Coordinate System Invariant Formulation of Fractional‐Dimensional Child‐Langmuir Law for a Rough Cathode-Reference-Cited by-同舟云学术

Coordinate System Invariant Formulation of Fractional‐Dimensional Child‐Langmuir Law for a Rough Cathode

Published:2023-04-14 Issue:7 Volume:2 Page:
ISSN:2751-1200
Container-title:Advanced Physics Research
language:en
Short-container-title:Advanced Physics Research

Author:

Zubair Muhammad¹^ORCID,Fatima Adeela²,Raheem Noreen²,Ang Yee Sin³^ORCID,Mehmood Muhammad Qasim¹²^ORCID,Massoud Yehia¹^ORCID

Affiliation:

1. Innovative Technologies Laboratories (ITL) King Abdullah University of Science and Technology (KAUST) Thuwal 23955‐6900 Saudi Arabia

2. MicroNano Lab Department of Electrical Engineering Information Technology University (ITU) of the Punjab Ferozepur Road Lahore 54600 Pakistan

3. Science Mathematics, and Technology (SMT) Cluster Singapore University of Technology and Design (SUTD) Singapore 487372 Singapore

Abstract

AbstractThis work presents an exact closed‐form analytical model of the space charge limited (SCL) current density for planar, cylindrical, and spherical geometries in fractional dimensional spaces (Fα) where α represents the fractional dimensions having a range 0 < α ⩽ 1. Decreasing value of α shows an increasing degree of surface roughness. This analytical model approaches Langmuir–Blodgett equations for sufficiently close anode (Ra) and cathode (Rc) radii for integer dimensions (α = 1). To calculate SCL current density for any geometry, variational calculus (VC) is used to derive the differential equations in fractional (α) dimensions. The effect of electrode radius ratios on space charge limited current is investigated here considering the surface roughness.

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/apxr.202200120

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