Journal of Crystallization Process and Technology, 2012, 2, 12-15
http://dx.doi.org/10.4236/jcpt.2012.21002 Published Online January 2012 (http://www.SciRP.org/journal/jcpt)
Analysis of μ-Czochralski Technique
Using Two-Dimensional Crystallization Simulator
Kuniaki Matsuki1, Ryusuke Saito1, Shuji Tsukamoto1, Mutsumi Kimura1,2, Ryoichi Ishihara3
1Department of Electronics and Informatics, Ryukoku University, Otsu, Japan; 2Joint Research Center for Science and Technology,
Ryukoku University, Otsu, Japan; 3Delft Institute of Microelectronics and Submicrontechnology, Delft University of Technology,
Delft, Netherlands.
Received December 4th, 2011; revised January 5th, 2012; accepted January 16th, 2012
ABSTRACT
-Czochralski technique has been analyzed using two-dimensional crystallization simulator. It is observed that the
temperature is relatively uniform in the entire Si region after the laser irradiation because the heat conductivity of the Si
region is much higher than that of the underneath SiO2. Grain growth advances from the grain filter to the channel re-
gion and continues until it collides with what advances from random nucleation in the channel region. When the initial
temperature is high, the random nucleation rarely occurs even under the supercooling condition, and the grain size be-
comes large. Moreover, it is qualitatively reproduced that the grain size increases as the irradiated energy of the laser
irradiation increases.
Keywords: -Czochralski Technique; Two Dimensional Crystallization Simulator; Grain Growth; Grain Filter;
Grain Size
1. Introduction
-Czochralski technique is a crystallization technique to
enlarge poly-Si grains in thin-film transistors (TFTs) not
only for flat panel displays and but also for general elec-
tronics [1,2]. In the -Czochralski technique, grain filters
are bored in underneath SiO2 films, amorphous-Si films
are deposited and filled into the grain filters, excimer laser
are irradiated to the amorphous-Si films, and grain growth
advances from the grain filter and to the channel regions.
Although the -Czochralski technique has been experi-
mentally analyzed in detail [3-6], the crystallization pro-
cess should be theoretically clarified.
Recently, a two-dimensional (2-D) crystallization simu-
lator has been developed and proposed as a practical eva-
luation tool for poly-Si TFTs [7]. In the 2-D crystallization
simulator, random nucleation, crystal growth velocity, la-
tent heat emission, and partial crystallization are modeled.
In this paper, we analyze the -Czochralski technique
using the 2-D crystallization simulator. We evaluate the
temperature, grain growth, nucleation, etc. We try to repro-
duce the dependence of the grain size on the irradiated
energy of the laser irradiation.
2. 2-D Crystallization Simulator
The 2-D crystallization simulator is minutely explained
in a previous paper [7]. Roughly speaking, the nucleation
rate is defined as a function of temperature following a
classical nucleation theory, and the crystal growth veloc-
ity is also defined as a function of temperature following
a classical crystal growth theory. The partial crystalliza-
tion model is used allowing the co-existence of the liquid
and crystal phases even in a finite element. The simulation
algorithm is composed of the phase transition and heat
transfer algorithms. The thermal properties of Si and SiO2
are listed in the previous paper.
The grain filters are located in underneath SiO2 films,
and grain seeds are put at the bottoms of the grain filters.
The depth and diameter of the grain filters are 250 nm and
50 nm. The grain seeds consist of fine grains formed dur-
ing explosive crystallization at the beginning of the laser
irradiation [3]. The channel regions are melt to the liquid-
Si, and initial temperature of the liquid-Si is varied. The
thickness of the channel regions is 250 nm. The nuclea-
tion, grain growth, and temperature are successively cal-
culated with the time after the laser irradiation. The cal-
culation area is more than 2.5 m. It should be noted that
the initial temperature is set instead of giving the irradi-
ated energy of the laser irradiation. The initial tempera-
ture is not the temperature at the laser irradiation, but the
temperature at the start of the crystallization simulation.
3. Simulation Results
The distribution of the temperature in the grain filter,

Analysis of μ-Czochralski Technique Using Two-Dimensional Crystallization Simulator 13
channel region, and underneath SiO2 is shown in Figure
1. Here, the initial temperature is 1800 K, and the time after
the laser irradiation is 80 ns. It is observed that the tem-
perature is relatively uniform in the entire Si region. This
is because the heat conductivity of the Si region, 0.25
WK–1·cm–1, is much higher than that of the underneath
SiO2, 0.014 WK–1·cm–1. As seen in Figure 1, the tempera-
ture at the top of the grain filter is slightly high owing to
the latent heat released during the grain growth from the
grain filter. Moreover, the temperature at the right side in
the calculation area is also slightly high owing to the latent
heat released during the grain growth from the random
nucleation, as seen in Figure 2(b).
The advance of the grain growth in the -Czochralski
process is shown in Figure 2. Here, the initial temperature
is 1800 K, and the time after the laser irradiation is 40 -
200 ns. It is observed that the grain growth advances from
the grain filter to the channel region. The random nuclea-
tion occurs, as seen in Figures 2(b) and (c), and the grain
growth continues until it collides with what advances from
random nucleation in the channel region, as seen in Fig-
ures 2(c) and (d). As a result, the center grain from the
grain filter is surrounded by the many grains from random
nucleation, as seen in Figure 2(d).
Figure 1. Distribution of the temperature in the grain filter, channel region, and underneath SiO2.
Figure 2. Advance of the grain growth in the -Czochralski process.

Analysis of μ-Czochralski Technique Using Two-Dimensional Crystallization Simulator
14
The dependence of the grain growth on the initial tem-
perature is shown in Figure 3. Here, the initial tempera-
ture is varied from 1700 K to 2200 K. The grain size is
small for the initial temperatures of 1700 K and 1800 K,
as seen in Figures 3(a) and (b). This is because the ran-
dom nucleation occurs in the channel region during the
grain growth from the grain filter. On the other hand, the
grain size increases for the initial temperature more than
1900 K as the initial temperature increases, as seen in Fi-
gures 3(c)-(e). This is because the grain growth advances
from the grain filter while the temperature in the channel
region is high and the Si stays liquid-Si. Since the nuclea-
tion rate is small considering that the time scales of the
laser irradiation and following cooling process are short,
the random nucleation rarely occurs even under the su-
percooling condition, and the grain size becomes large.
The dependence of the grain size on the initial tempe-
rature is shown in Figure 4. Here, the initial temperature
is varied from 1700 K to 2400 K. It is qualitatively repro-
duced that the grain size increases as the initial tempera-
ture increases, which corresponds to the irradiated energy
of the laser irradiation. This result is consistent with ex-
perimental results [8].
4. Conclusions
-Czochralski technique has been analyzed using 2-D cry-
stallization simulator. It was observed that the tempera-
ture is relatively uniform in the entire liquid-Si after the
laser irradiation because the heat conductivity of the Si
region is much higher than that of the underneath SiO2.
Grain growth advances from the grain filter to the channel
region and continues until it collides with what advances
from random nucleation in the channel region. When the
initial temperature is high, the random nucleation rarely
occurs even under the supercooling condition, and the grain
size becomes large. Moreover, it was qualitatively repro-
duced that the grain size increases as the irradiated energy
of the laser irradiation increases.
It is obvious that the lateral grain growth such as -Czo-
chralski technique cannot be reproduced using one-dimen-
sional crystallization simulator, whereas it is expected that
Figure 3. Dependence of the grain growth on the initial temperature.

Analysis of μ-Czochralski Technique Using Two-Dimensional Crystallization Simulator 15
Figure 4. Dependence of the grain size on the initial tempe-
rature.
it can be reproduced using three-dimensional simulator,
which consumes terribly long computation time. It is mean-
ingful that the lateral grain growth can be at least qualita-
tively reproduced using two-dimensional crystallization,
which consumes acceptable computation time, although a
certain cross section is only considered.
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