A series of two-dimensional electron gas (2DEG) structures have been grown with the 2DEG only 28 nm from the surface. The effects of growth temperature and δ-doping density have been investigated, and a comparison has been made between AlAs and Al 0 . 3 Ga 0 . 7 As barriers. A mobility of 340,000 cm 2 V - 1 s - 1 at 4 K has been measured for a shallow 2DEG with an Al 0 . 3 Ga 0 . 7 As barrier, which is the highest reported for such a structure.