EC-5.4 Conductors, Semiconductors and Insulators

What this is and why it exists

Conductors, semiconductors and insulators are not three kinds of thing. They are one continuum read at three points, and the reading is the band gap.

No gap at all and the material always conducts. A very large gap and it never does. A gap of about an electron volt and it does neither reliably.

That middle case sounds useless. It is the entire basis of the industry. A material that can be persuaded either way is a material you can build a switch from. A switch is what a computer is made of.

This topic also settles something that surprises people in a laboratory. Heating a metal makes it conduct worse; heating a semiconductor makes it conduct better. Same heat, opposite answers, and both for good reasons.

The vocabulary

• Intrinsic semiconductor — a pure one, with no deliberate impurity added.
• Carrier — anything that carries charge through the material, meaning an electron or a hole.
• Carrier concentration — how many carriers there are per unit volume.
• Mobility — how readily a carrier moves through the material under a field.
• Scattering — the collisions that stop a carrier accelerating freely.
• Lattice scattering — scattering off the vibrations of the atoms themselves.
• Impurity scattering — scattering off foreign atoms in the crystal.
• Compound semiconductor — one made from two or more elements rather than one.

The mental model

The classification is one sentence. A conductor has bands that overlap, so there are always electrons free to move and no gap to cross. An insulator has a gap far too wide for thermal energy to lift an electron across. A semiconductor has a gap small enough that a few make it across anyway.

Nothing else distinguishes them. Not appearance, not hardness, not price.

In a pure semiconductor, some electrons at any temperature above absolute zero happen to have enough thermal energy to cross the gap. Each one that does leaves a hole behind. So in a pure crystal there are exactly as many electrons in the conduction band as holes in the valence band, and both carry current. This is intrinsic conduction, and it is weak.

Now the temperature question, which is worth getting right.

Heating a semiconductor frees more carriers. More electrons make it across the gap, the carrier concentration rises steeply, and resistance falls. The gain in carriers overwhelms everything else.

Heating a metal frees nothing, because a metal already has every carrier it is going to get. The only thing heat does is make the lattice vibrate harder, which scatters the carriers more, so resistance rises.

Same cause, opposite effect, because one material has carriers to gain and the other does not.

That brings in mobility. A carrier in a field does not accelerate freely; it is knocked about constantly and settles at an average velocity. Two things do the knocking. Lattice vibrations, which get worse as temperature rises. And impurities, which matter most when the carrier is moving slowly, so they dominate at low temperature. The two working against each other is why mobility rises, peaks and then falls as a sample is warmed from very cold.

Finally, why silicon. Its gap is workable, it is abundant, and — the decisive one — it grows a stable insulating oxide on its own surface. Germanium is the better conductor and lost the argument on the oxide. That oxide is what makes a gate insulator and a protective layer practical. The industry chose a material for its rust.

Combining elements from either side of silicon in the periodic table gives compound semiconductors with different gaps, some of them direct. That is where light-emitting devices, very high frequency transistors and efficient solar cells come from.

What you should now be able to explain or do

• Classify a material from its band gap and say what each class does.
• Explain intrinsic conduction and why electron and hole counts are equal in a pure crystal.
• Say why heating helps a semiconductor and hurts a metal.
• Describe the two scattering mechanisms and why mobility peaks with temperature.
• Give the real reason silicon won, and say what compound semiconductors are for.

Check yourself