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?

Short answer

The short answer based on the step-by-step solution: (a) For CdS and CdTe, CdS will have a larger band gap due to the higher electronegativity of Sulfur compared to Tellurium. (b) For GaN and InP, GaN will have a larger band gap because both Gallium and Nitrogen are higher in the periodic table than Indium and Phosphorus, respectively. (c) For GaAs and InAs, GaAs will have a larger band gap as Gallium is higher in the periodic table than Indium.

Step-by-step solution

a) CdS or CdTe#

Both semiconductors have the same element, Cadmium (Cd), but differ in the second element, Sulfur (S) and Tellurium (Te). Sulfur is higher in the periodic table (2nd period) than Tellurium (5th period), and has a higher electronegativity than Tellurium. Based on the trends mentioned above, semiconductors with higher electronegativity atoms typically have larger band gaps. Therefore, CdS will have a larger band gap than CdTe. Answer: CdS

b) GaN or InP#

To compare these semiconductors, we need to look at the elements involved. Ga (Gallium) and In (Indium) are in the same group (13) of the periodic table. However, Ga is higher than In. Between N (Nitrogen) and P (Phosphorus), N is higher in the periodic table (2nd period) than P (3rd period). GaN has one element higher in the periodic table than InP, making it more likely that GaN has the larger band gap. Therefore, GaN will have a larger band gap than InP. Answer: GaN

c) GaAs or InAs#

For these semiconductors, the second element is the same, Arsenic (As). We need to compare the first elements: Ga (Gallium) and In (Indium). Ga is in a higher position in the periodic table (4th period) than In (5th period). Based on the trends mentioned above, GaAs will have a larger band gap than InAs. Answer: GaAs

Key concepts

Periodic Table Trends

When investigating the properties of semiconductors, one useful tool is understanding the trends in the periodic table. Elements are arranged in a systematic way, showcasing trends that can predict behaviors and characteristics of compounds.
Some key periodic table trends include:

• Atomic size: Generally, atomic size increases as you move down a group but decreases as you move across a period from left to right.
• Ionization energy: The energy required to remove an electron increases across a period and decreases down a group.
• Electronegativity: Tends to increase across a period and decrease down a group. It’s crucial when determining bond types and characteristics such as band gaps in semiconductors.

Understanding these trends is vital when comparing elements like Gallium and Indium or Sulfur and Tellurium, as seen in semiconductor compounds. Elements higher in electronegativity generally lead to larger band gaps in semiconductors.

Electronegativity

Electronegativity is a key concept in chemistry that affects many properties, including the behavior of semiconductors. It measures the tendency of an atom to attract a bonding pair of electrons.
Some important points about electronegativity:

• Elements with higher electronegativity values are more effective in pulling electrons towards themselves.
• This has direct effects on the structure and stability of compounds they form. This results in materials with certain electronic properties, such as larger band gaps.
• On the periodic table, electronegativity increases across a period from left to right and decreases down a group.

In semiconductors like Cadmium Sulfide (CdS) versus Cadmium Telluride (CdTe), the higher electronegativity of sulfur leads to a larger band gap compared to tellurium.

Gallium Nitride

Gallium Nitride (GaN) is an important semiconductor known for its wide band gap. This makes it a preferred material in various high-power and high-frequency applications.
Here are some key aspects of GaN:

• Wide band gap: Approximately 3.4 eV, which allows GaN to handle high voltages and temperatures. Its wide band gap also leads to efficient light emission, making it ideal for LED technology.
• High thermal conductivity: GaN effectively dissipates heat, which is crucial in power devices.
• Excellent mechanical stability: Its robust structure makes it less prone to damage under stress or temperature variations.

Compared to Indium Phosphide (InP), GaN’s wide band gap results from its constituent nitrogen, which has a higher electronegativity than phosphorus, contributing to GaN’s superior electronic properties.

Cadmium Sulfide

Cadmium Sulfide (CdS) is a semiconductor material distinguished by its unique electronic properties. It is used in various applications, from photovoltaics to sensors.
Key features of CdS include:

• Band gap: About 2.42 eV, allowing it to absorb visible light efficiently, which is why it's used in solar cells.
• Photoconductivity: CdS becomes more conductive when exposed to light, making it valuable in optoelectronic devices.
• Toxicity concerns: Cadmium compounds can be toxic, necessitating careful handling and disposal.

In comparison to other compounds such as Cadmium Telluride (CdTe), the higher electronegativity of sulfur gives CdS a larger band gap, which affects its electrical and optical behavior.

Indium Phosphide

Indium Phosphide (InP) is a semiconductor material recognized for its high-speed and high-frequency capabilities. It's often used in telecommunication and fiber optics.
Here are some important attributes of InP:

• Band gap: InP has a direct band gap of about 1.34 eV, suitable for efficient electron-hole pair generation.
• High electron mobility: This allows for fast electron movement, beneficial in high-speed electronic devices.
• Thermal stability: InP’s composition allows it to perform reliably even at elevated temperatures.

Although GaN and InP are in the same group, GaN’s larger band gap makes it more applicable for devices needing higher power and thermal capacity. In contrast, InP is chosen for its exceptional electron mobility,