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 $2\mu \mathrm{m}$ long sample, and of one-fifth for a $5\mu \mathrm{m}$ 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 ( $\simeq 1\mu \mathrm{m}$ in our case) of the inherent inhomogeneity of hopping transport, obtained from percolation theory.