## 1 Introduction  
Graphene is a planar sheet of sp\({}^{2}\) bonded carbon atoms with single atomic thickness [1]. It is increasingly popular due to its splenidd properties. Excellent intrinsic mobility of about 200,000 cm\({}^{2}\cdot\) V\({}^{-1}\cdot\) s\({}^{-1}\)[2], current density tolerance of about 10\({}^{8}\) A/cm\({}^{2}\)[3] and thermal conductivity in the order of 5 \(\times\) 10\({}^{3}\) W/m\(\cdot\) K [4] are among the few important properties of graphene that make it a promising candidate for a vast number of applications, such as ULSI (Ultra-Large Scale Integration) interconnects, transparent conductive coatings, photodetectors, optical modulator, sensors, metrology, etc., and many others. Specifically, graphene with different numbers of layers have different potential applications. Single-layer or mono-layer graphene (SLG) is used as the top electrodes of semi-transparent organic solar cells fabricated by [PERSON] et al. [5], as the transparent conductive anode in OLEDs (Organic Light-Emitting Diodes) investigated by [PERSON] et al. [6], as field-effect transistors studied by [PERSON] et al. [7], etc. [PERSON] et al. [8], [PERSON] et al. [9], [PERSON] et al. [10] and [PERSON] et al. [11] reported the applications of few-layer graphene (FLG) in thin-film transistors (TFTs), capacitive touch panels, touch screens and micro/nanometer-scale heat spreaders, respectively. On the other hand, multi-layer or many-layer graphene (MLG) films are used as thermal interface materials in photovoltaic (PV) solar cells, optoelectronic, photonic devices and systems [12]. MLG films are also used as superconductors reported by [PERSON] et al. [13] and as fillers in polymer composite reported by [PERSON] [14] and [PERSON] et al. [15], etc. Several graphene growth methods have been reported since its discovery in 2004 by [PERSON] et al. [1]. Beginning from a scotch-tape technique [1] in order to mechanically exfoliate graphene flakes, many growth techniques have been reported [16; 17; 18], such as graphite sonication [19], epitaxial growth [20], graphene oxide reduction [21], etc. The chemical vapor deposition (CVD) technique produces large area graphene with high quality and low mass production, which otherwise is a big challenge for other growth methods [16; 22; 23]. The CVD method uses a variety of carbon sources, including gaseous [7; 24; 25; 26] and liquid [27; 28] precursors. Use of amorphous carbon as a solid source for graphene synthesis on Cu was reported by [PERSON] et al. [29]. However, their method involved graphene growth on a several micron-thick copper foil, and the graphene so obtained needs to be transferred onto the required substrate, which might introduce defects. Recently, we demonstrated the feasibility of the crystallization of amorphous carbon (a-C) below sputtered copper (Cu) thin film, which acts as a catalyst to obtain graphene on the top surface of the Cu film experimentally [30]. This graphene synthesis method is PVD (Physical Vapor Deposition) based, which is novel as both a carbon source and a metal catalyst are deposited using the sputtering method. Unlike other methods, such as conventional CVD (Chemical Vapor Deposition), where much of the gaseous carbon source is wasted and the synthesis temperature is very high, this PVD-based method provides low cost and direct transformation of pure carbon species underneath the copper film into graphene on the top of copper film at temperatures acceptable for the semiconductor industry, with better control over the number of layers and the quality of the grown graphene. Therefore, it can potentially be useful for enhancing the conductivity and reliability performance of ULSI copper interconnects. In order to optimize the above-mentioned PVD-based process, the key process parameters (also known as factors) must be identified. One-factor-at-a-time (OFAT) experimentation is the most common method to identify the key factors, in which only one factor or variable is varied at a time while keeping others fixed [31].