p-n Junctions and Diodes

Describes p-n junctions, rectification and current in semiconductor diodes.

Conceptual context

A p-n junction forms when p-type and n-type semiconductor regions meet. Carriers initially diffuse across the contact, leaving fixed ions behind and creating a depleted region with an internal electric barrier. That barrier is not a mechanical wall; it is an electrostatic energy landscape. A diode uses this asymmetric landscape. Forward $V_d$ lowers the effective barrier and lets $I$ grow rapidly, while reverse bias reinforces the barrier and leaves only a small leakage-like response. The device therefore acts as an electrical one-way valve, but with a curved, temperature-dependent characteristic rather than a perfect switch.

🟢 Essential level

A diode rectifies because applied $V_d$ changes the internal barrier of a p-n junction differently for the two polarities.

At equilibrium, diffusion builds an internal barrier and a region with very few mobile carriers near the junction. When the anode is positive relative to the cathode, the effective barrier is reduced, majority carriers cross more easily, and $I$ rises very sharply. When the polarity is reversed, the barrier widens and majority-carrier transport is almost entirely blocked. $T$ matters because it sets $V_T$, the voltage scale that decides how strongly the current responds to the same electrical push. Rectification therefore means turning an alternating drive into a preferred current direction through asymmetric transport, not creating energy, not enforcing a perfect threshold, and not behaving like an ideal switch. It is like a revolving door that pushes easily in one direction but barely yields in the other: almost all the traffic ends up flowing the way the door favors.

🔵 Formal level

Basic formulas

The basic quantitative description uses the ideal diode equation. $I$ depends on $V_d$, $I_s$, $n$ and $V_T$; a small forward change in $V_d$ can produce a large change in $I$. This creates an exponential I-V curve in forward operation and a nearly flat reverse branch before breakdown.

Ideal diode equation

The thermal scale is obtained from $T$, $k_B$ and $q$. This is why the same diode shifts its I-V curve when heated and why $n$ must be read together with thermal voltage rather than as a decorative fit parameter.

Thermal voltage

At equilibrium, the junction has a $V_bi$ linked to $N_A$, $N_D$ and $n_i$. Higher doping usually raises the barrier logarithmically and changes the depleted region.

Built-in barrier potential

Real student questions

Why do people say a diode drops 0.7 V? It is a practical rule for some silicon diodes at particular currents, not a physical constant.

Can there be current under reverse voltage? Yes. A small $I_s$ exists, and large reverse voltage may cause breakdown.

Why does $T$ change everything? Because $V_T$ and carrier generation depend on thermal agitation.

Is $W$ empty material? No. It contains fixed ions and electric field, but few mobile carriers.

Final synthesis

A p-n junction rectifies because $V_d$ tilts an internal asymmetric barrier. $I$ is the collective response of carriers, temperature, doping and power limits.