Electronic Conduction in Ti/Poly-TiO2/Ti Structures

Recent intensive investigations on metal/metal oxide/metal structures have targeted nanometric single grain oxides at high electric fields. Similar research on thicker polycrystalline oxide layers can bridge the results to the prior literature on varistors and may uncover novel ionic/electronic features originating from the conduction mechanisms involving grain boundaries. Here, we investigate electronic conduction in Ti/poly-TiO2−x/Ti structures with different oxygen vacancy distributions and describe the observed features based on the motion and rearrangement of the ionized oxygen vacancies (IOVs) on the grain facets rather than the grain interiors. Containing no interface energy barrier, Ti/poly-TiO2/Ti devices demonstrate high resistance ohmic conduction at biasing fields below 5 × 106 V.m−1; higher fields drive the samples to a distinctly nonlinear and hysteretic low resistance status. The observed threshold is two orders of magnitude smaller than the typical resistance switching fields reported for the nanosized single grain memristors. This is consistent with the smaller activation energies reported for the IOV motion on the rutile facets than its interior. The presented model describes the observed dependence of the threshold field on the relative humidity of the surrounding air based on the lower activation energies reported for the hydroxyl-assisted IOV motion on the rutile facets.


Crystal structure of the grown TiO2 layers
The XRD pattern obtained from the titanium substrate after oxidation at in air is given in Fig. S1. The pattern demonstrates peaks related to the metal substrate and the rutile layer grown; no other TiOx phase is detect. A comparison of counts recorded for different peaks clarifies that the polycrystalline rutile layer mainly consists of {110}faceted crystallites. Figure S1. The XRD pattern of the thermally grown TiO2 on a Ti substrate at 650 ; the patter exhibits rutile and titanium peaks only.

Conduction monitoring during the filament formation and dissolution processes
Further experimental data is provided on the formation and dissolution of the conductive filaments in Ti/ poly-TiO2/Ti structures.
After a long stay at zero bias conditions, a step voltage is applied to the Ti/poly-TiO2/Ti samples. As shown in Fig. S2 a-d, an AC voltage waveform is added to the step biasing, which facilitates online monitoring of the device dynamic conductance (Gd) as well as the static conductance (Gs). According to Fig. S2 a and c, the A-sample operates almost like a normal resistor as its static and dynamic conductances remain nearly constant within the biasing field range examined. However, Fig. S2b and d show that the B-sample performs differently as its dynamic conductance varies with time after biasing field application. This interesting feature of Bsamples point to a number potential applications; e.g., the conductance of the device can be used as a measure of the time elapsed after the biasing voltage is switched on.
In another set of experiments, a constant DC biasing field, enough for filament formation, is applied to a B-sample. A small AC component added to the biasing field facilitates the online monitoring of the dynamic conductance of the device. Time is allowed for the device

Dynamic
Static current to reach its steady state level as shown in Fig. S2 b. Then, the temporal variations of the device current is recorded when the DC biasing field is suddenly dropped to different lower levels. The AC component of the biasing field is kept unchanged. The results are presented in Fig. S3 a-d. Based on these experimental results, the dynamic resistance of the device at any point in time is calculated and graphically presented in Fig. S4. The experimental results presented here are consistent with the filament formation and dissolution mechanism described in the manuscript.

Is the observed asymmetric I-V diagram caused by a junction energy barrier?
The I-V diagrams obtained for B-samples are vividly asymmetric and rectifying. The results of the following calculations rule out the possibility of this asymmetry being caused by a junction barrier: Thermionic emission through a junction barrier results in a current given by 51 : (S1) wherein is the ideality factor, q is the electronic charge, and is given by: in which is the junction area, is the Richardson constant, and is the energy barrier established at the junction. and follow from equations (S1) and (S2) : and are calculated graphically from the semi-logarithmic I-V diagrams given as insets in Fig. 2c and d. The graphical work is presented in Fig. S5 a-b. The obtained and are given in Table-S1; values larger than 20 show that the observed I-V diagrams are distinct from those related to the thermionic emission over junction barriers.

Figure S5. Graphical calculations resulting
and from the semi-logarithmic I-V diagrams; the calculation results are given in Table S1. Table S1. and values partly describing the IV diagrams given in Fig. S5.