A4 · Semiconductor basics

The pn Junction: A Border That Builds Its Own Barrier

What happens when you join n-type and p-type? Step through how majority carriers cross over, and the fixed ions left behind raise a barrier that stops the diffusion on its own.

Follow the junction to equilibrium

The left is p-type (holes), the right is n-type (electrons). Step forward and watch carriers cross while fixed ions are exposed. When does the net current stop?

Tap to step forward.

Equilibrium condition and barrier

Jdiff >> Jdrift

The concentration difference is enormous. Holes want to cross right, electrons left. There is no barrier yet.

Net diffusion is large

At contact, diffusion begins

The n-side is overwhelmingly rich in electrons, the p-side in holes. Across the border this concentration difference is so large that, the moment they touch, electrons pour into the p-side and holes into the n-side. This is exactly the diffusion seen in A3.

Departure exposes the fixed ions

Even after carriers cross, the dopant atoms that gave them up are locked in the lattice and cannot move. As in A2, the n-side donors that gave up electrons remain as positive ions, and the p-side acceptors that took holes remain as negative ions. The region near the border thus becomes a depletion layer, emptied of carriers and holding only fixed charge, and a built-in field pointing toward the p-side stands up between the two fixed charges.

ObserveJdrift = Jdiff (Jnet = 0)

At equilibrium, drift and diffusion cancel exactly.

ChooseVbi = (kTq) ln(?)

The built-in potential goes as the log of the doping product over ni squared.

Fill inNA xp = ?

The total fixed charge on each side of the depletion layer is equal.

On your ownVbi = (kTq) ln(?)

The heavier the doping, the higher the barrier.

The barrier stops diffusion: equilibrium

The built-in field pushes the crossing carriers back. This drift grows opposite to the diffusion, and the moment the two become equal in size as well, the net current falls to zero. This is exactly the cancellation foreshadowed in A3. At that point the depletion width and the built-in potential barrier Vbi stop growing, and their size is set by the doping on each side. This border, which built its own barrier to stop the diffusion, is the heart of the diode.

Back to the first screen

Just after contact, the net diffusion was enormous. As carriers crossed, fixed ions were exposed and the built-in field grew, and that barrier pushed the diffusion back by drift. The moment the two matched in size, the net current was zero and the depletion layer and barrier stopped growing. Without anything done from outside, the border built its own barrier and made an equilibrium. The fixed dopant ions of A2 and the drift-diffusion cancellation of A3 meet in one place to shape the heart of the diode.

In a pn junction, majority carriers cross the border by diffusion, and where they leave, fixed dopant ions are exposed (positive on the n-side, negative on the p-side). This fixed charge raises a carrier-free depletion layer and a built-in potential barrier Vbi. When the drift from the barrier exactly cancels the diffusion, the net current is zero at equilibrium, with Vbi = (kT/q) ln(NA ND / ni²).

What comes next

Now you hold the barrier. The next group, B, applies an external voltage to it. Forward bias lowers the barrier and carriers pour through; reverse bias raises it and blocks the flow. This one-way asymmetry is the diode I-V curve and rectification.