Comments on "A New Derivation of the Law of the Junctions"

• Published in: IEEE transactions on education Vol. 64; no. 2; pp. 202 - 204
• Main Author: Hong, Brian
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bipolar transistors; Carrier density; Curricula; Depletion; Derivation; Electrical engineering; Electrical junctions; Electrochemical potential; Engineering education; engineering mathematics; Equilibrium; Equilibrium conditions; Equivalence; Fermi-Dirac statistics; Mathematical model; Minority carriers; P-n junctions; physical modeling; Quantum mechanics; Semiconductor devices; Semiconductor junctions; Solid state devices; Solid state physics; Textbooks; Thermal energy
• ISSN: 0018-9359; 1557-9638
• DOI: 10.1109/TE.2020.3025362

Contribution: This brief comment highlights some crucial assumptions behind the "law of the junction" that are overlooked by the above paper and argues that the proposed derivation is not actually a "new" derivation at all. Background: The "law of the junction" is one of the most significant and useful results within the field of solid-state devices. The above paper is likely to confuse readers, particularly those who are undergraduate electrical engineering students studying semiconductor device physics for the first time. This is especially so because of the abstract nature of the underlying quantum mechanics framework and solid-state physics models (subjects which the typical student at that level lacks a substantial background in) as well as the plethora of tedious equations in the curriculum. Research Questions: What core physical concepts are essential to a fundamental yet intuitive understanding of the law of the junction? Methodology: Several key features of how semiconductor junctions behave under bias are explained. References to well-known textbooks are provided where appropriate. Findings: The above paper's primary mistake is its assertion that its derivation does not rely on the assumption of thermal equilibrium. However, the law of the junction is equivalent to a calculation of depletion-edge minority carrier concentrations using Maxwell-Boltzmann statistics-a distribution which only holds under thermal equilibrium conditions. More rigorously, in a nondegenerate semiconductor, Fermi-Dirac statistics (which governs electrons) reduces to Boltzmann statistics only when the electrochemical potential is spatially uniform, a condition equivalent to having no net flow of thermal energy-the very definition of thermal equilibrium.