Shubnikov-de-Haas oscillation is observed in a polarization-doped three-dimensional electron slab in a graded AlxGa1-xN semiconductor layer. The electron slab is generated by the technique of grading the polar semiconductor alloy with spatially changing polarization. Temperature-dependent oscillations allow us to extract an effective mass of m*=0.21m(0). The quantum scattering time measured (tau(q)=0.3 ps) is close to the transport scattering time (tau(t)=0.34 ps), indicating the dominance of short-range scattering. Alloy scattering is determined to be the dominant mechanism-limiting mobility; this enables us to extract an alloy-scattering parameter of V-0=1.8 eV for the AlxGa1-xN material system. Polarization-doping presents an exciting technique for creating electron slabs with widely tunable density and confinement for the study of dimensionality effects on charge transport and collective phenomena.