About this previous year paper
This question paper evaluates a student's understanding of semiconductor physics, energy band theory, electronic devices (PN junctions, transistors, MOSFETs), wave mechanics, and charge transport mechanisms. The exam is structured into three comprehensive sections, testing conceptual clarity, problem-solving skills, and deeper analytical reasoning.
SECTION A — Short Answer Questions (14 Marks)
Seven questions × 2 marks each
This section checks fundamental theoretical understanding of device physics.
Topics Covered:
1. Thermal Equilibrium Condition
Explains how carrier concentration, Fermi level, and recombination-generation balance remain constant in a semiconductor under equilibrium.
2. PN Junction Reverse Bias Energy Band Diagram
Requires sketching band bending, widened depletion region, increased barrier potential, and electric field direction.
3. Relation Between α and β in a Transistor
Given α = 0.98, calculate β using:
β = α / (1 – α)
4. Electroluminescence
Discusses the principle where recombination of electrons and holes emits photons (basis of LEDs).
5. de Broglie Principle of Duality
States the wave–particle duality of matter with λ = h/p.
6. Properties of MOS Capacitor
Key features: accumulation, depletion, inversion, oxide capacitance, and threshold voltage behavior.
7. Drift Current vs Diffusion Current
Differentiate motion due to electric field (drift) vs carrier concentration gradient (diffusion).
SECTION A checks conceptual clarity and precision in definitions.
SECTION B — Analytical Descriptive Questions (21 Marks)
Attempt any three × 7 marks each
This section requires explanation, diagrams, and reasoning.
1. Photoelectric Effect & Particle Nature of Light
Explain Einstein’s equation (hν = Φ + KE), threshold frequency, and how discrete photon energy proves particle nature.
2. Intrinsic vs Extrinsic Semiconductors
Discuss carrier concentration, Fermi level position, dopants (donor/acceptor), and I–type, N–type, P–type semiconductors.
3. Small-Signal Model of PN Junction Diode
Explain dynamic resistance, incremental changes, diode linearization under AC, and equivalent circuit.
4. Stability Factor in Transistor Biasing
Define stability factor S, its importance, why unstable biasing causes thermal runaway, and methods to improve bias stability.
5. C-V Characteristics of MOS Transistor
Plot and explain accumulation, depletion, and inversion regions; oxide capacitance; threshold voltage.
SECTION C — Long Answer / Analytical Questions (35 Marks)
One question from each part × 7 marks
3. Quantum Mechanics & Band Theory
Option A – Schrödinger Equation in Infinite Potential Well
Explain quantized energy levels, wave functions, effect of well width on energy, and confinement.
Option B – Allowed & Forbidden Bands (Kronig–Penney Model)
Illustrate formation of energy bands, band gaps, periodic potential, and qualitative/rigorous explanation from model results.
4. Doping & Carrier Transport
Option A – Doping and Energy Band Gap Changes
Explain donor/acceptor levels, shift in Fermi energy, narrowing/widening of band gap, and effect on conductivity.
Option B – Continuity Equation
Derive using drift and diffusion currents, charge conservation, and recombination-generation processes.
5. Carrier Transport, Diode Equation & Einstein Relation
Option A – Einstein Relation
Derive D/μ = kT/q and explain physical importance in diffusion and mobility.
Option B – PN Junction Diode I-V Relation
Derive Shockley diode equation:
I = I₀ (e^{qV/ηkT} – 1)
Discuss forward & reverse bias behavior.
6. Transistor Modeling & Biasing
Option A – Ebers–Moll Model for PNP Transistor
Explain large-signal model, forward/reverse biasing, current equations, and equivalent circuit.
Option B – Biasing Schemes & Voltage Divider Bias
List all schemes:
• Fixed bias
• Collector-to-base bias
• Voltage-divider bias
• Emitter bias
Explain voltage divider bias with diagram, derivation of stability, and operating point selection.
7. JFET & MOSFET Characteristics
Option A – JFET Biasing Schemes
Explain various biasing types:
• Self-bias
• Voltage-divider bias
• Fixed-bias
• Current-source bias
Option B – Enhancement-Type P-Channel MOSFET
Discuss structure, operation (VSG > Vt), channel formation, transfer and drain characteristics with diagram.