Observation of Partially Suppressed Shot Noise in Hopping Conduction

We have observed shot noise in the hopping conduction of two dimensional carriers confined in a p-type SiGe quantum well at a temperature of 4K. Moreover, shot noise is suppressed relative to its ``classical'' value 2eI by an amount that depends on the length of the sample and carrier density, which was controlled by a gate voltage. We have found a suppression factor to the classical value of about one half for a 2 $\mu$m long sample, and of one fifth for a 5 $\mu$m sample. In each case, the factor decreased slightly as the density increased toward the insulator-metal transition. We explain these results in terms of the characteristic length ($\simeq 1\mu$m in our case) of the inherent inhomogeneity of hopping transport.