Solid-state materials and band theory — match each item to its band-structure characteristic List I (Material / dopant) A. Copper (a good conductor) B. Rubber (an electrical insulator) C. Antimony doped into Si/Ge (Group V donor) D. Boron doped into Si/Ge (Group III acceptor) List II (Band-structure effect) 1. Produces a discrete energy level just above the valence band (acceptor level) 2. Produces a discrete energy level just below the conduction band (donor level) 3. Large forbidden energy gap (typical of insulators) 4. Valence and conduction bands overlap (typical of good conductors)
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AA-4, B-3, C-2, D-1
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BA-4, B-1, C-2, D-3
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CA-3, B-4, C-2, D-1
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DA-4, B-3, C-1, D-2
Answer
Correct Answer: A-4, B-3, C-2, D-1
Explanation
Introduction / Context:This matching question tests fundamental solid-state physics as used in electronics: how intrinsic materials and dopants shape band structures and hence conductivity. Conductors, insulators, and doped semiconductors can be recognized by simple band diagrams and the placement of donor/acceptor energy levels relative to the conduction and valence bands.
Given Data / Assumptions:
- Copper represents a metallic conductor.
- Rubber represents an insulating polymer with a large band gap.
- Antimony (Sb, Group V) acts as a donor in Si/Ge.
- Boron (B, Group III) acts as an acceptor in Si/Ge.
Concept / Approach:In metals, the valence and conduction bands overlap or a partially filled band exists, so electrons move freely. Insulators show a large forbidden gap between valence and conduction bands, limiting carrier excitation. In semiconductors, doping introduces discrete energy levels: donors (Group V) add levels just below the conduction band; acceptors (Group III) add levels just above the valence band, easing promotion of carriers with modest thermal energy.
Step-by-Step Solution:
Copper → overlapping bands → maps to statement 4.Rubber → large forbidden gap → maps to statement 3.Antimony (donor) → discrete level just below E_c → maps to statement 2.Boron (acceptor) → discrete level just above E_v → maps to statement 1.Verification / Alternative check:Introductory band diagrams for metals, insulators, and doped semiconductors consistently show these placements. Device physics texts use the same donor/acceptor level locations to explain n-type and p-type behavior and the ease of thermal ionization at room temperature.
Why Other Options Are Wrong:
- Assigning rubber to donor/acceptor levels confuses intrinsic insulation with doped semiconductor behavior.
- Placing “overlap” on rubber or dopants contradicts their basic roles.
- Swapping donor/acceptor positions in energy band diagrams reverses n-type vs p-type physics.
Common Pitfalls:Mixing up “discrete level near E_c” (donor) and “near E_v” (acceptor); assuming all good conductors simply have tiny gaps rather than true band overlap; forgetting that polymers like rubber are wide-gap insulators.
Final Answer:A-4, B-3, C-2, D-1