Distribution-function analysis of mesoscopic hopping conductance fluctuations

Abstract

Variable-range hopping ͑VRH͒ conductance fluctuations in the gate-voltage characteristics of mesoscopic gallium arsenide and silicon transistors are analyzed by means of their full distribution functions ͑DF's͒. 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 fieldeffect 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. ͓S0163-1829͑96͒10227-7͔

Coulomb Blockade and Transport in a Chain of One-Dimensional Quantum Dots

“…(10) describes the statistics of G in an ensemble of wires at a given T. However, fluctuations of comparable magnitude would appear in the same wire as T varies [29,30,37]. They would be superimposed on the backbone dependence G / T a .…”

Conductance fluctuations in one‐ and two‐dimensional localized systems

“…In our model, this behavior can be derived from Eqs. (9) and (11). Experimental data also follow this law [11].…”

“…Medina and Kardar [9,10] found a universal distribution with a variance growing as r 2=3 in 2D systems. On the experimental side, Hughes et al [11] measured the distribution function of the conductance in the variable-range hopping regime of mesoscopic gallium arsenide and silicon transistors. They claimed that their data could be explained with the prediction of Raikh and Ruzin [5].…”

Activated hopping transport in anisotropic systems at low temperatures

“…From (14), an activated T dependence of conductivity (σ ∝ c ) is obtained. Additional information on the conduction mechanism in the activation regime can be obtained from the probability distribution function (PDF) of the conductance fluctuations [19]. The hopping transport generally implies strong fluctuations as any external parameter (e.g., the chemical potential) varies because of an extremely broad distribution of elementary resistors composing the network [20].…”

“…Note that the geometrical constraint due to reducing dimensionality generally enhances fluctuations (see Ref. [19] and references therein), and leads ultimately to large non-self-averaging fluctuations in 1D [21].…”