Question

Consider an electron with an energy of 2 ev impinging on a potential barrier with 20 ev and a width of 3 . What is the tunneling probability?

Answer 1

Tunnel Effect: - particle with kinetic energy E strikes a barrier with height
U0 > E and width L
- classically the particle cannot overcome the barrier
- quantum mechanically the particle can penetrated the barrier and
appear on the other side
- then it is said to have tunneled through the barrier
examples: - emission of alpha particles from radioactive nuclei by tunneling
through the binding potential barrier
- tunneling of electrons from one metal to another through an oxide
film
- tunneling in a more complex systems described by a generalized
coordinate varying in some potential
phys4.5 Page 1
approximate result: - the transmission coefficient T is the probability of a particle
incident from the left (region I) to be tunneling through the
barrier (region II) and continue to travel to the right (region III)
- depends exponentially on width of barrier L and the difference
between the particle kinetic energy and the barrier height
(U0-E)1/2 and mass of the particle m1/2
example: - An electron with kinetic energy E = 1 eV tunnels through a
barrier with U0 = 10 eV and width L = 0.5 nm. What is the
transmission probability?
- the probability is small, even for a light particle and a thin
barrier
- but it can be experimentally observed and used in devices