Semiconductors have

Question

Semiconductors have

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Option B: Negative coefficient of resistivity

Explanation & Concepts:
Semiconductors exhibit a negative temperature coefficient of resistivity (TCR), meaning their electrical resistivity decreases as temperature increases. This property arises because thermal energy excites more charge carriers from the valence band to the conduction band, significantly increasing conductivity despite increased lattice scattering.

Working Principle: In a semiconductor, the number of free charge carriers is highly temperature-dependent, governed by the Boltzmann distribution. As temperature rises, the rate of carrier generation ($n_i$) increases exponentially according to $n_i \propto e^{-\frac{E_g}{2kT}}$. This increase in carrier concentration far outweighs the reduction in carrier mobility caused by lattice vibrations (phonons), resulting in a net decrease in resistivity.

Key Formulas: $\rho(T) = \rho_0 [1 + \alpha(T - T_0)]$, where $\alpha; $n_i = \sqrt{N_c N_v} e^{-\frac{E_g}{2kT}}$ — Intrinsic carrier concentration vs temperature

Key Points: Metals have a positive temperature coefficient (resistivity increases with temperature).; Semiconductors have a negative temperature coefficient (resistivity decreases with temperature).; At absolute zero (0 K), pure semiconductors behave as perfect insulators.; The energy band gap ($E_g$) determines the thermal sensitivity of the material.

Advantages: Allows for sensitive temperature sensing (Thermistors).; Enables variable conductance control in electronic devices.

Disadvantages: Thermal instability in power electronic circuits.; Requires cooling/heatsinks for high-power semiconductor applications.

Applications: Thermistor manufacturing for temperature measurement.; Integrated circuits and transistors.; Solar cells and photovoltaic converters.

Additional Info: The negative coefficient is a direct consequence of the exponential increase in the number of charge carriers (electrons and holes) as thermal energy exceeds the bandgap.. Option C refers to conductors (like Copper), and Option A describes materials like Manganin or Constantan used in precision resistors.

Answer: B is correct — Semiconductors possess a negative temperature coefficient of resistivity because the increase in charge carrier density with temperature dominates over the decrease in carrier mobility.

Exam Tip: Remember: Metals (conductors) gain resistance as they heat up, whereas Semiconductors (intrinsic) become better conductors as they heat up due to thermal excitation of electron-hole pairs.

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Option A: Zero coefficient of resistivity

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Option C: Positive coefficient of resistivity

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Option D: Infinite coefficient of resistivity

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