# Radiofrequency Performance Analysis of Metal-Insulator-Graphene Diodes
## 2 MIG Device and Modeling  
A physics-based model was calibrated with experimental data describing the static and dynamic performance of a MIG diode reported elsewhere [13]. The cross-section of the MIG diode used as a reference here and first reported in [4] is presented in Figure 1a. The fabrication process has been reported in detail in [4] and can be summarized as follows: The device consists of a Ti/Al alloy embedded metal electrode working as the anode, a TiO\({}_{2}\) dielectric grown by atomic layer deposition (ALD) with a thickness (\(t_{\text{ox}}\)) of 6 nm separating the top graphene layer from the anode and substrate, yielding an oxide capacitance per unit area \(C_{\text{ox}}=e_{\text{ox}}e_{0}/t_{\text{ox}}\), considering \(e_{\text{ox}}=9\). A Ni cathode (20 nm tick) is located at one end of the graphene layer. The graphene layer length (\(L\)) is 2 \(\upmu\)m and its width (\(W\)) is 80 \(\upmu\)m. The fabrication process was conducted using optical contact lithography on a high-resistivity Si substrate (\(\approx\)5 k\(\Omega\)cm) with a 1 \(\upmu\)m thermal SiO\({}_{2}\) layer. The embedded metal layers forming the anode (180 nm Al, 20 nm Ti) were deposited (by e-beam evaporation followed by lift-off) in 200 nm deep trenches etched into the SiO\({}_{2}\) layer (via reactive ion etching). The dielectric was then deposited with an oxygen plasma process and the required rails for contacting the anode were opened through the TiO\({}_{2}\) layer with Ar plasma and sealed with 20 nm Ni. The graphene layer grown by chemical vapor deposition on copper foil was transferred to the device structured using a PMMA support layer. Oxygen plasma was used for graphene patterning, and the cathode (20 nm Ni, 100 nm Al) was fabricated by sputtering deposition and lift-off. After the graphene had been transferred onto the substrate, a characterization was performed using Raman spectroscopy, which confirmed that the transferred material consisted of single-layer graphene. Additionally, the carrier mobility was estimated to be in the range of 2000-3000 cm\({}^{2}\)/Vs using a four-probe measurement setup [4]. The DC characteristics of the device were obtained by applying a voltage between \(-1\) V and \(1\) V (cf. Figure 1b), whereas the RF power detection was characterized by using an RF power source at a selected operation frequency (_f_) under zero-bias conditions [13]. The large-signal compact model describing the thermionic transport within the MIG diode is based on the Dirac-Schottky model and includes image force lowering effects at the potential barrier. For the electrostatics, it considers the charge conservation principle and includes quantum capacitance and interface effects. Further technical details and specific model formulation are discussed in [16]. The resulting current density-voltage curve at a temperature of 295 K, showing the transition from reverse bias to forward bias, is presented in Figure 1b. A good agreement was achieved between the model and experimental results for both negative and positive biases. The large-signal equivalent circuit of the MIG diode, including the extrinsic elements representing the parasitics due to metallic pads and dielectric surroundings, is presented in Figure 2[16]. The dynamic phenomena of the internal graphene charge are described by the bias-dependent \(C_{\text{int}}\). On the other hand, the transport is governed by the effects of the barrier formed at the graphene-insulator interface, modeled through a two-dimensional (2D) modified Dirac-Schottky equation [17], represented as the density current source \(J_{\text{th}}\) (current/device area). The extrinsic elements were extracted by applying a de-embedding procedure [18]. \(C_{\text{pa/pc}}\) represent the anode/cathode parasitic capacitance, both due to the substrate. \(C_{\text{f/fp}}\) is the parasitic diode fringe/pad capacitance, and \(R_{\text{a/c}}\) and \(L_{\text{a/c}}\) are the parasitic resistances and inductances associated with the anode and cathode pads, respectively [16].