Partially suppressed shot noise in hopping conduction: observation in SiGe quantum wells

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 4 K. Moreover, shot noise is suppressed relative to its "classical" value 2eI by an amount that depends on the length of the sample and the carrier density. We have found a suppression factor to the classical value of about one-half for a 2 &mgr;m long sample, and of one-fifth for a 5 &mgr;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 ( approximately 1 &mgr;m in our case) of the inherent inhomogeneity of hopping transport, obtained from percolation theory.