For each of the following pairs of semiconductors, decide which has the smaller band gap energy, \(E_{g}\), and then cite the reason for your choice. (a) C (diamond) and Ge (b) AlP and InAs (c) GaAs and \(\mathrm{ZnSe}\) (d) \(\mathrm{ZnSe}\) and \(\mathrm{CdTe}\) (e) \(\mathrm{CdS}\) and \(\mathrm{NaCl}\)

Semiconductor materials are substances that possess a conductivity level between that of conductors (like copper) and insulators (such as glass). Their unique property of varying conductivity under different conditions makes them vital in electronic components, especially in devices like transistors, diodes, and solar cells. The band gap energy, denoted as \(E_{g}\), is a fundamental characteristic of semiconductors. This energy gap between the valence band, filled with electrons, and the conduction band, where electrons can move freely to conduct electricity, vastly influences the electronic and optical properties of the material.

In the context of a semiconductor's band gap, materials with a smaller \(E_{g}\) become more easily conductive as the energy required to excite an electron from the valence to the conduction band is less. For instance, germanium (Ge) has a smaller band gap than diamond (carbon), which means that Ge can conduct electricity at lower energy input compared to diamond. This makes Ge a more suitable material for some semiconductor applications. Understanding the size of the band gap is crucial as it determines the response of semiconductors to light and temperature, thus defining their role in electronic circuits and photovoltaic devices.

Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons. When considering compound semiconductors, which consist of two or more elements, the difference in electronegativity between these atoms can influence the band gap energy of the material. A greater difference generally means that the material will have a more pronounced polar character, potentially increasing the band gap energy.

For example, the pair of aluminum phosphide (AlP) and indium arsenide (InAs) demonstrates this concept well. The smaller electronegativity difference between indium (In) and arsenic (As) results in a smaller band gap for InAs compared to AlP. Electronegativity difference plays a significant role during the formation of bonds and consequently affects the electronic structure of the compound. When assessing semiconductor properties, it’s often seen that materials with smaller electronegativity differences between their constituent atoms have smaller band gaps, thus making them more conductive at lower energy levels. This concept can help students predict and compare the conductive behavior of different semiconductors.

Covalent bonding involves the sharing of electrons between atoms and is a predominant force within many semiconductor materials. The strength of these covalent bonds directly impacts the band gap energy of a semiconductor. Stronger covalent bonding within a crystalline lattice usually translates into a larger band gap since more energy is required to break the bond and move an electron to the conduction band.

Take the case of carbon in its diamond form, for example. Carbon atoms form a rigid, tightly-bonded lattice, exemplifying very strong covalent bonds. This strong bonding results in a high band gap energy for diamond, making it an electrical insulator under normal conditions. On the contrast, germanium has weaker covalent bonds due to its larger atomic radius and lesser bond energy, resulting in a lower band gap energy and making it a better semiconductor than diamond. Understanding the nature of covalent bonding is critical for students learning about semiconductor materials, as it helps explain why some substances have higher band gap energies and different electrical properties.