Long-range random potential in thin-film structures

Dimensional quantization effects in the thermodynamics of conductive filaments

“…The screening radius r s ∼L∼10 nm is determined by distance L between the metal electrodes due to their electron redistribution. The redistribution is dictated by the condition of tangential component of the electric field vanishing in the presence of charged CF [24]. That screening mechanism does not depend on material properties and should not be confused with the Debye screening.…”

“…The screening radius r s ∼ L ∼ 10 nm is always limited to the distance between the metal electrodes due to their electron redistribution. 12 With these parameters, Eq. ( 5) yields the number of electrons in a single CF, Λ/e ∼ 5 − 50.…”

A thermodynamic theory of filamentary resistive switching

“…Furthermore, a realistic analysis takes into account that CF charging simultaneously creates the corresponding image charges in metal electrodes, which screens the lateral electric field at distances of the order of h from CF. 15 As a result, r max under the logarithm in Eq. ( 1) should be replaced with h, which makes it fully independent of a particular circuit design.…”

“…Therefore, nucleation of the next embryos at the tip becomes easier, and the probability of formation of a narrow CF is determined by the first nucleation event at the threshold voltage given in Eq. (15). The radial growth of a just formed narrow CF with r ∼ r min is described in Sec.…”