Subtopic: Crystal Lattices, Band Theory & Superconductivity
Question Statement:
A phosphorous doped silicon semiconductor ( doping density: 1017/cm3) is heated from 100C to
200C. Which one of the following statements is CORRECT ?
Options:
(A) Position of Fermi level moves towards conduction band
(B) Position of dopant level moves towards conduction band
(C) Position of Fermi level moves towards middle of energy gap
(D) Position of dopant level moves towards middle of energy gap
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2013 Q.20)**
**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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