Low temperature electron mobility and concentration under the gate of $AlGaN∕GaN$ field effect transistors

High electron mobility field effect transistors were fabricated on $AlGaN∕GaN$ heterostructures and their magnetoresistance was measured at $4.2K$ up to $10T$ with simultaneous modulation of the gate potential. Low and high magnetic field data were used to determine the electron mobility $(μ)$ and concentration $(n)$⁠, respectively, in the gated part of the transistor channel. With these measurements we present a method to determine $μ$ and $n$ under the gate of a transistor, which does not require knowledge of the transistor gate length, access resistance, threshold voltage, or capacitance. We discuss applications of this method for nanometer and ballistic transistors.