Key idea: What causes Zener breakdown?

Zener breakdown occurs in a reverse-biased $p$-$n$ junction when the electric field across the depletion region becomes extremely large, causing electrons to tunnel across the junction.

Condition for very high electric field

The electric field in the depletion region becomes very large when:

• the junction is heavily doped, and
• the depletion layer is very thin (narrow).

This is because heavy doping reduces the depletion width, and for a given reverse voltage, a smaller width gives a larger electric field: $E \approx \frac{V}{d}$ where $d$ is the depletion width.

Evaluate the options

• A: heavily doped and have wide depletion layer
  Incorrect. Heavy doping does not give a wide depletion layer; it gives a narrow one.

• B: lightly doped and have narrow depletion layer
  Incorrect. Light doping generally produces a wide depletion layer.

• C: heavily doped and have narrow depletion layer
  Correct. This is exactly the condition for Zener breakdown.

• D: lightly doped and have wide depletion layer
  Incorrect. This condition is associated more with avalanche breakdown, not Zener breakdown.

Final answer

Therefore, Zener breakdown occurs in a $p$-$n$ junction when both sides are heavily doped and the depletion layer is narrow.