1. Lecture VII Tunneling

2. Tunneling An electron of such an energy will never appear here! classically E kin = 1 eV 0 V-2 Vx

3. Potential barriers and tunneling According to Newtonian mechanics, if the total energy is E, a particle that is on the left side of the barrier can go no farther than x=0. If the total energy is greater than U 0, the particle can pass the barrier.

4. Tunneling – quantum approach Schroedinger eq. for region x>L Solution:

5. Potential barriers and tunneling Two solutions: or Normalization condition: Solution: The probability to find a particle in the region II within

6. Potential barriers and tunneling

7. example Let electrons of kinetic energy E=2 eV hit the barrier height of energy U 0 = 5 eV and the width of L=1.0 nm. Find the percent of electrons passing through the barrier? T=7.1·10 -8 insulator semiconductor metal A If L=0.5 nm.then T=5.2 ·10 -4 !

8. Scanning tunneling electron miscroscope

12. Image downloaded from IBM, Almaden, Calif. It shows 48 Fe atoms arranged on a Cu (111) surface Scanning tunneling electron miscroscope

13.  particle decay Approximate potential - energy function for an  particle in a nucleus.

14. Tunneling Nuclear fusion ( synteza ) is another example of tunneling effect E.g. The proton – proton cycle