Problem 67 - Chemistry: The Central Science

Question

For each of the following pairs of semiconductors, which one will have the larger band gap: (a) \(\mathrm{CdS}\) or \(\mathrm{CdTe}\) (b) GaN or InP, (c) GaAs or InAs?

Step-by-Step Solution

Answer

The comparison of the band gaps for each given pair is as follows: (a) \(\mathrm{CdS}\) has a larger band gap than \(\mathrm{CdTe}\), (b) GaN has a larger band gap than InP, and (c) InAs has a slightly larger band-gap compared to GaAs. This is determined by comparing the electronegativity differences between the elements forming each semiconductor.

Step 1: (a) Comparing \(\mathrm{CdS}\) and \(\mathrm{CdTe}\)

To compare CdS and CdTe, we should look at the difference in electronegativity between the elements combined to form these semiconductors. Electronegativity values are as follows: - \(\mathrm{Cd}\): 1.69 - \(\mathrm{S}\): 2.58 - \(\mathrm{Te}\): 2.1 Electronegativity difference for \(\mathrm{CdS}\): \(|1.69 - 2.58| = 0.89\) Electronegativity difference for \(\mathrm{CdTe}\): \(|1.69 - 2.1| = 0.41\) Since greater electronegativity difference usually implies a larger band gap, \(\mathrm{CdS}\) will have a larger band gap compared to \(\mathrm{CdTe}\).

Step 2: (b) Comparing GaN and InP

To compare GaN and InP, we will again look at the difference in electronegativity between the elements combined to form these semiconductors. Electronegativity values are as follows: - \(\mathrm{Ga}\): 1.81 - \(\mathrm{N}\): 3.04 - \(\mathrm{In}\): 1.78 - \(\mathrm{P}\): 2.19 Electronegativity difference for GaN: \(|1.81 - 3.04| = 1.23\) Electronegativity difference for InP: \(|1.78 - 2.19| = 0.41\) Since a greater electronegativity difference generally implies a larger band gap, GaN will have a larger band gap compared to InP.

Step 3: (c) Comparing GaAs and InAs

To compare GaAs and InAs, we will again look at the difference in electronegativity between the elements combined to form these semiconductors. Electronegativity values are as follows: - \(\mathrm{Ga}\): 1.81 - \(\mathrm{As}\): 2.18 - \(\mathrm{In}\): 1.78 Electronegativity difference for GaAs: \(|1.81 - 2.18| = 0.37\) Electronegativity difference for InAs: \(|1.78 - 2.18| = 0.40\) Since a greater electronegativity difference generally implies a larger band gap and the difference is small, we can say that both GaAs and InAs might have similar band gap values. However, in this case, InAs will have a slightly larger band-gap compared to GaAs due to higher electronegativity difference.

Key Concepts

Understanding Band Gap in Semiconductors

The concept of a band gap is pivotal in semiconductor physics, as it determines how a semiconductor behaves when subjected to an external voltage. Band gap is the energy difference between the valence band (highest energy electrons that are still bound to an atom) and the conduction band (lowest energy electrons that can move freely).
This gap defines a material’s ability to conduct electricity.
In simple terms, a larger band gap generally means the material is a better insulator, while a smaller band gap indicates that the material can more easily conduct electricity.

• A semiconductor with a large band gap requires more energy to move an electron from the valence band to the conduction band.
• Conversely, a small band gap means less energy is needed for the same transition, and the material will readily conduct electricity.

The size of the band gap can significantly influence the applications of the semiconductor.
Materials with specific band gaps are selected based on the intended use, such as electronic devices or photovoltaic cells in solar panels.

Role of Electronegativity in Determining Band Gap

Electronegativity, the tendency of an atom to attract a bonding pair of electrons, is a crucial factor in understanding the electronic properties of compounds.
It plays a significant role in determining the band gap of compound semiconductors.
A comparably higher electronegativity difference between the atoms in a compound often leads to a larger band gap.

• When the electronegativity difference is greater, the atomic bonds in a compound become more ionic rather than covalent.
• This increased ionic characteristic causes the energy levels of the valence and conduction bands to be further apart, thereby increasing the band gap.

For example, in the exercise solution, CdS has a larger electronegativity difference compared to CdTe, which directly translates to a larger band gap.
Understanding these differences is essential for predicting and engineering the electronic properties of semiconductors.

Exploring Compound Semiconductors

Compound semiconductors are materials composed of two or more elements, which often belong to groups III, IV, and V of the periodic table.
These compounds can form crystals with unique properties that make them extremely useful in a variety of electronic and optoelectronic applications.
For instance:

• GaN (Gallium Nitride) and GaAs (Gallium Arsenide) are popular in the electronics industry due to their specific band gap properties.
• They are suitable for light-emitting diodes (LEDs), lasers, and high-efficiency solar cells.

Compound semiconductors achieve their unique properties by balancing the electronegativity and atomic size of their elements.
This creates a tailored electronic structure suitable for high-speed electronic components and devices.
The ability to combine different elements results in varied applications, making compound semiconductors versatile in advanced technology sectors.