A high electron mobility transistor (HEMT) structure grown by molecular beam epitaxy consisting of a 2-nm In0.3Ga0.7As channel limited by a thick GaAs layer at the bottom and a 5-nm Al0.3Ga0.7As spacer at the top has been characterised by transmission electron microscopy (TEM) and high-resolution electron microscopy (HREM). The carrier supplier of this structure is a Si delta-doped layer centred within a 1.7-nm wide GaAs quantum well grown on the spacer. (200) dark field (DF) TEM and HREM show well-defined InGaAs/GaAs and AlGaAs/InGaAs interfaces. The interface abruptness, the InGaAs layer thickness and its In composition have been quantitatively determined by strain measurements from [110] HREM images. The compositional profile obtained confirms an average InGaAs layer thickness of 7 group III monolayers (ML). All the layers are pseudomorphic, without dislocations or stacking faults. An inhomogeneous intensity distribution in DF TEM along the Si delta-doped GaAs layer suggests lateral Si segregation or strain modulation of which no evidence has been found by HREM. HREM reveals, however, an unusually large average lattice contraction at the position of the delta-doped layer which can be explained by atoms occupying non-lattice sites (DX centres).