The crystallization by laser of amorphous or microcrystalline silicon films allows to obtain thin, high-quality, polycrystalline Si films, being a very promising method for diminishing costs in the microelectronic and solar cells sectors. During a laser crystallization process, light is partially absorbed in the amorphous silicon film, heating the sample and, if the temperature rises high enough, causing the reorganization of the film structure into a crys- talline one. In this work we show both experimental results on the crystallization of non-hydrogenated silicon thin-films performed by a continuous wave infrared laser are included, as well as a study of the process with a simple finite elements (FEM) numerical model based in the dimensional non-linear heat transfer equation with a steady heat source

Canteli Pérez Caballero, David

Molpeceres Álvarez, Carlos Luis

Morales Furió, Miguel

Muñoz Martín, David

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

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Finite element method modeling applied to laser 
crystallization of amorphous silicon 
David CANTELI (1), David MUNOZ-MARTIN (1), Miguel MORALES (1), Carlos 
MOLPECERES (1) 
1. Centro Láser, Universidad Politécnica de Madrid, Alan Turing 1, 28031 Madrid, Spain. 
Contact name: David Canteli (david.canteli@upm.es). 
ABSTRACT:  
The crystallization by laser of amorphous or microcrystalline silicon films allows to obtain 
thin, high-quality, polycrystalline Si films, being a very promising method for diminishing 
costs in the microelectronic and solar cells sectors. During a laser crystallization process, 
light is partially absorbed in the amorphous silicon film, heating the sample and, if the 
temperature rises high enough, causing the reorganization of the film structure into a crys-
talline one. 
In this work we show both experimental results on the crystallization of non-hydrogenated 
silicon thin-films performed by a continuous wave infrared laser are included, as well as a 
study of the process with a simple finite elements (FEM) numerical model based in the 
dimensional non-linear heat transfer equation with a steady heat source. 
 Key words: Laser crystallization, polycrystalline silicon, FEM modelling. 
 
1.- Introduction 
Laser crystallization and annealing of amor-
phous silicon (a-Si) to produce high quality 
crystalline-silicon thin films has been a sub-
ject of great interest for applications as thin-
film transistors, sensors, or solar cells. Espe-
cially in the latter field, as thin-film polycrys-
talline silicon solar cells have long been con-
sidered a potential competitor to wafer-based 
silicon devices. Electron-beam and laser crys-
tallization of a-Si are regarded as the most 
promising methods for fabricating thin-film 
polycrystalline silicon solar cells from crystal-
lization of amorphous material. With the aim 
of improving the efficiency and lowering the 
cost of these solar cells, intensive research has 
been done to enhance the quality of laser crys-
tallized silicon films deposited on low-cost 
substrates such as glass. 
A major advantage of laser crystallization and 
annealing over conventional heating methods 
is its ability to induce rapid heating and cool-
ing of thin surface layers. During laser crys-
tallization, laser energy is used to heat the 
amorphous or microcrystalline silicon thin 
film, melting it and changing the microstruc-
ture to crystalline silicon (poly-Si) as it cools. 
Phase change from a-Si to c-Si thus depends 
on the absorbed energy from the incident la-
ser-pulse.  
Different laser sources has previously been 
used in laser crystallization experiments of a-
Si, as pulsed excimer lasers emitting in the 
UV range or pulsed Nd:YAG lasers (532 nm, 
355nm and 1064 nm) [1-4], although the best 
results have been obtained with continuous 
wave (CW) lasers emitting in the IR range [5-
7]. Also, as a way to understand the physics 
underlying the process, it usual to found 
works about crystallization modelling [8, 9]. 
In this work we show the results of experi-
ments with a CW infrared laser source, as well 
as a thermal study by FEM modelling of the 
laser crystallization. 
2.- Crystallization experiments 
The samples used consisted of Borofloat 33 
glass substrates with a buffer layer of about 
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200 nm and 10 microns of hydrogenated 
amorphous silicon (a-Si:H) deposited by 
PECVD. The samples are thermally annealed 
previous to the laser treatment to effuse the 
hydrogen from the a-Si:H. During the laser 
crystallization process the samples are heated 
up to 700ºC with a heater plate to prevent 
cracks due to thermal stress in the substrate. A 
continuous wave (CW) laser emitting at 980 
nm has been used in the experiments. The la-
ser have a cylindrical lens, leading to a line 
spot of  2,16 cm (Gaussian) × 19,6 cm (Top 
hat), allowing the crystallization of large ar-
eas. Laser beam is scanned along the sample 
at a constant speed. The samples were mor-
phologically characterized by optical and 
electronic microscopies, and its internal struc-
ture was studied by Raman and XRD spec-
troscopy. 
2.1.- Crystallization results 
A parametrization of the silicon laser crystal-
lization was performed for process velocities 
ranging from 0 to 25 mm/s. Fig 1 show the pa-
rameter window obtained for different veloci-
ties and laser light intensities.  
 
Fig 1: Parameter window for the silicon laser 
crystallization process. 
For too low intensities (show as blue dots in 
the figure) the film surface do not show any 
change. As the laser intensity increases, small 
areas appear in the sample surface, corre-
sponding to a partial melting and a subsequent 
solidification of the silicon. That is the begin-
ning of the liquid phase crystallization process 
(see Fig 2). For slightly higher intensities the 
sample crystallizes completely in crystal 
grains of great area (up to mm2). Finally, too 
high intensities (green dots in Fig 1) led to the 
dewetting of the silicon film (i.e. the separa-
tion of the Si film from the glass substrate). 
 
Fig 2: Onset of the silicon melting (left) and 
crystallized samples (right) obtained for dif-
ferent process parameters. 
3.- Finite elements method (FEM) 
modelling 
To have a better understanding of the crystal-
lization process we used a finite elements 
method (FEM) model. Using COMSOL Mul-
tiphysics Software we developed a 2D station-
ary model based in the non-linear heat transfer 
equation, taking the laser as a Gaussian heat 
source, and including the phase change for sil-
icon at 1687 K (show as a red line in Fig 3).  
We selected some of the parameters used in 
the experiments and calculate the temperature 
distribution for a stationary process in the 
whole system (silicon film + glass substrate). 
Fig 3 show the model results using a maxi-
mum optical intensity of 2700 W/cm2 and a 
process velocity of 8.3 mm/s. As can be seen 
in the temperature profile, as the laser reaches 
a sample point the temperature of that point 
rise quickly, being slightly over the melting 
temperature for about half a second, and cool-
ing afterwards. 
 
Fig 3: Temperature in the sample (top) and at 
a point versus time (bottom) obtained from the 
FEM model for a maximum optical intensity of 
2700 W/cm2 and a process velocity of 8.3 mm/s 
10ª Reunión Española de Optoelectrónica, OPTOEL17 
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The obtained temperatures are consistent with 
the experimental results. From the calcula-
tions we concluded that the irradiation time 
(i.e. the process speed) is identified as a key 
variable in the crystallization process. In addi-
tion, the model can predict the start of the liq-
uid phase crystallization process with diode 
laser, and can be used to study the thermal 
conditions for the onset of the dewetting of the 
silicon. 
4.- Conclusions 
In this work we present a study of the influ-
ence of irradiating time and laser power in la-
ser crystallization of amorphous silicon thin 
films, using continuous wave IR laser source 
emitting at 980 nm. Different results are show 
for different process parameters, but laser-an-
nealed films with high crystalline quality 
(grains of several mm wide) have been ob-
tained.  
A simple thermal finite element model (FEM) 
has been developed in COMSOL Multiphys-
ics to simulate the process by solving numeri-
cally the two dimensional non-linear heat 
transfer equation with a steady heat source. 
The local temperature evolution in the irradi-
ated area given by the FEM model show good 
agreement with the experiment results. The 
numerical model developed helps to under-
stand the physics underlying and determine 
the process parameters in which crystalline 
silicon is obtained without damage or ablation 
of the silicon surface. 
Acknowledgements: This work has been sup-
ported by the Spanish Ministry of Economy 
and Competitiveness under projects HELLO 
(ENE2013-48629-C4-3-R) and CHENOC 
(ENE2016-78933-C4-4-R). We also want to 
acknowledge Prof. Stephan Gall and Prof. 
Ono Gabriel from the HZB for their help. 
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Finite element method modeling applied to laser crystallization of amorphous silicon

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Finite element method modeling applied to laser crystallization of amorphous silicon

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