  It is shown that the observed Quantum Hall Effect in epitaxial layers of
heavily doped n-type GaAs with thickness (50-140 nm) larger the mean free path
of the conduction electrons (15-30 nm) and, therefore, with a three-dimensional
single-particle spectrum is induced by the electron-electron interaction. The
Hall resistance R_xy of the thinnest sample reveals a wide plateau at small
activation energy E_a=0.4 K found in the temperature dependence of the
transverse resistance R_xx. The different minima in the transverse conductance
G_xx of the different samples show a universal temperature dependence
(logarithmic in a large range of rescaled temperatures T/T_0) which is
reminiscent of electron-electron-interaction effects in coherent diffusive
transport.
