AlGaN/GaN quantum well (QW) structures are grown on c-plane sapphire substrates by molecular beam epitaxy. Control at the monolayer scale of the well thickness is achieved and sharp QW interfaces are demonstrated by the low photoluminescence linewidth. The QW transition energy as a function of the well width evidences a quantum-confined Stark effect due to the presence of a strong built-in electric field. Its origin is discussed in terms of piezoelectricity and spontaneous polarization. Its magnitude versus the Al mole fraction is determined. The role of the sample structure geometry on the electric field is exemplified by changing the thickness of the AlGaN barriers in multiple-QW structures. Straightforward electrostatic arguments well account for the overall trends of the electric-field variations. (C) 1999 American Institute of Physics. [S0021- 8979(99)07719-1].