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Ch.12 - Solids and Solid-State Materials
Chapter 12, Problem 101

Considering only electronegativity, rank the LED semiconductors made of solid solutions in order of increasing bandgap energy. Al0.40Ga0.60As, Al0.25Ga0.75As, Al0.05Ga0.95As

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Understand that the bandgap energy of a semiconductor is influenced by the electronegativity of the elements involved. Higher electronegativity differences typically lead to larger bandgap energies.
Identify the elements involved in the given solid solutions: Aluminum (Al), Gallium (Ga), and Arsenic (As).
Recognize that Aluminum (Al) has a higher electronegativity than Gallium (Ga), which means that increasing the proportion of Al in the solid solution will generally increase the bandgap energy.
Compare the given solid solutions based on their Al content: Al_{0.05}Ga_{0.95}As, Al_{0.25}Ga_{0.75}As, and Al_{0.40}Ga_{0.60}As.
Rank the solid solutions in order of increasing bandgap energy based on their Al content: Al_{0.05}Ga_{0.95}As < Al_{0.25}Ga_{0.75}As < Al_{0.40}Ga_{0.60}As.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electronegativity

Electronegativity is a measure of an atom's ability to attract and hold onto electrons in a chemical bond. In semiconductor materials, differences in electronegativity between constituent elements can influence the electronic properties, including the bandgap energy. Higher electronegativity typically correlates with stronger bonding and can lead to variations in the energy levels of the material.
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Bandgap Energy

Bandgap energy is the energy difference between the valence band and the conduction band in a semiconductor. It determines the electrical conductivity and optical properties of the material. In general, a larger bandgap energy means that the material can absorb higher energy photons, which is crucial for applications in optoelectronics, such as LEDs.
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Solid Solutions in Semiconductors

Solid solutions in semiconductors refer to mixtures of different semiconductor materials that form a single-phase crystal structure. The composition of these solid solutions affects their electronic properties, including the bandgap energy. For example, varying the ratio of aluminum to gallium in AlxGa1-xAs alters the bandgap, allowing for tuning of the material's optical and electronic characteristics.
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A photovoltaic cell contains a p–n junction that that converts solar light to electricity. An optimum semiconductor would have its band-gap energy matched to the wavelength of maximum solar intensity at the Earth's surface. (a) What is the color and approximate wavelength of maximum solar intensity at the Earth's surface? Refer to the figure for Problem 12.102.

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