**4. Discussion and Conclusions**

In this study, we reported the domain wall conductance by inclined domain walls in LNO thin films, which could be applied as a new multi-level non-volatile memory cell based on out-of-plane ferroelectric switching, by the precise tuning of the inclination and thus the conductance state. We investigated further the temperature dependence as well as the temporal dependence on erase voltage application and concluded that the main contribution to the current is space-charge-limited.

We obtained evidence the current to be dominated by a polaron gas formation at such inclined domain wall and confined by the band bending from the temperature dependence of the conductance. Upon local inversion, generally, charge carrier injection is discussed, even though it has been speculative for a long time. Assuming such charge carriers are injected at the DW, which are needed to compensate the inclined DW of the spike-domain-like nucleus, free charge carriers—electrons—are generated, which will condensate into similarly charged and, hence, screening electron polaronic, states inside the single crystal material. Such a transition has been observed in bulk material, e.g., by optical time-resolved spectroscopy, to happen within 200 fs [37]. Yet, at a CDW these values can be significantly larger due to the smaller energy gap between conductance band and Fermi energy. However, as the band-bending is not large enough to create a 2DEG, which would be apparent with much higher mobility conductivity, we assume a 2D polaron gas (2DPG) is obtained. Bound polarons will very

rapidly be trapped by iron impurities. Upon pure-diffusion transport, thus without an external electric field, the average mean free path of the bound polaron until trapping with FeLi is < tNbLi4<sup>+</sup> ≥ 100 Å and for the free polaron is < tNbNb4<sup>+</sup> ≥ 80 Å. These values were derived by interpolation from the data of Mhaouech and Guilbert [35] under consideration of the smaller iron impurity concentration cFe = 1017 cm−<sup>3</sup> and a niobium antisite defect concentration of cNbLi = 10<sup>21</sup> cm<sup>−</sup>3. Upon drift condition, these values can be larger. Hence, the bound polaron has a larger mean free path. However, the hopping rate of bound polarons is only wNbLi4<sup>+</sup> = 10<sup>7</sup> s−1. Assuming the hopping rate to depend mainly on the nearest neighbor distance, like w~er[Å], we can calculate, that the hopping rate of free polarons is two orders of magnitude larger, hence wNbLi4<sup>+</sup> = 109 s<sup>−</sup>1. Thus, the electric current with free polaron transport as in Mg:LNO can be significantly larger. This again explains why, for the case of bulk material only, congruent Mg:LNO revealed a conductance upon UV illumination. For the ultrathin LNO films in use in this study, even undoped material can give measureable conductance.

The model explains why an asymmetric electrode condition can result in the efficient switching between an HRS and LRS. Upon the negative pulse application, the carrier density reduces, which destabilizes the inclined domain wall formation and finally reduces the conductance of the wall further. However, this process requires relatively high electric fields and times due to the low mobility of the charge carriers. Hence, the study suggests that Mg:LNO and thinner films can significantly improve the performance of the tunable non-volatile memory.

The thin-film lithium niobate resistive switching effect based on charged ferroelectric domain walls formation and erasure offers interesting advantages over conventional filament-based resistive switching, which can be interesting for neuromorphic computing applications.

**Author Contributions:** Investigation, T.K., B.W.; resources, A.H., L.M.E.; writing—review and editing, T.K.; supervision, L.-Q.C., L.M.E. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Cluster of Excellence "Center of Advancing Electronics Dresden" and the DFG Research Grant HA 6982/1-1. We also acknowledge open access funding support by the publication fund of TU Dresden.

**Acknowledgments:** The authors would like to acknowledge the support of NanoLN for the provision of the lithium niobate thin film samples, H. Hui (Shandong University) for helpful discussions, and S. Johnston as well as Z.X. Shen (Stanford) for measurement support. B.W. acknowledges the support by the NSF-MRSEC grant number DMR-1420620. The effort of L.-Q.C. is supported by National Science Foundation (NSF) through Grant No. DMR-1744213.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**


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