1. Tunneling

2. Energy Barrier  Kinetic energy is used to overcome potential energy. More for motion past barrier Less creates turning point  Objects with less energy should not cross high potential regions. E 1 < U 0 failure E 2 > U 0 success x1x1 x2x2 U0U0 E2E2 E1E1

3. Quantum Wave  Wave duality permits particles to behave as waves.  Waves can enter a barrier but lose intensity on entry. Exponential decrease Depends on energy U 0 -E Depends on barrier width w  Reduced amplitude reflects the probability of barrier penetration. U0U0 A0A0 AwAw w

4. Tunneling Probe  Optical microscopes are limited by light diffraction. About 500 nmAbout 500 nm  Electron microscopes are also diffraction-limited. Debroglie wavelengthDebroglie wavelength About 0.2 nmAbout 0.2 nm  Tunneling between a sharp tip and sample measures gap. Resolves 0.001 nmResolves 0.001 nm About 1% of atomic diameterAbout 1% of atomic diameter

5. STM  A scanning tunneling microscope (STM) uses a tunneling current to make images of atoms. next 7 nm x 7 nm image: Cs atoms on GaAs (NIST)