Subtopic: Crystal Lattices, Band Theory & Superconductivity
Question Statement:
A junction is formed between a metal on the left and an n-type semiconductor on
the right. Before forming the junction, the Fermi level EF of the metal lies below
that of the semiconductor. Then which of the following schematics are correct for
the bands and the I-V characteristics of the junction?
(A)
(B)
(C)
(D)
EF
EF
Conduction Band
Valence Band
Metal
n-type semiconductor
EF
Conduction Band
EF
Valence Band
Metal
n-type semiconductor
I
V
-V0
I
V
-V0
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.57)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Solid State Physics** within *Section 7: Solid State Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Solid State Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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