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

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Na4

■ As we add atoms, energy levels get closer together.

■ With one electron per atom, bonding orbitals always filled, antibonding always empty.

Ener

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Solid Sodium

Nan

...

...

■ For a bulk solid, n is very large (1023...)■ Spaces between levels vanish, forming

a continuous “band” of energy levels.

...

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Band Diagram

Filled

Empty

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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

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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

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Band Diagrams

MetalSemiconductor

Insulator

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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

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■ 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

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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

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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

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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