Shot noise in long conductors

Abstract

Using the 'drift-diffusion-Langevin' equation we show that, at least in one geometry, finite-frequency shot noise is of the order of the 'full' shot noise $2eI$ provided the sample is either short or long enough, $L > L_0(ω)$. Here $L_0(ω) = D'/\lph ω$ with $D'$ the effective diffusion coefficient, $\lph$ the electron-phonon energy relaxation length with energy transfer $eV$, and $ω$ the observation frequency. For example, in a typical 'zero frequency' experiment, actually performed at 10 KHz, shot noise may be large for $L$ larger than a few centimeters. At 100 MHz shot noise may be large for any length of the sample. The physical reason for this result -- a competition between the equilibration length and the dynamic screening length -- is discussed in the text.