Doping, Majority Carriers, and Mass Action
Pentavalent donor impurities create n-type material with electrons as majority carriers; trivalent acceptors create p-type material with holes as majority carriers. At thermal equilibrium, carrier concentrations obey the mass-action law.
Why this shows up in the exam
Identifying n-type and p-type semiconductors · Finding a minority-carrier concentration · Checking charge neutrality after doping
Learn the idea
Donors make n-type material, acceptors make p-type material, but the doped crystal remains electrically neutral. A donor supplies an extra electron and an acceptor leaves a mobile hole. Doping changes which carrier is abundant, not the net charge of the complete crystal.
🧠 Memory hook: Donor gives electron; acceptor creates hole; the crystal stays neutral.
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_i² — mass-action law for a semiconductor in thermal equilibrium
- n approximately N_D or p approximately N_A — majority-carrier approximation for fully ionized, strongly extrinsic material
How to approach it
- 1Identify the impurity valency first
- 2Name majority and minority carriers
- 3Use np = ni squared for the missing concentration
Common slip-ups that cost marks
- •Calling n-type material negatively charged
- •Saying holes in n-type material are supplied by donors
- •Replacing np = ni squared by n + p = ni
🌟 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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