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A3 · Semiconductor basics

Drift and Diffusion: The Two Hands That Move Carriers

There are only two ways for carriers to move: drift, pushed along by an electric field, and diffusion, spreading out because of a concentration difference. In this unit you switch each one on separately and see how the total current comes together.

Switch on the mechanisms one at a time

The horizontal bar is the semiconductor and the gold dots are carriers. Switch on only the electric field and an orange arrow appears as every dot is pushed in one direction; set up only a concentration difference and the dots spread from the crowded region by the blue boundary line toward the empty side. Switch the buttons to check what it takes to draw the total current in full.

Switch the mechanism with the buttons.
Current density J
J = q n μ E
The electric field pushes every carrier the same way. The average drift velocity is the mobility times the electric field.
Half the picture

The pushing hand: drift

Apply an electric field and carriers are pulled along by its force. Because they keep colliding inside the crystal, though, they cannot speed up without limit; on average they settle at a steady drift velocity. That velocity is proportional to the field, and the constant of proportionality is called the mobility, so the more carriers there are and the more easily they move, the larger the drift current.

The spreading hand: diffusion

Even left alone, carriers jiggle randomly because of heat. Where they are crowded on one side, more of them cross the boundary from inside to outside than from outside to inside, so a net flow arises from the crowded side to the empty side with no push at all. This flow is proportional to the concentration gradient, and the constant of proportionality is the diffusion coefficient. Both coefficients come from the same thermal motion, so diffusion and drift are tied together 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 sum of the two terms.
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 flowing at a point is the drift term plus the diffusion term. Usually one of them dominates, but there is a special state in which the two terms are equal in size and opposite in direction. Then the net current is 0, 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 electric field on, and with only a concentration difference, the carriers clearly moved, yet each was only half the picture. The total current is the pushing drift plus the spreading diffusion. And when the two become equal in size and opposite in direction, cancelling each other exactly, the net flow stops, and that standstill sets up the barrier of the junction. Two hands move the carriers, and the operation of a device is always a tug-of-war between them.

Carrier current has two terms. Drift is the flow pushed by an electric field, J = q n μ E, and diffusion is the flow spreading down a concentration gradient, J = q D (dn/dx). The total current is their sum, and the two coefficients, both rooted in the same thermal motion, are tied by the Einstein relation D = (kT/q)μ. When the two terms cancel, the net current is 0 and equilibrium is reached.

What comes next

The stage where the two hands meet is the next unit. Join n-type and p-type and carriers diffuse across the boundary, while the fixed ions left behind set up an electric 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.