Wentzel-Kramers-Brillouin approach

From a simple Wentzel-Kramers-Brillouin (WKB) approach [2], the tunneling current increases exponentially as the thickness of the Si02 decreases. MOSFET is the capacitance-operated device. The source-drain current of the MOSFET depends on the gate capacitance ... 

In the case of not having a potential barrier independent of the distance, like in the Eckart potential, some approximations can be proposed. The Wentzel, Kramer, and Brillouin (WKB) approach is a clear example to overcome the problem. If the energy equation inside the potential barrier is... 

For an arbitrary continuous potential barrier, an approximate general expression for transition probability (barrier permeability) can be derived using the approach of ZWAAN-KEMBIE /60/, which is a generalization of the familiar BWK (BRILLOUIN-WENTZEL-KRAMERS) method/6l/. 

This approach is named after its founders—Wentzel (1926), Kramers (1926), Brillouin (1926a,b), and Jeffreys (1925). The WKBJ method is one of the powerful approximate approaches of quantum mechanics. Although in the present discussion we are concerned only with its application to obtaining approximate eigenvalues for bound states of the onedimensional Schrodinger equation, such application does not cover all of its range and its force. 

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