Predicting Equation of Transient Position-Probability Density for Nano-Tunnel Problem in SET

Abstract:

This analytic investigation intends to study the nano-tunnel problem of the single electron transistor (SET), which is the most important component in the nano-electronics industry. With a combined effort of quantum mechanics and similarity parameter, the PDE equation of transient position-probability density is attained and can be applied to predict the electron’s position inside the nano tunnel. Also, appropriate initial and the boundary conditions are set up in accordance to the actual electron behavior for solving this PDE of probability density function. Thereafter, a simple, closed-form solution for the probability density is obtained and expressed in terms of the error function for a new similarity variable η. In conclusions, this is an innovative approach by using the Schrödinger equation directly to solve the nano-tunnel problem. Moreover, with the aids of this analytic position-probability-density solution, it is illustrated that the free single electron in the SET’s tunnel can only appear at some specified regions, which are defined by a dimensionless parameter η within a range of 0≤η≤2. This result can be served as a valuable design reference for setting the practical manufacture requirement.

• Periodical: Applied Mechanics and Materials (Volumes 284-287)
• Pages: 2570-2574
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.284-287.2570
• Online since: January 2013
• Authors: Sheam Chyun Lin, Hsien Chang Shih
• Keywords: Nano Tunnel, Probability Density, Quantum Mechanics, Set, Similarity Parameter

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