Mobility, Conductivity, and Resistivity
Mobility is drift-speed magnitude per electric-field magnitude. For electron concentration n and hole concentration p, their conventional-current contributions add to give the total conductivity.
Why this shows up in the exam
Calculating sample conductivity or resistivity · Comparing electron and hole contributions · Relating drift velocity to applied field
Learn the idea
Semiconductor conductivity is the sum of electron and hole charge transport. An electric field gives electrons and holes drift speeds. More carriers or greater mobility produces more current for the same field, so conductivity increases and resistivity decreases.
🧠 Memory hook: Carrier count times mobility, add both types, then multiply by e.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- mu = v_d / E — magnitude definition of carrier mobility
- sigma = e (n mu_e + p mu_h) — conductivity including electron and hole contributions
- rho = 1 / sigma — resistivity as the reciprocal of conductivity
How to approach it
- 1Convert every carrier density to the same volume unit
- 2Include both carrier terms unless one is stated negligible
- 3Check that sigma has unit siemens per metre
Common slip-ups that cost marks
- •Subtracting electron and hole conductivity contributions
- •Confusing mobility with drift velocity
- •Forgetting to invert conductivity when resistivity is asked
🌟 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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