Concept:

In Zener breakdown (tunneling), the band gap narrows with temperature, making tunneling easier and lowering \( V_Z \) (negative coefficient). In Avalanche breakdown (impact ionization), increased lattice vibrations reduce carrier mean free path, requiring higher voltages to cause breakdown (positive coefficient).

Formula:

$$\frac{d V_Z}{d T} < 0 \quad (\text{Zener: Negative Coefficient}) \quad \text{vs} \quad \frac{d V_{\text{BR}}}{d T} > 0 \quad (\text{Avalanche: Positive Coefficient})$$

Solution:

• Zener (\( < 6\text{ V} \)): Higher temperatures narrow the band gap \( E_g \), enabling field-assisted tunneling at lower reverse voltages (\( \frac{d V_Z}{d T} < 0 \)).



• Avalanche (\( > 6\text{ V} \)): Higher temperatures increase phonon scattering, shortening the carrier mean free path and requiring a higher voltage to achieve ionizing collisions (\( \frac{d V_{\text{BR}}}{d T} > 0 \)).

Why other options are incorrect:

• Option A: Avalanche breakdown has a positive temperature coefficient, not negative.
• Option B: Zener breakdown has a negative temperature coefficient, not positive.
• Option C: This inverts the temperature coefficients for the two mechanisms.