  We perform the investigations of the resonant tunneling via impurities
embedded in the AlAs barrier of a single GaAs/AlGaAs heterostructure. In the
$I(V)$ characteristics measured at 30mK, the contribution of individual donors
is resolved and the fingerprints of phonon assistance in the tunneling process
are seen. The latter is confirmed by detailed analysis of the tunneling rates
and the modeling of the resonant tunneling contribution to the current.
Moreover, fluctuations of the local structure of the DOS (LDOS) and Fermi edge
singularities are observed.
