Concept:

Avalanche breakdown requires minority carriers to gain kinetic energy equal to the ionization energy over their mean free path \( \lambda \). Higher temperatures increase lattice vibrations, shortening \( \lambda \) and requiring a stronger electric field (higher voltage) to cause impact ionization.

Formula:

$$E_{\text{kinetic}} = q \mathcal{E} \lambda \ge E_{\text{ion}} \implies \text{As } T \uparrow, \lambda \downarrow \implies \mathcal{E}_{\text{crit}} \uparrow \implies V_{\text{BR}} \uparrow$$

Solution:

• Higher temperature increases thermal lattice scattering (shorter mean free path \( \lambda \)).



• Because carriers undergo more frequent collisions, they require a stronger electric field to accelerate to the threshold energy needed for impact ionization.



• Therefore, a higher reverse voltage is needed to trigger breakdown, resulting in a positive temperature coefficient.

Why other options are incorrect:

• Option A: The energy band gap narrows with temperature; it does not widen.
• Option C: Minority carrier concentration increases with temperature due to thermal generation.
• Option D: Avalanche breakdown is an impact ionization process, not laser emission.