Transient kinetics of nucleation and crystallization: Part I. Nucleation
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Analytical results obtained for the transient kinetics of nucleation enable one to interpret N(gd,t), the accumulated number concentration of clusters at the instrumentally detectable size, gd. The new results enable one to extract kinetic and thermodynamic parameters of nucleation from experimentally measured cluster concentrations and to test nucleation theories experimentally. An approach to estimate the mean time to form the first nucleated cluster in a given sample is also presented.
I. INTRODUCTION When an amorphous material is heated to a certain temperature, atoms may rearrange themselves to form small crystalline clusters. The phase transformation from amorphous (a-) to crystalline (c-) phases is generally considered to be initiated by a nucleation process, and the Gibbs free energy change for this nucleation process is determined by the gain in volume free energy for atoms in the crystalline phase relative to the amorphous phase and by the cost of the free energy necessary to form an interface between the crystalline cluster and the amorphous matrix.1'2 Phase transformations from a- to c-phases or vice versa have various technological applications, one of which is processing of a - S i films or layers to obtain high quality SOI (Silicon on Insulator) structures. To obtain high quality SOI, lateral solid-phase epitaxial (LSPE) growth of a - S i films deposited on Si substrates with SiO 2 patterns has been extensively investigated as a promising technique.3 Random nucleation in the a-Si, however, can compete with LSPE so that the growth of a single crystal over SiO2 is currently limited to length scales smaller than about 10 fim.3 A similar problem arises in enlarging grain sizes of a polycrystalline film from an a - S i film by thermal annealing.4'5 The effective time lag for nucleation is often taken as the maximum length of a period of annealing during which random nucleation and thus random crystallization is supposed not to occur.4 The technological importance of transient nucleation has stimulated extensive experimental studies of nucleation and crystallization of a-Si. 4 " 6 The fundamental parameters characterizing nucleation and crystallization have to be extracted from experimental data based on theoretical formulations for the transient kinetics. The time required to form a specified crystallized volume fraction is the measure of the stability of an amorphous phase7 and has to be evaluated based on theoretical expressions for the transient rate of nucleation and timeJ. Mater. Res., Vol. 6, No. 10, Oct 1991
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dependent crystallized volume fraction. In view of its importance, it is surprising to find that little theoretical analysis of transient kinetics of nucleation has been performed8"14 in the past two decades. The present work presents new theoretical results for the transient kinetics of nucleation and time-dependent crystallized volume fraction. II. TRANSIENT KINETICS OF NUCLEATION IN THE CRITICAL REGION Results presented below and in P
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