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Modified WKB Approximation for Fowler-Nordheim Tunneling Phenomenon in Nano-Structure based Semiconductors

In modern fabrication techniques, it is possible to fabricate nanostructure based semiconductor devices whose dimensions are much more comparable to the de Broglie wavelength of the electron. Therefore the concept of tunneling is a key point parameter in the design and fabrication of nanoelectronic devices. Particle tunnels through barrier particularly in the presence of high electric field or when barrier is thin. Leakage in the nano MOSFET devices is due to the tunneling phenomena of high energy electron through the super narrow oxide barriers. The theory of tunneling from metal was given by Fowler and Nordheim. Fowler-Nordheim tunneling is the wave-mechanical tunneling of electrons through a triangular barrier created at the surface of metal by applying a very high electric field. In this paper, modeling of Fowler-Nordheim tunneling is presented using modified WKB approximation method. Using this approximation method, tunneling of electron from metal as well as from semiconductor is studied and it is found that tunneling transmission coefficient differs from WKB approximation by a factor of 2–2.5.