3. Summary of physics principles Waves and particles are related – photo electric effect

4. Schrödinger equation gives us empty states and quantum numbers Fermi function tells us if the state is filled Boltzmann equation describes how the distribution of states evolves in space and time Velocity modulation helped win World War II and demonstrates the Boltzmann equation

5. Energy bands With more than one atom, one has to inquire about possible interaction between individual particles. Think of two race cars (or two witches) – the one behind uses less energy if it is following very closely behind the first one. Splitting of individual energy levels yielding a band.

6. Probability density functions from two adjacent atoms in close juxtaposition causes interaction and splitting of the lowest state yielding a band. separatedclose together band

7. Valence band – the top most energy band containing electrons Conduction band – the energy band just above the valence band Electrons in the conduction band can move from one location to another

8. Why did the chicken cross the road? Aristotle: It is the nature of chickens to cross roads. Issac Newton: Chickens at rest tend to stay at rest, chickens in motion tend to cross roads. Albert Einstein: Whether the chicken crossed the road or the road moved beneath the chicken depends on your frame of reference. Werner Heisenberg: We are not sure which side of the road the chicken was on, but it was moving very fast. Wolfgang Pauli: There already was a chicken on this side of the road.

9. Periodic table

10. Simple three-dimensional unit cell

12. Find the volume density of atoms in a simple cubic crystal.

14. Find the density of atom material in a simple cubic crystal –assume that each atom touches each other.

15. lattice plane & Miller indices

17. 1) If all the planes are parallel in the material, the material is called a single crystal material. 2) If there are regions where the planes are parallel in the material and there are other regions of the material where they are parallel in a different direction, the material is called a polycrystalline material. 3) If there are no regions containing parallel planes, the material is called an amorphous material.

19. Surface charge density at the edge

20. Vector directions normal to the plane in cubic lattices

21. Diamond (silicon) lattice -1/4 shown

22. Czochralski method of “growing” crystals 1916-1918

24. Dry oxidation process silicon oxygen Oxygen diffuses into the silicon

25. Wet oxidation process silicon water

26. Defects – 2 dimensional representation

27. Controlled impurities -- doping

28. Ion implantation

30. ions move Mel Widner BS, MS, PhD U. of Iowa

31. Movie to illustrate the evolution of the various charge densities.

32. ion electron