The Background to Resonant Tunnelling Theory

The concept of tunnelling is almost as old as quantum mechanics itself. Oppenheimer (1928) wrote a paper on a hydrogen atom in an electric field as early as 1927. He calculated the rate of dissociation of the hydrogen atom and developed a method for determining the transition probabilities between two almost orthogonal states of the same energy. This method was to be rediscovered years later by Bardeen (1961) and applied to many particle tunnelling between two metals separated by a thin oxide layer. It is normally referred to as the Bardeen transfer hamiltonian method and it is important in tunnelling theory. The most familiar example of tunnelling is undoubtedly the radioactive decay of a nucleus by α-particle emission. The enormous range of lifetimes observed experimentally for radioactive decay is a consequence of the sensitivity of the transmission coefficient to variations in the tunnel barrier. For the same reason, a wide range of lifetimes should also be expected for tunnelling in semiconductors even though the potential barriers are much smaller.