Statement I: By doping silicon semiconductors with pentavalent material, the electrons density increases.
Statement II: The n-type of semiconductor has a net negative charge.
In the above statements, choose the most appropriate answer from the options given below:

To analyse the two given statements, we first recall the basic ideas of semiconductor physics.

A pure silicon crystal is called an intrinsic semiconductor. Silicon atoms have four valence electrons, so every atom forms four covalent bonds with its neighbours, and at 0 K no free charge carriers exist in the crystal lattice.

Whenever we deliberately introduce a small amount of an impurity into this pure lattice, the process is called doping. The impurity atom is called a dopant. The nature of the dopant decides whether the material becomes n-type or p-type.

Now let us examine Statement I:

We dope silicon with a pentavalent element such as phosphorus (P), arsenic (As) or antimony (Sb). A pentavalent atom possesses

$$5$$

valence electrons. Four of these electrons pair up with the four neighbouring silicon atoms to form covalent bonds exactly as the silicon atoms do. The fifth electron, however, does not find a bonding partner. This extra electron is only very weakly bound (its ionisation energy is of the order of $$0.01\;\text{eV}$$), so at room temperature it is easily promoted into the conduction band where it becomes a free charge carrier.

Therefore, for every pentavalent dopant atom we obtain one additional conduction electron. If the concentration of dopant atoms is $$N_D$$, the concentration of extra electrons generated is also approximately $$N_D$$. Hence the electron density $$n$$ in the crystal increases:

$$n_{\text{new}} = n_{\text{intrinsic}} + N_D \;.$$

This confirms that Statement I — “By doping silicon semiconductors with pentavalent material, the electrons density increases” — is true.

We now consider Statement II:

The silicon crystal originally contains an equal number of positive and negative charges, so it is electrically neutral. When a pentavalent atom donates its fifth electron to the conduction band, the atom itself becomes a positively charged ion (donor ion) with charge $$+e$$. Simultaneously, the freed electron carries charge $$-e$$. Thus for every donor atom we add equal magnitude positive and negative charges. Mathematically, for each dopant:

$$(+e) + (-e) = 0 \;.$$

The total charge in the crystal therefore remains

$$\text{Net charge} = 0 \;.$$

Because of this compensating mechanism, an n-type semiconductor, although rich in negative charge carriers (electrons), is still electrically neutral as a whole. It does not possess a net negative charge. Consequently, Statement II — “The n-type of semiconductor has a net negative charge” — is false.

Combining the two results, we see that Statement I is true while Statement II is false. This situation corresponds exactly to Option B in the list provided.

Hence, the correct answer is Option B.