Kinetic Modeling of Grain Growth in Polycrystalline Silicon Films Doped with Phosphorus and Boron
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KINETIC MODELING OF GRAIN GROWTH IN POLYCRYSTALLINE SILICON FILMS DOPED WITH PHOSPHORUS AND BORON H.-J. Kim and C.V. Thompson Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 ABSTRACT In previous work it has been shown that doping of silicon with P or As leads to enhanced rates of grain growth while doping with B has little effect, except in compensation of the effect of P or As. Here we report a detailed study of the effects of P doping on normal grain growth in silicon films. We also outline a kinetic model for grain growth which is consistent with the various observed effects of dopants. This model is based on the assumption that dopants primarily affect grain boundary mobilities and that grain boundary motion occurs through parallel diffusive and non-diffusive processes. It is further assumed that the rate of the diffusive process is proportional to the vacancy concentration which is a known function of the electron concentration. INTRODUCTION For an increasing number of applications of polycrystalline silicon films in VLSI technology, the grain structure of the films is an important factor affecting its physical and electrical properties. During post-deposition heat treatments, grain sizes, size distributions, and textures can gradually change due to grain growth. Therefore, control of grain growth is important for obtaining desired grain structures for specific applications. It has been reportedt" that doping with phosphorus or arsenic leads to increases in the rates of grain growth by up to several orders of magnitude when compared with undoped Si. Boron, on the other hand, has little effect. Dopant-induced enhancement of grain growth is thought to stem from increases of the atomic mobility of grain boundaries. 4 Wada and Nishimastul and Mei et. al. 2 have explained the enhancement in terms of an increase in self-diffusion of Si. We have previously reported 4 that P or As enhanced grain growth can be partially or fully compensated through codoping with B, strongly suggesting that grain growth enhancement can be attributed to an increase in the extrinsic free carrier concentration in Si. It is well known that rates of migration of structural defects (e.g., impurity diffusion 5 , self-diffusion 6 , dislocation motion7 , oxidation 8 , and crystallization of amorphous Si 9) are also affected by shifts of the Fermi level. In these cases atomic movement has been associated with defects which have energy levels inside the band gap of Si. In previous experimental work4 we have focussed on the effects of dopants on secondary grain growth in Si films. Here, we report on the effects of P and B on normal grain growth. We also describe a kinetic model for dopant-enhanced grain growth which is based on the role of charged defects and which can be used to explain experimental results for Si films doped with P and B for wide ranges of dopant contents and temperatures. RATES OF NORMAL GRAIN GROWTH The rate of normal grain growth can be described by dr (1) dt--=MAF wh
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