Hopping conductivity beyond the percolation regime probed by shot-noise measurements

Abstract

We have observed suppression of shot noise in the variable-range hopping regime for a twodimensional electron gas whose localization length, ξ, is controlled by a gate voltage. We have found that the suppression factor F (Fano factor) is approximately inversely proportional to the length of the system L (F = L * 0 /L) for a broad range of values of ξ/L * 0 , where L * 0 is the characteristic length. In the case ξ/L * 0 << 1, we have identified L * 0 with the distance L0 between the hard hops along the sample length. On the other hand, when ξ is of the order of L * 0 , we have observed that L * 0 does not agree with L0 calculated from the percolation model of hopping. We attribute this discrepancy to a breakdown of that model and to a reconstruction of the hopping paths.

Finite-size effect in shot noise in hopping conduction

“…With this goal we chose the frequencies at least two orders of magnitude higher than in previous experiments [11,12,16]. Also the heterostructure used was relatively clean, so that the samples did not exhibit sizeable mesoscopic fluctuations even at low-T and strong depletion.…”

“…In long enough samples, the experiments in 2D VRH regime [11,12] find that the Fano factor decays with the sample length roughly as F ∝ L −1 . This behavior is qualitatively explained by the averaging of the Poissonian noises associated with different hops, analogous to noise averaging in a one-dimensional array of N identical tunnel junctions F = 1/N [13].…”

“…In the VRH conduction regime, however, the hopping rates are spread exponentially wide, so that only the most resistive hops (so called hard hops) are important for the noise averaging [11,12]. A typical distance between these hard hops, known as a correlation length L C of the critical cluster [9], represents a length scale for the Fano-factor [11,12] …”

Full shot noise in mesoscopic tunnel barriers

“…A wide variety of noise behaviors due to localized states in mesoscopic systems have been studied both theoretically [13][14][15][16] and experimentally. [17][18][19][20][21] On the other hand, a clear demonstration of the shot noise behavior of an ideal tunnel barrier is still missing for semiconductor systems. In this paper, we report our observation of such a behavior in semiconductor tunnel barriers under various measurement configurations.…”

“…These results are similar to those from other groups. 17,19,20 the data requires information of the microscopic details ͑e.g., coupling between localized states and contacts͒ of the barrier. Figure 3 shows the results of similar measurements on four different barriers of the smaller size.…”