By compositionally grading AlGaN layers over different thicknesses, high mobility electron gases are produced by polarization-induced doping. Temperature dependent Hall and capacitance-voltage measurements were performed on these AlGaN layers, and two degrees of freedom are found for choosing the carrier concentration of these slabs. Carrier mobilities determined from Hall measurements are observed to be much higher than impurity doped structures of similar carrier densities. Alloy and phonon scattering are determined to be the major contributors limiting the mobility of the electron in the graded layers. This form of polarization-induced doping offers an attractive alternative to the traditional doping techniques, and may be used for highly conductive AlGaN layers with high Al composition, both for lateral and vertical transport.