*3.4. Conductance Type Extraction*

The conduction type was investigated by I–V measurements by linearization with typical mechanisms. In Figure 4a, the I–V measurements are plotted according to space-charge-limited current (SCLC) theory, which predicts I∼V<sup>2</sup> in a log–log plot. A fit is given, which shows a perfect fit over almost two voltage magnitudes. In Figure 4b the I–V curve is linearized according to Shottky thermioninc emission (STE). A good fit can be seen in a medium voltage range, but both for a small and large voltage significant deviations are visible. Similarly, in the case of Poole–Frenkel (PF) linearization given in Figure 4c, we obtain a reasonable fit for medium voltages, but discrepancies for very low and high voltages. Yet, it would be not sufficient to formally exclude these two transport mechanisms. Likewise, the linearization with Fowler–Nordheim (FN) tunneling does not give a decent fit. In the LRS we obtain a flat line. Hence, the first three transport mechanisms still have to be considered. Thus, we used the abrupt junction approximation, which assumes a pn-junction with an abrupt doping profile [31] Even though the main advantage of this method is to understand impedance upon a DC bias, it is still helpful to analyze the plain DC I–V curves as dlog(I)/dV is independent on most parameters, especially the contact area; it is, hence, more robust, especially upon temperature changes, and it is possible to differentiate between FN and PF. Hence, in Figure 4d, the I–V curves in a temperature range T between 300 K and 340 K are given. Only SCLC and PF [both dlog(I)/dV <sup>∼</sup> <sup>V</sup><sup>−</sup>1] can describe such a curve, whereas STE [dlog(I)/dV <sup>∼</sup> V−3/4] cannot describe this behavior. Yet, in the case of PF, a very strong component <sup>∝</sup> <sup>V</sup>−1/<sup>2</sup> should also be present, which cannot be seen in the measurements. The I–V SCLC curve fit is almost perfect over two orders of magnitude and, thus, significantly better than those of PF and STE.

**Figure 4.** Conductance type analysis on CDWs in LNO (**a**) SCLC I–V plot; (**b**) STE I–V plot; (**c**) PF I–V plot; (**d**) derivative plot. The I–V curves show the first cycle and the stationary cycles after 20 cycles. The off-state was obtained by applying V <sup>=</sup> <sup>−</sup>210 V until the current is reduced to 10−<sup>8</sup> A.

So far, we have solely discussed electronic transport. Yet, especially, resistive switching is generally an interplay of both ionic and electronic current contributions. Hence, it is necessary to further rule out scenarios of mixed electronic–ionic conduction. We use the Nernst–Ernstein equation to analyze whether ionic conduction is a significant contribution, which is given by Δ = τeDE/kT, with τ the diffusion time and D the diffusion constant. Using a conservative value of D <sup>∼</sup> 10−<sup>18</sup> m2/s, which is derived from experimental values of lithium transport in LixSi [32], the estimated ionic movement over 100 ms is about <sup>∼</sup>0.8 nm at a field of 2 <sup>×</sup> 107 <sup>V</sup>/m and room temperature T <sup>=</sup> 300 K, which is about three orders of magnitude smaller than the film thickness. Reported values for the ionic transport diffusion constants in LNO (e.g., Li, H, D, Na, Mg) at elevated temperatures and interpolated to room temperature are significantly smaller. Hence, we can exclude ionic current having a major share.

The conduction in DWs, thus, follows the Mott–Gurney equation (Child's law) [33]: I(T) = Aeff 9εμ(T)V2/8d3 with Aeff the effective contact area, d the thickness of the dielectric film, ε the static permittivity, and μ(T) the mobility of the major charge carrier. Using the current extracted from cAFM measurements, we can derive a mobility of about 5 <sup>±</sup> 3 <sup>×</sup> 10−<sup>2</sup> cm2/Vs, which is in good agreement with previously reported macroscopic photo-induced current measurements [34]. The temperature dependence in an SCLC transport regime is solely determined by the temperature dependence of the mobility of the major charge carrier.
