If np and ne is the number of holes and electrons respectively in an intrinsic semiconductor then:
- A.npne = 1
- B.np > ne
- C.np = ne
- D.np < ne
Show answer
Correct answer: C. np = ne
Explanation
The correct answer is C, the number of holes equals the number of electrons. In an intrinsic, that is a chemically pure, semiconductor every free electron is produced by breaking a covalent bond, and breaking a bond leaves behind exactly one hole, so electrons and holes are created strictly in pairs and their concentrations must be equal. Option A is wrong because a product of two concentrations cannot equal a bare number one; the product is fixed by temperature and the band gap, not by unity. Option B is wrong because holes can outnumber electrons only in a p-type crystal, which needs a trivalent dopant. Option D is wrong because electrons outnumber holes only in an n-type crystal, which needs a pentavalent dopant. Equal numbers are therefore the signature of the pure crystal, and any inequality means doping has taken place.