Distribution Function Analysis of Mesoscopic Hopping Conductance Fluctuations

TL;DR

This paper analyzes mesoscopic VRH conductance fluctuations using distribution functions, validating theoretical models and exploring magnetoconductance behavior in Si MOSFETs with respect to geometry and magnetic field effects.

Contribution

It provides experimental validation of the distribution function approach for VRH conductance fluctuations and applies it to magnetoconductance analysis in mesoscopic devices.

Findings

Distribution functions match theoretical predictions for different geometries.

Mean square fluctuation size varies with temperature as per Lee's model.

Magnetoconductance exhibits non-monotonic behavior influenced by device geometry.

Abstract

Variable-range hopping (VRH) conductance fluctuations in the gate-voltage characteristics of mesoscopic GaAs and Si transistors are analyzed by means of their full distribution functions (DFs). The forms of the DF predicted by the theory of Raikh and Ruzin have been verified under controlled conditions for both the long, narrow wire and the short, wide channel geometries. The variation of the mean square fluctuation size with temperature in wires fabricated from both materials is found to be described quantitatively by Lee's model of VRH along a 1D chain. Armed with this quantitative validation of the VRH model, the DF method is applied to the problem of magnetoconductance in the insulating regime. Here a non-monotonic variation of the magnetoconductance is observed in Si MOSFETS whose sign at low magnetic fields is dependent on the channel geometry. The origin of this defect is discussed within the framework of the interference model of VRH magnetoconductance in terms of narrowing of the DF in a magnetic field.