Semiconductor Electronics: Materials, Devices and Simple Circuits

Physics · Class 12

Lesson 12 of 12 · 14 min

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Must-know facts

18 facts

  1. 1Resistivity: metals 10⁻² to 10⁻⁸ Ω m, semiconductors 10⁻⁵ to 10⁶ Ω m, insulators 10¹¹ to 10¹⁹ Ω m.
  2. 2Band gap: insulators Eg > 3 eV, semiconductors Eg < 3 eV, metals Eg ≈ 0 or overlapping bands.
  3. 3Eg: C (diamond) 5.4 eV, Si 1.1 eV, Ge 0.7 eV, Sn 0 eV (a metal).
  4. 4Si and Ge crystal: 4N valence electrons, 8N states split into a full valence band (4N) and an empty conduction band (4N) at 0 K.
  5. 5Intrinsic: nₑ = nₕ = nᵢ; current I = Iₑ + Iₕ.
  6. 6Lattice spacing: C 3.56 Å, Si 5.43 Å, Ge 5.66 Å.
  7. 7Donors (n-type): As, Sb, P (pentavalent). Acceptors (p-type): In, B, Al (trivalent).
  8. 8Energy to free a donor electron: about 0.01 eV in Ge and 0.05 eV in Si.
  9. 9n-type: nₑ ≫ nₕ; p-type: nₕ ≫ nₑ; always nₑnₕ = nᵢ².
  10. 10Example 14.2: 1 ppm As in Si gives nₑ ≈ 5 × 10²² m⁻³ and nₕ ≈ 4.5 × 10⁹ m⁻³.
  11. 11Depletion region thickness: about one-tenth of a micrometre.
  12. 12Barrier height: (V₀ − V) in forward bias, (V₀ + V) in reverse bias.
  13. 13Cut-in voltage: about 0.7 V for Si and 0.2 V for Ge.
  14. 14Forward current in mA; reverse saturation current in µA.
  15. 15Dynamic resistance rd = ΔV/ΔI; Example 14.4 gives 10 Ω forward and 1.0 × 10⁷ Ω reverse.
  16. 16Rectifier output frequency for 50 Hz input: 50 Hz half-wave, 100 Hz full-wave.
  17. 17Full-wave with a centre tap: two diodes, each rectifying half the secondary voltage; the bridge circuit uses four diodes.
  18. 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

Saying n-type material is negatively charged because it has extra electrons.

Every free electron came from a donor that is now a fixed positive ion. Doped crystals stay neutral overall.

Choosing boron or aluminium to make n-type silicon.

n needs a donor with five valence electrons (P, As, Sb). The valency-3 elements (B, Al, In) accept electrons and make p-type.

Thinking doping raises both electron and hole numbers.

nₑnₕ = nᵢ² stays fixed, so raising the majority carriers lowers the minority carriers below nᵢ.

Mixing up diffusion and drift at the junction.

Diffusion is driven by the concentration difference (majority carriers crossing); drift is driven by the junction field (minority carriers swept across). In equilibrium they cancel.

Saying reverse bias narrows the depletion layer.

Reverse bias adds to the barrier (V₀ + V) and widens the depletion layer; forward bias lowers it to (V₀ − V) and narrows it.

Expecting the reverse current to grow steadily with reverse voltage.

Below breakdown it saturates at a few µA, set by the supply of minority carriers, not by V.

Giving a full-wave rectifier the same output frequency as its input.

Two pulses per input cycle: 50 Hz in gives 100 Hz out for full-wave, and 50 Hz for half-wave.

Putting the filter capacitor in series with the load.

The capacitor goes in parallel with RL (an inductor, if used, goes in series). Larger C × RL means less ripple.

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.
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