For an intrinsic semiconductor, how does temperature affect the number of free electrons and holes present?

Introduction / Context:
Temperature strongly influences carrier concentration in semiconductors. For intrinsic materials, thermal energy controls how many electrons are promoted from the valence band to the conduction band, simultaneously creating holes. Understanding this trend is essential for sensor design and for predicting leakage currents in devices.

Given Data / Assumptions:

• Intrinsic semiconductor with no intentional doping.
• Uniform temperature across the sample.
• Thermal equilibrium conditions.

Concept / Approach:
The intrinsic carrier concentration n_i increases rapidly with temperature due to the exponential dependence on bandgap and thermal energy. When an electron gains sufficient energy to cross the bandgap, it becomes a free electron in the conduction band and leaves behind a hole in the valence band. Thus, both electrons and holes increase with temperature, keeping n = p = n_i at equilibrium.

Step-by-Step Solution:
1) Consider thermal generation of electron-hole pairs.2) As temperature rises, more pairs are generated per unit time.3) Therefore, the concentrations of both electrons and holes increase together in intrinsic material.

Verification / Alternative check:
Experimental I–V measurements of diodes show increased reverse saturation current with temperature, reflecting higher intrinsic carrier concentration. This aligns with the theoretical temperature dependence of n_i.

Why Other Options Are Wrong:

• Decreases: Opposite of the true trend for intrinsic materials.
• Stays the same: Only approximately valid over very narrow ranges, not generally true.
• 0oC: This is not a trend description and is irrelevant as an option.
• None of the above: Incorrect because the correct trend is an increase.

Common Pitfalls:
Confusing intrinsic behavior with doped behavior can lead to mistakes. While mobility may decrease with temperature, the dominant effect on intrinsic conductivity is the steep increase in carrier concentration.

Final Answer:
Increases.