Problem 71 - Chemistry: The Central Science in SI Units, Global Edition

Question

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

Step-by-Step Solution

Answer

For each pair of semiconductors, the one with the larger band gap is: (a) CdS, with a band gap of 2.42 eV, (b) GaN, with a band gap of 3.4 eV, and (c) GaAs, with a band gap of 1.43 eV.

Step 1: Find the Band Gaps

Look up the band gap values for each of the given semiconductors in a reference book or reliable online source. (a) CdS: The band gap is 2.42 eV. CdTe: The band gap is 1.44 eV. (b) GaN: The band gap is 3.4 eV. InP: The band gap is 1.35 eV. (c) GaAs: The band gap is 1.43 eV. InAs: The band gap is 0.36 eV.

Step 2: Compare the Band Gaps

Compare the band gaps of each pair to determine which semiconductor has a larger band gap. (a) CdS vs CdTe: CdS has a band gap of 2.42 eV, while CdTe has a band gap of 1.44 eV. Since 2.42 eV > 1.44 eV, CdS has a larger band gap. (b) GaN vs InP: GaN has a band gap of 3.4 eV, while InP has a band gap of 1.35 eV. Since 3.4 eV > 1.35 eV, GaN has a larger band gap. (c) GaAs vs InAs: GaAs has a band gap of 1.43 eV, while InAs has a band gap of 0.36 eV. Since 1.43 eV > 0.36 eV, GaAs has a larger band gap.

Step 3: Write the Results

After comparing the band gaps, note down which semiconductor has a larger band gap for each pair. (a) In the pair of CdS and CdTe, the semiconductor with the larger band gap is CdS. (b) In the pair of GaN and InP, the semiconductor with the larger band gap is GaN. (c) In the pair of GaAs and InAs, the semiconductor with the larger band gap is GaAs.

Key Concepts

Semiconductors

Semiconductors are materials that have a conductivity level which is in between that of a conductor and an insulator. This means they can conduct electricity, but not as well as metals like copper or silver. Semiconductors are unique because their conductivity can be controlled through various techniques such as doping—adding impurities to the material—or by applying electric fields.

The most common semiconductors include silicon and germanium, but compounds like GaN (Gallium Nitride) and InP (Indium Phosphide) are also frequently used in electronic devices. These materials are fundamental in the production of transistors, solar cells, light-emitting diodes (LEDs), and integrated circuits.

• Silicon is the most widely used semiconductor due to its abundance and effective electronic properties.
• Compound semiconductors like GaAs (Gallium Arsenide) offer faster electronic speeds compared to silicon.

In the exercise, you observed pairs of compound semiconductors compared based on their band gaps, helping to determine their electronic properties and potential applications.

Electrical Conductivity

Electrical conductivity in semiconductors is unique because it can be altered by changing conditions like temperature or by adding impurities. In their pure form, semiconductors have very few charge carriers, which are essential for conduction. When they are doped, which means adding a small amount of another element, the number of charge carriers increases, thus improving conductivity.

• In semiconductors, increased temperature can lead to more free carriers since heat energy helps bridge the band gap.
• N-type semiconductors have an abundance of electrons, whereas P-type have more holes.

In terms of band gaps, a smaller band gap means that electrons can move more easily across the valence to the conduction band, enhancing conductivity. This is why the size of the band gap was key in the exercise to compare different semiconductors.

Energy Levels

Energy levels in semiconductors are crucial for understanding how they function. In these materials, the electrons occupy certain energy bands. The two most important ones are the valence band and the conduction band. The valence band is filled with electrons that are bound to atoms, while the conduction band is where free electrons reside that can move and conduct current.

The key feature of semiconductors is the energy gap (band gap) between these two bands. This gap determines the energy required to move an electron from the valence band to the conduction band.

• A small band gap means electrons need less energy to move, which usually increases conductivity.
• A larger band gap means the semiconductor may have better insulating properties, but less conductivity.

The exercise demonstrated how semiconductors with different band gaps—like CdS with a larger band gap compared to CdTe—perform differently in applications based on this energy level difference.