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By exploiting the difference in spontaneous and piezoelectric polarization between GaN and compositionally graded layers of strained AlGaN, we demonstrate three-dimensional electron slabs of tunable widths ͑30-100 nm͒ and densities ͑1-5 ϫ 10 18 cm 3 ͒. Removal of ionized impurity scattering results in relatively high mobilities limited by alloy scattering at low temperatures, and by a combination of alloy and polar optical phonon scattering at room temperature. Owing to the tunabledoi:10.1063/1.2168253 fatcat:vthev7dxvff3dnu6ta5dbyqlte