1.1.2 · D5Electricity & Charge Basics
Question bank — Understand conductors, insulators, and semiconductors
This bank hunts the exact misconceptions the topic invites: the meaning of the band gap (the energy wall electrons must climb from the valence band to the conduction band), the difference between ==resistivity (material-only) and resistance == (shape too), and the opposite temperature behaviour of metals versus semiconductors. If any of those terms feel shaky, re-read the parent note first — every reveal below assumes you can picture the ladder-and-balcony image.
True or false — justify
A semiconductor always conducts about halfway between a conductor and an insulator.
False — a cold, pure semiconductor is nearly an insulator; its value is being switchable by heat, light, or doping, not being permanently middling.
Insulators contain no electrons.
False — they are full of electrons, but those electrons are tightly bound and cannot cross the large band gap ( eV), so they never reach the conduction band.
Heating any material lowers its resistance.
False — this holds for semiconductors (more carriers ) but reverses for metals, where hotter atoms scatter electrons more, shrinking the collision time and raising .
Resistivity and resistance are two names for the same thing.
False — resistivity is a material-only property; resistance also depends on the object's length and cross-section.
In a conductor the valence and conduction bands overlap.
True — that overlap means electrons are effectively already in the conduction band (), so current flows with almost no push.
Doping raises the melting point of silicon, which is why it conducts better.
False — doping changes conductivity by adding carriers (), not by changing the material's physical toughness; melting point is irrelevant here.
A pure (intrinsic) semiconductor creates electrons and holes in equal numbers.
True — each electron promoted to the conduction band leaves behind exactly one hole, so they are generated as pairs (this is why the exponent carries a factor of 2).
Copper conducts because it has a small band gap that electrons hop across.
False — copper is a metal with overlapping bands (); there is no gap to hop, so free electrons are always available.
Silver conducts better than copper, so all our chips should be made of silver.
False — chips need controllable conduction (switching), which raw metals cannot offer; that is why doped silicon, not silver, computes.
An n-type semiconductor carries a net negative electric charge.
False — the extra donor electrons are balanced by the fixed positive donor ions left behind, so the material stays electrically neutral overall.
Spot the error
"Silicon has eV and germanium eV, so germanium is the better insulator."
The gap value for germanium is wrong — it is about eV (smaller than silicon), so germanium conducts more easily, not less; eV is insulator territory.
", so a longer wire has lower resistance."
The formula is inverted — it is ; a longer wire means more collisions and thus higher resistance, and a fatter one (bigger ) lowers it.
", so doubling the applied voltage doubles the conductivity."
Conductivity depends on , , and — none of which is voltage; a bigger field raises current density , but itself stays fixed.
"The carrier density follows ."
The exponent is missing its factor of 2 — it is , because an electron and a hole are created together and the gap energy is split between the pair.
"Because conductivity is , an insulator with has conductivity ."
Inverting gives , an extremely small number — an insulator has tiny conductivity, matching its refusal to carry current.
"A material at Ω·m is clearly a conductor."
That value sits in the semiconductor range (– Ω·m); conductors live near , about ten orders of magnitude lower.
Why questions
Why does the exponent in have a 2 rather than a 1?
Because thermal excitation makes an electron–hole pair at once; the energy is effectively shared between the two carriers, halving the cost per carrier in the exponent.
Why does resistivity, not resistance, appear in material tables that classify solids?
Resistance changes with the sample's shape, so it can't fairly compare materials; resistivity is intrinsic, letting a copper block and a copper thread report the same .
Why does adding a pinch of impurity change conductivity so dramatically?
Intrinsic silicon has very few carriers (), so donating even extra swamps the original count, multiplying by roughly a million.
Why do metals get more resistive when heated while semiconductors get less?
In a metal is already fixed, so hotter atoms just scatter electrons more (smaller , bigger ); in a semiconductor heat mainly creates new carriers ( climbs exponentially), which wins decisively.
Why is it controllability, not raw conductivity, that makes silicon the basis of computing?
A wire only carries current; a doped p–n junction can be switched on and off by voltage, and stacking millions of such switches (transistors) is what performs logic.
Why is the band gap called an energy "wall" rather than a physical distance?
It measures the minimum energy an electron must gain to jump from the valence to the conduction band — an amount of energy (in eV), not a length; the ladder-height image is about energy, not space.
Edge cases
At absolute zero, how does a pure semiconductor behave?
Like a near-perfect insulator — with no thermal energy, , so essentially no carriers exist to cross the gap.
What happens to a semiconductor's resistivity as temperature rises toward very high values?
It keeps falling as carriers multiply, so it behaves more and more like a conductor — the reverse of a metal, which would only grow more resistive.
Is a material with band gap exactly a conductor or a semiconductor?
A conductor — a zero (or overlapping) gap means the conduction band is always populated, so free electrons exist even at low temperature with no ladder to climb.
Does an insulator ever conduct?
Yes, under extreme conditions — a large enough voltage can force electrons across the gap (dielectric breakdown, like a spark through air), but under normal use it blocks current.
If you cool a copper wire close to absolute zero, what happens to its resistance?
It drops, because fewer atomic vibrations mean fewer collisions (larger ), the opposite of a semiconductor which would lose its carriers and become more resistive.
Can holes actually move, or is only the electron real?
Holes move as genuine positive charge carriers — as a neighbouring electron shifts to fill a vacancy, the empty spot travels the other way, so the hole carries current just like a real particle.
Recall Fast self-test
Cover every answer, run the list once, and tally your reasons (not just verdicts). Metal heated ::: resistivity goes up (more scattering). Semiconductor heated ::: resistivity goes down (more carriers). Correct carrier formula ::: . Correct resistance formula ::: . What makes silicon special ::: controllable switching via doping, not raw conductivity.
Related deep dives worth pairing with this trap set: Electric Charge and Current, Ohm's Law and Resistance, Energy Bands in Solids, Semiconductor Diodes and Transistors, Temperature Coefficient of Resistance.