Height distribution of equipotential lines in a region confined by a rough conducting boundary

Abstract

Abstract.This work considers the behavior of the height distributions of the equipotential lines in a region confined by two interfaces: a cathode with an irregular interface and a distant flat anode.Both boundaries, which are maintained at distinct and constant potential values, are assumed to be conductors. The morphology of the cathode interface results from the deposit of 2 × 10 4 monolayers that are produced using a single competitive growth model based on the rules of the Restricted Solid on Solid and Ballistic Deposition models, both of which belong to the Kadar-Parisi-Zhang (KPZ) universality class. At each time step, these rules are selected with probability p and q = 1 − p. For several irregular profiles that depend on p, a family of equipotential lines is evaluated. The lines are characterized by the skewness and kurtosis of the height distribution. The results indicate that the skewness of the equipotential line increases when they approach the flat anode, and this increase has a non-trivial convergence to a delta distribution that characterizes the equipotential line in a uniform electric field. The morphology of the equipotential lines is discussed; the discussion emphasizes their features for different ranges of p that correspond to positive, null and negative values of the coefficient of the non-linear term in the KPZ equation.Height distribution of equipotential lines in a region confined by a rough conducting boundary2

The role of Hurst exponent on cold field electron emission from conducting materials: from electric field distribution to Fowler-Nordheim plots

“…To overcome this difficulty, we developed an algorithm to round off the sharpest projections and replace the real WM surface with an equipotential surface, Φ E (very similar to the previous one), that is calculated from the numerical solution of the Laplace equation using a finite-difference scheme (Liebmann method - see Supplementary Information ). For practical applications, this approximation corresponds, for instance, to the condition in which good Spindt arrays 22 are produced by slowly increasing the voltage such that the sharpest tips “burn off.” Our numerical solution has been shown to yield an FEF for ideal protuberances that is in very good agreement with the results of previous analytical, finite-element and multigrid methods 23 24 25 .…”

“…For practical applications, this approximation corresponds, for instance, to the condition in which good Spindt arrays [22] are produced by slowly increasing the voltage such that the sharpest tips "burn off." Our numerical solution has been shown to yield an FEF for ideal protuberances that is in very good agreement with the results of previous analytical, finite-element and multigrid methods [23][24][25].…”

Hallmarks of the Kardar–Parisi–Zhang universality class elicited by scanning probe microscopy

“…A related result was obtained in Ref. [43], where the profile statistics of equipotentials, which are akin to the output profile in SPM techniques, generated by self-affine conducting surfaces yield a large skewness for a growth model in the regime of the linear Edwards-Wilkinson universality class [7], for which S = 0.…”

“…For a fixed growth time, we observed that both skewness and kurtosis increase with the tip size, since the lowest height contributions are being depleted, but values consistent with KPZ (S=0.4 to 0.5 against 0.43 and K=0.3 to 0.5 against 0.35) are observed for R T comparable to ξ; see also discussion on figure 3 for time dependence. A related result was obtained in [43], where the profile statistics of equipotentials, which are akin to the output profile in SPM techniques, generated by self-affine conducting surfaces yield a large skewness for a growth model in the regime of the linear Edwards-Wilkinson universality class [7], for which S=0.…”