MODEL Transistor The transistor is modeled generically by a heavily simplified virtual-source (short-channel) MOSFET model . Although this model was first defined for Silicon transistors, it has been successfully adapted to numerous other contexts, including Graphene and Gallium Nitride devices, both HEMTs and MOSHEMT+VO₂ HyperFETs . Following Khakifirooz , the drain current ID is expressed {W}=Q_{ix_0}v_{x_0}F_s where Qiz₀ is the charge at the virtual source point, vx₀ is the virtual source saturation velocity, and Fs is an empirically fitted “saturation function” which smoothly transitions between linear (Fs ∝ VDS/VDSSAT) and saturation (Fs ≈ 1) regimes. The charge in the channel is described via the following semi-empirical form first proposed for CMOS-VLSI modeling and employed frequently since (often with modifications, eg ): Q_{ix_0}=C_nV_\ln\left[1+\exp\left\{-V_T}{nV_}\right\}\right] where Cinv is an effective inversion capacitance for the gate, nVthln10 is the subthreshold swing of the transistor, VGSi is the transistor gate-to-source voltage, VT is the threshold voltage, and Vth is the thermal voltage kT/q. For precise modeling, Khakifirooz includes further adjustments of VT due to the drain voltage (DIBL parameter) and the gate voltage (strong vs weak inversion shift), as well as a functional form of Fs. For a first-pass, we will ignore these effects, employ a constant VT, and assume the supply voltage is maintained above the gate overdrive such that Fs ≈ 1. However, we will add on a leakage floor with conductance Gleak. Altogether, the final current expression (for the analytical part of this analysis) is {W}=nv_{x_0}C_V_{th}\ln\left[1+\exp\left\{-V_}{nV_{th}}\right\}\right]+}{W}V_