Effect of probe size on electrical noise due to conductivity fluctuations

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Abstract
Increases in spectral noise density associated with small probe size are investigated. It is shown that conductivity fluctuations give fluctuating dipole fields. The dipoles near the electrodes lead to large noise for small electrodes. This dependence of noise on probe size is investigated for several geometries including the case where noise is produced at the surface of a three-dimensional medium. Also the effect of boundary conditions is considered. It is found that with a finite size sample one may simply treat a conductivity fluctuation as causing some average resistance change when probe size is comparable to sample sizes, but the dipole effect is important for small probes.