## 2 Materials and Methods  
Thin Cu-doped TiN\({}_{x}\)O\({}_{y}\) films (x \(\sim\)0.82, y \(\sim\)1.43) was fabricated using the atomic layer deposition (ALD) and fully characterized by standard experimental techniques, which revealed the films' structure, chemical composition, optical and transport properties and are reported elsewhere [8]. TiCl\({}_{4}\) liquid precursor, NH\({}_{3}\) gas, background O\({}_{2}\) and background Cu-atoms were used as the input components for the growth process performed in the Picosun SUNALETM (Picosun Oy, Masala, Finland) R-200 ADVANCED reactor at 420 \({}^{\circ}\)C. There were two groups of samples: G1 lightly-(or unintentionally) Cu-doped and G2 highly-(or intentionally) Cu-doped. In both cases, the Cu-atoms were brought into the ALD chamber by forming gas. The likely source of the copper impurities was the forming gas tank brass outlet. However, the reactor chamber was passivated with 100-120 nm Al\({}_{2}\)O\({}_{3}\) prior to loading and growing the G1-samples, while the G2-samples were grown right after the exposure to the Cu-carrying forming gas, i.e., without Al\({}_{2}\)O\({}_{3}\) passivation of the ALD reactor.  
Resistors studied in this work were formed from the lightly Cu-doped TiN\({}_{x}\)O\({}_{y}\) films (G1-samples) [8] that were grown on a mirror finished 500 \(\upmu\)m thick CT-32-1 Sital (SIT) wafer, which is a Mg-doped, quartz-like polycrystalline ceramic with dielectric constant 9.7-10 and loss tangent of 0.0005 (at 10 GHz). The TiN\({}_{x}\)O\({}_{y}\) resistor active area (body) was defined by optical lithography followed by plasma etching in RIE-1701 Nordson MARCH using a gas mixture of CF\({}_{4}\) (15 sccm)/O\({}_{2}\) (3 sccm) at 250 W RF power and 250 mTorr pressure for 2 min. The resistors' electric contacts were formed as the second layer metallization by aligned optical lithography using negative photoresist AZ nLOF 2035 and e-beam evaporation of Ti (5 nm)/Cu (1 \(\upmu\)m)/Ti (5 nm)/Au (50 nm), followed by lift-off. We fabricated two groups of resistors: short (1-square, 30 \(\times\) 30 \(\upmu\)m) and long (3-square long, 90 \(\times\) 30 \(\upmu\)m), with the same geometry of the routing and pads. The layout shown in Figure 1 was designed for both DC and high-frequency measurements. Source Meter 2634b (Keithley Instruments, LLC, Solon, OH, USA) connected to the EMPX-HF (Lake Shore Cryotronics, Westerville, OH, USA) probe station was used for DC resistance measurements at quasi-stationary varied temperatures 10-300 K.  
The resistors' morphology and EDX spectra for Mg, Al, Ti, Cu, O and N were investigated by using TM4000 Plus (Hitachi, Japan) in the BSE mode with an acceleration voltage of 20 kV equipped with an EDX XFlash Detector 630 Hc (Bruker, Germany). The sample was mounted with a carbon conductive double coated SEM adhesive on a SEM sample stub. Since no metal coating was applied to the sample surface prior to taking the SEM measurements, the surface charging occurred despite using the charge suppression scan mode of the SEM. In order to investigate the chemical composition of the specimens and the uniformity of the distribution of elements over the surface, the above listed elements mapping was performed over the resistor body, contacts and surrounding area, and they were visualized and quantified by using the Quantax 70 (Bruker, Billerica, MA, USA) software. The acquisition time was 5 min for all samples.  
We investigated the Cu-TiN\({}_{x}\)O\({}_{y}\) resistors high-frequency transmission properties by measuring their S-parameters at 0.01-26 GHz using the ZNB (Rohde & Schwarz, Munich, Germany) vector analyzer and MPI TS150 (MPI Corporation, Taiwan) probe station. The numerical simulations of the copper routing structure high-frequency behavior were performed by using the CST Microwave Studio environment. We used a simple model of resistor and capacitor connected in parallel to model the Cu-TiN\({}_{x}\)O\({}_{y}\) resistor body and fit theoretical curves to the experimental data for S-parameters.