## 4 Discussion  
We fabricated and measured 1-square and 3-square resistors from the ALD-grown Cu-TiN\({}_{x}\)O\({}_{y}\) film with Au-finished metal traces of the Cu-routing for DC and RF characterization. The DC sheet resistance equals 220 \(\pm\) 8 \(\Omega/\square\), and the intrinsic TCR is -400 ppm/\({}^{\circ}\)C, which is comparable to NiCr resistors and almost two orders of magnitude smaller than the values reported for TiN single-crystal films [10]. Compared to the monocrystalline TiN the Cu-TiN\({}_{x}\)O\({}_{y}\) resistance is roughly 20 times higher [11]. However, due to the TiN\({}_{x}\)O\({}_{y}\)/Ti/Cu interface contact reliability issues (ageing), the extrinsic TCR of the resistors became considerably higher over the course of 18 months. Initially the extrinsic R(T) dependence showed only a slight increase at low temperatures; however, this trend increased substantially due to the ageing effect (Figure 2a). A more detailed analysis that separated the resistor body from the contact contribution to the net resistance revealed that the contact resistance increased dramatically and became a non-linear function of temperature after 18 months (Figure 2b). At the same time the intrinsic (resistor physical body) resistance remained stable below 200 K and decreased only slightly above 200 K.  
We studied the non-linearity of the resistors and found that it increased as they aged: U\({}_{10}\) decreased almost five times at low temperature (Figure 3b). Non-liner polynomial fits of the resistors' \(I\)-\(V\) curves measured at different temperatures showed that all significant coefficients of non-linear terms in (2) increased significantly at low temperatures while  
Figure 7: Measured two-port S-parameters for the following: 1-square (blue and red) and 3-square (black and green) resistors and their theoretical values were obtained using 2D coplanar micro-strip lines model for copper routing and lumped model of resistor and capacitor connected in parallel (for the Cu-TiN\({}_{x}\)O\({}_{y}\) resistor body). The best matching is achieved with the Cu-TiN\({}_{x}\)O\({}_{y}\) thin film sheet resistance of the following: 250 \(\Omega/\square\) for 1-square and 215 \(\Omega/\square\) for 3-square resistors with 15 fF and 5 fF bypass capacitors, respectively. The left and right \(y\)-axes correspond to the magnitude of the reflection and transmission coefficients of the RF power. the linear term coefficient, i.e., conductance decreased 20% in the early measurements and up to 100% in the latest studies (Figure 4). The non-linear divergence of the contact resistance at low temperature is believed to be due to a TiO\({}_{\text{x}}\) potential barrier gradually formed at the interface between the TiN\({}_{\text{x}}\)O\({}_{\text{y}}\) film resistor body and Cu/Ti metallization at the contact areas. It is plausible that the titanium adhesion layer became oxidized over the course of 18 months via the oxygen scavenging (gettering) mechanism from the underlying TiN\({}_{\text{x}}\)O\({}_{\text{y}}\) film. Since the non-linearity of _I-V_ curves significantly increased at low temperatures and the R(T) itself became increasingly non-linear, we suggest there is an increasing admixture of the tunneling and/or thermionic current components in resistors measured after 18 months, i.e., the contact gradually transforms from Ohmic to TiO\({}_{\text{x}}\)-barrier type. However, the resistors' _I-V_ curves do not saturate yet, which, for example, would be typical for the back-to-back (B2B) Schottky diodes [12]. Therefore, we believe that the parasitic TiO\({}_{\text{x}}\) potential barrier is leaky. This uncertainty in device performance sets our future work goal of resolving the contact ageing problem by eliminating the Ti/TiN\({}_{\text{x}}\)O\({}_{\text{y}}\) interface, as the TiN\({}_{\text{x}}\)O\({}_{\text{y}}\) thin film resistor itself seems to be stable and capable of functioning at high-power density.