Intuition The one core ideaPure silicon locks up all its electrons in bonds, so nothing is free to carry current. N-type doping sneaks in atoms with one spare electron each, and because that spare is barely held, it floats free and lets the crystal conduct — while the crystal stays electrically neutral overall.
This page assumes you have seen none of the notation used in the parent topic. We build every letter, subscript, and picture from the ground up, in an order where each idea rests on the one before it. If a symbol appears in the main topic , it is defined here first.
Before any symbol, fix the mental image. An atom is a tiny positive core (nucleus + inner electrons) surrounded by outer electrons. Only the outermost electrons ever do chemistry or carry current — everything else is spectator.
Definition Valence electronsThe valence electrons are the electrons in the outermost shell of an atom — the only ones available to form bonds or wander off.
Picture: the outer ring of dots in the figure above.
Why the topic needs it: the entire difference between silicon (4 valence electrons) and phosphorus (5) is one valence electron. That single extra electron is the whole story of N-type doping.
Definition Group IV and Group VThe group number of an element (Roman numeral) tells you its valence-electron count.
Group IV = 4 valence electrons → silicon (Si), the host crystal.Group V = 5 valence electrons → phosphorus (P), arsenic (As): the donors .
Picture: count the dots on the outer ring — Group IV has 4, Group V has 5.
Why the topic needs it: doping works by substituting a Group-V atom into a Group-IV lattice. The mismatch of exactly one electron is what produces a free carrier.
Intuition The whole trick in one line5 − 4 = 1 1 is the free electron. Everything else on this page explains why that 1 is free and how many we get.
A covalent bond is two atoms sharing a pair of electrons to complete their outer shells.
Picture: a shared line of two dots sitting between two atom cores.
A lattice is the regular, repeating 3-D grid of atoms in a crystal. Each silicon atom bonds to 4 neighbours , using all 4 of its valence electrons.
Picture (drawn flat for clarity): every silicon holds hands with 4 others; no hand is free.
Why the topic needs it: in pure silicon every electron is used up in a bond, so nothing moves — that is why pure silicon barely conducts. When a Group-V atom joins, only 4 of its 5 electrons find a bond; the 5th has no partner. Look at the orange electron with no line to it in the figure — that is the future free carrier.
Definition Free (mobile) electronA free electron is one not locked in any bond — it can drift through the crystal when you apply a voltage.
Picture: the waving, unbonded electron in the figure above, able to hop away.
Definition Charge carrierA carrier is any mobile charge that can move to make current. In N-type, the carriers are these free electrons — negatively charged. This is why we call the material N-type (N for negative movers).
Why the topic needs it: "conductivity" literally means "how many carriers can move, and how easily". No free carriers → no current.
When the 5th electron leaves, the phosphorus core is now short one electron , so it carries a net +1 charge. It cannot move — it is locked in the lattice.
N D + N D + fixed, positive donor ion left behind after its spare electron has run off.
The subscript D Donor .
The superscript + Picture: a "+" sticker frozen at the lattice site where the electron used to be.
Intuition Charge bookkeeping (never skip this)For every free electron (− 1 + 1 electrically neutral overall . "N-type" describes the sign of the movers , not the net charge.
Now the letters that appear in every formula. All are concentrations — how many of something per cubic centimetre (cm − 3 cm 3
Definition The four population symbols
n free electrons per cm 3 n egative).p holes per cm 3 p ositive). A hole is an empty bond slot that behaves like a mobile + n i intrinsic carrier density: how many carriers pure silicon makes on its own from heat alone. Subscript i i ntrinsic. For Si, n i ≈ 1.5 × 1 0 10 cm − 3 N D donor doping density : how many donor atoms per cm 3
Intuition Why so many symbols?To control conductivity by design we must count carriers. N D n p n i
The bar chart above shows the punchline of the whole topic in numbers: after doping, n ≈ N D p pushed down far below n i
The main note draws a band diagram — a vertical energy axis where "higher up" means "electron has more energy and is freer". These letters live on that axis.
Definition Energy levels on the band diagram
E C conduction band — the energy an electron must reach to be free and conduct. Subscript C C onduction.E D donor energy level — where the spare electron sits before it is freed. It lies just below E C E D ≈ 26 50 meV E D E C E F Fermi level — a reference energy telling you where electrons "prefer to sit". In N-type it shifts up toward E C ; that upward shift is the fingerprint of N-type material.
Definition The electron-volt (eV)An eV is a unit of energy convenient at the atomic scale. 1 meV = 0.001 eV E C 1.12 eV 40× larger than the 26 meV
Definition Conductivity ingredients
σ conductivity : how easily the material conducts. Bigger σ q = 1.6 × 1 0 − 19 μ n electron mobility : how fast electrons drift per unit electric field. Subscript n μ p hole mobility , the same for holes.
They combine as σ = q ( n μ n + p μ p ) Why the topic needs it: this is the formula that turns "n ≈ N D point of doping.
Covalent bonds and lattice
Free electron plus fixed ion ND+
Mass action law n p = ni squared
Read it bottom-up: valence electrons feed the group idea and the bond idea, which together explain the donor, which produces a free electron plus a fixed ion, which feed the counting and energy pictures, which finally assemble into the N-type topic.
Cover the right side and see if you can state each before revealing.
What does "valence electrons" mean? The outermost electrons of an atom — the only ones that bond or carry current.
How many valence electrons do Group IV and Group V atoms have? 4 and 5 respectively.
Why does a Group-V donor produce a free electron? It only needs 4 electrons for bonds; the 5th has no partner and floats free.
What does N D + The fixed, immobile positive donor ion left behind after the spare electron leaves.
Is N-type material negatively charged? No — it is electrically neutral; each free electron is matched by a fixed +
What is n i The intrinsic carrier density — carriers pure silicon makes from heat alone, ≈ 1.5 × 1 0 10 cm − 3
What do n p Free-electron and hole concentrations (per cm 3
What is E C The conduction-band bottom; an electron there is free to conduct.
Where does E D E C Just below it, only about 26–50 meV down.
Why does room temperature ionise nearly all donors? Because k B T ≈ 26
What does the mass-action law n p = n i 2 At fixed temperature the product of electron and hole counts is constant.
What is σ = q ( n μ n + p μ p ) Conductivity = charge × (carrier count × mobility), summed over electrons and holes.
Ready? Continue to the parent: N-type doping with donor atoms . Related foundations worth a look: Intrinsic vs Extrinsic Semiconductors , Mass-action law and carrier concentrations , Fermi level and its shift with doping , Conductivity and carrier mobility , and the mirror case P-type doping with acceptor atoms (boron) which leads into PN Junction formation .
