Question

For each of the following pairs of semiconductors, which one will have the larger band gap: (a) InP or InAs, \((\mathbf{b})\) Ge or AlP, (c) Agl or CdTe?

Short answer

In conclusion, for each pair of semiconductors, the following has a larger band gap: (a) InP with a band gap of \(1.34 eV\), (b) AlP with a band gap of \(2.45 eV\), and (c) Agl with a band gap of \(3.2 eV\).

Step-by-step solution

a) InP or InAs

To compare the band gaps of InP and InAs, we need to first find the values of their band gaps. You can either look up values from a reference book or search online. We get the following values: Band gap of InP: \(1.34 eV\) Band gap of InAs: \(0.36 eV\) Now comparing the values, we find that InP has a larger band gap (1.34 eV) than InAs (0.36 eV).

b) Ge or AlP

Similarly, for the pair Ge and AlP, we need to find the values of their band gaps. We get the following values: Band gap of Ge: \(0.66 eV\) Band gap of AlP: \(2.45 eV\) Comparing the values, we find that AlP has a larger band gap (2.45 eV) than Ge (0.66 eV).

c) Agl or CdTe

Finally, for the pair Agl and CdTe, we need to find the values of their band gaps: Band gap of Agl: \(3.2 eV\) Band gap of CdTe: \(1.5 eV\) Comparing the values, we find that Agl has a larger band gap (3.2 eV) than CdTe (1.5 eV). In conclusion, InP has a larger band gap than InAs, AlP has a larger band gap than Ge, and Agl has a larger band gap than CdTe.

Key concepts

InP vs InAs

Indium Phosphide (InP) and Indium Arsenide (InAs) are both compound semiconductors that belong to the III-V group of the periodic table. These materials are crucial in electronics, particularly in devices like LEDs and lasers. The band gap of a material is an essential property as it determines its electrical conductivity and optical properties.

For InP, the band gap is about 1.34 eV, while for InAs, it's much lower at 0.36 eV. A larger band gap means the material is less conductive but more effective at emitting light, making InP suitable for high-frequency and high-speed electronics. Conversely, InAs, with its smaller band gap, is more sensitive to infrared light and finds applications in photodetectors and thermoelectric devices.

Thus, the choice between InP and InAs depends on the intended application, balancing conductivity and speed with light emission and sensitivity.

Ge vs AlP

Germanium (Ge) and Aluminum Phosphide (AlP) represent another interesting comparison when it comes to semiconductor band gaps. Germanium, a group IV element, has a modest band gap of 0.66 eV, making it a highly conductive semiconductor. This property is why historically, Ge was among the first materials used in transistors. Its lower band gap makes it excellent for early-stage electronics but less effective than modern materials that can operate at higher frequencies and voltages.

On the other hand, AlP, an III-V compound, boasts a significant band gap of 2.45 eV. This wide band gap contributes to AlP's excellent optical properties, making it useful in optoelectronics. Larger band gaps are crucial for stability across a range of temperatures and are beneficial for devices that operate in harsh environments. While Ge is excellent for conductive applications, AlP is preferred in scenarios demanding high resistivity and optical transparency.

Ultimately, the decision between Ge and AlP hinges on their application, whether conductivity is prioritized or higher optical performance and stability are essential.

AgI vs CdTe

Silver Iodide (AgI) and Cadmium Telluride (CdTe) are semiconductor materials used in various advanced technology sectors. They are compared based on their band gaps to determine suitability for different applications.

AgI possesses a large band gap of approximately 3.2 eV. This substantial band gap makes AgI less conductive under standard conditions but enhances its use in applications that require materials capable of handling high-energy photons. Fields like meteorology make use of AgI's properties in cloud seeding and other specialized optical applications.

CdTe, with a band gap of 1.5 eV, strikes a balance between low-energy conductivity and optical activity. CdTe is prominently used in solar cells due to its efficient absorption of sunlight and its capacity to convert light into electricity effectively.

The choice between AgI and CdTe revolves around whether high-energy optical interactions or effective solar energy conversion is the priority, illustrating the diversity and specialized roles of semiconductors.