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In this letter, carrier transport in gradedAl$\mathrm{_x}$Ga$\mathrm{_{1-x}}$N with a polarization-induced n-type dopingas low as ~ 10$\mathrm{^{17}}$ cm$\mathrm{^{-3}}$ is reported. The gradedAl$\mathrm{_x}$Ga$\mathrm{_{1-x}}$N is grown by metal organic chemical vapordeposition on a sapphire substrate and a uniform n-type doping without anyintentional doping is realized by linearly varying the Al composition from 0%to 20% over a thickness of 600 nm. A compensating center concentration of~10$\mathrm{^{17}}$ cm$\mathrm{^{-3}}$ was also estimated. A peak mobility of900 cm$\mathrm{^2}$/V$\mathrm \cdot$s at room temperature is extracted at an Alcomposition of ~ 7%, which represents the highest mobility achieved inn-Al$\mathrm{_{0.07}}$GaN with a carrier concentration ~10$\mathrm{^{17}}$cm$\mathrm{^{-3}}$. Comparison between experimental data and theoretical modelsshows that, at this low doping concentration, both dislocation scattering andalloy scattering are significant in limiting electron mobility; and that adislocation density of <10$\mathrm{^7}$ cm$\mathrm{^{-2}}$ is necessary tooptimize mobility near 10$\mathrm{^{16}}$ cm$\mathrm{^{-3}}$. The findings inthis study provide insight in key elements for achieving high mobility at lowdoping levels in GaN, a critical parameter in design of novel power electronicstaking advantage of polarization doping.

Electron Mobility in Polarization-doped Al$\mathrm{_{0-0.2}}$GaN with a Low Concentration Near 10$\mathrm{^{17}}$ cm$\mathrm{^{-3}}$