Photoacoustic study of explosive boiling and lift-off of a thin water droplet layer from a Si
substrate heated by a KrF laser
Sergey I. Kudryashova)
Department of Chemistry and Biochemistry, Florida State University, Tallahassee,
Florida 32306-4390
Susan D. Allenb)
Department of Chemistry and Biochemistry, Florida State University and Department of Electrical and Computer Engineering, FAMU/FSU College of Engineering,
Tallahassee, Florida 32310-6046
The mechanism of explosive boiling and lift-off of a thin layer of water droplets
from a Si substrate heated by a nanosecond KrF laser was studied using a contact
photoacoustic technique. The photoacoustic response increases rapidly with increasing laser fluence above a threshold laser fluence of 0.20 J/cm2 to an asymptotic value on the order of the water critical pressure. The acoustic pressure buildup
and lift-off of the thin water layer can be explained by the strong near-spinodal
non-linearity of the thermal expansion coefficient and spinodal decomposition (explosive boiling) of the superheated water.
I. INTRODUCTION
Laser-induced explosive boiling of superheated liquids on a nanosecond time scale is currently
employed in laser cleaning of surface micro- and nano-scale particulates,1 various biomedical applications such as laser surgery, corneal sculpturing and gall stone fragmentation,2 laser chemistry3 and material science.4 Explosive boiling of superheated liquids is, therefore, an important
fundamental problem in the study of highly non-equilibrium, transient extreme states of matter.
The explosive boiling of liquids occurs under certain superheating and external applied pressures (hydrostatic, transient compressive or tensile pressures, or combinations thereof).5-17 The
different methods of external pressure application correspond to several typical experimental geometries of laser-induced explosive boiling: a bulk absorbing liquid with a free boundary,6 a bulk
absorbing liquid with a rigid transparent boundary7 and a bulk transparent liquid on a rigid absorbing substrate8-13. While there have been numerous experimental and theoretical investigations5-17, a clear understanding and proper control of these particular cases of explosive boiling
are still under development. Moreover, the interesting and practical case of a thin layer of a
transparent liquid on a rigid absorbing substrate, which is important in steam laser cleaning
(SLC) of particulates from critical surfaces,1 has not yet been studied in detail.14-17
In this work we report a photoacoustic (PA) study of explosive boiling and lift-off of a thin
water droplet layer from a Si wafer heated by a nanosecond KrF laser using rear side contact
mode recording of the laser-generated acoustic transients in the Si wafer both for dry and “wet”
Si surfaces. By subtracting the small “dry” PA signal from the corresponding large “wet” signal,
the PA response of superheated water was measured as a function of the heating laser fluence.
The rapid, threshold-like increase of this response at a laser fluence of 0.20 J/cm2 and its subsequent leveling off at a value of the order of the water critical pressure as the fluence is increased
to approximately 0.4 J/cm2 are attributed to the spinodal (near-critical) behavior of superheated
water including the strong non-linearity of the thermal expansion coefficient of thermodynamically unstable, superheated water that undergoes instantaneous spinodal decomposition (explosive boiling and expansion ) near its spinodal curve. Under spinodal decomposition conditions
1
the acoustic generation was found to occur into the superheated water layer near the rigid Si
boundary, resulting in an unipolar, compressive acoustic transient up to the Si ablation threshold
near 1.4 J/cm2. These photoacoustic studies were also employed to explain lift-off of a thin water
layer on a laser-heated Si substrate.
II. ACOUSTIC GENERATION AT AN INTERFACE BETWEEN A THIN WATER
LAYER AND SOLID SI HEATED BY A NANOSECOND UV LASER RADIATION
Nanosecond UV laser heating of Si with an optical reflectivity RS(T), laser intensity I(t) and
typical pulse length LAS20 ns occurs into a near-surface Si layer during the laser pulse in a
steady-state regime with regard to interband optical excitation of electron-hole pairs, their ambipolar diffusion, Auger recombination, electron-phonon and anharmonic phonon-phonon relaxation, with the subsequent heating of the crystalline lattice.18,19 In contrast to the visible wavelength (indirect bandgap) region, the optical properties of Si in the ultraviolet (direct bandgap)
region are not strong functions of temperature and the optical absorption depth for Si at, for example, 248 nm (1/6 nm),20 is much smaller than the thermal or electron-hole plasma diffusion
depths for nanosecond laser pulses. For the Si surface covered with a thin, continuous UV transparent water layer, this type of laser heating results in thermal fluxes from the water/Si interface
into the bulk Si and the water layer proportional to the corresponding thermal conductivities,
S(T) and L(T), respectively, of solid Si and liquid water (up to the natural limit of superheating
of the liquid, corresponding to the spinodal curve of water5)
(1)
  S (T )(dT ) x 0   L (T )(dT ) x 0  (1  R S ) I (t ) .
dx
dx
The ratio of the thermal fluxes in the liquid and solid phases, , equals the ratio of their products
Cp1/2,19 where CpL,S and L,S are the heat capacities and thermal diffusivities of water and Si, respectively. For the Si/water system the  value changes 15% from the mean value of 0.08 in the
broad temperature range of 300-643 K nearly up to the critical temperature of water, Tcrit=647 K,
as the CpL(T)4.2 J/cm3, CpS(T)2 J/cm3, L(T)1.510-3 cm2/s and S(T)0.3-0.7 cm2/s change
only slightly at these temperatures.5,21 Therefore, the indirect laser heating of the transparent water layer nearly up to its critical point by the absorbing Si substrate can be represented, to a good
approximation, by the direct heating of a normal absorbing liquid with an “absorption coefficient” of order of /(LLAS)1/2 by a laser pulse with an effective intensity of (1-RS)I(t). Under
these conditions cooling of water near the interface may occur quite rapidly because of the high
thermal conductivity of Si and very small thickness of the superheated water layer,
LdepL(LLAS)1/20.05 m, relative to that of the near-surface heated Si layer, LdepS(SLAS)1/21
m, where Ldep is the characteristic energy deposition depth in either media during the laser
pulse.
The expected subnanosecond explosive boiling of a nanometer-scale, near-surface superheated
water layer at near-spinodal temperatures22 should not significantly affect the gradual rise of the
interface temperature with increasing I(t) during the laser pulse due to its small thickness, although the latent heat of boiling for water is considerable.5,20 The vapor/droplet mixture layer resulting from spinodal decomposition provides significant thermal isolation of the entire water
layer from the hot Si substrate and the further continuous growth of the “bare” Si surface temperature. Boiling of the superheated water layer, i.e. bubble nucleation and growth, occurs outward
from the Si surface as a result of the initial accumulated superheating of the layer, predominantly
on the tiny near-surface bubbles (spinodal density fluctuations) acting as nucleation centers.
2
For nanosecond laser pulses the acoustic generation mode at the water/Si interface is quasistatic because of the acoustically “thin” transient energy deposition depth, i.e., size of the corresponding acoustic source LdepLdepS+LdepL«ClSLAS, where ClS is the Si longitudinal acoustic velocity (8.4103 m/s for [100] direction).21 This is in contrast to the “inertial” acoustic generation
mode more typical for shorter laser pulses, particularly at longer laser wavelengths
(Ldep»ClSLAS).19 Depending on the thickness of the water layer LL and the water longitudinal
acoustic velocity ClL, quasi-static acoustic generation may occur at: 1) the acoustically “free” water/Si boundary for LL«ClLLAS with permanent rarefaction of the superheated water layer LdepL
during the heating laser pulse or 2) the acoustically “rigid” water/Si boundary for a thick (bulk)
water layer (LL»ClLLAS) or for subnanosecond explosive boiling of water with a characteristic
nucleation time *min,22 when LL»ClL*min. In the case of the “free” water boundary, PA pressure
transients P1(t) consist of contributions from acoustic sources in the heated Si layer (PfS(t)) and
the superheated water layer (PfL(t)), following a time derivative of the sum of their weighted
thermoelastic stresses, L(T)KadL(T)L(T)(T-300) and S(T)KadS(T)S(T)(T-300), expanded
along the ultrasound propagation distance ClSt in bulk Si and are qualitatively represented by the
following expression (for a more accurate theory see Ref.19):
S
L
S
L
1 d [σ (T (t )) Ldep (t )  σ (T (t )) Ldep (t )]
S
L
P1 (t )  S
 Pf (t )  Pf (t ) ,
(2)
dt
Cl
where KadS(T), KadL(T)=L(T)[ClL(T)]2, S,L(T), L(T) and T are, respectively, the solid Si and water adiabatic linear bulk modulii of elasticity, temperature coefficients of the thermal expansion,
mass density of water and the temperature at the water/Si interface. In the case of the “rigid” water boundary, occurring for “bulk” water or at laser fluences above the threshold for explosive
boiling of water on a sub-ns time scale, the PA transients P2(t) have a “combined” nature
S
S
1 d [σ (Tspin (t )) Ldep (t )]
S
L
P2 (t )  S
 σ L (Tspin (t ))  Pf (t )  Pr (t ) ,
(3)
dt
Cl
represented by the PfS(t) term, as the Si surface remains acoustically “free”, and the PrL(t) term,
corresponding to the thermoelastic stress in water L(T(t)) and following its temporal profile.19
(For a general analysis of acoustic generation at an impedance boundary see Ref.19).
At water/Si interface temperatures far from the critical point of water, acoustic generation at
the interface is expected to occur in the “free boundary” mode and the water and Si acoustic responses are predominantly thermoelastic. We estimate that PfSSLdepS/ClSLAS for T480 K<Tcrit,
S(480 K)3.510-6 K1, KS(480 K)11011 Pa,21 LdepS0.7 m (calculated using the “SLIM”
computer code23), ClS8.4103 m/s21 and LAS20 ns, is approximately 0.3 MPa and an estimate
of PfLL(T)LdepL/ClSLAS yields about 0.1 MPa for L(480 K)1.610-3 K1, L(480 K)1103
kg/m3, ClL(480 K)1.2103 m/s,21 LdepL0.05 m and the same values of T, ClS and LAS. Bubble
nucleation will not occur on a smooth Si surface until Tspon480 K (Fig.1) because of significant
spatial limitation of the maximum critical bubble radius, r, in the hot water layer by the thickness,
LdepL0.003-0.1 m, according to the following nucleation condition5
2δγ(T )
PL (T )  PSAT (T ) 
,
(4)
r (1  V L (T ) / V V (T ))
where PL, PSAT, VV and VL are, respectively, the pressure in the liquid phase (in this case, transient acoustic pressure PL), the saturated water vapor pressure at the water/Si interface at the given
T, the temperature dependent molar volumes of vapor and liquid water;  is the water surface ten-
3
sion and an accommodation coefficient, 0<1, accounts for heterogeneous boiling on a smooth
Si surface. Indeed, the left-hand term in Eq. (4) becomes positive only for T480 K due to the
rapid growth of PSAT with increasing temperature to 2 MPa, equilibrating the last term at the
right side for (480 K)410-2 N/m,21 and r on the order of LdepL0.05 m. This temperature estimate for nucleation of bubbles in water on a smooth Si surface is consistent with the nucleation
temperature of 52030 K for bulk water measured recently on sub-s time scale using optical reflectance from a smooth Si substrate,13 and an estimate of Tspon470 K for water given elsewhere.5 This type of boiling does not really have an “explosive” character as a water vapor bubble growth to a radius of 0.09 m at these temperatures lasts tens of nanoseconds with a typical
velocity of several m/s (e.g. 3.6 m/s10), consistent with the velocity of a thermal wave in water of
the order of (L/LAS)1/21-10 m/s.
More pronounced explosive boiling in water on a smooth Si surface corresponds to the complete filling of a superheated water layer with vapor bubbles of radius rLdepL0.05 m on the
nanosecond time scale of the heating laser pulse (nucleation time LAS), which yields steadystate nucleation rate, J1/r3, on the order of 1023 cm-3s-1. Steady-state heterogeneous nucleation
on a smooth surface is5


1  cos
6γ
16πγ 3f(  )
,
(5)
J het N 2 / 3
exp 
2
L
V 2
2
(2  PL /PSAT )πmf(  )
3
kT
(
P
P
)
(1
V
/V
)
SAT
L


where N, , m, k are the density of molecules in liquid water, the contact angle for water on a Si
surface, the water molecular mass, and the Boltzmann constant, respectively;
f()=0.25(1+cos)2(2-cos) is a correction factor to the activation energy for critical bubble formation. In the case of heterogeneous boiling, Tspon under these conditions is approximately 580
K,5 in reasonable agreement with the 563 K,15 measured by optical transmission on a time scale
of 100-200 ns. At temperatures close to 580 K, an estimate of solid Si acoustic response (PfS)
gives about 0.6 MPa for the S, KS, LdepS, ClS and LAS values given above, which is still higher
than the estimated PfL (0.3 MPa for L(573 K)4.210-3 K1, L(573 K)7102 kg/m3, ClL(573
K)9102 m/s,5 and LdepS0.05 m). It is to be noted that 580 K is quite close to the spinodal
curve of water, where the minimum spinodal temperature Tspin0.92Tcrit595 K at positive PL
(Fig.1), and 580 K may be considered as an approximate spontaneous nucleation threshold Tspon
of water on a smooth surface under nanosecond laser heating.
The Tspon value of water is a function of ambient experimental conditions (e.g., external static
pressure9 or heating rate T/t) and temperatures well above 580 K may be experimentally
achieved under certain conditions as Tspin may increase at times (TspinTspon)/(T/t) much shorter
than the instantaneous  value in this temperature range. Although homogeneous boiling occurs
nearly instantaneously on the time scale of LAS (the minimum nucleation time min10-11-10-10
s)22,24 and at very high nucleation rates J1038 cm-3s-1 near the spinodal curve at r=0,5 the maximum temperature can be equal to the critical temperature of water at very high heating rates
[(T/t)min»(TcritTspin)]. Energy coupling to water from the solid starts to be a technical problem in this regime because of the sparse fluid structure (so-called “gas of droplets”) at the critical
point.5
The instantaneous thermal expansion of superheated water in the proximity of the spinodal
curve results from the strong spinodal non-linearity of L(T) as (V ) P   (Fig.2), correT
sponding also to instantaneous explosive boiling due to the dual “liquid/vapor” nature of spinodal
decomposition products.5 Therefore, more efficient thermoelastic generation should occur in the
4
superheated water during spinodal decomposition relative to that in solid Si, while the acoustic
pressure buildup occurs at the acoustically “rigid” water/Si boundary, similar to the case of bulk
water,11,12 as ClLmin«LL even for a micron-thick water layer. At the same time, min10-11-10-10
s22,24 seems to be long enough to result in a quasi-static acoustic generation regime in water as
LdepL«ClSmin. Another expected feature of acoustic generation near the spinodal curve is that
acoustic rarefaction of the vapor/droplet mixture in the LdepL layer proceeds relatively slowly because of its low sound velocity.25
As the explosive thermal expansion of superheated water under spinodal conditions imparts a
mechanical momentum to a “cooler” water overlayer with nearly zero surface tension at the water/(vapor/droplet mixture) boundary, this overlayer loses mechanical contact with the Si substrate and lifts off inertially. This phenomenon was recently studied using molecular dynamics
simulations of nm-thick superheated water layers on a Au surface at T103 K, with lift-off starting 30-90 ps after a step function temperature increase of the Au surface, 22 in a good agreement
with the characteristic time of spinodal decomposition, min10-10 s.24 Lift-off laser fluence
thresholds for water and 2-propanol and the corresponding plume velocities of order of tens of
m/s were recently reported for variable liquid layer thicknesses and different laser fluences.26
This lift-off effect was also experimentally observed earlier in the form of a thin liquid disk in
nanosecond laser ablation of bulk absorbing liquids with a free boundary, 6 assuming that maximum superheating occurs below the liquid surface. This observation may result from a relatively
large optical absorption depth for the liquid combined with significant surface evaporative cooling,27 providing explosive expansion and rupture in the bulk liquid with removal of the cooler
liquid overlayer.
It should be noted that a thin water layer on a Si substrate is expected to have a nonhomogeneous, droplet-like structure because of the relative surface tension of water and the nanometer-thick oxide film present on Si wafers exposed to ambient air.1,28-29 The interface temperature in Eq. (1) can increase during laser heating as the thin layer of micron-thick water droplets
is not as effective a heat sink as a homogeneous liquid film. To achieve the same temperature, incident laser fluences should be increased relative to the “dry” Si surface by a factor of (1+) in
the presence of a homogeneous water film, but by (1+S) for the droplet-covered Si surface,
where S is the portion of the covered surface and the temperature equilibration time between
“dry” and “wet” Si spots is on the order of 1 ns for a heating laser pulse of several tens of ns.
More importantly, the droplet-like structure of a water layer deposited on a Si surface may significantly affect the optical properties of the interface. At 248 water is transparent, however, and
does not change the absorptivity of Si. Neither does the reflectance/scattering change as the
own water reflectance nm is about 2-3%,21 but optical interference and, especially, focusing effect of micron-thick water droplets seem to be important. Fortunately, as a photoacoustic response of the interface is expected to be proportional also to a surface size of a boiling area, the
latter effect is negligible as well as the average interference effect for irregular-shaped water
droplets.
Thus, despite the basic understanding of spinodal phenomena in liquids and the availability of
the corresponding general theory,1-17,22,24-25 there are still open questions of detailed understanding and proper control of these effects in various applications. In this work the current knowledge
of spinodal behavior of superheated water has been employed in photoacoustic studies to explain
the threshold-like acoustic pressure buildup and lift-off of a thin water layer on a laser-heated Si
substrate.
5
III. EXPERIMENT
A 248-nm, 20-ns KrF excimer laser beam (Lambda Physik, LPX 210) was apertured in its
central part by a 1-cm wide vertical slit and was focused (f=10 cm) at normal incidence onto a
0.25-mm thick Si(100) wafer dosed with water. The laser beam has nearly rectangular and gaussian fluence, F, distributions in the horizontal (X) and vertical (Y) directions (Fig.3) with characteristic dimensions of x=4 and y=1.1 mm, respectively. Laser energy (0.2 J/pulse (3%) after the
aperture) was attenuated by color filters (Corning Glass Works) and was measured by splitting
off a part of the beam to a pyroelectric detector (Gentec ED-500).
In photoacoustic studies the Si wafer was attached to the front surface of a fast 1.5-mm thick,
8-mm wide acoustic transducer (PZT ceramic, effective bandwidth of 3-10 MHz, with a 3-mm
thick protective brass disk) by means of a thin vacuum grease layer providing acoustic contact
between the wafer and transducer. A LeCroy 9360 storage oscilloscope (50- inputs) triggered
by a fast Si photodiode, detecting a part of the excimer laser beam scattered from the entrance
slit, was employed simultaneously to measure the laser pulse energy using the same calibrated
photodiode and to record the PA transients within the operating time window of the acoustic
transducer (the first 300 ns). These transients were delayed by 1.15 s due to the protective brass
disk. Photoacoustic measurements were performed at different laser fluences both for dry and wet
(dosed with water) Si surfaces, with the former (dry) case providing a reference signal as the
acoustic source is localized into the Si wafer.
A water dosing system described elsewhere1 consists of a source of pressurized nitrogen with
a triggered valve, connected to a bubbler immersed in a glass flask filled with heated deionized
water and directed onto the Si surface through a heated output nozzle. The dosing system (gas
pressure of 0.7 bar, flask water and nozzle temperatures of 40 oC, dosing pulse of 0.3 s) was employed to deposit a water layer on the Si wafer placed at a distance of 5 cm from the nozzle. According to previous observations,1,28 the deposited water layer consists of separate droplets
(Fig.4) as the several nanometer-thick native silicon oxide surface film on the Si wafer has
dewetting properties relative to water with an expected contact angle of 20-45o.29 Deposition, laser removal and natural drying of a water layer were monitored in real time by observing the optical reflectance/scattering of a HeNe probe laser focused on the center of the irradiated area
(Fig.5). Preliminary measurements of a deposited water mass performed with a absorbent CaSO4
(drierite) and drying times defined by an instant of recovery of HeNe reflectivity in a center of a
dosing area on the Si surface (Fig.5) exhibit their linear increase with increasing dosing pulse
length, Tdose, within the range of 0.1-1 s at the total deposition rate of 0.007 g/s (Fig.6). Studying
a transversal distribution of water on the Si wafer from the corresponding measurements of drying times across the dosing area at different Tdose, an average thickness of the water layer about
0.4 m has been estimated in a particular case of Tdose=0.3 s using the known mass of water deposited and neglecting transportation losses. Though a real average diameter of water droplets
(i.e., droplet’s height, LL) is a time-dependent value due to permanent nucleation and Ostvald ripening processes, its approximate magnitude about 1.5 m can be obtained for the latter case, dividing the average layer thickness by the surface coverage S30% (Fig.6), which is a product of
an average droplet square and surface density of droplets acquired making snapshots of the dosed
Si surface (cf. Fig.4).
In the photoacoustic experiments the excimer laser was fired 0.06 s after the end of each deposition step, accounting for the approximately 40-ms delay for the dosing jet to propagate the 5-cm
distance between the nozzle and the Si substrate surface. The gas valve and the excimer laser
6
were triggered manually in a single-shot mode with the corresponding delays generated using a
pulse generator (Stanford Research Systems DG 535). Inspection of irradiated spots was made
with an optical microscope (Mitutoyo WH).
IV. RESULTS OF PHOTOACOUSTIC MEASUREMENTS AND INTERFACE TEMPERATURE CALCULATIONS
Characteristic nearly symmetrical bipolar PA transients were obtained for the acoustically free
water/Si boundary and the dry Si boundary at different laser fluences, F, in the range of 0.1-0.24
J/cm2 (Fig.7). The first positive pulse corresponds to compressive pressure, Pcomp, resulting from
thermal expansion of the laser-heated near-surface layers of water and Si, and the second negative pulse corresponds to rarefaction (tensile pressure, Prare) in these transient regions because of
their cooling at the end of the laser pulse.19,30 The broadening of the waveforms by nearly five
times compared to the laser pulse length LAS of 20 ns (FWHM) (Fig.3) and decreased amplitudes
are largely attributable to dissipative losses in the 3-mm protective brass disk, thin layer of vacuum grease, epoxy glue fixing the PZT element in the acoustic transducer, and reflections at all interfaces in the acoustic delay line. As is shown in Fig.7, PA transients with and without a water
layer have similar temporal shapes with somewhat higher rarefaction pressure amplitudes up to
the threshold laser fluence Fb0.200.04 J/cm2 defined as the fluence value where the PA transients obtained for the water/Si boundary start to exhibit much higher amplitudes relative to a dry
Si surface (Figs.7,8) and the strongly asymmetric waveform shapes with the predominance of a
compression amplitude. These waveforms are similar to those recorded in the photoacoustic studies of superheated water boiling on a Si surface in bulk water.11 Moreover, visual lift-off of the
water layer appears in the form of a several mm-long water plume (vapor/droplet mixture) at fluences above Fb. Following the discussion in Section II, these data correspond to the explosive
boiling (spinodal decomposition) of superheated water.
As the acoustic pressure at the laser-heated water/Si boundary is additive [cf. expressions
(2,3)], the separate contributions, PfS and PrL, of the acoustic sources in superheated water and
solid Si may be evaluated, starting from the boiling threshold Fb, by subtracting Pcomp and Prare
values, measured in the case of “dry” Si, from the Pcomp and Prare amplitudes for the “wet” Si surface, at the same incident laser fluences. We have also taken into account a nearly double increase of acoustic pressure amplitudes of the compressive acoustic waves transmitted from water
into a bulk Si for the pressure transmittances water/Si and Si/water31
 water/Si  2
,
 2N
,
(6)
N  1 Si/water
N 1
where N=[L(T)ClL(T)]/[SClS]0.07 is the impedance ratio for water and solid Si at normal conditions. PrL values obtained after subtraction, were halved and then were divided by the factor S,
corresponding to nearly 30% at Tdose=0.3 s (Fig.6). The resulting dependence PrL(F) is presented
in Fig.9.
The transition from acoustic generation at the free water/Si boundary to that at the constrained one can be quantitatively described by a ratio of Pcomp and Prare amplitudes for the “pure”
water acoustic response. The ratio as well as both Pcomp and Prare values are affected by diffraction of the 100-ns (FWHM) acoustic pulse component detected in the protective brass disk
(Fig.7). The acoustic pulse has a nearly plane wavefront in the near acoustic field (Z/Zdiffr0.2)
due to the wide laser spot on the Si wafer surface in our PA measurements, where the characteristic diffraction length equals Zdiffrxy/2ac15 mm and the characteristic wavelength, ac, of the
7
100-ns detected acoustic pulses for the brass longitudinal acoustic velocity Clbrass4.4103 m/s21
is equal to about 0.5 mm. The expected Pcomp/Prare ratio in the near acoustic field at Z/Zdiffr0.2
should be about 0.7 for bipolar symmetrical acoustic pulses and 3-3.5 for unipolar compressive
acoustic pulses, respectively.19 In the latter case the diffraction effect results in a 30% reduction
of Pcomp amplitude and in appearance of a spurious rarefaction pulse with an amplitude of nearly
25% from the initial Pcomp value.19 These expectations are consistent with our experimental observations in Fig.10, exhibiting, on average, 0.70.3 at F<0.24 J/cm2 and 3.00.2 at F=0.4-1.4
J/cm2.
To explain these results, the maximum Si surface temperature, Tmax, and its transients have
been calculated as a function of F using the computer code “SLIM”23 to solve a non-steady-state
thermal conduction equation with temperature-dependent solid Si parameters. The temperature
dependence of the thermal conductivity of solid Si was taken as 1.58103T-1.23 W/cmK,32 while
the heat capacity, optical reflectivity, R, and absorption coefficient at 248 nm were assumed to be
constant (1.99 J/cm3K, 0.6, 1.65106 cm-1 for the solid and 2.4 J/cm3K, 0.68, 1.8106 cm-1 for the
liquid phases of Si, respectively).20-21,32 In contrast to similar calculations in the visible wavelength (indirect bandgap) region, the optical properties of Si in the ultraviolet (direct bandgap)
region are not strong functions of temperature. These calculations give correct values of the Si
surface temperatures for the onset of Si melting and ablation (Tm=1689 K, Tboil3.6103 K)21
consistent with the experimentally observed acoustic responses of dry Si for melting (0.5
J/cm2)30,33 and ablation (1.4 J/cm2)30,34 thresholds. Furthermore, as shown in Section II, thermal
fluxes in water and solid Si near the interface may be accounted in the temperature calculations
for a dry Si surface in the temperature range of 300-643 K, just multiplying F in the “wet” Si case
by the factors of (1+S) or (1+) for droplet and continuous coverage, respectively. Transients of
interface temperature may also be adapted in the same way for the “wet” Si case, increasing the
effective fluence by this value. The resulting dependence of Tmax(F) calculated for the case of a
water/Si interface is presented in Fig.9.
V. DISCUSSION
Our temperature calculations show that Tmax(6.20.6)102 KTspin(PL)Tcrit is achieved during the tail half of the excimer laser pulse near the threshold fluence Fb0.20 J/cm2 for the rapid
compressive acoustic pressure buildup (Fig.9) and lift-off of the pre-deposited water layer. A
numerical estimate of PrL value near this threshold was done on the basis of the corresponding PfS
value, accounting for comparable PfS and PrL values (PrL/PfS2) at F0.24 J/cm2Fb (Fig.8), as
the L(T) thermal coefficient has not well-defined character near the spinodal curve. The PfS estimate taken in the form SLdepS/ClSLAS for T600 K, S(600 K)3.710-6 K1, KS11011 Pa,21
LdepS0.4 m and other parameters (ClS,LAS) given in the Section II, equals about 0.6 MPa. This
value, in its turn, yields the real PrL value 8 times higher, taking into account PrL/PfS2 ratio at
F0.24 J/cm2, the partial (30%) water coverage of the Si wafer surface at Tdose=0.3 s (Fig.6) and
the linear dependence of Pcomp on Tdose [Fig.11(a)], the double acoustic pressure increase at the
water/Si interface (see expression (6)) and the diffraction correction about 2 relative to PrL values
at higher fluences (Fig.10), resulted from the small vertical width of a boiling area,
Ythr=y{ln[F/Fb]}1/2, for laser fluences near the boiling threshold Fb, which gives Z/Zdiffr ratio
about 0.5. This estimate PrL5 MPa is well consistent with the pressure values PL of 10 MPa at
Tspin6.2102 K (Fig.1). The reported transition from acoustic generation at the free water/Si
8
boundary to the rigid one above the threshold, followed by the acoustic pressure buildup, may
provide one more evidence of explosive boiling of water as the 1.5-m height LL of water droplets corresponds to their characteristic rarefaction time of 2 ns, which is much longer than the
characteristic time of spinodal decomposition min10-11-10-10 s,22,24 but much shorter relative to
the laser pulse length LAS of 20 ns (Fig.3). These facts allow quite unambiguous identification of
the explosive boiling nature of the threshold Fb.
According to PrL(F) curve in Fig.9, PrL starts to grow rapidly at Fb, approaching to a plateau at
F0.4 J/cm2. On this plateau PrL value estimated from a ratio of relative PrL magnitudes at 0.4
J/cm2 and 0.24 J/cm2, being about 5 after the diffraction correction (about 2) of the latter, multiplied by the value PrL(0.24 J/cm2)5 MPa, yields about 25 MPa. This value is on the order of the
water critical pressure (Pcrit22 MPa),21 and may mean the achievement of the critical point of
water, passing along the spinodal curve. This thermodynamic transition seems to be quite possible at moderate laser heating rates of (0.5-3)102 K/ns achievable in our experiments at the transient temperature T620 K for the fluence range of 0.24-1.4 J/cm2 [Fig.11(b)]. Indeed, with increasing heating rate T/t, temperatures TTspin+(T/t)min well above Tspin620 K (till
Tcrit=647 K21) may be achieved on a time scale of spinodal decomposition time min. A gradual
decrease of  along the spinodal curve of water seems to occur as the 8% temperature rise in the
range T=(0.92-1.0)Tcrit (Fig.1) corresponds to the nearly double growth of F from Fb to 0.39
J/cm2 in the beginning of the PrL plateau (Fig.9) or at the corresponding maximum Pcomp/Prare in
Fig.10. Moreover, the further superheating of water above its critical temperature seems to occur
very slowly as a function of F because of a poor thermal conductivity of a supercritical nearsurface “gas of droplets”,5 thermally isolating the hot Si surface. Furthermore, early thermal isolation of the hot Si substrate by the supercritical vapor/droplet mixture results in reduction of a
heat-affected zone LdepL in the liquid, i.e. capacity of the corresponding acoustic source. Thus, accounting for gradually increasing energy deposition into the superheated water layer as a function
of F resulted in higher “real” acoustic pressures, the PrL “plateau” may result from simultaneous
reduction of a heat-affected zone in water compensating the pressure growth.
The prominent minimum at F0.5 J/cm2 is presented on the “plateau” of PrL(F) curve in Fig.9
(see also the corresponding maximum in Fig.10). The reason for this minimum may be Si melting
above the corresponding threshold of 0.5 J/cm2 under dry conditions,30,33 i.e. at the fluence higher
by factor of (1+)1.08 for the Si surface dosed with water, as is shown by Tmax(F) curve in
Fig.9. The melting effect results in a negative rarefaction pressure due to molten Si contraction,
thus changing the thermodynamic stability limit (both pressure and temperature) of superheated
water under these conditions. Finally, decrease of PrL value (or Pcomp/Prare ratio) is present at
F>1.4 J/cm2, where raw Pcomp values start to increase slowly relative to that of Prare in the “dry”
case (Fig.8) in agreement with experimental evidences for ablation of “dry” Si, starting in the fluence range 1.1-1.4 J/cm2,30,34 but clear understanding of an acoustic generation regime for this
water-confined ablation of Si is still lacking.35
It is noteworthy that PrL(F) in Fig.9 has a similar shape (the steep threshold-like rise and the
following “plateau”) as fluence dependences of a compressive acoustic pressure at the water/Si
interface reported earlier for the case of bulk water.11,12 Nevertheless, the experimentally measured compressive pressure values on the corresponding plateaus in those works were considerably lower (1-5 MPa)11,12, than our estimate PrL25 MPa. This contradiction can not be explained
by different experimental geometries in this and other works,11,12 i.e., for example, by frequencydependent dissipative losses in bulk water (ac/f22510-15 Hz2m1),21 not exceeding several
percents for 100-ns or 40-ns acoustic pulses and 3-cm or 1-mm acoustic propagation distances,
9
respectively, used in these experiments,11,12 or by a diffraction effect, which is much weaker in
water. The most probable reason for this acoustic pressure discrepancy is a rough surface of Ag
or Cr metallic substrates11,12 having exhibited boiling temperatures of 400-500 K well below the
critical temperature of water. This strong effect of substrate surface roughness was recently found
for laser-induced water boiling on smooth and rough Si substrates which have boiling temperatures of 430 and 520 K, respectively.13 Accounting for higher Si reflectivity of 0.6 at 248 nm
work against 0.4 at 532 nm calculated using tabulated optical constants of Si20 and nearly 30%
lower temperatures for a 20-ns laser pulse relative to a 8-ns one,36 water boiling threshold of 0.08
J/cm2, reported13 for the 532-nm laser wavelength and 8-ns pulse width, is consistent with that of
0.20 J/cm2 obtained in this work.
To explain these experimental results, a consequent scheme of events taking place between
explosive boiling of water and lift-off of the liquid layer has been proposed. According to this
scheme, at first, simultaneous explosive boiling and expansion of a superheated water layer adjacent to a hot Si surface occurs under spinodal conditions on a time scale of min10-11-10-10 s.22,24
Since the superheated, unstable water layer with a thickness LdepL(Lmin)1/23-10 nm formed
during min is acoustically “thin” as LdepL«ClLmin10-100 nmLL, expansion or, in other words,
acoustic relaxation of the layer, would be significant during min, resulting in a maximum acoustic pressure, which approaches at this stage to PrL(Tspin)KadL(VL/V0L)TspinLdepL/ClLmin102
MPa (Fig.12) for KadL2103 MPa estimated using the reported21 values L(300 K)1103 kg/m3
and ClL(300 K)1.4103 m/s as well as (VL/V0L)Tspin1-2 at T590-647 K estimated5 from the
van der Waals equation of state. This process occurs in a dynamic mechanical equilibrium with
simultaneous compression of a top layer of cooler water, providing space for expansion of superheated water and a potential energy of elastic deformation to the latter. As a result, in the case of
a relatively thick water layer during min or so superheated water expands rapidly to a quasiequilibrium state of the vapor/droplet mixture near the spinodal curve at pressure PrL(t) up to Pcrit
(Fig.12). The following acoustic relaxation (thermal expansion) of the mixture starts at
t2LL/ClL, i.e. after redistribution of the compressive stress during tLL/ClL over the entire top
cooler water layer, reflection of the compressive wave at the free water/air boundary as a tensile
wave and the following rarefaction of the cooler compressed water layer phase until t resulting
in a permanent displacement of its center-of-mass (lift-off). It proceeds with a corresponding liftoff velocity, Vlift, which is inversely proportional to LL because of effective spreading of the compressive potential elastic energy over the whole liquid layer,22,26 and occurs slowly due to
P/VTspin=0 in the proximity of the spinodal curve.5 Due to a difference in acoustic impedances
of cooler water and its vapor/droplet mixture the coming rarefaction wave is predominantly reflected at their boundary in a compression phase and thus bounces forth and back in the cooler
water layer as compression or rarefaction waves, coming each time to the water/mixture boundary as a rarefaction wave (because of two - external and internal - free boundaries of the cooler
water layer) and decaying gradually. Therefore, due to the steady-state influence of the rarefaction acoustic wave on the vapor/droplet mixture a reverse switching of acoustic generation to the
“free” water/Si boundary mode takes place at t. Because of much lower acoustic generation efficiency at a free liquid boundary relative to that at the “rigid” one for nanosecond acoustic pulses,19 the acoustic pressure drops to one MPa or less soon after t and, therefore, the time interval
t may be concerned with an effective acoustic pulse length (Fig.12) depending on LL, i.e. about 2
ns for the 1.5-m thick water droplets, which low-frequency, 10-MHz component was detected in
this work because of strong frequency-dependent attenuation of the acoustic pulse in the protective brass disk. Unfortunately, only this second, relatively long (tt) and low-amplitude
10
(PrL(t)Pcrit) phase of the acoustic pulse can be detected usually by the present photoacoustic,
photodeflection and surface-plasmon probe techniques,11,12,14-15 especially in a “bulk” water geometry, when the estimated ultrasound penetration depth, ac-1, equals to about 40 m at f1 GHz
and 0.4 m at f10 GHz for the non-linear attenuation coefficient ac/f22510-15 Hz2m1.21 The
first, ultrafast (tmin) and high-amplitude (PrL(t)102 MPa) acoustic pulse phase corresponding
to spinodal decomposition of a superheated liquid might be studied in a future with a subpicosecond temporal and micrometer spatial resolution using the optical microscopy variant37 of a
femtosecond pump/probe technique, while quite accurate pressure measurements in the multiGHz frequency range seem to be possible employing the existing picosecond ultrasonics techniques.38
Main factors determining parameters of a lift-off process of a thin transparent liquid layer
from a hot absorbing solid substrate can be deduced straightforwardly from the proposed scheme.
First of all, this is a degree of superheating of a liquid, corresponding to its thermodynamic state
on the corresponding spinodal curve and assuming its strong thermal expansion resulting in a
high compressive stress for a top cooler liquid layer. Then, a thickness of the superheated liquid
layer seems also to affect a value of a potential elastic energy of the cooler liquid layer. Finally, a
thickness of the entire liquid layer is the last factor determining a lift-off onset and the corresponding velocity.
VI. CONCLUSIONS
In conclusion, in this work a mechanism of explosive boiling and lift-off for a thin layer of
water droplets on a Si substrate heated by a KrF laser was studied using a contact photoacoustic
technique. By subtracting the small PA signal measured for a dry Si wafer from the large total PA
signal for the wet Si surface, the PA response of superheated water was evaluated. The sharp
threshold-like increase of this response was shown to be concerned with the spinodal (nearcritical) non-linearity of the thermal expansion coefficient and spinodal decomposition of superheated water, while the following “plateau” may correspond to achievement of the critical point
of water. Main aspects of acoustic generation in this experimental geometry under near-critical
(spinodal) conditions are discussed.
1
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21
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12
34
W.P. Leung, and A.C. Tam, Appl. Phys. Lett. 60, 23 (1992); Y.F. Lu, M.H. Hong, and T.S.
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35
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36
M. Mosbacher, V. Dobler, H.-J. Muenzer, M. Bertsch, N. Chaoui, J. Siegel, J Solis, C.N. Afonso, R. Oltra, D. Baeuerle, P. Leiderer, and J. Boneberg, in Particles on Surfaces 7, edited by K.L.
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a)
Permanent address: Institute for High Energy Densities, Joint Institute of High Temperatures of
Russian Academy of Science, 127412 Moscow, Russia, electronic mail: sergeikudryashov@hotmail.com, sergeikudryashov@chat.ru
b)
Electronic mail: sdallen@mailer.fsu.edu
PACS: 43.35.Ud, 81.70.Cv, 64.70.Fx, 64.60.My
FIG.1. P,T-phase diagram of water constructed using the tabulated data5,20: binodal curve
(solid circles, solid line), spinodal curve (solid squares, solid line), liquid/vapor equilibrium
curves for bubble radiuses of 3 (open rhombs), 10 (open triangles), 30 (open squares) and 100
(open circles) nm.
FIG.2. Relative temperature-dependent change of thermophysical parameters of water.
FIG.3. (a) Intensity profile of the KrF laser; (b) gaussian distribution of F in the X and Y directions.
FIG.4. Snapshot of the “wet” Si surface at Tdose=0.3 s.
FIG.5. Transients of HeNe reflectance/scattering from the Si surface dosed with water with (1)
and without (2) excimer laser irradiation and the corresponding electrical pulse for the dosing
valve (3) of duration Tdose=0.3 s.
FIG.6. Deposited water mass, drying time and Si surface coverage (the product of square and
surface density of water droplets) as a function of Tdose.
FIG.7. PA transients: (a) for “wet” Si at F=0.24 (1), 0.36 (2), 0.39 (3), 0.92 (4) J/cm2 and (b)
for dry Si at F=0.4 (1), 0.5 (2), 0.9 (3), 2.3 (4) J/cm2. The arrows show the operational time window for the 1.5-mm PZT acoustic transducer as well as the PA signal delay in the acoustic delay
line.
FIG.8. Pcomp and Prare as a function of F for dry and “wet” Si surfaces.
FIG.9. PrL values for water as a function of F (left axis); dependence of maximum water/Si
interface temperature Tmax on F (right axis).
FIG.10. Pcomp/Prare ratio for the water acoustic response as a function of F.
FIG.11. (a) Pcomp as a function of Tdose at F=2.4 J/cm2; (b) laser heating rate T/t for the water/Si interface at T620 K as a function of F.
FIG.12. A schematic profile of the transient acoustic pressure on the laser-heated water/Si interface under spinodal decomposition conditions. Boiling onset, tboil, corresponds to an instant of
Tspin620 K on the water/Si interface during the heating excimer laser pulse; other notations are
given in the text.
13
Pcrit=22.1 MPa
P (MPa)
20
10
0
-10
-20
Tcrit=647 K
-30
400
500
600
T (K)
L
L
L
L
L
L
 (T)/ (273)
1000
 (T)/ (273)
 (T)/ (273)
L
L
Cl (T)/Cl (273)
100
L
L
CP (T)/CP (273)
10
1
Tcrit=647 K
0,1
300
400
500
T (K)
14
600
I(t) (arb.u.)
1,0
a)
0,8
20 ns
(FWHM) 1,0
b)
F(X)
F(Y)
0,6
0,5
0,4
0,2
0,0
0,0
0
30 60 90
t (ns)
-10 -5 0
5 10
X,Y (arb.u.)
15
30
2
25
0,6
o
20
15
0,3
0,0
10
1
5
3
Valve voltage (V)
R(633nm,30 ,s-pol.)
0,9
0
0
1
2
3
4
Tdose (s)
coverage (%)
mass (g),drying time (s)
70
2
10
1
10
mass
drying time 10
coverage
0
10
0,1
1
10
Tdose (s)
a)
10
0
P(t) (mV)
P(t) (mV)
20
1
2
3
-10
-20
1,4
b)
0
1
2
3
-5
4
-10
4
1,2
5
1,6
1,2
1,4
t (s)
t (s)
16
1,6
Pcomp, Prare (mV)
20
Dry
Pcomp
Prare
15
Wet
Pcomp
Prare
10
5
boiling
threshold
0
0,1
0,2
1
2
F (J/cm )
L
Pr
Tmax
3000
2500
2000
L
20
10
1500
boiling
threshold
1000
Tcrit=647 K
0
0,1
0,2
2
F (J/cm )
17
1
500
Tmax (K)
Pr (arb.u.)
30
Pcomp/Prare (arb.u.)
4
2
boiling
threshold
0
0,1
0,4
1
2
Pcomp (mV)
40
dT/dt(620K) (K/ns)
F (J/cm )
a)
30
20
10
300
200
100
0
0,0 0,3 0,6 0,9
0,2
1
F (J/cm )
explosive boiling
and expansion of
superheated layer
102
rarefaction of
cooler liquid layer
101
1
10-1
3
2
Tdose (s)
acoustic pressure (MPa)
b)
free liquid
boundary
free liquid
boundary
rigid liquid
boundary
tboil min
t*
t (ns)
18