EC-6.1 Carriers, Doping and Concentration

What this is and why it exists

Doping is the idea the whole industry rests on. Adding a vanishingly small quantity of another element changes a material's conductivity by orders of magnitude, predictably and permanently.

How small? One impurity atom per million silicon atoms is a heavy dose. Nothing else in engineering gives that much leverage for that little intervention.

The relationship worth carrying out of this topic is short. The electron and hole concentrations multiply to a constant that depends only on the material and the temperature. Raise one and the other falls to compensate. Almost every concentration question later is that statement plus arithmetic.

The vocabulary

• Doping — deliberately adding a controlled impurity to change conductivity.
• Donor — an impurity with a spare valence electron, which it gives up easily.
• Acceptor — an impurity short of a valence electron, which leaves a hole.
• n-type — doped so that electrons are the abundant carrier.
• p-type — doped so that holes are the abundant carrier.
• Majority carrier — whichever carrier doping has made abundant.
• Minority carrier — the other one, present in far smaller numbers.
• Fermi level — the energy at which a state has a one in two chance of being occupied.
• Charge neutrality — the fact that a doped region carries no net charge overall.

The mental model

Silicon has four valence electrons and bonds to four neighbours, with every electron accounted for. Doping breaks that arrangement deliberately, in one of two directions.

Add an atom with five valence electrons. Four go into bonds and the fifth has nothing to do. It is held so loosely that ordinary room-temperature thermal energy frees it. That leaves a fixed positive ion behind and a mobile electron in the conduction band. The material now has far more electrons than holes: n-type.

Add an atom with three. One bond is left incomplete. A neighbouring electron slides in to fill it, leaving the vacancy where it came from, and the vacancy moves. The material now has far more holes than electrons: p-type.

Notice what happened. In neither case did the material gain net charge. The impurity atom is neutral. It contributed a mobile carrier and kept a fixed opposite charge. That is charge neutrality, and writing it down is the fastest way to find an unknown concentration or catch an arithmetic slip.

Now the distinction that matters more than it first appears. Doping fixes which carrier is abundant, but a great deal of device behaviour depends on the rare one. A transistor is a device built almost entirely on what the minority carrier does after being injected somewhere it does not belong. So the small number is not a rounding error to be dropped; it is often the answer.

The mass action relation ties them together: the two concentrations multiply to a constant fixed by the material and the temperature. Doping a region heavily n-type does not merely add electrons; it actively suppresses holes. That is a consequence people forget, and it is exactly why a junction works.

One more piece of vocabulary that pays off later. The Fermi level marks the energy at which a state is as likely to be occupied as not. In an undoped crystal it sits near the middle of the gap. Doping n-type moves it up toward the conduction band; doping p-type moves it down toward the valence band. On a band diagram, its position tells you the doping without any calculation. That is why every band diagram in the next few topics draws it.

What you should now be able to explain or do

• Say what a donor and an acceptor each do, and which type each produces.
• Name the majority and minority carrier in a given doped region.
• Use the fact that the two concentrations multiply to a constant.
• Write charge neutrality for a doped region and use it as a check.
• Read the doping of a region from where the Fermi level sits on a band diagram.

Check yourself