Semiconductor Electronics

2.1 Core concepts

• Before 1948, electron-flow devices were vacuum tubes (diode, triode, tetrode, pentode); they are bulky, need ~100 V, have low reliability — solid-state semiconductor devices replaced them because charge supply happens within the solid (NCERT §14.1, p. 323-324).
• On the basis of conductivity: metals have ρ ~ 10−2 to 10−8 Ω m; semiconductors ρ ~ 10−5 to 106 Ω m; insulators ρ ~ 1011 to 1019 Ω m (NCERT §14.2, p. 324).
• Semiconductors of interest are elemental (Si, Ge) and compound (inorganic like GaAs, CdS, CdSe, InP; organic like anthracene; organic polymers like polyaniline) (NCERT §14.2, p. 324-325).
• Energy-band picture: in a solid, electron energy levels of neighbouring atoms form continuous bands — the valence band (lower, filled by valence electrons) and the conduction band (upper); the gap between top of VB (EV) and bottom of CB (EC) is the energy band gap Eg (NCERT §14.2, p. 325-326).
• Three cases from band theory: (a) Metals — CB and VB overlap, or CB is partially filled; (b) Insulators — Eg > 3 eV, no thermal excitation possible; (c) Semiconductors — small finite Eg < 3 eV, so at room temperature some electrons can cross over to CB (NCERT §14.2, Fig. 14.2, p. 326-327).
• For Si and Ge crystal of N atoms there are 4N valence electrons in 8N available outer-orbit states; at the lattice spacing, these split into two bands separated by Eg (NCERT §14.2, p. 325).
• Intrinsic semiconductor (pure Si, Ge): diamond-like lattice with each atom covalently bonded to 4 neighbours. At T = 0 K behaves as an insulator. At T > 0 K, thermal energy breaks some covalent bonds, producing free electrons in CB and equal-numbered holes in VB (NCERT §14.3, p. 327-329).
• A hole is a vacancy left by an electron in a broken covalent bond and behaves like an apparent free particle of effective positive charge +q (NCERT §14.3, p. 327).
• In an intrinsic semiconductor ne = nh = ni (intrinsic carrier concentration), and the total current I = Ie + Ih (NCERT §14.3, eqns 14.1 and 14.2, p. 327-328).
• Generation–recombination equilibrium: under steady state, rate of thermal generation of carriers equals their rate of recombination (electron colliding with a hole) (NCERT §14.3, p. 328).
• Extrinsic semiconductor: deliberate addition (doping) of a small (~ppm) impurity of nearly the same size as the host atom to increase conductivity manifold. Two dopant types in Si/Ge: pentavalent (As, Sb, P) and trivalent (In, B, Al) (NCERT §14.4, p. 329-330).
• n-type: pentavalent dopant gives one weakly-bound extra electron (ionisation energy ~0.05 eV for Si, ~0.01 eV for Ge — much less than the band gap of 1.1 eV for Si and 0.72 eV for Ge); donor atom donates this electron to CB. Electrons are majority, holes minority; ne >> nh (NCERT §14.4, p. 330-331, eqn 14.3).
• p-type: trivalent dopant accepts an electron, creating a hole in VB; acceptor atom becomes effectively negative. Holes are majority, electrons minority; nh >> ne (NCERT §14.4, p. 331, eqn 14.4).
• Law of mass action (electron–hole concentration product): nenh = ni2 in thermal equilibrium for any (intrinsic or extrinsic) semiconductor; crystal stays overall electrically neutral (NCERT §14.4, eqn 14.5, p. 332).
• In the band diagram of doped material the donor level ED lies just below EC; the acceptor level EA lies just above EV (NCERT §14.4, Fig. 14.9, p. 331-332).
• Energy gaps reported: C (diamond) 5.4 eV, Si 1.1 eV, Ge 0.7 eV; Sn 0 eV (a metal). This explains why C is an insulator while Si and Ge are intrinsic semiconductors despite having the same lattice (NCERT §14.4, p. 332; Example 14.1, p. 329).
• p-n junction formation: in the same wafer one region is doped p-type and another n-type. Two processes occur — diffusion (holes p → n, electrons n → p, due to concentration gradient) and drift (carriers driven by the electric field of the depletion region). At equilibrium diffusion current = drift current and net current is zero (NCERT §14.5, p. 333).
• Depletion region: as carriers diffuse across, immobile ionised donors leave a positive space-charge on the n-side and ionised acceptors leave a negative space-charge on the p-side; thickness ~ one-tenth of a micrometre. This sets up a barrier potential V0 opposing further diffusion (NCERT §14.5, Fig. 14.10-14.11, p. 333-334).
• Forward bias (p to +, n to −): applied V opposes V0, so depletion width and effective barrier (V0 − V) decrease; majority carriers cross the junction (minority carrier injection); current is in mA (NCERT §14.6.1, p. 334-335).
• Reverse bias (n to +, p to −): applied V adds to V0, so depletion width and effective barrier (V0 + V) increase; only a small drift current (~μA) due to minority carriers flows; nearly voltage-independent up to breakdown (NCERT §14.6.2, p. 335-336).
• V-I characteristics: forward current is negligible until the threshold/cut-in voltage (~0.2 V for Ge, ~0.7 V for Si), after which it rises sharply (exponentially). In reverse bias, current is a small reverse saturation current (~μA); at breakdown voltage Vbr it suddenly increases (NCERT §14.6.2, Fig. 14.16, p. 336-337).
• Dynamic resistance rd = ΔV/ΔI; in forward bias rd ~ a few Ω, in reverse bias ~107 Ω (NCERT §14.6.2, eqn 14.6 and Example 14.4, p. 337).
• Rectification: since a diode conducts only when forward biased, it converts ac into pulsating dc. Half-wave rectifier uses one diode and gives output only during one half-cycle (NCERT §14.7, Fig. 14.18, p. 338).
• Full-wave rectifier uses two diodes with a centre-tap transformer; D1 and D2 conduct in alternate half-cycles, giving an output for both halves of the input ac (NCERT §14.7, Fig. 14.19, p. 338-339).
• A capacitor in parallel with RL acts as a filter: it charges to peak rectified voltage and discharges slowly through RL (time constant ∝ CRL). Large C gives a steady dc nearly equal to peak voltage; widely used in power supplies (NCERT §14.7, p. 339-340; Fig. 14.20).
• Output frequency depends on rectifier type: a half-wave rectifier reproduces the input frequency (one pulse per ac cycle, so 50 Hz → 50 Hz output), whereas a full-wave rectifier delivers two pulses per cycle so the output ripple frequency is twice the input (50 Hz → 100 Hz). This is a recurring distinction tested by NCERT exercises (NCERT §14.7, p. 339; Exercise 14.6).
• The depletion-region width in a typical silicon p-n junction is of order 0.1 µm; despite being so thin it sets up an internal field strong enough (~10⁵ V cm⁻¹) to balance the chemical-potential difference between p- and n-regions at equilibrium (NCERT §14.5, p. 333).
• In reverse bias the small reverse saturation current arises from minority carriers — electrons in the p-region and holes in the n-region — which the depletion-region field happily sweeps across; this is why the reverse current is almost independent of the applied voltage but depends strongly on temperature (NCERT §14.6.2, p. 336).
• Forward-bias current in a diode follows the exponential Shockley-like behaviour above the cut-in voltage — that is why textbook V–I curves show a knee at ~0.7 V (Si) followed by a near-vertical rise; below the knee, current is negligibly small (NCERT §14.6.2, Fig. 14.16, p. 337).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 14.1 — energy band positions of a semiconductor at 0 K with EC, EV and Eg labelled (p. 326).
• Fig. 14.2 — band-gap pictures for (a) metal (overlap), (b) insulator (Eg > 3 eV), (c) semiconductor (small Eg) (p. 326).
• Fig. 14.4 / 14.5 — 2-D lattice of Si/Ge showing covalent bonds and the hole-electron generation and hole-motion mechanism (p. 328).
• Fig. 14.7 / 14.8 — pentavalent (donor) and trivalent (acceptor) atoms substituted in the Si lattice; commonly used schematic with +ve core and electron, and −ve core and hole (p. 330-331).
• Fig. 14.9 — band diagram showing the donor level ED just below EC for n-type and the acceptor level EA just above EV for p-type (p. 332).
• Fig. 14.10 / 14.11 — formation of the p-n junction: diffusion and drift, and the resulting depletion region with barrier potential V0 (p. 333-334).
• Fig. 14.13 / 14.15 — diode under forward bias (barrier reduced to V0 − V) and reverse bias (barrier raised to V0 + V) (p. 335-336).
• Fig. 14.16 — circuit for studying V-I characteristics and the typical V-I curve of a silicon diode showing cut-in at ~0.7 V and a reverse saturation current (p. 336).
• Fig. 14.18 — half-wave rectifier circuit with transformer secondary and load RL and output waveform (p. 338).
• Fig. 14.19 — centre-tap full-wave rectifier with diodes D1 and D2 and output waveform across RL (p. 339).
• Fig. 14.20 — full-wave rectifier with a capacitor in parallel with RL acting as a filter; smooth dc output (p. 340).

2.4 Common confusions / NTA trap points

• Eg ranges: metals Eg ≈ 0, semiconductors 0.2-3 eV (Si 1.1, Ge 0.7), insulators > 3 eV (C ~5.4 eV). Students mix up which class has the smallest/largest gap — remember the order (Eg)C > (Eg)Si > (Eg)Ge.
• n-type majority/minority: in n-type, electrons are MAJORITY but the dopant is PENTAVALENT (P/As/Sb). NTA frequently swaps "pentavalent" with "trivalent" to trap students.
• Hole charge: a hole is the absence of an electron in a bond — its effective charge is +q, but the material as a whole remains neutral because the acceptor/donor cores carry the opposite charge.
• Cut-in voltage values: 0.2 V for Ge, 0.7 V for Si — easy to swap.
• Reverse current is voltage-independent (in μA) only up to breakdown; at breakdown it rises sharply. Students wrongly assume it is always negligible.
• Output frequency: half-wave rectifier output frequency equals input frequency (50 Hz → 50 Hz), but a full-wave rectifier output frequency is twice the input (50 Hz → 100 Hz).
• Depletion-region direction of internal field: the built-in field points from the n-side to the p-side (i.e. from + to − space charge), opposing further diffusion of majority carriers. Many students draw the arrow the wrong way.
• Conduction in metal vs semiconductor with temperature: metals' resistivity rises with T (more lattice scattering), but semiconductors' resistivity falls with T (more thermally generated carriers). NTA exploits this contrast.
• nₑnₕ = nᵢ² always — even in heavily doped material. If nₑ is raised by donor doping, nₕ falls accordingly so that the product is fixed at any given temperature.
• Diode is not Ohmic: V–I curve is non-linear, so dynamic resistance rd = ΔV/ΔI varies along the curve. Treating Ohm's law I = V/R as applicable to a diode is wrong.
• The capacitor filter does NOT change input frequency; it merely smooths the pulsating dc. Full-wave output already has frequency 2ν; the filter does not double it further.

2.5 Key formulas table