Intuition The one core ideaPure silicon has no spare charges to carry current; boron sneaks in with one missing bond, and that missing spot — a hole — moves like a positive charge. Everything else on the parent page is just the bookkeeping that counts how many holes (p n n p = n i 2
This page assumes nothing . Before you can read the parent ... — sorry, before you read the parent — you need each symbol below to feel obvious. We build them in order, each one leaning on the one before.
Before "doping" means anything, you must picture an atom the way a chemist does: a tiny heavy nucleus in the middle, and electrons orbiting in shells around it.
Definition Valence electronThe valence electrons are the electrons in the outermost shell — the only ones that reach out and form bonds with neighbours. Inner electrons are buried and never take part in chemistry or conduction.
Look at the figure: silicon (Si) has 4 electrons in its outer ring, boron (B) has 3. That single difference — 4 vs 3 — is the seed of the entire topic. Hold onto it.
Intuition Why we only care about the outer shellConduction is electrons moving between atoms . Only the outermost electrons are close enough to a neighbour to be shared or handed over. So from now on, "electron" almost always means "valence electron."
A covalent bond is two electrons shared between two neighbouring atoms , gluing them together. Draw it as a line (a pair of dots) sitting between two atoms.
Definition Crystal latticeA lattice is the repeating, orderly grid in which the atoms sit. In silicon each atom has 4 neighbours and forms 4 bonds — one per valence electron.
In the left panel every silicon atom has used all 4 of its valence electrons in 4 bonds. Nothing is free to move → pure silicon barely conducts. This "everything locked" state is exactly what the parent's parking-lot analogy describes.
Intuition Why "locked bonds" = insulator-ishA moving electric current needs a charge that can travel . If every electron is pinned inside a shared bond, none can wander. The whole trick of doping is to break this perfect locking — either by adding a spare electron (n-type) or a spare empty spot (p-type).
Now the right panel of the figure above: replace one silicon with boron . Boron brought only 3 electrons, so one of the 4 bonds around it is left short one electron . That gap is the hole.
A hole is a missing electron in a covalent bond . Because a neighbouring electron can slide in to fill it — leaving its old spot empty — the empty spot appears to travel. A travelling empty spot in a sea of negative electrons behaves exactly like a mobile +1 charge .
Intuition Why a "missing thing" counts as a positive chargeA complete bond is neutral. Remove one electron (charge − 1 = + 1
Common mistake "A hole is a proton."Why it feels right: it's positive, and protons are positive.
The fix: the hole never involves the nucleus. It is purely an absence of a valence electron . The protons never move.
Definition Elementary chargeq q one electron or one proton : q = 1.6 × 1 0 − 19 C − q + q
B − ion is an atom that has gained or lost an electron, so it is no longer neutral. When boron accepts an electron to complete its bond it becomes B − fixed atom with net charge − 1 cannot move — unlike the hole it released.
The figure shows the balance the parent insists on: one fixed B − mobile hole (moves, positive). Add them: ( − 1 ) + ( + 1 ) = 0 moves is positive — that is why it's called p -type.
Intuition Why "mobile vs fixed" is the whole confusion-busterStudents think "lots of positive holes ⇒ positive block." No: every positive hole was born from a negative acceptor ion that stays behind. The net charge is zero; only the mobility is one-sided.
Now we need numbers, not just pictures. Semiconductor physics counts how many carriers sit in each cubic centimetre.
Definition Concentration symbols
n free electrons per cubic centimetre (cm − 3 p free holes per cubic centimetre.n i intrinsic concentration : in pure silicon, thermal jiggling breaks a few bonds and each break makes one electron + one hole together . So in pure Si, n = p = n i n i ≈ 1.5 × 1 0 10 cm − 3
Intuition Why electrons and holes come in pairs (in pure Si)Break one bond → the escaped electron is a free electron and the vacated spot is a free hole. One event, two carriers. That is why pure material has exactly equal counts. See Intrinsic Semiconductors for this baseline.
Definition Doping concentrationsN A N D
N A acceptor atoms (like boron) added per cm − 3 N D donor atoms (like phosphorus, N-type doping with donor atoms (phosphorus) ) added per cm − 3 N A − actually ionized (grabbed an electron, become B − N A − ≈ N A
The parent throws three equations at you. Here is what each symbol string is literally saying, in words, so the parent's derivation reads like a sentence:
Intuition Why a square root shows up at allCombining n p = n i 2 p = n + N A quadratic in p p 2 a x 2 + b x + c = 0 N A n i 4 n i 2 p ≈ N A
Recall Quick self-check on the symbolsIf N A = 1 0 16 n i = 1.5 × 1 0 10 4 n i 2 N A 2 N A 2 = 1 0 32 4 n i 2 = 9 × 1 0 20 1 0 11 p ≈ N A
μ Mobility μ μ p μ n μ Drift and Diffusion Currents .
σ Conductivity σ σ ≈ q p μ p ( Ω cm ) − 1
Intuition Why we ignore electrons inσ σ q p μ p q n μ n p ≈ 1 0 16 n ≈ 1 0 4 trillion times smaller. Dropping it is honest.
Atom and valence electrons
Covalent bond and lattice
Charge q and ions B minus
Mobile hole vs fixed ion neutrality
Charge neutrality p = n + N A
Mass action n p = n i squared
Hole concentration formula
Mobility and conductivity sigma
Cover the right side. Say each aloud before revealing.
What does "valence electron" mean, and how many does silicon vs boron have? Outermost-shell electrons that form bonds; silicon 4, boron 3.
What is a covalent bond, in one line? Two electrons shared between two neighbouring atoms, drawn as a line between them.
Define a hole and say why it acts positive. A missing electron in a bond; the surrounding neutral-minus-a-negative behaves as a mobile + 1
What is q The elementary charge, q = 1.6 × 1 0 − 19 C
Why is boron written B − It accepted an electron so it has net − 1
Why is a p-type crystal neutral despite many positive holes? Each mobile + 1 − 1
What do n p n i Free electrons/cm³, free holes/cm³, and the pure-silicon carrier count (where n = p = n i
Difference between N A N A − N A N A − N A
In words, what does n p = n i 2 Electrons times holes always equals the intrinsic value squared, at equilibrium.
Why does a square root appear in the hole formula? Combining the two equations gives a quadratic in p
What do μ σ μ σ = q p μ p