Day 4: Device physics I: bands, doping, and the PN junction
What makes silicon a semiconductor
Silicon atoms bond into a regular crystal lattice, sharing electrons in covalent bonds. Quantum mechanics smears the allowed electron energies into bands: a filled valence band, an empty conduction band, and a forbidden band gap between them (~1.12 eV for silicon). Electrons must gain at least the gap energy to jump up and become free to carry current.
That gap size is the whole story of why materials differ. Conductors have overlapping bands (carriers everywhere, always). Insulators have a huge gap (nothing crosses). Semiconductors sit in between: a gap small enough that heat, light, or clever doping can put a controllable number of carriers into the conduction band. Control is the key word — a device is a semiconductor whose conduction you can *switch*.
Doping: intrinsic vs extrinsic
Pure (intrinsic) silicon has very few free carriers at room temperature. Doping deliberately adds impurities: donors like phosphorus have a spare electron → n-type silicon with electrons as majority carriers; acceptors like boron leave a missing bond, a hole, → p-type silicon with holes as majority carriers. How fast those carriers move under a field is their mobility (electrons are faster than holes — one reason NMOS is stronger than PMOS).
The band gap as a step
Picture electrons at the bottom of a staircase (valence band) that must climb a step (the band gap) to reach a walkway where they can move freely (conduction band). Intrinsic silicon makes the step tall and lonely. Doping is like pre-placing a crowd of electrons (n-type) or empty footholds/holes (p-type) right at the top — now only a nudge is needed to get current flowing.
The PN junction in equilibrium
Put p-type and n-type silicon in contact and something beautiful happens on its own. Electrons diffuse from the n-side into the p-side and holes the other way, recombining near the boundary and leaving behind charged, carrier-free dopant ions. That exposed charge forms a depletion region with a built-in potential (~0.7 V in silicon) whose field opposes further diffusion. At equilibrium, diffusion and drift exactly cancel — no net current.
Under bias: the diode
Apply voltage and the balance breaks. Forward bias (p positive) shrinks the depletion region and lowers the barrier — above ~0.7 V, current rises steeply. Reverse bias (p negative) widens the depletion region and raises the barrier — only a tiny leakage flows. Current in one direction, blocked in the other: that asymmetry is the diode, and you'll measure its exponential shape tomorrow.
Key terms
- Band gap
- The forbidden energy range between valence and conduction bands (~1.12 eV in Si); its size classifies conductor/semiconductor/insulator.
- Conduction / valence band
- The (mostly empty) band where electrons move freely, and the (mostly full) band they leave behind.
- Donor / acceptor
- Dopants that add a free electron (donor → n-type) or a hole (acceptor → p-type).
- Majority / minority carrier
- The dominant carrier in a doped region (electrons in n-type, holes in p-type) and the sparse opposite type.
- Mobility
- How quickly a carrier drifts per unit electric field; electron mobility exceeds hole mobility in silicon.
- Depletion region
- The carrier-free zone at a junction, filled with fixed ionized dopant charge and a built-in field.
- Built-in potential
- The equilibrium voltage across the depletion region (~0.7 V in Si) that balances diffusion against drift.
Before moving on, you should be able to
Why does a depletion region form at a PN junction even with no applied voltage?
