The switching characteristics of As$_{10}$ Ge$_{15}$ Te$_{75}$ thin film were investigated under d.c. bias. And the frequency dependence of the conductivity was analysed with regard to the temperature dependence, in order to find the physical properties of the As$_{10}$ Ge$_{15}$ Te$_{75}$ thin film ; a characteristic relaxation time (.tau.$_{0}$ ), the spatial density of defect states (N), and the localized wavefunction (.alpha.$^{-1}$ ). It was formed that the threshold voltage depends on thickness, electrode distance, annealing time and temperature, respectively. The threshold voltage is increased as the thickness and the electrode distance is increased, while the threshold voltage is decreased in proportion to the increased annealing time and temperature.