Study of fractality nature in VO2 films and its influence on metal-insulator phase transition

The mechanisms underlying the origin of fractal shape of inclusions of a new phase in VO2 films during metal-insulator phase transition are discussed. The obtained results show that hysteresis of the temperature dependence of resistance R(T) significantly depends on the film morphology and texture. Moreover, some fractal features are observed. To determine the fractal dimension D of the structural elements of the studied films from their images, different fractal analysis approaches were preliminary compared and discussed. As a result of the film image treatments, the boundaries of the structural elements were found to have fractal dimensions of 1.3 to 1.5 or higher and to correlate with the shape of R(T). The fractal boundaries indicate the dominant role of elastic stress on the phase transition of films, which is confirmed by numerical modeling. Based on these results, an analytical model is proposed that relates the free energy of a film to the fractal dimension of its constituents. Depending on the ratio of the elastic and interface specific energies, the position of the free energy minimum F corresponds to a certain fractal dimensionality D. A small interface energy leads to a higher fractal dimension making the initial phase more stable. This conclusion explains well all the effects observed experimentally in VO2. The obtained results provide a better understanding of the influence of structure and morphology on other properties of the studied films.