A single-barrier GaAs/AlAs/GaAs heterostructure, with self-assembled In-based quantum dots incorporated in the AlAs tunnel barrier, exhibits a series of resonant peaks in the low temperature current–voltage characteristics. We argue that each peak arises fromsingle-electrontunneling through thediscrete zero-dimensionalstate of anindividualInAs dot. We use the tunneling for fine probing of the local density of states in the emitter-accumulation layer. Landau-quantized states are resolved at magnetic field B∥ as low as 0.2 T. Spin-splitting of the dot electron states has been observed forB⊥I.