Last reviewed 16 Sept 2026 · 7 min read
Energy bands and classification of solids
In solids, atomic energy levels form bands: the valence band (filled with bound electrons) and the conduction band (free electrons), separated by the forbidden energy gap .
| Material | Band gap | Conduction |
|---|---|---|
| Conductors (copper, aluminium) | Bands overlap — no gap | Very high; resistivity increases with temperature |
| Insulators (glass, rubber, diamond) | Large gap (several eV, e.g. diamond about 5.5 eV) | Negligible |
| Semiconductors (silicon, germanium, GaAs) | Small gap — Si ≈ 1.1 eV, Ge ≈ 0.7 eV at room temperature | Moderate; resistivity decreases with temperature (negative temperature coefficient) |
Silicon dominates electronics because of its lower leakage current, higher operating temperature and abundant, stable oxide (SiO₂).
Intrinsic semiconductors
- Pure semiconductor crystals (Si and Ge are tetravalent — four valence electrons forming covalent bonds).
- At absolute zero, they behave as insulators; at room temperature, thermal energy breaks some bonds, creating electron–hole pairs.
- A hole is the vacancy left by an electron — behaves as a positive charge carrier.
- In intrinsic material, electron concentration = hole concentration (intrinsic carrier concentration), which rises sharply with temperature.
Extrinsic semiconductors (doping)
Doping — adding small, controlled amounts of impurities to increase conductivity.
| Type | Dopant | Majority carriers | Minority carriers | Examples of dopants |
|---|---|---|---|---|
| n-type | Pentavalent (donor) impurities — donate a free electron | Electrons | Holes | Phosphorus, arsenic, antimony |
| p-type | Trivalent (acceptor) impurities — create holes | Holes | Electrons | Boron, aluminium, gallium, indium |
- The material remains electrically neutral overall (donor/acceptor ions balance the carriers).
- Mass action law: (in equilibrium).
Current mechanisms
- Drift current — movement of carriers under an electric field; (electron mobility is higher than hole mobility).
- Diffusion current — movement of carriers from high to low concentration.
PN junction diode
When p-type and n-type regions are joined:
- Majority carriers diffuse across the junction and recombine, leaving immobile ions — forming the depletion region (no free carriers).
- An internal electric field (barrier potential) builds up, opposing further diffusion: approximately 0.7 V for silicon and 0.3 V for germanium (at room temperature).
Biasing
| Bias | Connection | Effect |
|---|---|---|
| Forward bias | p to positive, n to negative | Barrier reduced, depletion region narrows; large current flows once voltage exceeds the cut-in (knee) voltage (≈ 0.7 V Si, 0.3 V Ge) |
| Reverse bias | p to negative, n to positive | Barrier increased, depletion region widens; only a tiny reverse saturation (leakage) current due to minority carriers — until breakdown |
Diode current equation
= reverse saturation current; = ideality factor (≈ 1 for Ge, 1–2 for Si); = thermal voltage ≈ 26 mV at 300 K (≈ 25 mV at room temperature in many texts).
- Dynamic (AC) resistance: (e.g. about 26 Ω at 1 mA for η = 1)
- Static (DC) resistance:
- Reverse saturation current roughly doubles for every 10 °C rise in temperature
- Forward voltage (at constant current) decreases by about 2 mV per °C (silicon)
Diode models
- Ideal diode — short circuit when forward biased, open when reverse biased.
- Constant voltage drop model — 0.7 V drop (Si) when conducting.
- Piecewise linear model — cut-in voltage plus forward resistance.
Breakdown
| Mechanism | Occurs in | Features |
|---|---|---|
| Zener breakdown | Heavily doped junctions with thin depletion region | High electric field pulls electrons from covalent bonds; typically at low voltages (below about 5–6 V); negative temperature coefficient |
| Avalanche breakdown | Lightly doped junctions | Carriers accelerated by the field ionise atoms by collision (multiplication); higher voltages; positive temperature coefficient |
Ordinary rectifier diodes must operate below their peak inverse voltage (PIV) rating; Zener diodes are designed to operate safely in breakdown.
Zener diode voltage regulator
Regulation is maintained while ; power in Zener .
The Zener holds output voltage nearly constant against changes in input voltage and load current.