Subtopic: Crystal Lattices, Band Theory & Superconductivity
Question Statement:
The temperature dependence of the electrical conductivity (𝜎) of three intrinsic
semiconductors A, B and C is shown in figure.
Let EA, EB and EC be the bandgaps of A, B and C, respectively. Which one of the
following relations is correct?
Options:
(A) EC > EA > EB
(B) EB > EC > EA
(C) EA > EB > EC
(D) EA > EC > EB
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.27)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Solid State Physics** within *Section 7: Solid State Physics* (1 Mark, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Solid State Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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