12-06-2012, 02:57 PM
SEMINAR ON TUNNELING PRINCIPLE
TUNNELING PRINCIPLE.doc (Size: 26.5 KB / Downloads: 28)
Tunneling is purely a neoclassical theory. It is based on the Heisenberg’s Uncertainty Principle. It can be inferred from the principle that one cannot be absolutely certain or uncertain about the happening of an event. That is the probability of happening of the event can neither be 1 or 0. It should be somewhere in between. Previously an orbit was defined as the place where an electron can be found but now it is defined as the place where there is maximum probability to find an electron. Consider that the probability to find the electron is 99.99%, and then the probability to find it outside its orbit which is its most preferred state of energy is .01 %, that is .0001.
This means that if there is a collection of 10000 electrons there will be a probability to find one electron outside its most preferred state of energy. The expectation increases as the number of electrons considered increases. The expectation is given by the equation: xf(x) where x denotes the number of items considered and f(x) is the probability density function. Hence if there is a collection of 108 electrons then it can be expected that 104 electrons will be outside its most preferred state of energy. These electrons have traveled outside their most preferred state against the laws of classical physics. Hence it can be seen that electrons can cross energy barriers without them having the energy to cross the barrier. This is the principle of Tunneling.
In a Josephson Junction there is a difference that instead of electrons it has quasiparticle, the cooper pair tunneling from the first superconductor to the second through the insulator region which poses an energy barrier to the flow of cooper pairs. If the barrier is sufficiently thin it cannot be said with certainty that the particle exist only on one side. However the wave function amplitude for the particle is reduced by the barrier so that the wave function can be reduced on the right hand side to the point that negligible tunneling occurs.