## 3 Results
Figure 2: Two sets of the Cu-TiN\({}_{\mathrm{x}}\)O\({}_{y}\) thin film resistors R(T) measurements taken 18 months apart in the year 2019 and 2021, accordingly. The width/thickness is 30 \(\upmu\)m/22 nm, and the lengths are 30 \(\upmu\)m and 90 \(\upmu\)m for the 1-square and 3-square resistors, respectively. The resistors are as follows: (**a**) extrinsic (measured) resistance and (**b**) extracted Cu-TiN\({}_{\mathrm{x}}\)O\({}_{y}\) sheet (\(R_{SH}\)) and TiN\({}_{\mathrm{x}}\)O\({}_{y}\)/Ti/Cu contact (\(R_{\mathrm{C}}\)) resistances. The current in Cu-doped TiN\({}_{x}\)O\({}_{y}\) resistors increases rather than saturates at higher voltages. This may cause a thermal runaway problem in these resistors when operating in real circuits, so we decided to explore the higher power handling capability of resistors and their maximum power handling capability at higher voltages. Figure 5 shows the results of the slow high-voltage stress test for long resistor with a 15 s bias voltage sweep from zero to maximum voltage. We began with a 11 V voltage cap and gradually increased it to 30 V in four consecutive tests using the same resistor. Continuous visible light emission (inset photos in Figure 5a) was observed for 10-15 s with maximum intensity near 12 V due to the resistor heating followed by a rapid irreversible resistance increase near 24 V in the seventh test. The light emission starts more or less uniformly over the resistor body, but then narrows down to the middle part of the body and then drifts as a focused light source towards the high-bias terminal at higher voltages. After seven high-voltage runs, the resistor ceases to emit light and changes its state to what we call a \"burnt\" state, characterized by a considerably higher sheet resistance; however, it does not break open even at 30 V and keeps functioning as a non-linear \(\sim\)100 k\(\Omega\)/\(\square\) resistor. Figure 4: T-dependence of the coefficients absolute values for non-linear polynomial fit of experimental \(I\)-\(V\) curves for the following: (**a**) 1-square and (**b**) 3-square resistors. All coefficients were positive except for \(B_{5}\), which was negative. Figure 3: Cu-TiN\({}_{x}\)O\({}_{y}\) resistors non-linearity: (**a**) definition of the non-linearity parameter U\({}_{10}\), which is the voltage that causes the differential resistance 10% change compared to its value at zero bias. In this particular example of I-V curve for 1-square long resistor measured at room temperature, U\({}_{10}\) = 3.191 V. (**b**) Resistors non-linearity parameter U\({}_{10}\) as a function of temperature measured 18 months apart. In order to find a physical explanation for the resistive state difference between normal and burnt resistors, we visualized their chemical composition by using the color-coded EDX data. Both working and burnt resistors have all their constituting elements (except for the nitrogen and oxygen) uniformly distributed over the active areas. The inset of Figure 5b shows the EDX data color map of the N-concentration distribution (in yellow) in resistor before (state-1) and after the burning test (state-3), as well as the line scans EDX data for nitrogen and oxygen along the burnt resistor. A noticeable N-gradient can be observed in the burnt resistor, indicating lower x-content in Cu-TiNxOy towards the high-bias terminal of the resistor. Since Cu-concentrations in both resistors do not exceed 1% and the resistors body is too thin (22 nm), the EDX Cu-signal was too weak to resolve the difference in Cu-concentration between the resistors. However, we believe that copper desorbed from the surface accompanied by the nitrogen depletion during the resistors burning test. Indeed, the remaining finite resistivity after the burning test (-0.4 \(\Omega^{\star}\)cm at 10 V) agrees well with the values for undoped TiNxOy with similar O-content (-1 \(\Omega^{\star}\)cm at y = 45%) published elsewhere [9].