Low-Frequency Noise Parameter Extraction Method for Single-Layer Graphene FETs

In this article, a detailed parameter extraction methodology is proposed for low-frequency noise (LFN) in single-layer (SL) graphene transistors (GFETs) based on a recently established compact LFN model. The drain current and LFN of two short channel back-gated GFETs ( ${L} = {300}$ and 100 nm) were measured at lower and higher drain voltages, for a wide range of gate voltages covering the region away from charge neutrality point (CNP) up to CNP at p-type operation region. Current–voltage ( IV ) and LFN data were also available from a long-channel SL top solution-gated (SG) GFET ( ${L} = {5}\,\,\mu \text{m}$ ), for both p- and n-type regions near and away CNP. At each of these regimes, the appropriate IV and LFN parameters can be accurately extracted. Regarding LFN, mobility fluctuation effect is dominant at CNP, and from there, the Hooge parameter $\alpha _{H}$ can be extracted, whereas the carrier number fluctuation contribution which is responsible for the well-known M-shape bias dependence of output noise divided by squared drain current, also observed in our data, makes possible the extraction of the ${N}_{T}$ parameter related to the number of traps. In the less possible case of a $\Lambda $ -shape trend, ${N}_{T}$ and $\alpha _{H}$ can be extracted simultaneously from the region near CNP. Away from CNP, contact resistance can have a significant contribution to LFN, and from there, the relevant parameter ${S}_{\Delta {R}}^{{2}}$ is defined. The LFN parameters described above can be estimated from the low drain voltage region of operation where the effect of velocity saturation (VS) mechanism is negligible. VS effect results in the reduction of LFN at higher drain voltages, and from there, the IV parameter $h\Omega $ which represents the phonon energy and is related to VS effect can be derived both from drain current and LFN data.