Consider a n-type semiconductor in which $$n_e$$ and $$n_h$$ are number of electrons and holes, respectively.
(A) Holes are minority carriers
(B) The dopant is a pentavalent atom
(C) $$n_e n_h \neq n_i^2$$
       (where $$n_{i}$$ is number of electrons or holes in semiconductor when it is intrinsic form)
(D) $$n_e n_h \geq n_i^2$$
(E) The holes are not generated due to the donors
Choose the correct answer from the options given below :

In an extrinsic semiconductor, one type of charge carrier is made the majority by adding a suitable impurity. If the dopant supplies extra electrons, the material becomes n-type.

Step 1 : Nature of majority and minority carriers
In an n-type semiconductor, electrons supplied by donor atoms are the majority carriers, while holes created by thermal generation are very few in number.
Thus statement (A) “Holes are minority carriers” is TRUE.

Step 2 : Kind of dopant required
A silicon or germanium atom has four valence electrons. To donate an extra electron we must insert an element from group V (P, As, Sb, etc.) which has five valence electrons. Such an atom is called a pentavalent donor.
Therefore statement (B) “The dopant is a pentavalent atom” is TRUE.

Step 3 : Applying the mass-action law
At thermal equilibrium, semiconductors (intrinsic or extrinsic) obey the mass-action law
$$n_e n_h = n_i^2 \quad -(1)$$
where $$n_i$$ is the intrinsic carrier concentration.
Hence the product $$n_e n_h$$ always equals, not differs from, $$n_i^2$$.

• Statement (C) “$$n_e n_h \neq n_i^2$$” contradicts equation $$(1)$$, so it is FALSE.
• Statement (D) “$$n_e n_h \geq n_i^2$$” is also inconsistent with $$(1)$$ (equality must hold), so it is FALSE.

Step 4 : Origin of the minority holes
In an n-type material, donor atoms produce extra electrons only. Holes arise solely from the thermal breaking of covalent bonds (electron-hole pair generation), exactly as in an intrinsic semiconductor. They are not created by the donor atoms.
Therefore statement (E) “The holes are not generated due to the donors” is TRUE.

Step 5 : Collecting the TRUE statements
TRUE : (A), (B), (E)
FALSE : (C), (D)

Comparing with the given options, Option C lists exactly (A), (B), (E).

Hence the correct answer is Option C.