We present a systematic study of the low-frequency noise in micron and submicron Hall devices made from Al(x)Ga(1-x)As/GaAs heterostructures. In a sample with feature size as small as 0.45 microm we observe a nonmonotonic temperature dependence of the noise power spectral densities (PSD's) at temperatures where surface states and deep-level excitations are frozen out. Near the temperature where the noise peaks, the PSD's can be described by a thermally activated two-level random telegraph signal, i.e., the 1/f noise originating from switching events in the highly doped Al(x)Ga(1-x) layer is resolved into a single Lorentzian spectrum.