Question

Gallium arsenide, GaAs, has gained widespread use in semiconductor devices that convert light and electrical signals in fiberoptic communications systems. Gallium consists of \(60 . \%^{69} \mathrm{Ga}\) and \(40 . \%^{71} \mathrm{Ga}\). Arsenic has only one naturally occurring isotope, \({ }^{75}\) As. Gallium arsenide is a polymeric material, but its mass spectrum shows fragments with the formulas GaAs and \(\mathrm{Ga}_{2} \mathrm{As}_{2} .\) What would the distribution of peaks look like for these two fragments?

Short answer

For GaAs fragment, the distribution of peaks will have a 60% abundance for \(^{69}\)Ga - \(^{75}\)As and a 40% abundance for \(^{71}\)Ga - \(^{75}\)As. For Ga₂As₂ fragment, the distribution of peaks will have a 36% abundance for \(^{69}\)Ga - \(^{69}\)Ga - \(^{75}\)As - \(^{75}\)As, a 24% abundance for \(^{69}\)Ga - \(^{71}\)Ga - \(^{75}\)As - \(^{75}\)As, a 24% abundance for \(^{71}\)Ga - \(^{69}\)Ga - \(^{75}\)As - \(^{75}\)As, and a 16% abundance for \(^{71}\)Ga - \(^{71}\)Ga - \(^{75}\)As - \(^{75}\)As.

Step-by-step solution

Determine the possible combinations of isotopes in GaAs fragment

Let's list down all possible combinations of Gallium and Arsenic isotopes in GaAs fragment: 1. \(^{69}\)Ga - \(^{75}\)As 2. \(^{71}\)Ga - \(^{75}\)As

Calculate the relative abundances for GaAs fragment

We multiply the abundances of the individual isotopes in each combination: 1. \(^{69}\)Ga - \(^{75}\)As: 0.60 * 1 = 0.60 or 60% 2. \(^{71}\)Ga - \(^{75}\)As: 0.40 * 1 = 0.40 or 40%

Determine the possible combinations of isotopes in Ga₂As₂ fragment

Let's list down all possible combinations of Gallium and Arsenic isotopes in Ga₂As₂ fragment: 1. \(^{69}\)Ga - \(^{69}\)Ga - \(^{75}\)As - \(^{75}\)As 2. \(^{69}\)Ga - \(^{71}\)Ga - \(^{75}\)As - \(^{75}\)As 3. \(^{71}\)Ga - \(^{69}\)Ga - \(^{75}\)As - \(^{75}\)As 4. \(^{71}\)Ga - \(^{71}\)Ga - \(^{75}\)As - \(^{75}\)As

Calculate the relative abundances for Ga₂As₂ fragment

We multiply the abundances of the individual isotopes in each combination: 1. \(^{69}\)Ga - \(^{69}\)Ga - \(^{75}\)As - \(^{75}\)As: (0.60 * 0.60) * (1 * 1) = 0.36 or 36% 2. \(^{69}\)Ga - \(^{71}\)Ga - \(^{75}\)As - \(^{75}\)As: (0.60 * 0.40) * (1 * 1) = 0.24 or 24% 3. \(^{71}\)Ga - \(^{69}\)Ga - \(^{75}\)As - \(^{75}\)As: (0.40 * 0.60) * (1 * 1) = 0.24 or 24% 4. \(^{71}\)Ga - \(^{71}\)Ga - \(^{75}\)As - \(^{75}\)As: (0.40 * 0.40) * (1 * 1) = 0.16 or 16% Now we have the distribution of peaks for both fragments: For GaAs fragment: 1. \(^{69}\)Ga - \(^{75}\)As: 60% 2. \(^{71}\)Ga - \(^{75}\)As: 40% For Ga₂As₂ fragment: 1. \(^{69}\)Ga - \(^{69}\)Ga - \(^{75}\)As - \(^{75}\)As: 36% 2. \(^{69}\)Ga - \(^{71}\)Ga - \(^{75}\)As - \(^{75}\)As: 24% 3. \(^{71}\)Ga - \(^{69}\)Ga - \(^{75}\)As - \(^{75}\)As: 24% 4. \(^{71}\)Ga - \(^{71}\)Ga - \(^{75}\)As - \(^{75}\)As: 16%

Key concepts

Isotope Distribution

When we use mass spectrometry to analyze a substance, we often look at isotopes to understand the distribution of different elements within the material. Isotopes are variations of elements that have different numbers of neutrons. This concept is essential in interpreting mass spectra because each isotope contributes to the peaks observed.
In the case of gallium arsenide,

• Gallium (Ga) has two main isotopes -
  • \(^{69}\text{Ga}\), with a natural abundance of 60%, and
  • \(^{71}\text{Ga}\), with a natural abundance of 40%.
• Arsenic (As), on the other hand, is typically found as \(^{75}\text{As}\), which is the only naturally occurring isotope.

This means that when we look at a mass spectrum of gallium arsenide (GaAs), we will see two main peaks corresponding to the different combinations of these isotopes:

• \(^{69}\text{Ga} - ^{75}\text{As}\) at 60% abundance due to \(^{69}\text{Ga}'s\) higher abundance.
• \(^{71}\text{Ga} - ^{75}\text{As}\) at 40% abundance.

Understanding isotope distribution helps us predict and interpret the peaks in mass spectrometry, crucial for identifying compounds like GaAs.

Gallium Arsenide

Gallium arsenide (\(\text{GaAs}\)) is a compound of gallium and arsenic with noteworthy properties that make it invaluable in electronics. It’s a favorite for semiconductor devices because it surpasses silicon in several ways.

• GaAs boasts superior electron mobility, resulting in faster electronic devices that are essential for high-frequency communication systems.
• It also has a direct band gap, meaning it can efficiently convert electric energy into light, which is pivotal for optoelectronic applications.
• Moreover, GaAs is more resistant to radiation damage, which is beneficial for space and military applications.

Mass spectrometry of GaAs involves analyzing fragments like GaAs and \(\text{Ga}_2\text{As}_2\). This helps in understanding the composition and quality of the material, essential for producing reliable semiconductor devices.

Semiconductor Materials

Semiconductor materials form the foundation of modern electronics. A semiconductor, like gallium arsenide, has electrical properties between conductors and insulators, making them crucial for controlling electronic circuits.

• Silicon is the most common semiconductor but GaAs is preferred in high-speed and optoelectronic applications due to its unique properties such as higher electron mobility.
• Semiconductors have adjustable conductivity, which is possible due to doping - the process of adding impurities to form p-type or n-type materials. This adjustability allows semiconductors to perform various functions inside electronic devices.
• Mass spectrometry aids in quality control of semiconductors by analyzing the isotopic composition and purity of materials like GaAs, ensuring they meet the stringent requirements of electronic manufacturers.

Understanding these properties and processes ensures the successful application of semiconductor materials in devices from smartphones to solar panels.