected zone is separated from the outer

boundary of a crystal by a layer of pristine crystal several

times thicker than the size of this zone. In earlier studies,

the effect of self-focusing was considered as a limit of the

maximum laser power [27]. However, later analysis dem-

onstrated that positive non-linearity responsible for self-

focusing is compensated by negative ionisation non-line-

arity at low ionisation levels.

Here, we show that the motion of the ionisation front in

the direction towards the laser beam propagation, first

discovered in studies of optical breakdown in gases [14], is

a major effect determining the size of the absorption vol-

ume at the laser fluence above the ionisation threshold level

Fthr. The ionisation threshold value is reached at the

beginning of the pulse if the total energy is well above that

necessary for ionisation. The beam is focused to the focal

spot area, Sf ¼ pr2f . Laser energy increases and the ioni-

sation front, the beam cross-section where the laser fluence

is equal to the threshold value, starts to move in the

direction opposite to the pulse propagation. The spatial

shape of the beam path is a truncated cone, so assuming the

flat-top shape of the pulse the intensity at any time is

independent of the transverse coordinates (see Fig. 1).

The analysis of this simplified geometrical model can be

found in [19]. Here, we present the final result for the

distance, z(tp), to which the ionisation front moves by the

end of the pulse. This distance depends on the focusing

parameters, focal spot radius, rf, focusing angle a, and ratio

of the total fluence to the threshold value, f ¼ Flas=Fthr as

the ratio of the maximum fluence to the threshold fluence

as the following:

38 L. Rapp et al.

123

z tp� �¼ rf

tgaf 1=2 � 1� �

: ð11Þ

One can see that if the total fluence equals that for the

threshold, f = 1, the ionisation time equals the pulse

duration [10, 28, 29], and thus there is no movement of the

ionisation front. These simple geometrical considerations

are in qualitative agreement with the experiments in

sapphire and silica. Indeed, the voids measured in silica

and sapphire in references [2–4] are slightly elongated;

from Eq. (11) one gets zSiO2m = 0.67rf and zAl2O3

m = 0.45rf.

Summing up the results of this section, we conclude that

the ionisation front motion at the laser energy well above

the ionisation threshold leads to a large decrease in the

absorbed energy density.

5 Formation of voidS at the AN Si/SiO2 interface

The experiments were conducted with 170 fs, 790 nm,

laser pulses from an MXR-2001 CLARK laser system.

Pulses with up to 2.5 lJ per pulse were focused using an

optical microscope (Olympus IX70) equipped with an oil-

immersion 1509 objective (NA = 1.45) The focal spots

were measured using a knife-edge technique with a sharp

edge of an Si [100] wafer etched at 54.748 to the surface

along the [111] direction and mounted on a nano-posi-

tioning stage. The focal spots were measured to have a

radius of 0.368 lm at the full width at half-maximum level.

The experiments were conducted with laser pulses of a

1 kHz repetition rate in a sample moved at a rate of

2 mm s-1 to guarantee a single shot per spot regime,

resulting in each of the shots located 2 lm apart.

Silicon is not transparent at 790 nm, the wavelength that

we used for the experiments. While the laser-induced

micro-explosion method was previously considered as

suitable only for transparent materials, we propose to

expand it into the unexplored domain of non-transparent

materials. To confine laser–matter interaction inside a

material, the distance ought to be far enough from the

crystal surface so that the interaction region can be con-

sidered as confined. The interaction of intense laser radi-

ation with matter when the beam is tightly focused inside a

transparent material is radically different from the case of

focusing the beam onto a surface. In the laser–surface

interaction the temperature has its maximum at the outer-

most atomic surface layer. If the absorbed energy density

in the surface layer is in excess of the ablation threshold,

the atomic bonding breaks and the ablated atoms leave the

surface. In the tightly focused interaction mode, the focal

zone with high energy density is confined inside a bulk of a

cold and dense solid. The laser-affected material remains at

the focal area inside the pristine material.

By growing a transparent oxide on the sample, laser-

induced confined micro-explosion can be applied to virtu-

ally any opaque material. The confinement conditions were

realised in silicon wafers by covering them by a 10-lm-

thick layer of dioxide of silicon (SiO2). SiO2 is transparent

to laser irradiation and allows for tightly focusing femto-

second laser pulses on the buried surface of the Si crystal.

The thickness of the SiO2 layer was not so deep for it to

develop large spherical aberrations with high NA focusing

optics and at the same time guarantee the absence of

optical breakdown at the surface.

The silicon crystal was exposed to a strong shock wave

induced by fs laser micro-explosion in confined geometry

[19]. Figure 1 shows a schematic representation of the

process and the realisation of an array of voids using

focused fs pulses at the Si/SiO2 interface. After processing,

the array was investigated by optical microscopy. Figure 2

presents an optical microscope image of a top view of the

sample of the laser-affected areas at the Si/SiO2 interface.

The dark dots in the picture are the voids. The voids are

observed through the SiO2 layer.

To analyse the dimensions of the voids and of the shock

wave-modified areas, we opened the sample using a focused

ion beam (FIB) technique. A FEI Helios 600 NanoLab

equiped with a Ga? ion column and separate electron column

was used. The sample was gold coated by sputtering (5 nm)

to avoid charging effects. The layer of SiO2 was removed, as

shown in Fig. 3a, and then the sample was characterised with

scanning electron microscopy (SEM). Figure 3b presents a

top view SEM image of the sample where the 10-lm-thick

SiO2 was removed. In the hole, we can see the Si surface and

arrays of voids. Voids were observed under the surface in the

region where the fs laser was focused. Figure 3c shows the Si

surface and the arrays of voids; on the side view, we can

observe the Si/SiO2 boundary.

Fig. 1 The path of the converging focused pulse as a truncated cone.

The motion of the ionisation front towards the beam propagation is

indicated by the red arrows

Confined micro-explosion induced by ultrashort laser pulse 39

123

Each of the regions irradiated by a single laser pulse at

the fluence above *1 J/cm2 contains a void located at the

focal spot. Figure 4 presents arrays of voids at the Si sur-

face produced by 300 nJ single laser pulses focused 2 lm

apart with a 1509 objective. On the top view, all the voids

had a circular shape and diameter of 250 nm.

On the area where the SiO2 layer was not completely

removed, cross sections were obtained using FIB cutting

through a void and then characterised with SEM. Figure 5

shows a side view of a void produced with energy of

700 nJ. The maximal horizontal length of the void in the

SiO2 region is 720 nm and in Si 550 nm. The vertical size

(including Si and SiO2) is 1.25 lm. A shock wave-modi-

fied Si surrounded the voids.

The thickness of the boundary between the transparent

oxidised layer and crystalline Si where the laser radiation is

focused is of the order of only 2 nm and can be clearly seen

on electron microscope. Material should be removed from

the energy deposition region to form a void involving a

denser shell surrounding the void. Therefore, the observation

of a large void is unequivocal evidence of creation of pres-

sure well in excess of the Young modulus of both materials,

YSiO2* 75 GPa for SiO2 and YSi * 165 GPa for Si.

The characterisation of the laser-affected area, the dense

shell surrounding the void and the shock wave-affected

area by transmission electron microscopy and by Raman

micro-spectroscopy will be discussed elsewhere.

6 Discussion

Preliminary electron diffraction patterns of laser and

shock-affected silicon reveal the presence of known high-

pressure silicon crystals and unknown, still unidentified

structures with inter-atomic distances which cannot be

attributed to any known modifications of silicon. The

experiments with the highest laser fluence, almost 40 times

Fig. 2 Optical microscope image of arrays of void made at the Si/

SiO2 interface viewed through the SiO2 layer produced fs-pulse laser

micro-explosion. The spacing between the voids is 2 lm

Fig. 3 a Side view schematic representation of the processed sample

and of the area milled using the focused ion beam (FIB). b SEM

image of the hole made in the SiO2 layer by FIB to reach the surface

of the Si layer, following the schematic in (a). c SEM image of the

side view of the milling by FIB of the SiO2 layer to reach the surface

of the Si layer

40 L. Rapp et al.

123

over the plasma formation threshold, revealed the inter-

esting phenomenon of twinning, when two separate crys-

tals shared the centre of their axial systems. This is well

known in mineralogy and also point to loading experiments

performed on germanium [34], but never observed for Si.

The natural question arises: How were these structures

formed from the disordered plasma state?

It is known that high-pressure phases created in DAC

after slow pressure release return to a low-pressure state.

However, in a micro-explosion, a solid is swiftly brought

up to the plasma state and then within record fast cooling

rates, 1014–1015 K/s, returned to the room condition. It

hence contains most probably residual stress. Thus, one of

the possible reasons for the observation of known high-

pressure structures inside laser-affected silicon might be an

ultrafast cooling. However, there might be also other

possible pathways for the formation of unconventional

structures in the unconventional and highly non-linear

conditions of confined micro-explosions.

An aperiodic incommensurate structure of barium was

discovered 14 years ago at a pressure of 0.01 TPa [30].

This structure consists of host and guest atoms (self-atoms

or impurities), which have different inter-atomic distance

(one per each structure). Later on, such structures were

uncovered either experimentally or/and computationally in

many other atomic groups of the periodic chart. The host–

guest structure can be formed from the random mixture of

the constituent atoms and it was demonstrated computa-

tionally that such structures may have many local minima

of enthalpy (at certain pressures) in contrast to conven-

tional periodic crystals which have only one. The important

prediction from these calculations is that the guest atoms

might enhance meta-stability of the structure after the

release of pressure. One may conjecture that the oxygen

atoms in the randomised plasma generated by confined

micro-explosion played the roles of such guest atoms. The

interesting prediction was made for the well-known simple

metal aluminium, which at 3.2 TPa transforms into a host–

guest structure where valence electrons form blobs in

between closely packed atomic cores [31]. We will study

all the possible ways for further interpretation of the

experimental results with regard to the observed transfor-

mation of silicon.

7 Summary

Let us summarise the main conclusions on ultrafast laser-

induced material modifications in confined geometry:

Fig. 4 Laser produced voids on an Si surface buried 10 lm beneath

the SiO2 surface of the oxidised wafer. The SiO2 was removed using

FIB milling, and the spacing between the voids is 2 lm: a SEM image

of FIB-opened section showing an array of voids produced by 170-fs,

800 nm, 300 nJ single laser pulses focused 2 lm apart with an 9150

objective; b Close view of a

Fig. 5 Schematic representation of the laser-induced micro-explo-

sion at the Si/SiO2 interface with the associated side view SEM image

of a void produced at the energy of 700 nJ

Confined micro-explosion induced by ultrashort laser pulse 41

123

• In conditions close, but below the optical breakdown

threshold, the femtosecond laser pulse creates optically

detectable changes in the refractive index. These

modifications in refractive index are short lived and

transient. The short-lived modification occurs due to

excitation of electrons of all constituent atoms. Perma-

nent modification occurs in the doped sites due to the

field of spontaneous polarisation.

• Femtosecond laser pulse tightly focused by high-NA

optics leads to absorbed energy density in excess of the

strength of any existing material. A void surrounded by

a compressed shell is formed as a result of the confined

micro-explosion in the focal volume.

• Warm dense matter at pressures exceeding TP and

temperatures of more than 100,000 K can be created in

the tabletop experiments, mimicking the conditions in

the cores of stars and planets.

• Confined micro-explosion studies open several broad

avenues for research, such as formation of three-

dimensional structures for applications in photonics,

studies of new materials formation and imitation of the

inter-planetary conditions at the laboratory tabletop.

Let us compare the main features of this exciting novel

method for the generation of extreme pressure/temperature

conditions—laser-induced confined micro-explosion, with

the traditional static (diamond anvil cell) and dynamic

(powerful ns-laser generated shock wave) methods—and

indicate future directions in micro-explosion studies.

Confined micro-explosion generates pressures exceed-

ing several TPa well over the upper limit of the DAC

method (BTPa) and higher than the strength of any existing

material. The laser-affected material remains confined,

readily available for the post-explosion investigation, in

contrast to the shock wave method where the all pressure-

affected material is dispersed after several nanoseconds of

its lifetime. One needs a conventional femtosecond laser

with *1 lJ pulses to produce confined micro-explosion in

the laboratory tabletop experiment. Note that both DAC

and shock wave methods are cumbersome, expensive and

require large-scale facilities.

The first experiments with micro-explosion proved the

feasibility of the new method. A new crystalline phase of

aluminium, bcc-Al, has been discovered [25, 32]. Molec-

ular oxygen was clearly identified by Raman spectra in

micro-explosion in GeO2 glass [33]. The results presented

in this paper show the possibility of the formation of novel

phases of silicon. These results also open the prospects of

modelling in the laboratory conditions in the cores of

planets and stars. It is obvious that the focus in micro-

explosion research has shifted to postmortem diagnosis of

shock-compressed material. Micro-Raman, X-ray and

electron diffraction, and AFM and STM studies with

resolution on the sub-micron level are needed for identifi-

cation of the new phases. Another challenge is to develop a

pump-probe technique with time resolution capable of

in situ observation of the shock front propagation inside a

crystal.

Summing up, the prospects for the fundamental study of

ultrafast laser–matter interaction and its technological

applications look extremely encouraging. As the technol-

ogy becomes smaller, less expensive, more robust, less

power-hungry and more energy efficient, it allows the

increased exploitation of ultrafast phenomena, ultimately

entering our everyday lives.

Acknowledgments This research was supported under Australian

Research Council’s Discovery Project funding scheme (project

number DP120102980). Partial support to this work by Air Force

Office of Scientific Research, USA (FA9550-12-1-0482) is gratefully

acknowledged. We also acknowledge the ANFF ACT Node for the

access to their FIB system.

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