In a semiconductor, heating gives valence electrons enough energy to jump across the small band gap into the conduction band. This creates many more free electrons and holes (charge carriers), so current flows more easily and resistance drops. Memory hook: "Heat unlocks carriers" - in a metal heat only adds traffic jams, but in a semiconductor heat first creates the cars.
In a metal, carrier number n is fixed, so heating adds scattering and resistance rises (positive alpha). In a semiconductor, heating creates many new electron-hole pairs, so n rises fast and resistance falls (negative alpha).
Your doubts, answered
Does the resistance of a semiconductor increase or decrease with temperature?
It decreases. As temperature rises, thermal energy breaks more covalent bonds and lifts electrons across the band gap into the conduction band. The number of charge carriers (n) increases sharply, so conductivity goes up and resistance goes down.
Why does a metal's resistance increase but a semiconductor's decrease with the same heating?
Resistivity is rho = m / (n e^2 tau). In a metal the carrier number n is already fixed (all valence electrons are free), so heating only lowers the collision time tau (more lattice vibrations, more scattering), and rho rises. In a semiconductor n rises very fast with temperature, and this large increase in n beats the small drop in tau, so rho falls.
What actually happens to the charge carriers when a semiconductor is heated?
Each broken bond releases one free electron and leaves behind one hole. So heating creates electron-hole pairs. The intrinsic carrier concentration ni grows roughly as ni is proportional to exp(-Eg / (2 k T)). More carriers means easier current flow and lower resistance.
Is the temperature coefficient of resistance for a semiconductor positive or negative?
Negative. Because resistance falls as temperature rises, the temperature coefficient of resistance (alpha) is negative for semiconductors (and for insulators). Metals have a positive alpha. This is why a thermistor made of semiconductor material is used to sense temperature.
Does the band gap size matter for this effect?
Yes. A smaller band gap Eg means electrons are lifted across more easily, so more carriers appear per degree of heating. That is why germanium (Eg about 0.7 eV) is more temperature-sensitive than silicon (Eg about 1.1 eV). Insulators have a very large Eg, so at normal temperatures almost no carriers cross and they stay poor conductors.
⚠️ The NEET trap ✗ Resistance of a semiconductor falls because the electrons move faster and collide less when heated. ✓ Resistance falls because the NUMBER of free carriers (n) increases hugely as bonds break and electrons cross the band gap. Heating actually increases collisions (tau falls), but the big rise in n dominates, so rho drops. 🧠 NTA loves testing WHY: the answer is 'more carriers', not 'faster electrons'. Faster/fewer collisions is the metal story reversed - do not mix it up.
Real NEET questions
NEET 2020
The solids which have the negative temperature coefficient of resistance are:
A · Semiconductors only
B · Insulators and semiconductors ✓
C · Metals
D · Insulators only
Solution: Step 1: A negative temperature coefficient means resistance decreases as temperature increases. Step 2: This happens when heating creates more charge carriers. Step 3: Both semiconductors and insulators gain carriers on heating (electrons crossing the band gap), so both have negative alpha. Metals have positive alpha because their carrier number is fixed and scattering increases. Answer: (B) Insulators and semiconductors.
NEET 2022
As the temperature increases, the electrical resistance:
A · Increases for both conductors and semiconductors
B · Decreases for both conductors and semiconductors
C · Increases for conductors but decreases for semiconductors ✓
D · Decreases for conductors but increases for semiconductors
Solution: Step 1: For a conductor (metal), n is fixed; heating increases lattice scattering, tau falls, so rho and R increase. Step 2: For a semiconductor, heating breaks bonds and creates many electron-hole pairs; n rises fast, so rho and R decrease. Answer: (C) Increases for conductors but decreases for semiconductors.
NEET 2018
In a p-n junction diode, change in temperature due to heating:
A · Does not affect resistance of p-n junction
B · Affects only forward resistance
C · Affects only reverse resistance
D · Affects the overall V-I characteristics of p-n junction ✓
Solution: Step 1: Heating a semiconductor generates extra electron-hole pairs everywhere in the junction. Step 2: More carriers change both the forward conduction and the reverse leakage (saturation) current. Step 3: Because both regions of behaviour shift, the whole V-I curve changes. Answer: (D) Affects the overall V-I characteristics of the p-n junction.
Resistivity rho = m / (n e^2 tau), where n is carrier number per unit volume and tau is the mean collision time. In a semiconductor n rises strongly with temperature as ni is proportional to exp(-Eg / (2 k T)), so rho falls even though tau also falls a little.
Why is a semiconductor an insulator at absolute zero?
At T = 0 K there is no thermal energy to lift electrons across the band gap. The conduction band is empty, so there are no free carriers and the material cannot conduct - it behaves like an insulator.
Is this why thermistors are made from semiconductors?
Yes. Because a semiconductor's resistance changes strongly and predictably with temperature (negative temperature coefficient), it makes a sensitive temperature sensor called a thermistor.
Does germanium or silicon change resistance faster with temperature?
Germanium, because its band gap (about 0.7 eV) is smaller than silicon's (about 1.1 eV). A smaller gap means more electron-hole pairs are generated for the same temperature rise, so germanium is more temperature-sensitive.
Do insulators also show decreasing resistance with temperature?
Yes, in principle. Insulators have a very large band gap, so at normal temperatures almost no electrons cross it. But at high enough temperatures some do, so insulators also have a negative temperature coefficient, just far weaker than semiconductors.
