In an N-type semiconductor, there are

Question

Prepp Team · Accepted Answer

N-type Semiconductor Fundamentals

An N-type semiconductor is a type of extrinsic semiconductor formed by adding a small amount of pentavalent impurity atoms to a pure (intrinsic) semiconductor like silicon (Si) or germanium (Ge).

Doping and Donor Impurities

The process of adding impurities to a pure semiconductor is known as doping. In the case of an N-type semiconductor, the impurities added are called donor impurities. These are elements from Group 15 of the periodic table, such as Phosphorus (P), Arsenic (As), or Antimony (Sb). These donor atoms have five valence electrons.

When a pentavalent impurity atom replaces a silicon or germanium atom in the crystal lattice, four of its five valence electrons form covalent bonds with the four surrounding semiconductor atoms.
The fifth valence electron is loosely bound to the donor atom. Because it requires very little energy (typically around $0.01 \text{ eV}$ for Ge and $0.05 \text{ eV}$ for Si) to break free from the donor atom, this fifth electron easily becomes a free electron in the conduction band.

Formation of Immobile Positive Ions

When the pentavalent donor atom donates its fifth electron to the conduction band, it loses a negative charge. Consequently, the donor atom itself becomes positively charged. Since this positively charged donor atom is fixed within the crystal lattice structure, it cannot move and is therefore referred to as an immobile positive ion.

These immobile positive ions are essential for maintaining charge neutrality within the bulk material, even though they do not contribute to current flow. They are distinct from the mobile charge carriers (electrons and holes).

Charge Carriers in N-type Semiconductors

In an N-type semiconductor:

Electrons are the majority carriers. This is because each donor atom contributes one free electron, significantly increasing the concentration of electrons in the conduction band compared to an intrinsic semiconductor.
Holes are the minority carriers. They are still present due to thermal generation (breaking of covalent bonds at room temperature), but their concentration is much lower than that of electrons.

The product of electron concentration ($n$) and hole concentration ($p$) is constant at a given temperature, following the mass action law: $n \cdot p = n_i^2$, where $n_i$ is the intrinsic carrier concentration. Since $n$ is very high in N-type semiconductors, $p$ must be very low.

Analyzing the Options

Let's evaluate the given options based on our understanding of N-type semiconductors:

Option 1: No minority carrier
This statement is incorrect. While electrons are the majority carriers in an N-type semiconductor, holes are always present as minority carriers due to thermal excitation across the band gap. There are never "no minority carriers" in any semiconductor at typical operating temperatures.
Option 2: Immobile negative ion
This statement is incorrect. Donor impurity atoms lose an electron and thus become positively charged, not negatively charged. These positive ions are immobile.
Option 3: Immobile positive ion
This statement is correct. As explained above, when a pentavalent donor atom gives up its loosely bound fifth electron, it becomes a fixed, positively charged ion within the crystal lattice.
Option 4: Holes as majority carrier
This statement is incorrect. In an N-type semiconductor, "N" stands for negative, indicating that electrons (which carry a negative charge) are the majority carriers. Holes are the majority carriers in P-type semiconductors.