  The local density of states of a degenerate semiconductor is investigated at
low magnetic fields. In order to realize this experiment, we designed a
strongly asymmetric double-barrier heterostructure with heavily doped contacts
and study the resonant tunneling transport through the lowest localized
(zero-dimensional) level in the quantum well. Fine structure in the tunneling
current as a function of bias voltage and magnetic field images mesoscopic
fluctuations of the local density of states in the emitter contact. Our
quantitative analysis demonstrates that the fluctuation pattern originates from
quantum interference of diffusive electron waves in the three-dimensional
disordered system on the length scale of the mean free path. Since the
fluctuations reflect the properties of the electron states below the Fermi
level, the observed mesoscopic effect is temperature insensitive.
