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The conducting filament forming voltage of stoichiometric hafnium oxide based resistive switching layers increases linearly with layer thickness. Using strongly reduced oxygen deficient hafnium oxide thin films grown on polycrystalline TiN/Si(001) substrates, the thickness dependence of the forming voltage is strongly suppressed. Instead, an almost constant forming voltage of about 3 V is observed up to 200 nm layer thickness. This effect suggests that filament formation and switching occurs for all samples in an oxidized HfO2 surface layer of a few nanometer thickness while the highly oxygen deficient thin film itself merely serves as a oxygen vacancy reservoir.
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Sharath et al. (2014) studied this question.
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