ATOMIC BONDING IN SOLIDS BONDING ENERGY, INTERATOMIC SPACING.
Bonding in Solids: Metals, Insulators, &...
Transcript of Bonding in Solids: Metals, Insulators, &...
Bonding in Solids: Metals, Insulators, &
SemiconductorsCHEM 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: 3s1
Na2
Na3
Ener
gy
Ener
gy
Na4
■ As we add atoms, energy levels get closer together.
■ With one electron per atom, bonding orbitals always filled, antibonding always empty.
Ener
gy
Solid Sodium
Nan
...
...
■ For a bulk solid, n is very large (1023...)■ Spaces between levels vanish, forming
a continuous “band” of energy levels.
...
Ener
gy
Band Diagram
Filled
Empty
Ener
gy
bonding
antibonding
nonbonding
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: sp3 hybrids, σ bonds
The Structure of Diamondone “cell”
The Structure of Diamondfour cells
Bonding in Diamond (pure sp3 carbon)
■ Pick one carbon atom and look at its bonds to four neighbor atoms.
■ Mix 4 sp3 orbitals from central atom with one sp3 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.
Filled “valence band”
Empty “conduction band”
Band gap energy
sp3-sp3 antibonding
sp3-sp3 bonding
X(element) → X(g) (atom)
Measuring the Band Gap
Eg
Energy
Abso
rban
ce
Wavelength
Eg
Ener
gy
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.
Semiconductors
■ 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
Semiconductors■ If the band gap becomes small enough,
some conductivity can be achieved.■ Band gaps:
● diamond: 580 kJ/mol● silicon: 105 kJ/mol● germanium: 64 kJ/mol
■ Pure Si or Ge can conduct at high T or if exposed to light.
Semiconductors
■ Energy from heat, light, etc.■ When electrons have been promoted,
the material will begin to conduct.
Add energy
promote e–’sEner
gy
Band Diagrams
MetalSemiconductor
Insulator
Ener
gy
Doped Semiconductors
■ Pure elemental semiconductors (Si, Ge, etc.) can only be used for devices where light or heat can be supplied to promote electrons.
■ Most useful devices are made using “doped” semiconductors.
n-Type Semiconductors
■ Initially, valence band is full, conduction band is empty
Add one e–
pure silicon
Ener
gy
■ An added e– must go in conduction band
n-Type Semiconductors
■ In a real material, we can’t add just one electron.
■ Extent of conductivity depends on # of electrons added.
Add e–’s
pure silicon
Ener
gy
n-Type Semiconductors■ 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).
Phosphorus doped into Si
+
The “left-over” electron easily escapes the positively-charged P atom and can roam through the silicon.
p-Type Semiconductors
■ Initially, valence band is full, conduction band is empty
■ Removing e– leaves a “hole” in valence band
Remove one e–
pure silicon
Ener
gy
p-Type Semiconductors
■ As for n-type, can’t really remove just one e–.
■ Number of electrons removed determines conductivity.
Remove e–’s
pure silicon
Ener
gy
p-Type Semiconductors■ 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.
Aluminum doped into Si
-
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.
Diamonds can be doped!
Colors in diamonds are due to impurity doping.
Graphite is a 2-Dimensional Net
Stacking of Layers — Only DispersionForces BetweenLayers
A Single graphene Layer (side view) — Strong CovalentBonds within Each Layer (sp2 carbon)
335 pm
141.5 pm
Graphite - Delocalized π Bonding
etc. etc.
etc.
What is the C–C bond order in
Graphite?(compare
C–C single-bond, benzene,
double bond and triple bond lengths)
C60 — A new Form of Carbon
Ball-and-stick model
the dominant “resonance structure”
C60 — Intermolecular PackingThere are strong covalent bonds within each C60 “buckyball”. The C60 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)
■ C60: Black, very soft, sublimes at 500 ˚C, electrical semiconductor, dissolves in nonpolar solvents to form purple solutions
Phase Diagram for Carbon