This is a rapid-fire misconception trap page for the parent topic. Each line below is a Question ::: Answer reveal. Cover the answer, commit to a reason (not just true/false), then check. The reasoning is the point — a bare "yes/no" earns nothing on an exam.
Before we start, three plain-word anchors we lean on everywhere (each defined here so nothing is used before it is built):
Every other symbol this page uses is spelled out in plain words below, before it appears in any question. Read this box slowly — it is the whole vocabulary.
Now, three visual anchors so nothing below is asserted without a picture behind it.
Figure s01 above is the whole subject on one board: filled VB (blue), empty CB (yellow), the forbidden gap Eg between. A conductor's bands overlap (no gap); an insulator's gap is a cliff; a semiconductor's is a hop-able step. The shallow donor level (just below CB) and acceptor level (just above VB) are the dashed chalk lines — sitting only ∼0.045 eV from their band, not a full Eg away.
The occupancy curve in figure s02 (the Fermi–Dirac distribution, see Fermi-Dirac Distribution) tells you the probability a state at energy E holds an electron. It drops from 1 (full) to 0 (empty) through a soft step centred on the Fermi levelEF — the energy with exactly 50% occupancy. For intrinsic Si the curve must leave the VB as full as it fills the CB, so by symmetry EF lands mid-gap. That is why mid-gap, not just that mid-gap.
Figure s03 sketches where σ=σ0e−Eg/2kBT comes from and how we read it. Carrier count is set by the Fermi function evaluated a distance Eg/2 (VB-top up to mid-gap EF) — that mid-gap distance is the origin of the factor 2. Taking ln straightens the exponential into a line of slope −Eg/2kB against 1/T.
Almost everyone gets these by reflex — and the reflex is often wrong. Say the reason.
A completely filled band can carry current if you just push hard enough with a big voltage.
False. Conduction needs an empty nearby state to move into. In a full band every seat is taken, so under a field electrons cannot gain net momentum — no matter the voltage. Emptiness, not force, is the missing ingredient.
Metals conduct better when you heat them up, just like semiconductors.
False. Metals already have carriers, so heating only adds lattice vibrations that scatter electrons → resistance rises. In semiconductors heating creates new carriers, so conductivity rises. Opposite mechanisms, opposite trends.
An intrinsic (undoped) semiconductor has zero conductivity at room temperature.
False. Its band gap is small (∼1 eV), so thermal energy promotes a modest number of electrons across it. Conductivity is tiny but non-zero; it becomes essentially zero only as T→0 K.
Donor electrons at 0.045 eV are released "for free" — every donor is ionized the instant the crystal is at room temperature.
False (careful!). Since 0.045 eV is still larger than kBT≈0.026 eV, a strict Boltzmann estimate gives only a fraction (∼e−1.7≈18%) ionized. In real doped crystals the donor level broadens and merges toward the band, so ionization is nearly complete — but "instant and total" is an idealisation, not a law.
n-type silicon carries a net negative charge because it has extra electrons.
False. Each donor atom gives up an electron but keeps its extra proton, becoming a fixed + ion. The crystal stays electrically neutral overall; it just has more mobile negative carriers.
In a p-type semiconductor, the positive holes are the same thing as protons.
False. A hole is a missing electron in the valence band — an absence that shifts around and behaves like a positive charge. No proton moves; the "particle" is bookkeeping for where an electron isn't.
Silicon (Eg=1.1 eV) is a better conductor than germanium (Eg=0.7 eV) at room temperature.
False. Smaller gap → easier thermal excitation → more intrinsic carriers. Ge's narrower gap makes it the more conducting of the two intrinsically (Si's larger gap is why it is nonetheless the industry workhorse — more stable, less leaky).
Adding more dopant always raises conductivity without limit.
False. Up to a point σ≈NDeμ grows with dopant. But heavy doping increases carrier scattering (lowering μ) and eventually the material behaves almost metallic ("degenerate"). Conductivity saturates rather than climbing forever.
Diamond and graphite are both carbon, so both are insulators.
False. Structure sets the band gap. Diamond's tetrahedral network has Eg≈5.5 eV (insulator); graphite's overlapping delocalised bands give it metal-like in-plane conduction. See Covalent Network Solids.
Each statement below hides one wrong link in the chain. Name it and fix it.
"Phosphorus in silicon donates a hole because it has one extra electron."
Error: hole → electron. An extra electron means it donates an electron, making it n-type. A hole would come from an atom with too few electrons (trivalent, like boron).
"Boron creates a donor level just below the conduction band."
Error: donor→acceptor, CB→VB. Boron is trivalent and accepts an electron, so it creates an acceptor level just above the valence band. Donor-below-CB describes pentavalent (n-type) dopants.
"Because n⋅p=ni2, doping keeps electrons and holes equal."
Error. The product stays fixed at ni2; the two are not kept equal. Doping raises one carrier and, by the same law, pushes the other far down. In n-type, n≫p.
"The factor of 2 in σ=σ0e−Eg/2kBT is there because there are two carriers."
Error (subtle). It is not "two carriers" loosely — it arises because the Fermi level sits mid-gap, so the energy from the top of the VB up to EF is Eg/2 (see figure s03). Carrier count follows the Fermi function at that mid-gap distance, giving the factor of 2 — not a headcount.
"An insulator has no conduction band, which is why current can't flow."
Error. It has a conduction band — it's just empty and separated by a large gap (>3 eV). The barrier is the gap size, not a missing band.
"Fermi level in intrinsic silicon lies inside the conduction band."
Error. The Fermi levelEF (the energy with 50% occupation probability, figure s02) lies near the middle of the gap for intrinsic material. Doping shifts it toward a band, but it stays within/near the gap, not inside the CB. See Fermi-Dirac Distribution.
"Heating an n-type semiconductor forever increases its majority-carrier advantage."
Error. At high enough T, thermally generated intrinsic pairs flood in and eventually swamp the fixed dopant carriers — the material re-enters the intrinsic regime and behaves as if undoped. See Thermistors.
The exam favourite: "explain why." One clean causal sentence beats a paragraph of hedging.
Why does a filled band contribute nothing to conduction while a half-filled band conducts well?
A filled band has no empty states, so electrons cannot shift to higher-momentum states under a field; a half-filled band has empty states right above the occupied ones, so electrons redistribute and carry net current.
Why does replacing 1 atom in 106 change conductivity by a factor of ∼106?
Intrinsic carriers are extraordinarily rare (only a few per 1013 atoms), so even a tiny dopant fraction adds vastly more carriers than nature supplied — small absolute number, enormous relative change.
Why do we plot lnσ against 1/T rather than σ against T?
Because σ=σ0e−Eg/2kBT becomes a straight line in those coordinates (figure s03), with slope −Eg/2kB — turning an exponential into a ruler-and-slope measurement of the band gap.
Why does the Fermi level sit mid-gap in intrinsic silicon rather than nearer one band?
Because the Fermi–Dirac curve (figure s02) is symmetric about EF: to have exactly as many electrons in the CB as holes in the VB, the 50% point must land halfway between them — dead centre of the gap.
Why is the donor ionization energy (~0.045 eV) so much smaller than the full band gap (~1.1 eV)?
The fifth electron is only loosely held by the donor ion's extra proton, orbiting far out in a huge hydrogen-like orbit screened by the crystal — a shallow, easily-broken bond, not the deep VB-to-CB leap.
Why is n-type silicon roughly 3× more conductive than p-type at equal doping?
Electrons in the CB have smaller effective mass than holes in the VB (band-curvature difference), so electron mobility μe≈1350 beats hole mobility μh≈450 cm²/(V·s) — about a factor of three.
Why does doping not violate charge neutrality even though it adds mobile carriers?
Every mobile electron left behind a fixed positive donor ion (and every mobile hole a fixed negative acceptor ion); mobile charge and fixed charge cancel, so the bulk stays neutral. See Crystal Defects.
Why can the same silicon crystal be made n-type in one region and p-type in another?
Because doping is local — you implant different impurities in different regions. Butting an n-region against a p-region builds a p-n junction, the heart of every diode and transistor.
The scenarios that break naive rules. Master these and you've mastered the topic.
At absolute zero (T=0 K), what is the conductivity of an intrinsic semiconductor?
Zero. With no thermal energy, not a single electron is promoted across the gap; the VB is perfectly full, the CB perfectly empty — indistinguishable from an insulator.
At absolute zero, are the donors in n-type silicon still ionized?
No. Without thermal energy the fifth electron stays bound ("frozen out") on its donor atom. The dopant carriers only appear once temperature climbs enough to ionize them — the low-T "freeze-out" regime.
What happens to a semiconductor's band gap as Eg→0?
The bands overlap and it becomes a conductor. A zero (or overlapping) gap is exactly the metallic case — no forbidden region means always-available empty states.
If a dopant had the same valency as silicon (e.g. germanium in silicon), what happens?
Neither n nor p-type. With four valence electrons it fits the bonding perfectly, contributing no extra electron or hole. It is an isoelectronic substitution, electrically almost neutral.
What if you dope silicon with equal amounts of donors and acceptors (ND=NA)?
They compensate — each donor electron falls into an acceptor hole. Net free carriers cancel, and the material behaves nearly intrinsic despite being heavily doped.
In the very high-temperature limit, does a doped semiconductor stay n- or p-type?
No — it goes intrinsic. Massive thermal generation of electron-hole pairs overwhelms the fixed dopant population; n≈p again and the dopant's identity stops mattering.
A material has Eg=3.0 eV exactly — conductor, semiconductor, or insulator?
A boundary case. ~3 eV is the fuzzy line between wide-gap semiconductor and insulator; classification depends on temperature and definition. GaN (3.4 eV), for instance, is deliberately used as a semiconductor in LEDs and power devices — proof that the cutoff is a chosen convention, not a physical wall.
Recall One-line self-test before you close the page
Cover everything: state (a) why full bands don't conduct, (b) why n-type is neutral, and (c) why lnσ vs 1/T is linear.
(a) no empty states to move into ::: (b) fixed + donor ions balance the mobile electrons ::: (c) the carrier count is exponential in −Eg/2kBT
