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We perform the investigations of the resonant tunneling via impuritiesembedded in the AlAs barrier of a single GaAs/AlGaAs heterostructure. In the$I(V)$ characteristics measured at 30mK, the contribution of individual donorsis resolved and the fingerprints of phonon assistance in the tunneling processare seen. The latter is confirmed by detailed analysis of the tunneling ratesand the modeling of the resonant tunneling contribution to the current.Moreover, fluctuations of the local structure of the DOS (LDOS) and Fermi edgesingularities are observed.Comment: accepted in Phys. Rev.

Acoustic phonon-assisted resonant tunneling via single impurities