602 × 10−19 C), n is the number of electrons captured, C is the
capacitance of the MIM capacitor, is the dielectric permittivity of the GeO2 film (approximately 6 ), is the thickness of the GeO x film (approximately 20 nm), and Ф is the capture cross-sectional area or the effective area of the conducting paths (nanofilament). ΔV is the voltage shift for capturing one electron and is approximately 1 V for the gate oxide (SiO2) with a thickness of 4.5 nm . However, the voltage shifts are 18 to 23.5 V, so the total number of electrons captured in the GeO x film after SBD is 18 to 23. The cross-sectional area of the cylindrical conducting filament in the GeO x film can be expressed as follows: (4) where D is the diameter of the nanofilament or NW. Considering Equations 2, 3, and 4, the diameter of the nanofilament is as follows: (5) and is found to be 37 to 42 nm under an operating PRI-724 mw mTOR inhibitor cancer current of 100 μA. The diameter can be reduced by decreasing the CC, particularly in the MOS structure (CC < 20 μA). In the case of CBRAM devices, many researchers
have reported filament diameters using different materials as well as structures [17, 48–50]. Rosezin et al.  reported a filament diameter of approximately 13.5 nm at a CC of 100 μA. Liu et al. [17, 49] reported a filament diameter of 20 nm with a CC of 1 mA. Yang et al.  reported a diameter of 20 nm at a low CC MycoClean Mycoplasma Removal Kit of 10 nA. However, the diameter investigated in this study is different from the reported values, which may be related to the different structure and materials. It is expected that this new method to calculate the diameter of defect paths in oxide-based resistive switching memory devices will be useful in the future. Figure 10 Evolution of voltage shift under constant current stress on the MIM structure. The voltage shift is caused by the filament or NW screening assay formation in the GeO x film. Conclusions Core-shell Ge/GeO x NWs were prepared by the VLS technique on Au NP-coated
Si substrate. Germanium-oxygen and oxygen vacancies, observed by XPS and broad PL spectra at 10 to 300 K, resulted in good resistive switching memory characteristics of the Ge/GeO x NWs in a MOS structure with a low self-compliance of <20 μA. Real-time observation of oxygen ion migration through a porous TE in an IrO x /GeO x /W structure and evolution of O2 gas during filament formation provided evidence for the resistive switching mechanism. Enhanced memory characteristics such as low-voltage operation (<4 V), low RESET current (approximately 22 μA), large resistance ratio (>103), pulse read endurance of >105 cycles, and data retention of >104 s were obtained for PMA devices because of its volatized nature and the ready formation of oxygen vacancies in the GeO x film. Furthermore, a nanofilament diameter of approximately 40 nm in the RRAM device was calculated using a new method.