# Critical Time to Nucleation: Graphite and Silicon Nanoparticle Generation by Laser Ablation

Authors: Sid Senadheera; Bo Tan; Krishnan Venkatakrishnan
Journal: Journal of Nanotechnology
 (2009)

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## Abstract

Femtosecond laser ablation hydrodynamics has been analyzed numerically. The nucleation process of two materials (silicon and graphite) in an expanding plume produced by a femtosecond laser ablation is analyzed within the framework of the Zeldovich-Raizer theory (RZ theory). RZ theory is the most appropriate theory applicable to an expanding plume created by a femtosecond laser ablation and has been used to estimate the critical times in the evolution of nanoparticle formation. However, there is no experimental result to directly substantiate the theoretical model on a fundamental level. This paper gives an experimental approach to prove theoretical predictions of critical times to nucleation in laser-ablated graphite and silicon plumes. The critical time to nucleation deduced using the RZ theory was found to be in close agreement with pulse frequency at which fibrous nanoparticle aggregates start to form for both materials. We experimentally showed that the nanoparticle aggregates were produced consistently when the pulse frequency corresponding to the femtosecond laser time interval was shorter than the critical time to begin nucleation. Therefore the nucleation time acts as a threshold time length to begin nucleation.


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## Body

## 1. Introduction

Nanoparticles  have  attracted intensive interest in the
nanotechnology applications due to their huge potentials
in medicine and new engineering materials. Several methods have been developed
to generate nanoparticles in large quantity, among which laser ablation is
desired because of simplicity in configuration and short process time.
Recently, femtosecond laser ablation has been investigated for nanoparticle
generation and it was observed that the nanoparticle structure generated by
femtosecond laser ablation presents unique characteristics, compared to
nanoparticles that are generated with conventional long pulse lasers. The
differences in ablation characteristics among femtosecond, picosecond, and
nanosecond lasers are discussed in detail in [1].Our recent research
revealed that fibrous nanoparticle aggregates can be created by laser ablation
of a target material in ambient atmosphere at room temperature [2]. To generate
nanoparticle aggregates with high yield, laser pulses must be fed to the target
material at a pulse frequency higher than the minimum value that was estimated
through our experiments. A theoretical analysis using a derivation of the
current hydrodynamic theory applied to laser-ablated silicon and carbon vapor plumes
finds that the critical time to nucleation agrees well with the observed
minimum pulse frequency at which aggregate formation begins.


## 2. Experimental Methodology

The experimental setup is shown
schematically in Figure1. We used a femtosecond laser capable of producing
variable pulse widths and pulse frequencies.
The laser source  is an all-diode-pumped, direct-diode-pumped Yb-doped fiber
oscillator/amplifier system capable of producing variable pulse energies up to
10 mJ at a pulse frequency between 200 kHz and 25 MHz. Average power varies
between 0–20 W. Arrays of
microvias were drilled into a graphite target and a blank silicon wafer with
laser beam at various pulse frequencies. The samples were then characterized
using scanning electrical microscopy (SEM). Large amounts of fibrous
nanostructures were observed surrounding the microvias, as shown in Figures 2
and 3.Figure 1
Setup for producing
femtosecond laser ablation sample.Silicon
nanoparticle aggregate growth with laser pulse frequency.
(a)(b)(c)Graphite
nanoparticle aggregate growth with laser pulse frequency.
(a)(b)(c)


## 3. Nanoparticle Production by Laser Ablation

We
observed that the formation of nanoparticle aggregates in silicon started at a
pulse frequency of about 2 MHz. Until this pulse frequency, the formation of
fibrous nanoparticle aggregates was not evident. At 2 MHz, aggregates are short
and coexist with
large amount of molten droplets. As the pulse frequency
increases, the amount of molten droplets reduces and the aggregates grow
longer, and finally form fibrous structures. For graphite, the formation of
aggregates begins at 1 MHz. On the graphite target surface, the fibrous
nanoparticle aggregates were denser at 1 MHz than those on a silicon wafer
surface at 2 MHz. The experimental results show that the minimum required pulse frequency to observe nanoparticle aggregates is
material dependent.To understand the formation of nanoparticle aggregates, it is
important to understand how they evolve with time after the laser ablation.
Characterizing our experimental results with an SEM, we observed that
individual nanoparticles are bonded with each other to form nanoparticle
aggregates, as shown in Figure4.Figure 4
Nanoparticle aggregate chains.As illustrated in Figure5,
during the laser ablation the material inside the plume evolves through several
physical states before condensation. In the first step, the laser light is
absorbed by free electrons due to inverse bremsstrahlung process in the semiconductor at the
top layer. This is followed by a fast energy transfer to the lattice owing to
electron-phonon coupling. After the energy transfer, a high temperature is
reached in the lattice. The interaction of intense ultrashort light pulses with
the target leads to a phase transformation (melting of surface, evaporation,
and plasma formation). At first, the very high heating rates cause a rapid
melting and the transition to an overcritical fluid. An overcritical fluid
occurs when the material is in a nonequilibrium state of high pressure and high temperature. The
rapidly increasing vapor pressure near the surface creates a large driving
force for vapor expansion. The high temperature and density lead to pressures
far exceeding the background gas pressure (of the order of 10–100 atm). The
unusually high fluid pressure causes the plume front to expand very rapidly
with time in a highly forward-directed pattern. At early times, the plume front
is spherical in nature, but as time evolves the plume front becomes sharpened Figure 6. Along with
sharpening, the expanding  plume front splits into a fast and a slow moving clouds indicating
plume splitting [3–6].Figure 5
Time evolution of a femtosecond plume.Figure 6
Constituents of the femtosecond plume.The expanding plume brings the hot-vaporized
material from the target to a critical state by a process known as supercooling
(cooling below the freezing point). Supercooling causes the vaporized material
inside the plume to saturate and then form nuclei. The critical vapor within
the plume (Figure6) becomes supersaturated,
leading to nanoparticle formation via condensation of nuclei. It has been shown
by several researchers that nanoparticles bond together linearly and form
similar structures to the fibers in nanoparticle aggregates [6] obtained by our
experiments. The fundamental parts of the creation and evolution of the plume
are shown in Figure 6. During condensation stage primarily formed nanoparticles
may coalesce incompletely, which leads to the formation of aggregates [6], such
as nanocrystal networks or nanofiber aggregates, and so on. Nanoparticle
aggregates have the structure of web-like material shown in Figures 2, 3. At
low pulse frequencies, in the range of KHz, condensates have a structure of
spherical nanoparticles, just after the condensation material that is still at
an elevated temperature. The cooling process down to ambient temperature is
very slow. This slow cooling process determines the physical structure of the
condensates according to the pulse frequency that the target is subjected to.


## 4. Analysis

The first theoretical analysis of condensation dynamics in
a rapidly expanding vapor was performed by Raizer et al.
Anisimov et al.  [7] and Anisimov and Luk'yanchuk [8] analyzed this theory with a modern perspective.  Raizer considered the self-consistent problem of vapor
condensation during expansion,  as applied to the problem of cosmic dust in star
formation regions. A constituent of the analysis is the classical theory of
nucleation and production of nanoparticle aggregates which was developed in [3, 8]. This theory of dynamic condensation of expanding vapor will be referred to
as the Raizer-Zeldovich
(RZ) theory, and is technically outlined in detail in [8]. An advantage of the
RZ theory is that it is a clear manifestation of the physics of the process,
and it also accounts correctly for the characteristic time scales for
production and the dimensions of resulting clusters produced after the
nucleation process. We use the RZ theory as a good theoretical model for
estimating the time scales for nucleation which will be explained soon. The RZ
theory has been applied (theoretically) to nanocluster production of silicon, germenium,
and carbon using laser ablation in [8, 9].During the phase transitional
period, nucleation rate of particles ablated by the femtosecond laser is given
byv. The time rate of change
of nucleation is given by dv/dt.  The
nucleation process maximizes at {|∂v/∂t|∣att=te}=0. The
instant of time te is when the
nucleation reaches maximum. The rate of formation of the nuclei is
proportional to cluster growth which leads to nanoparticle  formation within the
advancing front of ablation laser plume Figure 6. According
to Raizer-Zeldovich theory, the rate of nucleation can be written  as (1)dvdt=Kv(1−x)[ρ(t)ρstart]⋅exp[−TvT1θ2],Kv=2σπm⋅[ρstartρL],v=16πσ3M23kB3qρL,θ=Teq−TTeq,Tv=16πσ3M23kB3qρL.To look at the formation of fibrous
3D nanoparticle aggregates, we have to look at the nucleation ratedv/dt. The behavior of the exponential
factor of the nucleation rate is an extreme sharp function of supercooling [6]
and is proportional to the term
exp[−(Tv/T)(1/θ2)]. Since we are only
interested in finding the minimum repetition rate to form nanoparticle aggregates
for graphite and silicon
for beginning nucleation, we analyze only the time parameter of (1). Theoretically,
we can see that the corresponding time where nucleation reaches it's maximum can be
graphically represented (Figure 6
). By separating the exponential part of the
equation,  we have (2)dvdt∝exp[−TvT1θ2].


## 5. RZ Theory and the Nucleation Process

There are few approaches to theoretically calculate the critical-time period toward nucleation.  Out of these, we chose the classical hydrodynamics approach given by the RZ theory. The
modern theories of nucleation represent only modifications of the classical theory, and
they still remain unsuitable for quantitative prediction of experimental results. In order to
create a universal description of supersaturated vapor nucleation, we need to get reliable
theory such as the RZ theory that has been tested for half a century with various
experiments. According to this theory, the nucleation rate during the critical time can be
written as:(3)dvdt=Const⋅exp[−TvT1θ2],which can be
numerically graphed as shown in Figure 7.Figure 7
Critical
time to nucleation in microsecond and repetition rate is in MHz.Figure7 shows that nucleation starts just above 0.65 microsecond for silicon. This critical time to nucleation corresponds
to a laser pulse frequency of 1.53 MHz, which agrees well with our experimental
observations where the silicon nanoparticle aggregates start to form at the
pulse frequency of 2 MHz. The calculation also shows that graphite has a longer
critical time of 1.11 microseconds,
which is longer than that of silicon’s. If the critical time to nucleation is
the time to make minimum aggregations of the target material, pulse frequency
at which graphite nanoparticles starts to aggregate should be lower than that
of silicon's. Again, the experimental results on graphite target support this
hypothesis and agree with the RZ theory.Pulse
frequency has a significant effect in creating nanofiber aggregates and keeping
them continually forming. For high pulse frequencies, ablation from consecutive
pulses happens before the material on the surface of the target cools down.
Therefore, the material that is ejected by a new pulse can have its ablated
material condense (or bond) with the ablated material from the previous pulse
which is still at a very high temperature. This is a possible explanation for
how the nanoparticle structures are built dense and vertically in Figures3, 4.


## 6. Conclusion

In our research, we measured the
critical times required to form nanoparticle aggregates for graphite and silicon
experimentally. We have elaborated how our experimental measurements for both
materials agreed well with those predicted by RZ theory. Although the RZ theory
has been previously supported experimentally by a few other researchers using
particle sizes and atomic front velocity, and so on, there is no definitive
evidence that gives strong experimental results to support the theory. One of
the most important features of this theory is the ability to predict the
critical time for nucleation. We showed how this important theoretical
parameter (time for nucleation during phase transformation) agreed with
experiment. Therefore, to the best of our knowledge, we have shown that
Raizer-Zeldovich theory has been proven for the first time at it's most fundamental
level in terms of time scale to a phase transition.



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*Source: 590763-2009-02-10.xml*