Chapter 1 · Animation 1 of 6 · Sections 1.2.1 to 1.2.3
Electrons, Holes and Doping in the Crystal
A two-dimensional picture of the silicon lattice: bonds break and re-form, holes move by bond electrons hopping, and donors and acceptors tip the balance between electrons and holes.
electron (in a bond or free)hole: a bond missing one electrongenerationrecombination flash
What to look for
A hole is not a particle that travels; it is a missing bond electron. Follow the ringed hole: each step is a bond electron jumping the other way.
In steady state the numbers fluctuate, but the time-averaged product n·p stays close to ni² whatever the doping. Compare the readout for the intrinsic, n-type and p-type crystals at the same temperature.
The charge check in the panel always balances: every free electron came either from a bond (leaving a hole) or from a donor (leaving P⁺), and every B⁻ ion has a hole somewhere.
The physics behind it
Thermal generation creates pairs at a rate that depends only on temperature; recombination removes them at a rate proportional to n·p. Balance gives n0p0 = ni² (eq. 1.2.3).
ni(T) = A1T3/2exp(−A2/T): about 10¹⁰ cm⁻³ at 300 K, and roughly 400 times larger at 400 K.
Donors (P, As, Sb) and acceptors (B) are ionized at room temperature: n0 ≈ ND or p0 ≈ NA, and the minority density is ni²/N (eqs. 1.2.4 to 1.2.7).