Journal of Crystal Growth 83 (1987) 115—121 115 North-Holland, Amsterdam KINETICS OF PHASE AND MORPHOLOGICAL CHANGES IN THIN FILMS E.I. TOCHITSKY and N.M. CHEKAN Institute of Electronics, Academy of Sciences of the Byelorussian SSR, Minsk, USSR Received 26 May 1986; manuscript received in final form 1 October 1986 The kinetics of phase and morphological transformations in thin films have been theoretically investigated. The finiteness of the film dimension in one direction results in a change of the time dependence of the transformed volume as compared with bulk material. By using the Kolmogorov—Avrami formalism, general expressions have been derived for the phase and morphological changes in films of arbitrary thickness for the cases of nucleation in the film bulk and on the film surfaces. It is shown that there exists a size effect which leads to a nonuniform transformation over the film thickness and to slowing down or speeding up of the transformation with decreasing film thickness, depending on whether nucleation takes place in the film bulk of on the film surfaces. 1. Introduction direction in ref. [8] to analyze bulk crystallization of a film of varying thickness. Experimental results of investigations of relaxa- tion processes taking place in films obtained by pulsed deposition techniques [1,2] during struct- 2. Formulation of the problem ural transformations [3] or solid-state reactions [4] indicate the formation of a fine-grained structure This paper is concerned with the kinetics of in the films. It seems that in passing to a more post-deposition phase and morphological changes equilibrium state, a large number of centres of a occurring in thin film, i.e. material of finite thick- new phase (nuclei) randomly disposed appear and ness 1. For a film of sufficiently small thickness, start to grow. By the term “phase” we mean some boundary effects become important resulting in a state of the film material characterized by a cer- nonuniform deposit change across the film thick- tam set of thermodynamic and structural parame- ness [8]. Therefore, the kinetics of phase and mor- ters. The term “phase” may denote an amorphous phological changes will be described by a distribu- or quasi-amorphous state of deposit, some particu- tion function of the amount of new phase over the lar crystallographic structure, a polycrystalline, film thickness q(x, I), where the axis x is directed textures or monocrystalline state, a supersaturated normal to the substrate, i.e. in the thin film di- solid solution, a film state with excess number of mension. In the general case, the distribution vacancies, a homogenized mixture of chemically function can be written as [8]: reacting materials, etc. The formation of a more equilibrium phase occurs via nucleation and q = 1 — exp~f[—1(T) V(x, T, t)] dT~, (1) growth of randomly distributed nuclei. This allows one to describe the kinetics of phase transforma- where V(x, i-, t) is the volume in which the ap- tions using the methods of Kolmogorov [5] or pearance of nuclei in the time interval T, T + dT Avrami [6]. However, account should be taken of inevitably leads to a point with the coordinate x the finite dimensions of a physical object undergo- getting into the new-phase region by the time t, ing phase and morphological changes [7]. The and 1(t) is the nucleation rate. In the formalism Kolrnogorov—Avrami method has been applied to of Avrami, V( x, T, t) implies “an extended physical objects with a bounded extent in one volume”, i.e. the volume which would be occupied 0022-0248/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)