Analytical and Numerical Modelling of Electron Transmission Probability Through Quantum Tunnelling Barriers in Nanoscale Diodes

Quantum tunnelling becomes critical in nanoelectronic devices as dimensions approach or fall below the electron mean free path, wherein the classical transport models are no longer sufficient to describe carrier behavior. Accordingly, transmission of electrons across barriers is analyzed in nanodiodes within this paper using three main approaches: the Schrödinger Equation Method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Transfer Matrix Method. These methods have been applied to various tunneling situations involving barriers of different height and width, as well as semiconductor material interfaces representative of state-of-the-art device architectures in capturing the wavelike nature of electron transport typical at nanometric scales. A comparison is carried out in regard to the accuracy, efficiency of computation, and physical insights gained through each approach. Strengths and weaknesses of the above-mentioned techniques will be considered in view a variety of barrier profiles and device structures. Calculations based on self-consistent potentials in Si and GaAs hetero-structures exhibit strong exponential behavior of the tunneling current and barrier parameters. Consistency between methods appears only under the following special conditions of barrier variation. These results are discussed in relation to the emerging importance of a new class of tunneling-based devices: MIMs, RTDs, and TFETs, all promising for next-generation electronic and optoelectronic systems. These findings provide a conceptual and practical basis for the understanding and designing of nanoscale devices where tunneling is a dominant transport mechanism, adding an important comprehensive perspective to quantum transport modeling in nanoelectronics.