S. Jesse et al.: Etching-enhanced ablation and the formation of a microstructure in silicon by laser irradiation in an SF6 atmosphere
heat of vaporization is several times larger than the heat
of melting and therefore dominates the energy balance.
For silicon, the heat of melting is 50 kJ/mol while the
heat of vaporization is 359 kJ/mol. Also, no atmosphere
or plume–surface interactions are considered. In this
model, the velocity and temperature of the solid–gas
front is governed by the energy absorption and heat trans-
fer characteristics of the target. The Drude–Zener theory
of optical absorption is used which is based on a linear
relation between absorptivity, A, and temperature, Ts.
The following two relations can be obtained:25
This model leads to Eq. (1) and fitted values of maxi-
mum front distance xf ס
46 m and drag coefficient
Geohegan20 observed a similar behavior for the abla-
tion of YBa2Cu3O7−x in 100 mtorr of oxygen with a
value of xf ס
3.0 cm and  ס
0.36 s−1. The initial
velocity of the plume
= xf
,
(6)
0
was in this case 1 cm/s. The initial velocity of the
plume due to ablation/etching of silicon in our case is
2.4 cm/s indicating that the pressure of the gases pro-
duced during etching is very high. However our drag
coefficient, , is 150 times larger than in the case of
ablation of YBa2Cu3O7−x. This difference reflects the
fact that the background gas pressure is almost 4000
times larger than in the YBa2Cu3O7−x experiments.
In summary, we have shown that the growth of the
cones is closely correlated with the evolution of the laser-
generated plume. This correlation is strong evidence that
the silicon-rich material that is removed by an ablation-
etching process from the microholes feeds the growth of
the cones near them. The interplay between the deepen-
ing of microholes and growing of cones was revealed,
showing a continuing evolution leading to a stage where
holes are so deep that insufficient material reaches the
cones to overcome the always ongoing ablation process.
Then, for a sufficiently large number of pulses, the cones
recede beneath the initial surface. It is shown that, at the
bottom of the microholes, ablation is greatly enhanced
due to multiple reflections and focusing of the laser beam.
AI = V L + c T ͒
,
(2)
͑
s
v
p s
−MLv
V = V exp
,
(3)
ͩ ͪ
s
0
kbTs
where I is the laser fluence, is the density of silicon, Lv
is the latent heat of vaporization, cp is the heat capacity,
V0 is the speed of sound in the material, M is the molar
mass, and kb is Boltzman’s constant. The equations are
then solved simultaneously to find Vs and Ts, the evapo-
ration front velocity and temperature. At a laser fluence
of 12 J/cm2 (the estimated intensity at the bottom of the
microholes), Vs is found to be 38.2 m/s. A rough estimate
of the time required to establish steady state evaporation,
tc, is given by
tc =
,
(4)
Vs2cp
where is the thermal conductivity. For the same high
laser fluence, this equation yields tc ס
5.8 ns. If it is
assumed that most of the evaporation takes place after the
establishment of a steady-state front and until the end
of the 25 ns pulse, this model gives an ablation rate of
0.6 m/pulse for a laser fluence of 12 J/cm2. This rate is
500 times higher than the ablation rate of a flat surface in
the presence of SF6.
The advance of the plume front as a function of time
can only be measured with the ICCD camera is approxi-
mately the first 100 ns because the ambient gas quickly
quenches the laser-induced fluorescent light. The pres-
sure at which these measurements were performed was
thousands of times higher than in other reported meas-
urements of plume expansion.20,21 At a pressure of
0.5 bar the plume front reaches 60 m before the back-
ground gas quenches the excitations producing the fluo-
rescent light. We have found that at these very early
stages of plume expansion, the drag-force model fits
better than the shock model originally described by
Zel’dovich and Raizer.26 In the drag-force model it is
assumed that the ablation products are moving as a whole
and that the background gas produces a viscous decelera-
tion of the plume proportional to the expansion velocity,
ACKNOWLEDGMENTS
This research was sponsored by the National Science
Foundation Grant No. DMR-9901238 and by the Oak
Ridge National Laboratory, managed by UT-Battelle,
LLC, for the U.S. Department of Energy under Contract
DE-AC05-00OR22725.
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d
= −
.
(5)
dt
1012
J. Mater. Res., Vol. 17, No. 5, May 2002
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