1Classifying Materials by Energy Bands
In a solid, electron energy levels merge into continuous bands rather than the sharp lines seen in a single atom. What separates a metal, a semiconductor, and an insulator is the size of the energy gap (Eg) between the highest filled band (valence band) and the next available band (conduction band).
- Metals: valence and conduction bands overlap, or the conduction band is partially filled — electrons flow freely, giving high conductivity.
- Insulators: a large gap (Eg > 3 eV) — electrons essentially never gain enough thermal energy to cross into the conduction band.
- Semiconductors: a small gap (Eg ≈ 1 eV — silicon is 1.1 eV, germanium 0.7 eV) — few electrons cross at room temperature, but enough to give useful, controllable conductivity.
2Intrinsic Semiconductors
A pure semiconductor crystal (silicon or germanium, undoped) is called intrinsic. At room temperature, thermal energy occasionally frees an electron from a covalent bond, leaving behind a hole — an effective positive charge carrier, since a neighbouring electron can hop in to fill it, shifting the "gap" like a bubble moving through liquid.
3Extrinsic Semiconductors: Doping
Deliberately adding a tiny, controlled amount of impurity — doping — dramatically boosts conductivity and lets you choose which charge carrier dominates.
- n-type: doped with a pentavalent impurity (phosphorus, arsenic — 5 valence electrons). Four electrons form covalent bonds with neighbouring silicon atoms; the fifth is loosely bound and easily freed, becoming a majority electron carrier. These dopant atoms are called donors.
- p-type: doped with a trivalent impurity (boron, indium — 3 valence electrons). Only three bonds can form, leaving one bond incomplete — a hole — which becomes the majority carrier. These dopants are called acceptors.
4The p-n Junction
Join a p-type and n-type semiconductor together, and near the junction, electrons from the n-side diffuse across and combine with holes on the p-side (and vice versa), leaving behind fixed, uncompensated ions. This creates a narrow depletion region with no free carriers, and a built-in electric field (potential barrier) that eventually stops further diffusion — this junction, once formed, is the basis of practically every semiconductor device.
5Semiconductor Diode and Rectification
A p-n junction with two terminals is a diode — it conducts current in essentially one direction only.
- Forward bias (p-side positive, n-side negative): the external field opposes the built-in barrier, shrinking the depletion region; once the barrier is overcome, current flows easily and grows rapidly with voltage.
- Reverse bias (p-side negative, n-side positive): the external field widens the depletion region, and only a tiny leakage current flows — practically zero for most purposes.
This one-way behaviour makes a diode a natural rectifier — converting AC to DC.
Half-Wave vs. Full-Wave
A single diode passes only one half of each AC cycle (half-wave rectification), blocking the other. Using two or four diodes in the right arrangement (a bridge rectifier) lets both halves of the cycle contribute to the output (full-wave rectification), giving a smoother, more usable DC output for the same input.
6Special-Purpose Diodes
- Zener diode: designed to operate safely in reverse breakdown, where voltage across it stays essentially constant (Vz) over a wide range of current — used deliberately as a voltage regulator.
- LED (Light Emitting Diode): in forward bias, electrons and holes recombine at the junction, releasing energy as light rather than heat; the emitted colour depends on the material's band gap.
- Photodiode: operated in reverse bias; incoming light generates electron-hole pairs, increasing reverse current proportionally to light intensity — used as a light sensor.
- Solar cell: a p-n junction with no external bias at all — light generates electron-hole pairs, and the junction's built-in field separates them, directly producing usable electrical power.
7Junction Transistor
A transistor sandwiches three doped regions in sequence — either n-p-n or p-n-p — creating three terminals: emitter (heavily doped, injects carriers), base (very thin, lightly doped), and collector (moderately doped, collects carriers).
8Transistor as Amplifier and Switch
Because a small change in base current produces a large, proportional change in collector current, a transistor can turn a weak input signal into a much stronger output — the basic principle of every electronic amplifier, from hearing aids to guitar amps.
Run a transistor at its extremes instead of its linear middle region — fully on (saturation) or fully off (cut-off) — and it behaves as an electronic switch, the building block for every digital logic circuit, including the ones in the next section.
9Digital Electronics and Logic Gates
Digital circuits work with only two voltage levels — logic 1 (HIGH) and logic 0 (LOW) — built from transistor switches combined into logic gates.
- AND: output is 1 only when both inputs are 1.
- OR: output is 1 if at least one input is 1.
- NOT: a single-input gate that simply inverts its input.
- NAND: AND followed by NOT — output is 0 only when both inputs are 1.
- NOR: OR followed by NOT — output is 1 only when both inputs are 0.
Why NAND and NOR Matter
Both NAND and NOR are "universal" gates — either one, on its own, can be combined to build every other logic gate (AND, OR, NOT included). This is exactly why real digital chips are built almost entirely from NAND or NOR gates.
Formula Summary
Intrinsic Carriers
n_e = n_h = n_i
Mass Action Law
n_e × n_h = n_i²
Transistor Currents
I_E = I_B + I_C
Common-Emitter Gain
β = I_C/I_B
Common-Base Gain
α = I_C/I_E
Solved Examples
Example 1 · Transistor Current Gain
In a transistor, the base current is 20 µA and the collector current is 2 mA. Find the current gain β and the emitter current.
Solution: β = IC/IB = 2000 µA / 20 µA = 100.
IE = IB + IC = 20 µA + 2000 µA = 2020 µA = 2.02 mA.
Example 2 · Band Gap and Light Absorption
Silicon has a band gap of 1.1 eV. Find the maximum wavelength of light that can generate an electron-hole pair in silicon.
Solution: A photon needs at least Eg of energy, so the longest usable wavelength is λmax = hc/Eg = (6.63×10⁻³⁴ × 3×10⁸) / (1.1 × 1.6×10⁻¹⁹) ≈ 1.13×10⁻⁶ m ≈ 1130 nm.
This falls just beyond visible light, in the near-infrared — which is why silicon solar cells and photodiodes respond well across most of the visible spectrum and a bit beyond.
Quick Check
1. In a p-type semiconductor, the majority charge carriers are:
Electrons
✓ Holes (correct)
Protons
Equal electrons and holes
2. A NAND gate is logically equivalent to:
OR gate followed by NOT
✓ AND gate followed by NOT (correct)
NOT gate alone
AND gate alone
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