Hysteresis loop construction for the metal-semiconductor phase transition in vanadium dioxide films

Thermal hysteresis of the reflectivity of vanadium dioxide films observed upon the metal-semiconductor phase transition is studied. The major hysteresis loop is assumed to form when the phase equilibrium temperature in film grains and the grain size vary and correlate with each other. Within the suggested concept of hysteresis loop formation, it is demonstrated that the major loop may be asymmetric, i.e., broadened (shifted) toward lower temperatures. Unlike hysteresis branches for VO₂ bulk single crystal, those for VO₂ films are extended along the temperature axis and may exhibit a step if the grain size distribution has several maxima. The validity of the concept is verified experimentally. It is also shown that atomic force microscopy (AFM) data for the grain size distribution can serve to determine the distribution parameters from the phase equilibrium temperatures without constructing a complete set of minor hysteresis loops, as was required before.