Controlling a three dimensional electron slab of graded Al$_{x}$Ga$_{1-x}$N

Polarization induced degenerate $n$-type doping with electron concentrations up to $\sim$10$^{20}$\,cm$^{-3}$ is achieved in graded Al$_{x}$Ga$_{1-x}$N layers ($x$: 0\%$\rightarrow$37\%) grown on unintentionally doped and on $n$-doped GaN:Si buffer/reservoir layers by metal organic vapor phase epitaxy. High resolution x-ray diffraction, transmission electron microscopy and electron energy loss spectroscopy confirm the gradient in the composition of the Al$_{x}$Ga$_{1-x}$N layers, while magnetotransport studies reveal the formation of a three dimensional electron slab, whose conductivity can be adjusted through the GaN(:Si) buffer/reservoir.