It is demonstrated that the formation of logarithmic-normal crystallite size distributions during crystallization of amorphous thin films can be a consequence of the dynamics of random nucleation and growth without the involvement of coarsening. Our analytical result is supported by experimentally observed crystallite size distributions during the crystallization of amorphous Si thin films obtained from transmission electron microscopy. [S0031-9007(97)05141-7] The phase transformation from the amorphous and liquid to the crystalline state, leading to the formation of polycrystalline materials, is of fundamental scientific and technological importance. As an example, the transition from an amorphous to a polycrystalline semiconducting film upon annealing is essential for processing electronic materials, such as thin film transistors [1,2] and solar energy converters [3]. Other examples are the formation of polycrystalline bulk Si material solidified via supercooling of a Si melt [4] or the deposition of polycrystalline Si films from the vapor phase [5]. All of these processes establish nonmonotonic crystallite size distributions that can be well approximated by a logarithmic-normal (log-normal) distribution [4]. The size distribution within a polycrystalline semiconductor material can have a significant impact on device performance. This is especially true for minority carrier devices with highly recombination-active grain boundaries [6].A fundamental understanding of the transition from an amorphous phase to the crystalline state is still far from complete. Previous studies concerned themselves merely with the understanding of the earliest stages of nucleation and growth. In this case, the amorphous phase can be treated to be infinite; size distributions thus monotonically decrease with grain size [7]. The depletion of the amorphous phase, however, significantly influences the dynamics of nucleation and growth and determines the subsequent development of the size distribution.In this Letter, we describe the time evolution of the cluster size distribution beyond the early stages of nucleation and growth. We demonstrate that the interplay between the dynamics of nucleation and growth results in a transition from monotonic size distributions in the early stages to nonmonotonic size distributions as a function of the grain radius r in the later stages similar to the log-normal distribution L͑ln r͒~exp͓2͑ln r 2 m͒ 2 ͞2s 2 ͔, where m and s represent the median and width of the distribution, respectively [8]. Our results thus reveal an alternative origin for the development of lognormal size distributions. This recognition is essential, since the formation of log-normal size distributions have generally been attributed to the coarsening process [9,10]. The physical concept described here has recently been proposed by the authors on an intuitive basis [11], and is here analytically established for the first time.The dynamic evolution of the crystallite size distribution in the early stages of random nucleation and gro...