1. Lecture XV Solid state dr hab. Ewa Popko

2. Measured resistivities range over more than 30 orders of magnitude Material Resistivity (Ωm) (295K) Resistivity (Ωm) (4K) 10 -12 “Pure” Metals Copper 10 -5 Semi- Conductors Ge (pure) 5  10 2 10 12 InsulatorsDiamond10 14 Polytetrafluoroethylene (P.T.F.E) 10 20 10 14 10 20 Potassium 2  10 -6 10 -10 Metals and insulators

3. Metals, insulators & semiconductors? At low temperatures all materials are insulators or metals. Semiconductors: resistivity decreases rapidly with increasing temperature. Semiconductors have resistivities intermediate between metals and insulators at room temperature. Pure metals: resistivity increases rapidly with increasing temperature. 10 20 - 10 10 - 10 0 - 10 -10 - Resistivity (Ωm) 1002003000 Temperature (K) Diamond Germanium Copper

4. Bound States in atoms Electrons in isolated atoms occupy discrete allowed energy levels E 0, E 1, E 2 etc.. The potential energy of an electron a distance r from a positively charge nucleus of charge q is V(r) E2E1E0E2E1E0 r 0 Increasing Binding Energy

5. Bound and “free” states in solids V(r) E2E1E0E2E1E0 The 1D potential energy of an electron due to an array of nuclei of charge q separated by a distance R is Where n = 0, +/-1, +/-2 etc. This is shown as the black line in the figure. r 0 0 + ++++ R Nuclear positions V(r) lower in solid (work function). V(r) Solid

6. Energy Levels and Bands + E +++ + position Electron level similar to that of an isolated atom Band of allowed energy states. In solids the electron states of tightly bound (high binding energy) electrons are very similar to those of the isolated atoms. Lower binding electron states become bands of allowed states. We will find that only partial filled band conduct

7. Solid state N~10 23 atoms/cm 3 2 atoms 6 atoms Energy band theory

8. Metal – energy band theory

9. At a temperature T the probability that a state is occupied is given by the Fermi-Dirac function n(E)dE The finite temperature only changes the occupation of available electron states in a range ~k B T about E F. where μ is the chemical potential. For k B T << E F μ is almost exactly equal to E F. Fermi-Dirac function for a Fermi temperature T F =50,000K, about right for Copper. The effects of temperature

10. Insulator -energy band theory

11. diamond

12. semiconductors

13. Intrinsic conductivity ln(  ) 1/T

14. ln(  ) Extrinsic conductivity – n – type semiconductor

15. Extrinsic conductivity – p – type semiconductor

16. Conductivity vs temperature ln(  ) 1/T

17. Actinium Aluminium (Aluminum) Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Bohrium Boron Bromine Cadmium Caesium (Cesium) Calcium Californium Carbon Cerium Chlorine Chromium Cobalt Copper Curium Darmstadtium Dubnium Dysprosium Einsteinium Erbium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium Gold Hafnium Hassium Helium Holmium Hydrogen Indium Iodine Iridium Iron Krypton Lanthanum Lawrencium Lead Lithium Lutetium Magnesium Manganese Meitnerium Mendelevium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Polonium Potassium Praseodymium Promethium Protactinium Radium Radon Rhenium Rhodium Rubidium Ruthenium Rutherfordium Samarium Scandium Seaborgium Selenium Silicon Silver Sodium Strontium Sulfur (Sulphur) Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten Ununbium Ununhexium Ununoctium Ununpentium Ununquadium Ununseptium Ununtrium Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium