EC-6.2 Drift, Diffusion and Carrier Transport

What this is and why it exists

Carriers move for exactly two reasons: something is pushing them, or there are more of them here than there.

Drift is the first and diffusion is the second. Every current in every semiconductor device is one, the other, or both. That is not a simplification for beginners; it is the complete list.

Diffusion is the one that surprises people, because nothing is pushing and the carriers move anyway. The reason is entirely statistical: random motion carries more carriers out of a crowded region than into it. It is also the diffusion equation from the mathematics module, arriving in its second home.

The vocabulary

• Drift — motion caused by an electric field.
• Drift velocity — the steady average velocity a carrier reaches under a field.
• Mobility — drift velocity per unit field; how readily a carrier moves.
• Diffusion — motion caused by a difference in concentration.
• Diffusion coefficient — how strongly a concentration difference produces current.
• Einstein relation — the fixed link between mobility and the diffusion coefficient.
• Generation — the creation of an electron and hole pair.
• Recombination — an electron and a hole meeting and both disappearing.
• Carrier lifetime — how long an injected excess carrier survives on average.
• Diffusion length — how far it typically gets before recombining.

The mental model

Drift first. Apply a field and carriers are pushed along it. They do not accelerate freely, because scattering interrupts them constantly, so they settle at a steady average velocity instead. That velocity is mobility multiplied by field, and the current follows from the carrier concentration and that velocity.

Both carrier types contribute, each in proportion to its own concentration and its own mobility. Add the two and you have the conductivity of the material. This is where the resistance of a doped region actually comes from, and it is worth writing once rather than accepting.

Diffusion second, and this is the part worth slowing down for.

Put more carriers in one place than another and do nothing else. Each carrier moves randomly, with no preferred direction. But there are more of them on the crowded side, so more happen to wander out of it than into it. The net result is a flow from high concentration to low, produced by nothing but numbers.

The current is proportional to how steeply the concentration changes with position, not to how high it is. A flat excess produces no diffusion current, however large.

The two mechanisms turn out not to be independent. Both arise from the same scattering, so mobility and the diffusion coefficient are locked together, and their ratio is fixed by temperature. That is the Einstein relation, and it means measuring one gives you the other for free.

Last, carriers do not last forever. Generation creates pairs by thermal energy; recombination destroys them when an electron meets a hole. In equilibrium the two rates match exactly, which is what keeps concentrations steady.

Inject an excess — as a forward-biased junction does — and it decays. The average survival time is the carrier lifetime. It sets how fast a device can be turned off, because the stored carriers have to go somewhere first.

An excess that is also diffusing spreads and decays at the same time, so it falls away over a characteristic diffusion length. That distance decides how thin a transistor's base has to be. It is the single most consequential number in the next few topics.

What you should now be able to explain or do

• Name the two transport mechanisms and write the current each produces.
• Explain why a field gives a steady velocity rather than acceleration.
• Explain diffusion without invoking any force.
• State what the Einstein relation says and why it is useful.
• Say what carrier lifetime and diffusion length each control in a real device.

Check yourself