## 1 Introduction  
Planar coils are widely used in radio-frequency (RF) applications as monolithic spiral inductors. To meet the fast-rising demand for high-performance integrated passive components in RF-integrated circuits (RFICs), a tremendous number of studies have been conducted to improve the performance of on-chip inductors on Si [1; 2; 3; 4] or GaAs substrates [5]. Recently, GaN-based wide bandgap compound semiconductors have drawn extensive attention in the field of high-efficacy lighting emitters and high-power electronic RF devices, yet there are scarce reports on the designs of inductors on the GaN platform [6; 7].  
Sapphire, commonly used as the substrate for GaN-based material heteroepitaxy, exhibits superior electrical insulating properties due to its ultra-wide bandgap and thereby stands out as an ideal substrate for integrated inductors, riding on the advantage of low magnetically-induced substrate loss. Therefore, to fabricate inductors on sapphire not only holds the potential to demonstrate high-performance inductors but also exhibits the feasibility of monolithic integration with the maturely developed GaN-on-sapphire platform, which would facilitate the development of GaN monolithic microwave integrated circuits (MMICs) and microwave integrated circuits (MICs) [8] in fields such as rail systems, ultra-high voltage power transmission, new energy vehicles and 5G base stations.  
Owing to its low resistivity, copper (Cu) is preferred over aluminum (Al) to fabricate on-chip integrated inductors on silicon or sapphire substrates [9]. Electron beam (E-beam) evaporation, sputtering, atomic layer deposition (ALD), and electrochemical and electroless deposition are the most common techniques to fabricate Cu-based coils [10]. Among these methods, electrochemical- and electroless-deposited Cu are often used by virtue of their low cost, stronger adhesion, higher deposition rate, and manufacturing feasibility for high-aspect ratio microstructures (e.g., micro-coils with thickness of 30 \(\upmu\)m) [11; 12]. However, the whole fabrication process can be tedious [13], which includes several steps of Cu seed layer electrodeposition, photolithography patterning, and seed layer etching. Additionally, the quality of Cu film fabricated by electrodeposition is generally inferior to that of evaporated or sputtered ones.  
In this paper, we have compared two categories of inductors on sapphire substrate based on evaporated or sputtered Cu and Al metal multilayers (Cr/Cu/Ti/Au, Cr/Cu/Ni/Au, Cr/Cu/Cr, and Cr/Al/Ti/Au). These inductors exhibit close \(Q\)-factors, out of the expectations for Cu-based inductors which are supposed to have higher performance than that based on Al. In-depth profile analysis on these multilayers reveals that the problem stems from the oxidation of Cu-based metal sublayers during the solution rinse and exposing to atmosphere, or forming alloys between the sublayers.  
In addition, complicated de-embedding procedures are always required in order to obtain accurate inductance, resonant frequency and \(Q\)-factor, which could be tricky and time-consuming when dealing with plenty of scattering parameters (\(S\)-parameters) of inductors with various layout parameters. Herein, a six-element equivalent physical model is proposed, which takes the parasitic effect of RF test structures into account. By fitting with the embedded measurement result, the model can be used to extract series and parasitic parameters rapidly.