A Model for CW Laser Recrystallization including Reflectivity Effects
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A MODEL FOR CW LASER RECRYSTALLIZATION INCLUDING REFLECTIVITY EFFECTS
I.D. CALDER Northern Telecom Electronics Ltd., P.O. Box 3511, Station C, Ottawa, Canada, KIY 4H7
ABSTRACT
A simple, practical model is developed for cw laser recrystallization of silicon and SO1 structures, taking into account spatial variations in The power absorption is assumed to be uniform within optical reflectivity. each of three regions: the central molten spot, the annular two-phase region, and an outer annulus to account for absorption in the solid phase. Analytic expressions are obtained for the radial and depth dependence of the temperature, for the melt depth, the melt radius, the melt threshold, the SOI structures crystallization threshold and the substrate melt threshold. are considered and comparison with some experimental results shows excellent agreement. INTRODUCTION
Many studies have been carried out on applications of cw laser annealing (LA) to semiconductor processing [1,2] and device fabrication [3,41. However, integration of this technique into a complete IC process requires quantitative modelling of the thermal cycle resulting from LA, and the Substantial work has been consequent effects on material properties. carried out on the modelling of the temperature distribution achieved during cw LA, beginning with a basic model [5,61 and later including the effects of high scanning speeds [7-9j, multilayer structures [10-12] and melting of the silicon [12,13]. If proper consideration is given to the problem of melting and recrystallization [12,131, the calculations become quite complex and time-consuming because of the variation in optical reflectivity from liquid, The objective of this work solid, and co-existing liquid and solid regions. is to develop a practical model for cw laser melting that yields simple analytic results and that can be an effective tool for materials research and process monitoring.
FORMULATION OF THE PROBLEM
We wish to model the temperature distribution due to a normally incident, circularly symmetric laser beam as illustrated in Figure I (a), where a 2 2 This heat flow gaussian distribution exp(-r /w ) is assumed. problem is nonlinear because the thermal conductivity is a function of temperature, and because the absorbed power distribution is a function of the surface temperature distribution. This situation occurs because the optical reflectivity is a function of melt depth, up to -30 nm, so that there is a rdgime in which the surface temperature is fixed at the melting point over a wide range of incident power densities [21. Initially, we treat the case of a stationary, circularly symmetric beam which is absorbed at the surface of a silicon sample, possibly through a A dielectric cap (which is assumed to only affect the reflectivity). linearized temperature O(T) is defined [6] and the thermal conductivity Mat.
Res.
Soc. Symp. Proc. Vol.
23 (1984)QElsevier Science Publishing Co.,
Inc.
508
of silicon is
assumed to be KMT)
= B/T for T < TM (the melting point)
and K = KL for T > TM.
The p
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