Lesson 12 of 12 · 14 min
Chapter review
Watch a class
The whole chapter on YouTube
Next Toppers - 12th ScienceWhole chapter · Hinglish
Diodes and logic gates, full chapter
Loading the full lesson
Must-know facts
18 facts
- 01Resistivity: metals 10⁻² to 10⁻⁸ Ω m, semiconductors 10⁻⁵ to 10⁶ Ω m, insulators 10¹¹ to 10¹⁹ Ω m.
- 02Band gap: insulators Eg > 3 eV, semiconductors Eg < 3 eV, metals Eg ≈ 0 or overlapping bands.
- 03Eg: C (diamond) 5.4 eV, Si 1.1 eV, Ge 0.7 eV, Sn 0 eV (a metal).
- 04Si and Ge crystal: 4N valence electrons, 8N states split into a full valence band (4N) and an empty conduction band (4N) at 0 K.
- 05Intrinsic: nₑ = nₕ = nᵢ; current I = Iₑ + Iₕ.
- 06Lattice spacing: C 3.56 Å, Si 5.43 Å, Ge 5.66 Å.
- 07Donors (n-type): As, Sb, P (pentavalent). Acceptors (p-type): In, B, Al (trivalent).
- 08Energy to free a donor electron: about 0.01 eV in Ge and 0.05 eV in Si.
- 09n-type: nₑ ≫ nₕ; p-type: nₕ ≫ nₑ; always nₑnₕ = nᵢ².
- 10Example 14.2: 1 ppm As in Si gives nₑ ≈ 5 × 10²² m⁻³ and nₕ ≈ 4.5 × 10⁹ m⁻³.
- 11Depletion region thickness: about one-tenth of a micrometre.
- 12Barrier height: (V₀ − V) in forward bias, (V₀ + V) in reverse bias.
- 13Cut-in voltage: about 0.7 V for Si and 0.2 V for Ge.
- 14Forward current in mA; reverse saturation current in µA.
- 15Dynamic resistance rd = ΔV/ΔI; Example 14.4 gives 10 Ω forward and 1.0 × 10⁷ Ω reverse.
- 16Rectifier output frequency for 50 Hz input: 50 Hz half-wave, 100 Hz full-wave.
- 17Full-wave with a centre tap: two diodes, each rectifying half the secondary voltage; the bridge circuit uses four diodes.
- 18A capacitor filter goes in parallel with RL; a large C × RL gives a steadier dc near the peak voltage.
Common traps
Where marks are lost
Formulas
9 to know
Resistivity and conductivity
ρ = 1/σ
ρ in Ω m, σ in S m⁻¹.
Band gap
Eg = EC − EV
Insulator > 3 eV; semiconductor < 3 eV.
Intrinsic carriers
nₑ = nₕ = nᵢ
Eq. 14.1; pure semiconductor.
Total current
I = Iₑ + Iₕ
Eq. 14.2; electron plus hole current.
Mass-action law
nₑnₕ = nᵢ²
Eq. 14.5; holds in thermal equilibrium for doped and pure material.
Donor concentration
ND = (atoms per m³) × (doping fraction)
1 ppm = 10⁻⁶; for n-type, nₑ ≈ ND.
Barrier under bias
forward: V₀ − V; reverse: V₀ + V
V₀ is the built-in barrier potential.
Dynamic resistance
rd = ΔV/ΔI
Eq. 14.6; small changes on the V-I curve.
Rectifier output frequency
half-wave: f; full-wave: 2f
50 Hz mains gives 50 Hz and 100 Hz.
Key terms
16 terms
- Valence band
- The band of energy levels holding the valence electrons; completely full at 0 K in Si and Ge.
- Conduction band
- The band above the valence band; electrons in it are free to move and carry current.
- Band gap (Eg)
- The energy between the top of the valence band and the bottom of the conduction band.
- Hole
- A vacancy in a covalent bond that acts as a mobile charge of +q.
- Intrinsic semiconductor
- A pure semiconductor, with equal numbers of free electrons and holes.
- Doping
- Adding a small, controlled amount of a suitable impurity to raise conductivity.
- Donor
- A pentavalent dopant that gives one free electron and becomes a fixed positive ion.
- Acceptor
- A trivalent dopant that takes an electron, creating a hole and becoming a fixed negative ion.
- Majority carriers
- The more numerous carriers: electrons in n-type, holes in p-type.
- Depletion region
- The layer at a p-n junction emptied of free carriers, holding only fixed ions.
- Barrier potential
- The potential difference across the junction that opposes further diffusion.
- Drift current
- Current from carriers pushed by the junction's electric field.
- Cut-in voltage
- The forward voltage beyond which diode current rises sharply: about 0.7 V (Si), 0.2 V (Ge).
- Breakdown voltage
- The reverse voltage at which the reverse current suddenly increases.
- Rectifier
- A circuit that turns alternating voltage into one-way (pulsating) voltage.
- Filter
- A capacitor or inductor that smooths the rectified pulses towards steady dc.