A comprehensive benchmarking method for the net combination of mobility enhancement and density-of-states bottleneck

In this letter, we propose a comprehensive benchmarking method to simultaneously address mobility enhancement and density-of-states bottleneck in advanced field-effect-transistors (FETs) with novel high-mobility (high- $\mu$ ) channel materials, where we focused on conventional covalent bonding semiconductors with pure and partially ionic character. This method relies only on the measured extrinsic transconductance of a long-channel FET in the saturation regime together with the source resistance, yielding the product of the effective mobility ( $\mu _{{eff}}$ ) and effective gate capacitance ( ${C}_{g\_{}{{eff}}}$ ). We tested this method in In x Ga1– x As quantum-well high-electron-mobility transistors (HEMTs) with various indium mole fractions, such as 0.53, 0.7, 0.8 and 1, as well as in Si n-FETs. We found that the In x Ga1– x As HEMTs with $\mu _{{eff}}$ over 10,000 cm2/ $\text{V}\cdot \text{s}$ at 300 K provided more than 20 times greater $\mu _{{eff}} \times {C}_{g\_{}{{eff}}}$ than Si n-FETs. More specifically, the product initially improved as ${x}$ increased, then showed a peak value of $10,300\,\,\mu \text{F}\cdot \text{V}^{-1}\cdot \text{s}^{-1}$ at ${x}$ of around 0.8, and degraded slightly beyond that composition. To verify the validness of the proposed method, we separately measured and analyzed ${C}_{g\_{}{{eff}}}$ and $\mu _{{eff}}$ using the split-CV technique, showing excellent agreement with the ones from the proposed method.