A general formula for the transmission coefficient through a barrier and application to I–V characteristic

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Abstract

A general formula providing the transmission coefficient through a given barrier, sandwiched by semiconductor reservoirs under bias is presented in terms of the incoming carrier energy and the logarithmic wave function derivative at the start of the barrier. Furthermore, the formula involves the carrier effective masses in the barrier and reservoir regions. The procedure employed is based on solving an appropriate Riccati equation governing the logarithmic derivative along the barrier width at the end of which it is known in terms of the carrier energy and applied bias. On account of the facility provided for obtaining the transmission coefficient we obtained the I–V characteristic of a quantum dot carved barrier, which exhibits a region of quite a large negative differential resistance together with a high peak to valley ratio. Under the circumstances, the possibility of developing a nanostructure switch utilizing a small variation in the applied bias exists.

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