Question

The avalanche breakdown voltage of a p-n junction:

• A. Increases with increase in doping and also with increase in band gap
• B. Decreases with increase in doping and also with decrease in band gap
• C. Increases with decrease in band gap and also with increase in doping
• D. Decreases with increase in band gap and also with increase in doping

Hint:

Remember:
Higher Doping $\rightarrow$ Thinner Depletion Layer $\rightarrow$ Lower Breakdown Voltage.
Smaller Bandgap $\rightarrow$ Less energy needed to generate electron-hole pairs $\rightarrow$ Lower Breakdown Voltage.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question asks about the dependency of the avalanche breakdown voltage of a p-n junction diode on two parameters: the doping concentration and the bandgap of the material.

Step 2: Key Formula or Approach:
Avalanche breakdown is caused by impact ionization under a strong electric field in the depletion region.
We must analyze how the depletion region width and electric field intensity change with doping, and how the energy required for impact ionization scales with the semiconductor bandgap.

Step 3: Detailed Explanation:

• Effect of Doping: Higher doping concentration decreases the depletion region width ($W \propto 1/\sqrt{N_d}$). A thinner depletion region increases the electric field strength for a given reverse-bias voltage. Consequently, carriers reach high kinetic energies over shorter distances, causing breakdown to occur at a lower reverse-bias voltage. Thus, breakdown voltage decreases with an increase in doping.

• Effect of Band Gap: To initiate impact ionization, a carrier must gain energy at least equal to the bandgap ($E_g$) of the semiconductor. A smaller band gap requires less energy to break covalent bonds, making avalanche multiplication easier at lower electric fields (and thus at lower reverse-bias voltages). Thus, breakdown voltage decreases with a decrease in band gap.

Step 4: Final Answer:
The avalanche breakdown voltage decreases with an increase in doping and also with a decrease in the bandgap, which corresponds to Option (B).