Intrinsic semiconductor behavior — effect of temperature on carriers in pure silicon As the temperature of a pure (intrinsic) silicon specimen increases, what happens to the concentrations of free electrons and holes?

Introduction / Context:Intrinsic semiconductors such as pure silicon conduct via thermally generated electron–hole pairs. Temperature strongly influences the intrinsic carrier concentration n_i, which in turn governs conductivity, mobility interplay, and device leakage characteristics.

Given Data / Assumptions:

• Material is intrinsic silicon (no intentional doping).
• Thermal equilibrium conditions apply.
• Temperature is increased within a range that does not cause material degradation.

Concept / Approach:In intrinsic semiconductors, electron concentration n equals hole concentration p, both equal to n_i. The intrinsic concentration varies roughly as n_i ∝ T^(3/2) * exp(−E_g / (2 k T)). As temperature T increases, the exponential factor dominates, rapidly increasing n_i, so both n and p increase equally.

Step-by-Step Solution:Start with charge neutrality: n = p = n_i for intrinsic silicon.Raise temperature → more thermal energy → more electron–hole pair generation.Therefore, both free electron and hole concentrations increase simultaneously.Thus, the correct qualitative statement is that both increase.

Verification / Alternative check:Measured conductivity σ = q (n μ_n + p μ_p) increases with temperature for intrinsic Si primarily because n_i increases rapidly, despite mobilities decreasing with temperature.

Why Other Options Are Wrong:(a) and (c) capture only one carrier type; in intrinsic material, electrons and holes are generated in pairs. (b) incorrectly suggests holes decrease.

Common Pitfalls:Confusing intrinsic behavior with doped (extrinsic) semiconductors, where one carrier type may dominate and temperature trends differ in certain ranges.

Final Answer:the number of free electrons and holes increases