Bonding in Solids: Metals, Insulators, & CHEM 107 T. Hughbanks Delocalized bonding in Solids Think of a pure solid as a single, very large molecule. Use our bonding pictures to try to understand properties. metals vs. nonmetals Sodium: 3s 1 Na 2 Na 4 Na 3 As we add atoms, energy levels get closer together. With one electron per atom, bonding orbitals always filled, antibonding always empty. Solid Sodium Na n......... Empty Band Diagram antibonding nonbonding For a bulk solid, n is very large (10 23...) Spaces between levels vanish, forming a continuous band of energy levels. Filled bonding
So why is sodium a metal? Bonding half ( bottom ) of band is filled up to the nonbonding point with two electrons per orbital. Antibonding half ( top ) is empty. Availability of empty delocalized orbitals at low energies allows electrons to move through the crystal, conducting electricity. Same ideas for thermal conductivity. Tungsten Half-filled 5d band & half-filled 6s band Interaction of metals with light? Metals are shiny and opaque. Absorb and re-emit light of many colors Continuous energy levels, so nearly any wavelength can be absorbed or emitted. Insulators Look at bonding in same way, try to explain differences between metals and insulators. Diamond: excellent electrical insulator, transparent, etc. Diamond is pure carbon, tetrahedral geometry: sp 3 hybrids, σ bonds The Structure of Diamond one cell The Structure of Diamond four cells
Bonding in Diamond (pure sp 3 carbon) Pick one carbon atom and look at its bonds to four neighbor atoms. Mix 4 sp 3 orbitals from central atom with one sp 3 orbital from each of the other 4. Get 8 new orbitals, 4 bonding and 4 antibonding. Bonding orbitals filled, antibonding empty. 109.47 Why an insulator? A band gap exists between the filled and unfilled orbitals. The gap is big; the bonding (and antibonding) interactions are strong. Empty conduction band Filled valence band sp 3 -sp 3 antibonding Band gap energy sp 3 -sp 3 bonding X(element) X(g) (atom) Measuring the Band Gap E g Absorbance E g Wavelength Insulators With a large band gap, a lot of energy is needed to promote an electron. Visible light photons too low in energy, so diamond is transparent. Electrons can t readily move through material, so no electrical conductivity. Similar idea for the thermal conductivity - at normal T, only low energy excitation possible. Small band gaps - properties are in some ways intermediate between those of metals and insulators Often doped with a small amount of a second element to provide either electrons or holes as charge carriers.
Si and Ge look the same as Diamond (w / longer bonds) Diamond, Silicon, & SiC If the band gap becomes small enough, some conductivity can be achieved. Band gaps: diamond: silicon: germanium: 580 kj/mol 105 kj/mol 64 kj/mol Pure Si or Ge can conduct at high T or if exposed to light. Add energy promote e s from heat, light, etc. When electrons have been promoted, the material will begin to conduct. Band Diagrams Doped Pure elemental semiconductors (Si, Ge, etc.) can only be used for devices where light or heat can be supplied to promote electrons. Metal Semiconductor Insulator Most useful devices are made using doped semiconductors.
n-type n-type Add one e Add e s Initially, valence band is full, conduction band is empty An added e must go in conduction band In a real material, we can t add just one electron. Extent of conductivity depends on # of electrons added. n-type Phosphorus doped into Si The added electrons can be promoted easily, so they can serve as charge carriers. How can we add electrons to Si? Dope with phosphorus. An electron is left-over after forming Si-P bonds. Typical n-type devices contain on the order of 0.00001% P (100 ppb). + The left-over electron easily escapes the positivelycharged P atom and can roam through the silicon. p-type p-type Remove one e Remove e s Initially, valence band is full, conduction band is empty Removing e leaves a hole in valence band As for n-type, can t really remove just one e. Number of electrons removed determines conductivity.
p-type Aluminum doped into Si The holes allow promotion of electrons within the valence band, so they serve as charge carriers. How can we remove electrons from Si? Dope with aluminum. Formation of Al-Si bonds steals an electron from Si. Small impurity levels, as for n-type. Properties of n & p type differ slightly. Most devices contain combinations of both. Diamonds can be doped! - Graphite is a 2-Dimensional Net 141.5 pm A Single graphene Layer (side view) Strong Covalent Bonds within Each Layer (sp2 carbon) Stacking of Layers Only Dispersion Forces Between Layers 335 pm Colors in diamonds are due to impurity doping. Graphite - Delocalized π Bonding A hole in the bonding electrons of the silicon is created in order to satisfy the Al atom octet. The hole easily escapes the negatively charged Al atom and roams through the silicon. C60 A new Form of Carbon etc. etc. etc. What is the C C bond order in Graphite? (compare C C single-bond, benzene, double bond and triple bond lengths) Ball-and-stick model the dominant resonance structure
C 60 Intermolecular Packing There are strong covalent bonds within each C 60 buckyball. The C 60 molecules are bound to each other by weaker dispersion forces Carbon; Properties Diamond: Transparent, extremely hard, melting point > 3000 C, electrical insulator, insoluble in all solvents (unless carbon reacts) Graphite: Black (shiny), extremely soft. melting point > 3000 C, electrical conductor, insoluble in all solvents (unless carbon reacts) C 60 : Black, very soft, sublimes at 500 C, electrical semiconductor, dissolves in nonpolar solvents to form purple solutions Phase Diagram for Carbon