Covalent Insulators and Chem 462 September 24, 2004 Diamond Pure sp 3 carbon All bonds staggered- ideal d(c-c) - 1.54 Å, like ethane Silicon, Germanium, Gray Tin Diamond structure Si and Ge: semiconductors Si is the purest element manufactured
Silicon and 3-5 Silicon (diamond-type) is related to the octet 3-5 semiconductors by replacing Si with, e.g., GaAs. Silicon vs. Carbon C-C single bonds (356 kj/mol) are much stronger than Si-Si bonds (230 kj/mol) occurrence of coal, hydrocarbons is reasonable no natural occurence of Si-Si bonds (can be synthesized, however) White Tin (β-sn) Stable under standard conditions, but unstable wrt a- Sn below 286 K at 1 atm pressure.
Crude picture for Bonding in Diamond 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. Why an insulator? A band gap exists between the filled Empty conduction band and unfilled orbitals. sp 3 -sp 3 antibonding Band gap energy Filled valence band sp 3 -sp 3 bonding The gap is big; the bonding (and antibonding) interactions are strong. Band Diagrams Metal Semiconductor Insulator
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 thermal conductivity - at normal T, only low energy excitation possible. Measuring the Band Gap Absorbance E g Wavelength E g If the band gap becomes small enough, some conductivity can be achieved. Band gaps: diamond: silicon: 580 kj/mol (l ~ 206 nm) 105 kj/mol (l ~ 1140 nm) germanium: 64 kj/mol (l ~ 1870 nm) Pure Si or Ge can conduct at high T or if exposed to light.
Thermal energy promote e s from heat (thermal equilibrium), gives (virtually Boltzmann-like) distribution of excited states where some electrons are promoted. When electrons have been promoted (heat, light), the material will begin to conduct. Intrinsic (pure, undoped) Moderate band gaps - conductivity is low but increases with temperature: [e][h] = K eq = e - G / RT = (e S / R)e - H / RT H E = E gap also [e] = [h] [e] = [h] (e S / 2R) e -Egap/ 2RT Conductivity is an activated process (E a = E gap /2) in a pure semiconductor. Plot lnσ vs. (1/T) to get slope = E gap /2 Metals vs Metals resistivities increase with T resistivities decrease with T However, note the huge difference in scales on these plots! Resistivities = ρ = 1/σ σ [e] = [h] Ge W Al Cu
Extrinsic (Doped) Pure elemental semiconductors (Si, Ge, etc.) can only be used for devices where light or heat can be supplied to promote electrons. More useful devices are made using doped semiconductors appropriate impurities are intentionally added to supply electrons (e.g., P) or holes (e.g., Al). n-type Dope with phosphorus. An electron is left-over after forming Si-P bonds. The added electrons are easily promoted from the donor levels at normal temperatures, so they can serve as charge carriers. Typical n-type devices contain on the order of 0.00001% P. Phosphorus doped into Si Si P +
n-type Add e donor levels pure silicon Initially, valence band is full, conduction band is empty Added e s must go in conduction band Extent of conductivity depends on # of electrons added. p-type Dope with aluminum. Formation of Al-Si bonds steals an electron from Si. The holes allow places for electrons to move into within the valence band, so they serve as charge carriers Shallow impurity levels, as for n-type - electrons easily promoted at normal temperatures. Properties of n & p type differ slightly. Most devices contain combinations of both. p-type Remove e acceptor levels pure silicon Initially, valence band is full, conduction band is empty Removing e s leaves holes in valence band Number of electrons removed determines conductivity.