1. Silicon
Effective mass

2. Energy bands –hydrogen atom
Another atom

3. Energy bands –hydrogen atom
Two atoms
interaction
One atom

4. Energy bands – analogy One car Two cars -- draft First car requires
more power (energy)

5. Covalent bonding # of electrons filled filled Atomic number Z element1 H 2 He 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne
# of electrons
filled
Covalent bonding
filled

6. Covalent bonding # of electrons filled Atomic number Z element 11 Na 28 1 12 Mg 13 Al 3 14 Si 4 15 P 5 16 S 6 17 Cl 7 18 Ar
# of electrons
filled
Covalent bonding

7. Energy bands – silicon +14 Electrons are tightly bound to the nucleus.
Electrons are weakly bound to the nucleus.

8. Two dimensional representation of covalent bonding

9. Periodic table is specified by quantum numbers
Most common
IV material
Most common
III & V compounds

10. Energy bands – silicon @ T = 0° K
Forbidden energy
+14
Valence band:
topmost energy band
containing electrons
Conduction band:
next higher energy band

11. Two dimensional representation of covalent bonding directional dependence

12. Two dimensional representation of covalent bonding
Electron jumps
to the conduction band
This leaves a vacancy
"hole"

13. Two dimensional representation of covalent bonding T > 0
hole
It appears that the vacancy is moving

14. Due to charged particles
Effective mass me* - +
Electric field -
Due to electric field
Due to charged particles

15. Recall the Davisson-Germer experiment
Energy of a photon Eph = h

16. Recall the Davisson-Germer experiment
Effective massI

17. Effective mass calculation of a free electron

18. Effective mass
positive and negative

19. Effective mass me* analogy
Negative
mass
Vacuum
Fluid
Ice cube
in water
Gravitational force
Effective mass me* analogy

20. Periodic potentials – limiting case Kronig-Penny model

21. Rabani Kronig-Penny model. people. bu
Rabani Kronig-Penny model. people.bu.edu/theochem/history/pdfs/ /rabani.pdf
Maximum is 1

22. Negative effective mass
Forbidden region
Negative effective mass
Positive effective mass

23. Energy bands – silicon @ T = 0° K
Conduction band
Valence band
1) Valence band filled
2) No free electrons
in conduction band
==> insulator