Exponents for 1/fnoise, near a continuum percolation threshold

Abstract

New bounds for the exponent characterizing the amplitude of the resistance noise near the percolation threshold of discrete random networks are found. The difference between the lower and upper bounds is very small, so that an accurate estimate of the noise exponent can be obtained in all dimensions. Continuum corrections to these exponents for the random-void class of systems are then calculated within the nodes-links-blobs model of percolating networks.

Percolative switching in transition metal dichalcogenide field-effect transistors at room temperature

“…3b and supplementary material for more detail), which makes identifying the transport mechanism at switching from T -dependence of σ alone a very difficult task. The exponents ν in N σ − σ scaling, however, provide a direct evidence of a percolative transport, with the noise peak signifying the percolation threshold at V g ≈ V c g [40,42,58]. Below the percolation threshold (V g < V c g : Region I), called the "dielectric regime", transport occurs by hopping or tunneling through disconnected metallic puddles [59], and approaches a finite device-dependent magnitude at low V g away from the threshold.…”

“…Hence despite compelling evidence of long range inhomogeneity in the charge distribution in MoS 2 FETs [21,22], its manifestation in transport remains indirect and confined only to low temperatures. A way to circumvent this difficulty involves measuring the lowfrequency noise, or 1 f -noise, in the channel conductivity σ, which also scales with p with independent characteristic scaling exponents [40,42], and diverges at the percolation threshold (p c ) [41]. A direct relation between the normalized noise magnitude N σ and σ thus eliminates the necessity to know either p or p c accurately.…”

“…Theoretically, clas-sical percolation-limited conductivity in metal-insulator composites is characterized by established critical exponents [21,24,25,[40][41][42][43][44], but the experimental difficulty lies in accurately determining the fraction p of the conducting region, or "puddles", embedded inside the insulating matrix. Hence despite compelling evidence of long range inhomogeneity in the charge distribution in MoS 2 FETs [21,22], its manifestation in transport remains indirect and confined only to low temperatures.…”

“…In the 2D lattice models of random resistor network, for example, ν ≈ 0.86 or 1.5, [REF: [40,45]] whereas in the continuum percolation framework, such as the "swisscheese model" [44], ν ≈ 3.2 for random void (RV, insulating voids in a conducting background) and ≈ 0.87 for inverted random void (IRV, weakly connected conducting regions in an insulating matrix), respectively [41,42]. In this work we have investigated the switching process in TMDC FETs by simultaneously measuring N σ and σ as the electrical transport is tuned from the strongly insulating to the quasi-metallic regime using a gate voltage.…”

“…At low carrier density, for example, hopping via single particle states trapped at short-range background potential fluctuations (∼few lattice constants [23]) is incompatible to the observation of classical percolative conduction that requires long-range inhomogeneity in charge distribution, created when linear screening of the underlying charge disorder breaks down [24][25][26][27]. Observations of metal-insulator transition [7,22] [21,24,25,[40][41][42][43][44], but the experimental difficulty lies in accurately determining the fraction p of the conducting region, or "puddles", embedded inside the insulating matrix. Hence despite compelling evidence of long range inhomogeneity in the charge distribution in MoS 2 FETs [21,22], its manifestation in transport remains indirect and confined only to low temperatures.…”