Electronics and Semiconductors

Electronics and Semiconductors

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Semiconductors are materials whose electrical conductivity lies between that of metals and insulators and can be tuned by doping, temperature, and electric field. Silicon (band gap Eg ≈ 1.1 eV) and germanium (Eg ≈ 0.67 eV) are the two textbook materials at 300 K.

Energy-band picture: the valence band holds bound electrons, the conduction band holds mobile electrons, and the forbidden energy gap (Eg) separates them. Intrinsic semiconductors have equal electrons (n) and holes (p) with n·p = nᵢ² (mass-action law). Doping with Group-V donors (P, As) creates n-type material (electrons as majority carriers); doping with Group-III acceptors (B, Ga) creates p-type material (holes as majority carriers).

A P-N junction forms a depletion region with built-in barrier (~0.7 V for Si, ~0.3 V for Ge). Under forward bias the diode conducts exponentially (Shockley equation); under reverse bias only a tiny saturation current flows until breakdown. A junction transistor (BJT) obeys I_C = β·I_B and α + β = 1.

High-yield pointers: (1) Thermal voltage V_T = kT/q ≈ 26 mV at 300 K — used in diode equations and amplifier biasing. (2) Half-wave rectifier efficiency ≈ 40.6%; full-wave bridge ≈ 81.2%. (3) Logic gates AND/OR/NOT and the universal gates NAND/NOR implement Boolean algebra.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Energy Bands and Material Classification

In the band theory of solids, allowed electron energies form continuous valence and conduction bands separated by a forbidden gap Eg. Conductors have overlapping bands or a partially filled conduction band. Insulators have Eg > 3 eV (≈ 5–10 eV), making thermal excitation negligible at room temperature. Semiconductors have Eg in the range ~0.1–3 eV, so a measurable number of electrons are thermally excited across the gap, leaving behind mobile holes. Silicon (Eg ≈ 1.12 eV), germanium (Eg ≈ 0.67 eV), and gallium arsenide (Eg ≈ 1.42 eV) are the standard examples.

Intrinsic vs Extrinsic Semiconductors

An intrinsic semiconductor is a pure crystal where n = p = nᵢ (intrinsic concentration, ~1.5 × 10¹⁰ cm⁻³ for Si at 300 K). Doping introduces impurities: a pentavalent donor (P, As, Sb) creates n-type material with electrons as majority carriers and a donor level just below E_C; a trivalent acceptor (B, Ga, In) creates p-type material with holes as majority carriers and an acceptor level just above E_V. The mass-action law n·p = nᵢ² holds at a given temperature, and the Fermi level lies near the band centre in intrinsic material, shifts toward E_C in n-type, and toward E_V in p-type.

P-N Junction Diode

At a P-N junction, holes diffuse from p to n and electrons from n to p, leaving behind ionised dopants that form a depletion region with a built-in barrier potential V_bi (≈ 0.7 V Si, ≈ 0.3 V Ge). The diode current follows the Shockley diode equation:

I = I_s · [exp(V / (η·V_T)) − 1], V_T = kT/q ≈ 25.85 mV at 300 K

In forward bias (p-side positive), the barrier is reduced and current rises exponentially past the cut-in voltage. In reverse bias only a small saturation current I_s flows until breakdown (Zener/avalanche), exploited by the Zener diode as a voltage regulator.

Rectifiers and Filters

A half-wave rectifier conducts during only one half-cycle of the AC input; its maximum efficiency is 40.6% and ripple factor is 1.21. A full-wave bridge rectifier uses four diodes to use both half-cycles, giving efficiency 81.2% and ripple factor 0.48. A capacitor filter smooths the pulsating DC; the peak inverse voltage (PIV) rating of each diode must exceed the transformer peak.

BJT Basics

A bipolar junction transistor has three regions — emitter, base, collector — in NPN or PNP form. The terminal currents obey I_E = I_B + I_C, the current gain β = I_C / I_B, and the relation α + β = 1 where α = I_C / I_E ≈ 1 for a well-designed transistor.

Exam Pattern (ECAT Physics)

ECAT Physics carries 30 MCQs (≈ 3 % weight for Electronics); questions usually test band-gap values, diode I-V identification, rectifier efficiency, and BJT current relations. Expect one or two numericals per paper on barrier potential, V_T, or β-based current calculations.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Deeper Band Theory and Carrier Statistics

The density of states in the conduction band and the Fermi–Dirac distribution give the electron concentration n = N_C · exp(−(E_C − E_F)/kT) and hole concentration p = N_V · exp(−(E_F − E_V)/kT). Multiplying yields the mass-action law n·p = nᵢ² = N_C·N_V·exp(−Eg/kT), which shows why the carrier product is temperature-dependent but independent of doping. Conductivity follows σ = n·q·μ_n + p·q·μ_p; because μ_n > μ_p in Si, n-type silicon has higher conductivity than p-type at equal dopant concentration.

Diode Edge Cases and Special Diodes

The Zener diode is reverse-biased into breakdown; below 5.6 V the mechanism is quantum tunnelling (Zener effect), above it is avalanche multiplication. A photodiode is operated in reverse bias; photon energy hν > Eg generates electron–hole pairs, so I ∝ incident light intensity. A light-emitting diode (LED) runs in forward bias; recombination across Eg emits photons of wavelength λ = h·c/Eg — choosing Eg selects the colour (GaAs ≈ 870 nm IR, GaP ≈ 565 nm green). A Schottky diode uses a metal–semiconductor junction with negligible depletion charge and very fast switching.

Transistor Configurations and Biasing

The three BJT amplifier configurations are common-emitter (CE), common-collector (CC) and common-base (CB), with very different voltage gain, current gain and input impedance. DC biasing is typically set by a resistive voltage divider so that V_out = V_in · R2/(R1 + R2), stabilising the Q-point against β variation and temperature drift. For field-effect devices, JFET and MOSFET (especially CMOS) are voltage-controlled, draw almost no gate current, and dominate digital ICs. A thyristor (SCR) latches on once triggered and stays on until current falls below the holding value — used in power control.

Logic Gates and Boolean Algebra

The seven basic gates implement Boolean functions: AND (Y = A·B), OR (Y = A + B), NOT (Y = Ā), NAND and NOR (universal gates), XOR and XNOR (parity/equality). De Morgan’s laws — Ā·B̄ = Ā + B̄ and Ā + B̄ = Ā·B̄ — let any Boolean expression be realised with NAND or NOR alone, which is the basis of CMOS logic.

Common Mistakes and Worked Example

Common mistakes: (1) Confusing majority and minority carriers after doping. (2) Using V_T = 25.85 mV in mV units while V is in volts — keep units consistent. (3) Assuming the depletion region has mobile charge — it only has ionised dopants. (4) Forgetting that rectifier efficiency compares DC output to AC input, not to peak.

Worked example: A Si diode (η = 2) at 300 K carries I = 1 mA at V = 0.65 V. Find the saturation current I_s using V_T = 26 mV. I ≈ I_s·exp(V/(ηV_T)) ⇒ I_s = I·exp(−V/(ηV_T)) = 10⁻³·exp(−0.65/0.052) = 10⁻³·exp(−12.5) ≈ 10⁻³ × 3.73 × 10⁻⁶ ≈ 3.7 × 10⁻⁹ A = 3.7 nA.

Practice Prompts

1. A silicon sample is doped with 10¹⁶ cm⁻³ phosphorus. Using μ_n = 1350 cm²/V·s, q = 1.6 × 10⁻¹⁹ C, compute σ and the resistivity ρ.
2. A full-wave bridge rectifier feeds a 1 kΩ load from a 12 V RMS secondary. Find the DC output voltage, PIV per diode, and ripple factor with a 1000 μF smoothing capacitor at 50 Hz.

Strategy for ECAT

Allocate one focused sitting to this topic — it is short, high-yield, and often yields a “free” mark from a direct formula recall question on β, V_T, or rectifier efficiency.

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