Board Previous Year Questions

How Boards Test This Chapter

Semiconductor Electronics is a dependable 4-6 mark CBSE topic. The recurring demands:

• 1 mark: band-gap comparisons; majority/minority carriers; name the dopant type; depletion region/barrier definitions; rectifier output frequency.
• 2 marks: energy-band diagrams of metal/insulator/semiconductor or intrinsic/n-type/p-type; effect of forward/reverse bias on barrier and depletion width; distinguish intrinsic from extrinsic.
• 3 marks: p-n junction formation (diffusion, drift, equilibrium) with diagram; V-I characteristics with circuit; half-wave OR full-wave rectifier with circuit + waveforms + working.
• 5 marks: the full journey — junction formation → biasing → characteristics → rectifier application, with all diagrams.

The questions below are Board-style previous-year questions with full step-by-step solutions embedded in the explanations. Attempt each before reading its solution. Years are attached only where attribution is certain; otherwise questions are tagged simply [CBSE Board].

The Statements and Diagrams Boards Reward (Model Answers)

Energy bands: valence band (VB, top $E_V$) filled at 0 K; conduction band (CB, bottom $E_C$) above; gap $E_g = E_C - E_V$. Metals: overlap/partial filling. Insulators: $E_g$ > 3 eV. Semiconductors: $E_g$ < 3 eV (C 5.4 / Si 1.1 / Ge 0.7 eV).

Intrinsic vs extrinsic: intrinsic — pure, $n_e = n_h = n_i$, feeble conduction; extrinsic — doped ppm-level; donors (pentavalent: As, Sb, P; level $E_D$ just below $E_C$) give n-type ($n_e \gg n_h$); acceptors (trivalent: In, B, Al; level $E_A$ just above $E_V$) give p-type ($n_h \gg n_e$); always $n_en_h = n_i^2$.

Junction formation (four steps): majority-carrier diffusion (holes p→n, electrons n→p) → immobile ion layers form the ~0.1 $\mu$m depletion region → its field (n→p) drives drift of minority carriers → equilibrium when drift = diffusion; barrier $V_0$ with n positive.

Biasing table: forward (p to +): barrier $V_0 - V$, depletion narrows, mA injection current beyond cut-in (0.2 V Ge / 0.7 V Si). Reverse: barrier $V_0 + V$, depletion widens, $\mu$A saturation until breakdown $V_{br}$.

Rectifiers: half-wave — one diode, output on positive half-cycles, ripple = input frequency. Full-wave — two diodes + centre tap (each diode on half the secondary), alternate conduction, ripple = 2 × input; capacitor filter (across $R_L$, large C, output near peak).

[Board Tip] Diagram marks are cheap and fixed: label $E_C$, $E_V$, $E_D$/$E_A$; mark depletion region and barrier in junction sketches; show BOTH input and output waveforms for rectifiers, aligned in time.

Board PYQ Set A: Short Answer (1-2 marks)

PYQ 1. Distinguish between intrinsic and extrinsic semiconductors on the basis of carrier concentrations. [CBSE Board]

Solution:

1. Intrinsic: pure material; carriers only from thermal bond-breaking; $n_e = n_h = n_i$.
2. Extrinsic: doped with ppm impurities; one carrier type dominates — $n_e \gg n_h$ (n-type, donors) or $n_h \gg n_e$ (p-type, acceptors); both obey $n_en_h = n_i^2$.

PYQ 2. Why is a semiconductor damaged when a strong current passes through it? [CBSE Board]

Solution:

1. Strong current → heavy Joule heating.
2. Excessive temperature breaks covalent bonds uncontrollably and can destroy the ordered doping/junction structure — the device is destroyed by overheating (NCERT's rated-value warning).

PYQ 3. Draw the energy-band diagrams of (i) n-type and (ii) p-type semiconductors at T > 0 K, marking the donor/acceptor levels. [CBSE Board]

Solution:

1. (i) n-type: $E_D$ drawn just below $E_C$; many electrons in CB (from donors), few holes in VB.
2. (ii) p-type: $E_A$ just above $E_V$; many holes in VB, few electrons in CB.
3. Labels $E_C$, $E_V$, $E_D$/$E_A$ carry the marks.

PYQ 4. What is the order of thickness of the depletion region, and why is it so named? [CBSE Board]

Solution:

1. ~0.1 micrometre ($10^{-7}$ m).
2. Named because the initial carrier migration depleted the region of its free charges — only immobile ionised donors (+, n-side) and acceptors (-, p-side) remain.

PYQ 5. How does the width of the depletion region change under (i) forward and (ii) reverse bias? Give reasons. [CBSE Board]

Solution:

1. (i) Forward: applied V opposes $V_0$ → effective barrier $V_0 - V$ → less space charge needed → width decreases.
2. (ii) Reverse: V adds to $V_0$ → barrier $V_0 + V$ → more exposed fixed charge required → width increases.

PYQ 6. In the V-I measuring circuits, why is a milliammeter used in forward bias but a microammeter in reverse bias? [CBSE Board]

Solution:

1. Forward current (minority-carrier injection) is of order mA.
2. Reverse current (minority-carrier drift/saturation) is of order $\mu$A — a milliammeter would read nothing.
3. Meter ranges must match the $10^3$ current asymmetry.

PYQ 7. State the factor on which the reverse saturation current of a diode chiefly depends, and the factor on which it does NOT. [CBSE Board]

Solution:

1. Depends on: the minority-carrier concentration — hence on temperature (thermal generation).
2. Not on: the applied reverse voltage (any small V already sweeps all minority carriers across).

PYQ 8. Write two advantages of semiconductor devices over vacuum tubes. [CBSE Board]

Solution:

1. Small size, low power consumption, low operating voltage (any two).
2. Long life and high reliability; no heated cathode or evacuated space needed.

Board PYQ Set B: Standard Numericals & Reasoning (2-3 marks)

PYQ 9. A pure Si crystal ($5 \times 10^{28}$ atoms m⁻³) is doped with 1 ppm pentavalent As. Calculate the electron and hole concentrations ($n_i = 1.5 \times 10^{16}$ m⁻³). [CBSE Board]

Solution:

1. $n_e \approx N_D = \dfrac{5 \times 10^{28}}{10^6} = 5 \times 10^{22}$ m⁻³.
2. $n_h = \dfrac{n_i^2}{n_e} = \dfrac{2.25 \times 10^{32}}{5 \times 10^{22}} = 4.5 \times 10^{9}$ m⁻³ (NCERT Example 14.2).

PYQ 10. The V-I characteristic of a Si diode gives V = 0.7 V at 10 mA and 0.8 V at 20 mA; at V = -10 V, I = 1 $\mu$A. Calculate the forward dynamic resistance and reverse resistance. [CBSE Board]

Solution:

1. $r_{fb} = \dfrac{0.1}{10 \times 10^{-3}} = 10$ ohm.
2. $r_{rb} = \dfrac{10}{10^{-6}} = 10^{7}$ ohm.

PYQ 11. C and Si have the same lattice structure; why is C an insulator but Si a semiconductor? [CBSE Board]

Solution:

1. C's bonding electrons occupy the 2nd orbit, Si's the 3rd — carbon's are far more tightly bound.
2. Band gaps: 5.4 eV (C) vs 1.1 eV (Si); thermal energy frees significant carriers only in Si (NCERT Example 14.1).

PYQ 12. Can a p-n junction be made by pressing polished p-type and n-type slabs together? Justify. [CBSE Board]

Solution:

1. No — surface roughness far exceeds the interatomic spacing (~2-3 angstrom).
2. Continuous atomic-level contact is impossible; the interface acts as a discontinuity for carriers (NCERT Example 14.3). Junctions must be grown within a single crystal.

Board PYQ Set C: Long-Answer Patterns (3-5 marks)

PYQ 13. Explain the formation of the depletion region and barrier potential in a p-n junction, with a diagram. [CBSE Board]

Solution:

1. Diffusion: concentration gradients drive holes p→n and electrons n→p.
2. Space charge: departing carriers expose immobile ionised donors (+, n-side) and acceptors (-, p-side) — the ~0.1 $\mu$m depletion region, empty of free carriers.
3. Field & drift: the space-charge field (n→p) sweeps minority carriers oppositely — the drift current.
4. Equilibrium: diffusion falls, drift grows until equal — no net current; the n-side sits positive relative to p by the barrier potential $V_0$, opposing further diffusion.

PYQ 14. Draw the circuit of a full-wave rectifier and explain its working. Why is the output frequency double the input frequency? [CBSE Board]

Solution:

1. Circuit: centre-tapped secondary; two diodes with p-sides to the winding ends, n-sides joined; load between the common point and centre tap.
2. Working: A positive → $D_1$ conducts; A negative → B positive → $D_2$ conducts. Alternate conduction, same direction through $R_L$.
3. Frequency: each input cycle yields two output humps (one per diode) → 100 Hz for 50 Hz input.

PYQ 15. With a circuit diagram, explain how the V-I characteristics of a p-n junction diode are studied in forward and reverse bias. Sketch the characteristics. [CBSE Board]

Solution:

1. Circuit: battery → potentiometer/rheostat (variable V) → diode; voltmeter across the diode; milliammeter (forward) or microammeter (reverse) in series.
2. Forward: negligible current until the cut-in (~0.7 V Si, ~0.2 V Ge), then exponential rise.
3. Reverse: flat $\mu$A saturation current, essentially voltage-independent up to breakdown $V_{br}$, where current rises sharply.
4. Sketch shows the knee at cut-in and the breakdown turn — with scales mA (up) and $\mu$A (down).

PYQ 16. Explain the role of a capacitor filter in converting the full-wave rectifier's output into a steady dc voltage. [CBSE Board]

Solution:

1. Capacitor across $R_L$ charges to the peak as each hump rises.
2. As the hump falls, it discharges slowly through $R_L$ — rate ∝ $1/(R_LC)$ — holding the output near the peak.
3. The next hump recharges it; with large C (large time constant) the ripple is small.
4. Output ≈ peak voltage with slight sawtooth ripple — the capacitor-input filter of practical power supplies.