Distribution-function analysis of mesoscopic hopping conductance fluctuations

Variable-range hopping (VRH) conductance fluctuations in the gate-voltage characteristics of mesoscopic gallium arsenide and silicon transistors are analyzed by means of their full distribution functions (DF's). 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 one-dimensional 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 nonmonotonic variation of the magnetoconductance is observed in silicon metal-oxide-semiconductor field-effect transistors whose sign at low magnetic fields is dependent on the channel geometry. The origin of this effect is discussed within the framework of the interference model of VRH magnetoconductance in terms of a narrowing of the DF in a magnetic field.