Question

Semi-conductor has phosphorus as impurity then it will have (A) \(\mathrm{n}_{\mathrm{e}}>\mathrm{n}_{\mathrm{h}}\) (B) \(\mathrm{n}_{\mathrm{e}}<<\mathrm{n}_{\mathrm{h}}\) (C) \(\mathrm{n}_{\mathrm{e}}=\mathrm{n}_{\mathrm{h}}\) (D) \(n_{e}=n_{h}=n_{i}\)

Short answer

In an n-type semiconductor, doped with phosphorus as an impurity, the number of free electrons will be greater than the number of holes. So, the relationship between electron concentration (\(n_e\)) and hole concentration (\(n_h\)) is given by \(n_e > n_h\). Therefore, the correct answer is (A).

Step-by-step solution

Understand n-type semiconductors

When a semiconductor is doped with phosphorus, it becomes an n-type semiconductor. This is because phosphorus has 5 valence electrons, which means it provides an extra free electron to the semiconductor. These extra electrons become mobile and contribute to the conductivity of the material. As a result, the electron concentration in the semiconductor (\(n_e\)) will increase while the hole concentration (\(n_h\)) will decrease.

Write the relation for an n-type semiconductor

In n-type semiconductors, the number of free electrons is greater than the number of holes. Therefore, we have the following relationship: \(n_e > n_h\)

Choose the correct answer

Based on the relationship we derived above, we can now choose the correct answer from the given options: (A) \(n_{\mathrm{e}} > n_{\mathrm{h}}\) So, the correct answer is (A).

Key concepts

Phosphorus Doping

Phosphorus doping hugely impacts the properties of a semiconductor. When phosphorus atoms are introduced into a semiconductor, they are there to donate extra electrons. This process is known as doping, specifically, it results in an n-type semiconductor.
Phosphorus has five electrons in its outer shell, but only four are needed to form covalent bonds with the silicon atoms in the semiconductor lattice. This leaves one electron free, which can move around the lattice, enhancing electron availability in the semiconductor.

• Increases conductivity by adding free electrons
• Helps in making semiconductors efficient in electronic devices

This free movement of additional electrons due to phosphorus doping directly affects the semiconductor's overall behavior.

Electron Concentration

The concentration of electrons, often denoted by \(n_e\), is a crucial factor in semiconductor performance. In an n-type semiconductor, phosphorus atoms increase the number of free electrons.
The higher the electron concentration, the more readily current can flow through the semiconductor, making it more conductive. This is due to the additional free electrons that have been introduced into the system.

• Contributes to increased electrical current
• Improves semiconductor efficiency

Understanding electron concentration helps explain why n-type semiconductors are more conductive compared to their undoped counterparts.

Hole Concentration

The term 'holes' in semiconductor physics refers to the absence of an electron, which behaves as a positively charged entity. Hole concentration is denoted by \(n_h\). In n-type semiconductors, the presence of excess electrons leads to a decrease in hole concentration.
This is because the infused electrons fill these positive holes, thereby reducing the number of holes available in the semiconductor.

• Decreases with an increase in doping
• Is lower than electron concentration in n-type semiconductors

Therefore, understanding hole concentration is essential to grasp how semiconductors manage their charge carriers.

Semiconductor Conductivity

Conductivity in semiconductors refers to their ability to allow electrical current to pass through them. When phosphorus doping occurs, it alters the conductivity of the semiconductor by adding free electrons.
The effective conductivity is primarily due to the increased number of charge carriers (electrons), as they enhance the flow of current.

• Elevated conductivity improves device performance
• Facilitates various applications in electronics

Understanding semiconductor conductivity is crucial for anyone studying electronics and materials science as it dictates how semiconductors are used in various applications.