Intuition The ONE core ideaA doped semiconductor has a huge crowd of one kind of moving charge and a tiny crowd of the other kind — but the two crowd-sizes, multiplied together, always equal the same fixed number n i 2 carrier is, why their product is locked, and why the crystal stays neutral .
This page assumes you have seen none of the notation on the parent page. We build every symbol from the ground, one at a time, each earning the next.
Definition Crystal, band, carrierA semiconductor (like silicon) is a solid where atoms sit in a regular grid and share electrons through bonds.
When a bond stays intact, its electron is "stuck" — it cannot carry current.
When heat breaks a bond, the freed electron can roam — it becomes a carrier .
The empty spot the electron left behind also moves around and behaves like a positive particle — a hole , also a carrier.
Intuition Why "carrier" is the right wordCurrent is just charge that moves . A stuck electron carries nothing. Only the freed electron and the hole it leaves behind can shuttle charge across the crystal — so we count those , and call them carriers . Everything in the parent topic is bookkeeping of how many of each we have.
n p
n free electrons packed into each cubic centimetre of crystal. Read it "electron concentration."p holes in each cubic centimetre. Read it "hole concentration."
The picture: imagine a 1 cm × 1 cm × 1 cm count the free electrons and the holes inside it.
Intuition Why a concentration, not a total count?The crystal could be any size. A number like "there are 40 electrons" is meaningless without a volume. Using "so many per cm³" makes the number a property of the material and its doping , not of how big your sample happens to be. That is why the whole topic speaks in concentrations.
The unit is written cm − 3 1/ cm 3 n = 1 0 16 cm − 3
n p Why it feels right: electrons carry charge, so n The fix: n p counts per volume — pure numbers divided by a volume, no coulombs attached. The charge comes separately from the symbol q
q q one electron or one hole:
q = 1.6 × 1 0 − 19 C C
An electron carries charge − q
A hole carries charge + q
q charge neutrality step adds up positive and negative charges and sets them equal. Every carrier and every ionized dopant carries exactly one unit q q both sides of that balance and cancels — which is why the neutrality equation ends up being about plain counts. You need q
n i perfectly pure (undoped) crystal at temperature T each broken bond makes exactly one free electron and one hole together. So in pure material:
n = p = n i n i intrinsic carrier concentration — how many of each carrier heat alone produces per cm³.
Intuition Why electrons and holes come in equal pairs hereA broken bond releases one electron and leaves one hole — never one without the other. So in a pure crystal the two counts must match. That shared value is n i Intrinsic carrier concentration $n_i$ for how n i
Intuition The superscript+ − N D + N A − all dopants have done this, so we use the full-ionization shortcut:
N D + ≈ N D , N A − ≈ N A
Intuition Why doping is the whole reason "majority/minority" existsIn a pure crystal n = p breaks the tie . See Doping — donors and acceptors and Fermi level position vs doping .
Definition Generation, recombination, equilibrium
Generation (G Recombination (R one electron AND one hole to meet , so its rate grows with both n p R = r n p r Thermal equilibrium : the crystal just sitting on a shelf, no light, no battery, long enough that generation and recombination exactly balance: G = R
n ⋅ p n × p G = r n p G forces the product n p Law of mass action .
Now that every symbol is defined, the parent's two master equations read in plain words:
Carriers electron n and hole p
Concentration per cm cubed
Intrinsic n i pure crystal
Majority vs minority split
Generation equals recombination
Law of mass action n p equals n i squared
Minority vs majority carriers
Read top to bottom: bonds give carriers, carriers get counted as concentrations, pure counting gives n i
Test yourself: cover the right side and answer before revealing.
What does a "carrier" physically mean in a crystal? A mobile charge — a freed electron or a hole — that can actually move current; stuck bond-electrons do not count.
What do the symbols n p Free-electron and hole concentrations, in number per cubic centimetre (cm − 3
What is q q = 1.6 × 1 0 − 19 C − q + q
Define n i n = p The intrinsic concentration; each broken bond makes one electron and one hole together, so counts are equal.
What do N D N A N D + N A − Donor and acceptor atom concentrations; the + / − ionized ones, ≈ N D ≈ N A
Why is the recombination rate proportional to n × p Recombination needs one electron to meet one hole, so its rate scales with the availability of both.
What does "thermal equilibrium" require? Generation and recombination exactly balance, with no light or applied voltage.
State the two master equations in your own words. Mass action (n p = n i 2
