Temperature coefficient of resistivity for semiconductors How does the resistivity of intrinsic or lightly doped semiconductors vary with temperature at ordinary temperatures?
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APositive temperature coefficient (resistivity increases with T)
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BNegative temperature coefficient (resistivity decreases with T)
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CMay be positive or negative depending on bias only
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DVery low and essentially zero at all T
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EOscillatory with T under DC bias
Answer
Correct Answer: Negative temperature coefficient (resistivity decreases with T)
Explanation
Introduction / Context:Unlike metals, semiconductors show strong temperature-dependent conductivity due to changes in carrier concentration and mobility. Recognizing the sign of the temperature coefficient is foundational for selecting sensors (thermistors), designing bias networks, and predicting device behavior across ambient conditions.
Given Data / Assumptions:
- Intrinsic or lightly doped semiconductor (e.g., Si, Ge) near room temperature.
- Dominant effect with rising temperature is an increase in thermally generated carriers.
- Moderate fields; no impact ionization or self-heating anomalies.
Concept / Approach:
The conductivity σ = e (n μn + p μp). In intrinsic material, n = p = ni, and ni increases steeply with temperature as ni ∝ T^(3/2) exp(−Eg/(2 k T)). Although carrier mobilities μ typically decrease with temperature due to enhanced phonon scattering, the exponential increase in ni dominates, causing σ to increase and thus resistivity ρ = 1/σ to decrease with T. Hence the temperature coefficient of resistivity is negative in the normal operating range.
Step-by-Step Solution:
Note ni(T) increases rapidly with T.σ(T) ∝ ni(T) despite μ(T) declining somewhat.Therefore ρ(T) decreases with T → negative temperature coefficient.Verification / Alternative check:
NTC thermistors exploit this behavior: resistance drops markedly as temperature rises, enabling temperature sensing and inrush current limiting (with proper design).
Why Other Options Are Wrong:
(a) describes metallic behavior; (c), (d), and (e) are not representative of semiconductor physics at ordinary temperatures under DC bias.
Common Pitfalls:
Confusing doped semiconductor trends at extreme doping levels or very low temperatures with the intrinsic/lightly doped regime.
Final Answer:
Negative temperature coefficient (resistivity decreases with T)