Electron tunneling in the tight-binding approximation
In this thesis, we treat tunneling similar to a scattering problem in which an incident wave on a barrier is partially transmitted and partially reflected. The transmission probability will be related to the conductance using a model due to Landauer. Previously tunneling has been treated using a simple barrier model, which assumes the electron dispersion is that of free electrons. In this model it is not possible to investigate tunneling in the gap between a valence band and a conduction band. We shall remedy this limitation by using the tight-binding model to generate a barrier with a gap separating a valence band and a conduction band. To do this, we constructed a model consisting of semi-infinite chains of A atoms on either side of a semi-infinite chain of B-C molecules. The B-C chain has a gap extending between the onsite energy for the B atom and the onsite energy for the C atom. Tunneling through the gap has been calculated and plotted. We present exact closed form solutions for the following tunneling systems: (i) A-B interface, (ii) A-(B-C) interface, (iii) A-B-A tunnel barrier, (iv) A-(B-C) interface with the orbitals on B having s-symmetry and those on C having p-symmetry, (v) A-(B-C)-A tunnel barrier.