$\mu_\mathrm{2T}(n)$: A Method for Extracting the Density Dependent Mobility in Two-Terminal Nanodevices

Measuring carrier mobility as a function of the carrier density in semiconductors using Hall effect is the gold standard for quantifying scattering mechanisms. However, for nanostructures, the Hall effect is not applicable, and the density dependence of mobility is generally inaccessible, rendering Hall effect measurements impractical. Here, we present $\mu_\mathrm{2T}(n)$, a new procedure allowing us to extract the density dependent mobility in two-terminal measured nano scale field effect transistors at zero magnetic field from conventional conductance vs gate voltage measurements. We validate $\mu_\mathrm{2T}$ against standard Hall measurements and then apply the procedure to 256 individual two-terminal InAs nanowire FETs, extracting information about the scattering mechanisms. To illustrate its broad utility, we reanalyze published data in which mobility had been treated as density independent. Our method represents a new powerful tool for optimization and development of nanomaterials crucial for a wide range of new technologies.