P-N Junction and Diodes

Syllabus: P-N junction, Zener diode, LED, photo diode and solar cell.

10 hand-picked visual resources on this topic, 2 of them little-known gems — under each card, look for See it. Every link is checked against the live site before it ships.

▶Interactive labThe p-n junction under bias

Built-in potential and depletion width

The depletion region widens under reverse bias and narrows under forward bias. Its width scales as the square root of the total junction voltage.

$V_{bi}=V_T\ln\!\left(\frac{N_AN_D}{n_i^{2}}\right)$
$W\propto\sqrt{V_{bi}-V}$
$C_j\propto\frac{1}{\sqrt{V_{bi}-V}}$

See it

Diode equation

Exponential in forward bias, saturating in reverse. A 60 mV change in bias multiplies the current by ten at room temperature.

$I=I_0\left(e^{V/\eta V_T}-1\right)$

Zener vs avalanche

Two different mechanisms with opposite temperature behaviour — which is how they are told apart in questions.

$\text{Zener: tunnelling, }\lesssim5\ \text{V, negative temp. coefficient}$
heavy doping, thin depletion region
$\text{avalanche}:\ V_Z\gtrsim7\ \text{V}$

Solar cell and photodiode

A photodiode operates in reverse bias as a current source proportional to light; a solar cell works in the fourth quadrant delivering power.

$I=I_L-I_0\left(e^{V/V_T}-1\right)$

LED and the direct-gap requirement

An LED is a forward-biased junction in which injected carriers recombine radiatively. That needs a direct band gap, which is why silicon — the material everything else is made of — cannot make one, and GaAs and its alloys can.

$\lambda=\frac{hc}{E_g}\ \Rightarrow\ \lambda(\mu\mathrm{m})=\frac{1.24}{E_g(\mathrm{eV})}$

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