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New physical approaches make fast-response non-volatile resistive memory (ReRAM) very attractive for digital, neuromorphic, and other data processing systems considered in many previous publications. Even though the effect of resistance and memory switching in metal-dielectric-metal structures is well known, the physical mechanisms underlying these phenomena are still vague. Considerable instability and insufficient reproducibility of electrical characteristics are the major factors that hold back the practical use of memristors. This problem can be solved by combining the theory of filaments and physics of amorphous wide-bandgap semiconductors which make up the majority of active memristor media currently being investigated. The properties of amorphous and crystalline nanostructures are radically different. Being rather specific, the characteristics of amorphous nanostructures are much dependent on the manufacturing technique. The methods of controlling the amorphous state and its stability are the subject of this paper. The conventional technique of electron-beam induced deposition is used to make the samples. Well-studied TiO2 is taken as a base material for active memristor media. The amorphous state of resultant coats is modified by varying the deposition temperature at an unvaried deposition rate, a residual vacuum-chamber pressure, and coat thicknesses. Sensitive surface plasmon resonance method, spectral technique, and total-external-reflection X-ray diffractometry are the tools to control the stability of the coats. In the experiment, we have observed the long and distinct relaxation of the optical parameters of amorphous layers and the manifestation of the development of an inhomogeneous amorphous layer.