## 1 Introduction  
Graphene is a low-dimensionality material which offers several advantages as an emerging electronic material in terms of high mobility (200,000 cm\({}^{2}\)/V-s) [1], high carrier concentration [2], high tensile strength (125 GPa) [3], and high thermal conductivity (\(\sim\)4000 W\(\cdot\)m\({}^{-1}\).K\({}^{-1}\)) [4]. In addition, graphene is inherently flexible, transparent, and chemically inert. Moreover, it has been adopted in several applications, such as bendable display technology, electrochemical energy storage devices, metal corrosion inhibitors, and signal processing and signal modulation applications [5; 6; 7; 8]. Graphene does not have a bandgap; as such, it has found limited applications as a logic gate [9; 10; 11; 12], although attempts have been made to form a bandgap with a bilayer graphene (BLG) structure [13]. On the other hand, due to its high mobility, there have been significant efforts toward the fabrication of graphene field-effect transistors (GFETs) for their application in high-frequency amplifiers, modulators, and resonators [14; 15; 16]. In addition, due to the sensitivity of graphene to physical and chemical stimuli, there are numerous reports of graphene-based physical and chemical sensors [17; 18; 19; 20]. There are several reported fabrication methods of graphene-based devices [21; 22; 23; 24; 25]. The choice of the fabrication method comes down to the final application and the required performance, as well as the available resources. High-performing GFETs typically consist of nanometer-length channels and reduced S/D capacitance techniques [26], and reported studies have achieved an extrinsic cutoff frequency (f\({}_{\rm T}\)) of 34 GHz, as well as an extrinsic maximum oscillation frequency (f\({}_{\rm max}\)) of 37 GHz with gate lengths \(<\)350 nm fabricated via electron beam lithography [26]. Gate electrodes for these devices are generally fabricated with a top [27], buried [28], or trench-filled (damascene process) [29] structure. Gate dielectric materials of ultrathin AlO\({}_{\rm x}\) (naturally grown or ALD), hBN (transferred), and other high-k materials are used in order to maximize the performance of these devices [30; 31; 32]. Additionally, the substrate that creates an interface with graphene is carefully selected to minimize adverse effects [33]. Published reports have shown that, even though high-volume production of such transistors results in a reasonably high number of working devices (high yield), the device-to-device variation and non-uniformity of their electrical characteristics remain quite high [34; 35; 36; 37; 38]. Non-uniformity (NU) is a value of device variation and can be calculated as NU = (max \(-\) min)/average. The value of non-uniformity can be used as a figure of merit of variability when not enough data exists to obtain a statistical meaningful normal distribution. For example, [PERSON] et al. reported the fabrication of 4500 top-gated GFETs with a yield of 75%, a median Dirac point of 4 V, and mobility of 40 cm\({}^{2}\)/V-s, but non-uniformity of 150% and 300% [34]. The observed device variation was explained by graphene defects during transfer, the strain of graphene, transfer polymer residue, and interface substrate effects [34; 35; 36; 39]. In contrast, in the design and fabrication of graphene-based THz resonators for communication systems and chemical/physical sensors, the dimensions of the proposed devices are in the micrometer range (1-100 s\(\cdot\)um) to meet the required performance of the application. THz resonators have been proposed through the hydrodynamic electron fluid concept applied to the Dyakonov and Shur (DS) instability [40; 41; 42]. THz radiation has been predicted in structures with high electron density and high-carrier-mobility materials with certain boundary conditions. The dimensions of these THz resonators are designed to match the targeted wavelengths at resonance [43].