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The resistive switching of an Ovonic threshold switch (OTS) material is characterized by Poole-Frenkel (PF) conduction and atomic rearrangement originating from chalcogen defects; thus, most OTS materials contain Se and/or Te. In addition to these chalcogen elements, As is included to form rigid amorphous networks. However, since As and Se are toxic, the development of As- and Se-free OTS materials is strongly desired. To realize As-free OTS materials that exhibit a comparable or even superior performance, a new strategy for material development should be established. In this study, we aimed to add Te to a HfO2 insulator to convert the electric conduction mechanism to PF conduction for realizing a selector function. The optical and electrical characteristics of Hf–O–Te ternary amorphous films with various Te contents were investigated. By changing the Te content, the optical bandgap was found to be tuned in the range of 0.46–5 eV, concomitantly with the modification of electrical properties. The electrical characteristics of the films demonstrated a strong compositional dependence, and Hf0.24O0.55Te0.21 was found to exhibit PF conduction, resulting in a selector function with a selectivity of approximately two orders of magnitude. These results indicate that the inclusion of a heavy chalcogen, such as Te, is effective in altering the conduction mechanism of transition-metal oxides and realizing a selector function.