Intrinsic Semiconductors and Temperature
A pure semiconductor is intrinsic and satisfies n = p = ni. Over the usual semiconductor range, increasing temperature raises ni strongly, so resistance falls even though carrier mobility may decrease.
Why this shows up in the exam
Comparing metal and semiconductor temperature behavior · Explaining thermal generation of carriers · Interpreting intrinsic conductivity trends
Learn the idea
An intrinsic semiconductor creates electrons and holes in equal numbers, and heating usually increases its conductivity. Thermal energy can lift a bound electron into the conduction band. That produces one mobile electron and one hole together, so both carrier populations rise as temperature rises.
🧠 Memory hook: Heating makes carrier pairs, so intrinsic resistance falls.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- n = p = n_i — electron and hole concentrations in an intrinsic semiconductor
- n_i proportional to T^(3/2) exp[-E_g/(2 k T)] — approximate strong temperature dependence of intrinsic carrier concentration
How to approach it
- 1Check whether the sample is explicitly pure or intrinsic
- 2Use n = p before substituting in conductivity
- 3Separate the carrier-number effect from the mobility effect
Common slip-ups that cost marks
- •Saying only electrons are produced by heating
- •Applying a metal's positive temperature coefficient to a semiconductor
- •Treating mobility increase as the reason conductivity rises
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A transistor has common-emitter current gain beta = 50. If base current is 20 microA, find collector current.
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