A3 · Semiconductor basics

Drift and Diffusion: The Two Hands That Move Carriers

There are only two ways to move a carrier: drift, which pushes, and diffusion, which spreads. Switch each on alone and watch how the full current is completed.

Switch each mechanism on, one at a time

The bar is a semiconductor and the dots are carriers. With only the field on, they are all pushed one way; with only a difference in concentration, they spread from crowded to empty. Which do you need to draw the full current?

Tap to switch the mechanism.

Current density J

J = q n μ E

The field pushes every carrier the same way. Drift speed is mobility times field.

Half the picture

The pushing hand: drift

Apply a field and carriers are drawn along it. But because they collide constantly inside the crystal, they never keep accelerating; on average they settle at a steady drift speed. That speed is proportional to the field, and the constant of proportionality is the mobility. The more carriers there are and the more easily they move, the larger the drift current.

The spreading hand: diffusion

Carriers jitter at random even when left alone. Where they crowd on one side, at that boundary more leave from inside than enter from outside. So even with no pushing force, a net flow appears from crowded to empty. This flow is proportional to the concentration gradient, and the constant of proportionality is the diffusion coefficient. Since the strength of the random motion has a common root, diffusion and drift are tied by the Einstein relation.

ObserveJdrift = q n μ E

Drift current is the product of carrier count, mobility and field.

ChooseJdiff = q D (?)

Diffusion current follows the concentration gradient.

Fill inJtotal = Jdrift + ?

The total current is the two terms added.

On your ownJtotal = q n μ E + ?

Complete it by adding the diffusion term to the drift term.

Their sum, and their cancellation

The total current at a point is the drift term plus the diffusion term. Usually one of the two dominates, but there is a special moment when they are exactly equal in size and opposite in direction. Then the net current is zero, and that very balance sets up the built-in potential of the pn junction in the next unit.

Back to the first screen

With only the field on, and with only a difference in concentration, the carriers clearly moved. But each was half the picture. The real total current is the pushing drift plus the spreading diffusion added together. And the moment these two become equal in size and opposite in direction, erasing each other exactly, the net flow stops, and that stopping builds the barrier of the junction. There are two hands that move carriers, and the behavior of a device is always the tug-of-war between them.

Carrier current has two terms. Drift is the flow pushed by a field, J = q n μ E; diffusion is the flow that spreads down a gradient, J = q D (dn/dx). The total current is their sum. Born of the same random motion, the two coefficients are tied by the Einstein relation D = (kT/q)μ. When the two terms cancel, the net current is zero and the system is at equilibrium.

What comes next

The stage where the two hands meet is the very next unit. Join n-type and p-type, and at the border carriers cross by diffusion, while the fixed ions left behind raise a field that pushes back by drift. Where the two cancel exactly, a depletion layer emptied of carriers and a built-in potential appear. That is the pn junction of A4.