Assertion–Reason (semiconductor properties): Silicon is less sensitive to temperature changes than germanium. Reason: The cut-in (turn-on) voltage in silicon is less than that in germanium.

Difficulty: Easy

Correct Answer: A is true but R is false

Explanation:


Introduction / Context:
Temperature sensitivity determines the stability of diodes and transistors. Silicon (Si) and germanium (Ge) differ in band gap and intrinsic carrier generation, producing different thermal behaviors and turn-on voltages.


Given Data / Assumptions:

  • Typical room-temperature band gaps: Si ≈ 1.12 eV, Ge ≈ 0.66 eV.
  • Typical diode cut-in voltages: Si ≈ 0.7 V, Ge ≈ 0.3 V (order of magnitude).
  • Comparison is for standard, undamaged devices under similar conditions.


Concept / Approach:
The intrinsic carrier concentration n_i grows roughly as exp(−E_g/(2kT)). A larger E_g (silicon) yields much lower n_i and a smaller temperature coefficient of leakage and parameters. Hence Si is less temperature-sensitive than Ge — the assertion is true. The reason claims Si has a smaller cut-in voltage than Ge, which is false; Si's cut-in is larger.


Step-by-Step Solution:

Relate temperature sensitivity to band gap: larger E_g → lower n_i → better thermal stability.Check cut-in voltages: V_γ(Si) ≈ 0.7 V > V_γ(Ge) ≈ 0.3 V.Therefore A is true; R is false; R cannot explain A.


Verification / Alternative check:

Leakage current vs. temperature curves show Ge rises much faster than Si, confirming higher sensitivity of Ge.


Why Other Options Are Wrong:

Options claiming R true contradict measured diode characteristics; options stating A false contradict band-gap arguments.


Common Pitfalls:

Confusing forward drop (cut-in) with thermal stability; they are related to material properties but not in the way stated by R.


Final Answer:

A is true but R is false

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