1. E bb **

2. E

3. Looking only at this region in the Rectangle:

4. We generated a Band Diagram If we include the relative number of orbitals, we make a Density of States DOS Diagram

5. We generated a Band Diagram If we include the relative number of orbitals, we make a Density of States DOS Diagram

6. We do the same thing again, starting with isolated atoms, Then turn on the bonding, then increase the number of interactions.

7. Mn P Polymeric unit P

10. An actual example, calculated using an M.O.theory Mn P P Polymeric unit %Mn in orbital (state) %P in orbital (state)

11. Using Band Diagrams: Conductivity Conductivity - in two flavors 1. Electronic conduction - electrons move typical of metals; example: Cu and Al very good conductivity “predicted” by band diagrams 2. Ionic conduction - ions move requires “ionic” material requires defects: vacancy and interstitial (Schottky and Frenkel types) example: AgI 2 and HgM 2 I 4

12. MOT analogies with Band Diagram - HOMO / LUMO and type of reactivity - Valence Band / Conduction band and - DE and Band Gap Empty bands filled bands conduction band valence band Metallic Conductor InsulatorSemi Conductor Large Band Gap small band gap no band gap

13. conduction band valence band Metallic ConductorInsulatorSemi Conductor Large Band Gap small band gap no band gap More typically simplified to show only “frontier” bands:  E < 10 kJ/mol  E ~ 10 -100 kJ/mol  E > 400 kJ/mol Fermi level  f ff ff

14. Pure Germanium How Defects Improve Semi-Conduction  E ~ 0.66 eV Gallium-Doped Ge small band gap Ga more Electropositive: Adds “Orbitals” At Higher Energy With Fewer Electrons Pure Ge Band Gap Gallium-Doping creates positive holes, as an acceptor band: A p-type semi-conductor

15. Pure Germanium How Defects Improve Semi-Conduction  E = 0.66 eV Arsenic-Doped Ge small band gap As is more Electronegative: Adds “Orbitals” At Lower Energy Partially Filled with Electrons Pure Ge Band Gap Arsenic-Doping creates negative holes, as a donor band An n-type semi-conductor

16. How Defects Lead to DevicesPN Junctions = Diodes Fermi level in n-type semi-conductor is at higher energy than for the p-type: Spontaneous flow of electrons in one direction only. Directional Flow of electrons --> current goes in one direction only small band gap ff ff n-typep-type

17. In a pn junction, current spontaneously flows in one direction

18. How Defects Lead to Devices Band Gap threshold can be exceeded by: energy as light - photoconductivity devices: - photocells, photovoltaic cells (GaAs) - solar cells (Si) - pn-junctions with suitable e f make Light Emitting Diodes (LED) energy as heat – thermoconductivity devices: - thermistors

19. How Defects Lead to Devices: Photocopy (Xerox) Process (photolithography) - uses photoconductivity of Selenium Se paper w/ image Ink (toner)

20. How Defects Lead to Devices: Thermochromic Materials - example based on HgM 2 I 4 materials

21. Replace S with I, Zn (at vertices) with Hg, Zn (in middle) with Cu Replace S with I, Zn (at vertices) with Hg Zn (in middle) with Ag Prototype Cubic ZnS (zinc blende), two adjacent cells

22. How Defects Lead to Devices: Thermochromic Materials - example based on HgM 2 I 4 materials - adding energy as heat creates defects Cu(+) vacancies (Schottky defects) and interstital sites (Frenkel defects) - defects change band gap, change color, change conductivity