CW Laser Crystallization of SOI Thermal analysis of the most critical parameters
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CW LASER CRYSTALLIZATION OF SOI Thermal analysis of the most critical parameters
J.M. HODE, J.P. JOLY, P. JEUCH LETI - Commissariat A l'Energie Atomique,
85 X - 38041 GRENOBLE Cedex France
ABSTRACT We present an overview of the thermal modeling of CW laser induced crystallization of SOI. The dynamical case for a three-layer structure is derived. Effects of the phase change (increase in reflectivity, latent heat) are also treated. Analytical expressions are given and the models are compared to experiment.
INTRODUCTION Thermal modeling of CW laser induced heating was pioneered by Lax (1) for heating of bulk material using a stationary beam. Several modifications have already been proposed in order to take account of the non-linearities of the problem and of the SOI structure. These non-linearities are induced by the temperature dependences of different physical parameters such as the thermal conductivity and diffusivity and the surface reflectivity. The variations of the thermal conductivity are incorporated using a change of variable known as the Kirchoff transformation (2). Since the thermal diffusivity of silicon shows little dependence versus temperature (6) beyond 600' C, this transformation can be used even in the dynamic case (for high enough pre-heating, which is the general case). But the strongest nonlinearities are induced by the phase change at the melting point : abrupt increase of the surface reflectivity and latent heat generation. We propose a review of three different models in order to give an overview of the difficult thermal problem involved in the CW laser induced crystallization of thin silicon films deposited on oxidized bulk silicon. The influence of the optical properties will be first treated with a static model and we will then report two dynamic models in order to derive the temperature distributions induced by a scanning CW laser beam and by a straight crystallization front generating latent heat. Each of these models decribes a three-layer structure similar to that of SOI: poly silicon (about.5 )i) deposited on oxidized (about 1 p) bulk silicon.
THE KIRCHOFF TRANSFORMATION Following Carslaw and Jaeger (2), as
a
we define the linear temperature rise
TK(t T= ) dt
(ToJ(Ž)
(TO
is
the pre-heating temperature)
We will show in a further publication that we can approximate 0 by a linear function of T in a wide range (about 500' C with good precision) below the melting point. This leads to 0 - 0M = a (T-T M) where TM is the melting temperature and 0M the corresponding linear temperature rise. For an easy use of this transformation, we give the variations of a and 0M versus To M (fig. 1). The variations of O(T) are also plotted for various values of To.
Mat. Res. Soc.
Symp. Proc. Vol.
23 (1984) OElsevier Science Publishing Co., Inc.
514
Fig I
:
Fi Z
:TRUE
TEMPERRTURE
C C
The Kirchoff transformation
0
20M
5=40 .
502
r32500 250 . PREHERTING ( *C )
500
250 PREHEATING
*C )
EFFECTS OF THE OPTICAL PROPERTIES It has been reported (3) that the formation of lamellae at the
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