Carrier concentration vs temperature in semiconductors As the temperature of a semiconductor increases, how does the average number of free charge carriers change?

Introduction / Context:The temperature dependence of carrier concentration underpins the behavior of diodes, transistors, and intrinsic sensors. Unlike metals, semiconductors become more conductive as temperature rises due to thermal generation of carriers.

Given Data / Assumptions:

• Intrinsic or lightly doped semiconductor.
• No breakdown or phase change within the temperature range considered.
• Standard bandgap Eg remains roughly constant over the range.

Concept / Approach:

Intrinsic carrier concentration ni follows ni ∝ T^(3/2) * exp(−Eg / (2kT)). As T increases, the exponential term grows rapidly, producing more electron-hole pairs. Even in doped materials, at sufficiently high T the intrinsic carriers dominate (intrinsic regime), increasing total carrier density.

Step-by-Step Solution:

Verification / Alternative check:

Conductivity σ = q (n μn + p μp) rises with T in intrinsic regime, as seen in temperature-dependent I–V of diodes and in intrinsic thermistors (NTC behavior).

Why Other Options Are Wrong:

A and C contradict fundamental semiconductor physics; D is too vague; E has no physical basis.

Common Pitfalls:

Transferring metal intuition to semiconductors; ignoring the dominance of carrier generation over mobility decrease at elevated temperatures.

Final Answer:

the average number of free charge carriers increases