The Poole-Frenkel laws and a pathway to multi-valued memory

Abstract

We revisit the mechanism of Poole-Frenkel non-ohmic conduction in materials of non-volatile memory. Percolation theory is shown to explain both the Poole and Frenkel dependencies corresponding to the cases of respectively small and large samples compared to the correlation radii of their percolation clusters. The applied bias modifies a limited number of microscopic resistances forming the percolation pathways. That understanding opens a pathway to multi-valued non-volatile memory and related neural network applications. arXiv:1906.07677v2 [cond-mat.dis-nn]

Percolation with plasticity for neuromorphic systems

“…An important conceptual point by Shklovskii 14,23,24 is that the applied voltage concentrates on the strongest resistor of a percolation cluster bond (resistor 1 in Fig. 2) suppressing it to the level of the next strongest (resistor 2 in Fig.…”

Pulse percolation conduction and multi-valued memory

“…3 and varies between different microscopic regions; they are exponentially higher for most resistive regions. The microscopic recharging while tacitly implied in the original non-ohmicity work, [8][9][10][11] was insignificant there due to the imposed steady state conditions, i. e. long enough time t τ max = τ 0 exp(ξ max ). 2) PWP systems violate all three of the above assumptions by: (a) opening a possibility of multiple (ℵ 1) electrodes 11 as signal entrances/ports and not assuming the system dimensions exceeding L c and requiring description beyond the standard percolation theory 11,19 ; (b) allowing for bias induced nonvolatile changes; and (c) operating under pulse shaped bias typical of neural networks (STDP).…”

“…The highest of those local fields produces the exponentially strong nonohmicity of percolation materials. [8][9][10][11] One distinct feature introduced here is that local electric fields in percolation bonds can be strong enough to structurally modify the underlying material through nonvolatile changes in its local resistivities; hence, percolation with plasticity (PWP).…”

Numerical modeling of nonohmic percolation conduction and Poole Frenkel laws

“…Non-ohmic conduction in disordered materials can be described in terms of the percolation theory. [1][2][3][4] Materials that exhibit percolation conduction include amorphous, polycrystalline and doped semiconductors, and granular metals. According to the percolation theory, the electric current flows along an infinite conducting cluster with topology resembling that of waterways formed in a flooded mountainous terrain.…”

“…The activation barriers W i are random, and the exponents ξ i = W i /kT vary in a broad interval ∆ξ ≈ ξ m 1, in which their probabilistic distribution ρ(ξ) is approximately uniform. [1][2][3][4] Here ξ m is the upper boundary of the distribution. Since the number of markedly different activation energies is of the order of ξ m and each cell of the cluster must include all representative resistors, one can estimate L ∼ aξ m .…”