## 3 Results and Discussions  
Theoretically, multilayer metal has a higher sheet resistance than that of pure metal, according to the formula as follows [19], which is used to estimate effective sheet resistance (\(R_{sheet}\)):  
\[R_{sheet}=\frac{1}{\frac{1}{\rho_{1}}+\frac{t_{2}}{\rho_{2}}+\frac{t_{3}}{ \rho_{3}}+\ldots+\frac{t_{n}}{\rho_{n}}} \tag{4}\]  
where \(n\) represents the \(n_{\text{th}}\) sublayer of the multilayer, \(t_{n}\) and \(\rho_{n}\) are the thickness and resistivity of the \(n_{\text{th}}\) sublayer, respectively. This can be attributed to the multilayer acting as parallel resistors [20]. Nevertheless, the theoretical conductivities of the multilayers approach those of the pure metals, for the contribution of the other sublayers is small as compared to that of the Cu or Al layer, which can be observed in Figure 2a. However, this was not the case for the samples in our measurement, with 23.2%, 18.6% and 24.8% reduction in conductivity for Cr/Cu/Ni/Au, Cr/Cu/Cr and Cr/Cu/Ti/Au, respectively, in comparison with the theoretical values. Oxidation of the metal and alloying  
Figure 2: (a) Conductivities of the Al and Cu-based metals; (b) HFSS simulation results of the \(Q\)-factors (solid line) and \(R\) (dashed line) of the inductors as a function of frequency. formed by the interdiffusion between the sublayers account for the deterioration in their electrical properties. In contrast, a reduction of only 1.6% for Cr/Al/Ti/Au was observed. According to the four-probe measurement result, the order of the conductivity from the greatest to the least was \(\sigma_{Cr/Cu/Cr}\), \(\sigma_{Cr/Cu/Ni/Au}\), \(\sigma_{Cr/Cu/Ti/Au}\), and \(\sigma_{Cr/Al/Ti/Au}\). Overall, Al-based multilayer has a close electrical conductivity to that of Cu-based multilayers, with little performance deterioration as compared to the pure metal, although pure Cu exhibits the highest electrical conductivity of about 1.5 times that of pure Al. Figure 2b presents the simulation results of the \(Q\)-factors and \(R\) of the inductors as a function of frequency. The disparities in the performance between Al and Cu-based inductors are tiny. The \(Q\)-factor reaches its maximum of 5.84 at 0.55 GHz for Cr/Cu/Cr, while the inductance mainly determined by the geometric parameters shows little susceptibility to different kinds of metallization systems. AES measurement was used to implement compositional and element analysis quantitatively, as displayed in Figure 3. Sapphire substrate is indicated by the cyan-shaded regions, exhibiting high atomic concentrations of Al and O elements. For Cr/Cu/Cr, chromium oxides on the surface exposed to the environment with low oxygen content were unsurprisingly detected (Figure 3b), which served as protective layers for the pattern underneath at the cost of deteriorating electrical conductivity of the multilayer. A 250 nm top Cr layer was employed in order to keep consistent thickness of other sublayers in the four control samples. In Cr/Cu/Ni/Au, the binary phase of Ni with  
Figure 3: In-depth profiles of (**a**) Cr/Al/Ti/Au; (**b**) Cr/Cu/Cr; (**c**) Cr/Cu/Ni/Au and (**d**) Cr/Cu/Ti/Au using Auger electron spectroscopy in combination with in-situ ion sputtering. Cu spreading throughout the entire conductor layer can be seen in Figure 3c, although 200 nm Ni was supposed to be an effective barrier layer. That is owing to the thermal energy facilitating the diffusion of Ni into Cu during the E-beam evaporation process. For Cr/Cu/Ti/Au, Ti barrier layer between Cu and Au was oxidized. This situation also happened for the sample with a thickened Au top layer of 200 nm, which denies the hypothesis that 50 nm Au is porous and too thin to be an effective protective layer whereby the Ti is directly exposed to the corrosive medium. It is found that oxidation of the Ti originates from the handover between sputtering and evaporation processes, during which oxygen inevitably adsorbed onto the surface of Cu. Excellent gettering properties of Ti require very low levels of residual water and oxygen.