We report quantum dots fabricated on very shallow 2-dimensional electron gases, only 30 nm below the surface, in undoped GaAs/AlGaAs heterostructures grown by molecular beam epitaxy. Due to the absence of dopants, an improvement of more than one orde
r of magnitude in mobility (at 2E11 /cm^2) with respect to doped heterostructures with similar depths is observed. These undoped wafers can easily be gated with surface metallic gates patterned by e-beam lithography, as demonstrated here from single-level transport through a quantum dot showing large charging energies (up to 1.75 meV) and excited state energies (up to 0.5 meV).
