Problem 73 - Chemistry: The Central Science in SI Units, Global Edition

Question

If you want to dope GaAs to make an \(\mathrm{n}\) -type semiconductor with an element to replace Ga, which element(s) would you pick?

Step-by-Step Solution

Answer

To dope GaAs and make an n-type semiconductor, suitable elements to replace Ga include Silicon (Si), Germanium (Ge), Tin (Sn), Phosphorus (P), and Antimony (Sb), as they have more than 3 valence electrons and similar atomic radii to Gallium.

Step 1: Identify group 14 and group 15 elements

Group 14 elements are Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), and Lead (Pb). Group 15 elements include Nitrogen (N), Phosphorus (P), Arsenic (As), Antimony (Sb), and Bismuth (Bi).

Step 2: Compare the atomic radii of Ga with the atomic radii of group 14 and group 15 elements

The dopant should have a similar atomic size as Gallium, to fit well within the GaAs crystal lattice and not disturb its structure. Gallium has an atomic radius of approximately 135 pm. The atomic radii of group 14 and 15 elements are as follows: Group 14: - \(C: 77 \, pm\) - \(Si: 118 \, pm\) - \(Ge: 122 \, pm\) - \(Sn: 140 \, pm\) - \(Pb: 175 \, pm\) Group 15: - \(N: 75 \, pm\) - \(P: 110 \, pm\) - \(As: 120 \, pm\) - \(Sb: 140 \, pm\) - \(Bi: 170 \, pm\)

Step 3: Eliminate unsuitable elements

Based on the differences in atomic radii between Ga and candidate elements, we can eliminate elements with significantly larger or smaller atomic radii from consideration: - Carbon (C) and Nitrogen (N) are too small, so they can be eliminated. - Lead (Pb) and Bismuth (Bi) are too large, so they can be eliminated as well.

Step 4: Choose the appropriate element(s) for doping GaAs

From the remaining elements (Si, Ge, Sn, P, As, and Sb), we would select the one(s) that have suitable atomic radii, as well as more than 3 valence electrons. The suitable elements are: - Silicon (Si) - Group 14, atomic radius 118 pm, and 4 valence electrons - Germanium (Ge) - Group 14, atomic radius 122 pm, and 4 valence electrons - Tin (Sn) - Group 14, atomic radius 140 pm, and 4 valence electrons - Phosphorus (P) - Group 15, atomic radius 110 pm, and 5 valence electrons - Antimony (Sb) - Group 15, atomic radius 140 pm, and 5 valence electrons These elements (Si, Ge, Sn, P, and Sb) could replace Ga in GaAs to create an n-type semiconductor.

Key Concepts

n-type semiconductors

In the world of electronics, semiconductors are crucial as they form the foundation of most electronic devices.
An n-type semiconductor is a type of extrinsic semiconductor where the charge carriers are majority electrons.
This is achieved by adding impurities, a process known as doping, to a pure semiconductor.
In this context, doping means the introduction of an element with more electrons than the semiconductor material itself.
When forming n-type semiconductors, elements from groups 14 and 15 are often used since they have extra electrons that can donate to the conduction band, making it easier for electricity to flow.
This is particularly applicable with materials like GaAs (Gallium Arsenide) which can be doped with elements that have more valence electrons to achieve the desired conductivity.

atomic radii comparison

When choosing an element for doping semiconductors, one crucial consideration is the atomic radii.
The reason for this is because the dopant must fit into the crystal lattice of the semiconductor material without disrupting its structure.
Atomic radii refer to the size of an atom, which determines how well a dopant can substitute a host atom in the lattice.
For instance, Gallium, a common component in semiconductors like GaAs, has an atomic radius of approximately 135 picometers (pm).
Therefore, when selecting dopants from group 14 or group 15 elements, one has to consider elements with similar atomic radii.

• Elements much smaller, like Carbon (77 pm) and Nitrogen (75 pm), can strain the lattice because they create voids or gaps due to size difference.
• In contrast, larger elements such as Lead (175 pm) or Bismuth (170 pm) exert pressure on the structure, potentially leading to distortions or defects.

Choosing elements with atomic radii close to that of Gallium (like Germanium, Arsenic, or Antimony) ensures structural stability while maximizing the effectiveness of doping.

group 14 elements

Group 14 elements in the periodic table are often featured in discussions about semiconductors due to their 4 valence electrons.
These include Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), and Lead (Pb).
Their positioning in the periodic table suggests that they can easily form covalent bonds with other group 14 elements.
Among these, Silicon and Germanium are particularly significant. Silicon (Si): - Widely used in the semiconductor industry, it forms the basis of most CPUs and other electronics. - Its suitable atomic size of 118 pm makes it a good candidate for replacing Gallium in GaAs semiconductors. Germanium (Ge): - Known for its electrical conductivity, it is sometimes used in high-speed circuits. - With an atomic radius of 122 pm, it can replace Gallium effectively without causing structural issues. While Tin (Sn) and Lead (Pb) also have potential uses due to their similar numbers of valence electrons, their larger atomic radii make them less suitable for precise applications.

group 15 elements

Group 15 elements are crucial in the context of doping semiconductors because they possess 5 valence electrons.
This sets them apart as potential candidates for n-type semiconductor formation.
Elements in this group include Nitrogen (N), Phosphorus (P), Arsenic (As), Antimony (Sb), and Bismuth (Bi).
The presence of an extra valence electron allows them to release more electrons into the conduction band when used as dopants.
For example, both Phosphorus and Antimony are commonly used to dope semiconductors: Phosphorus (P): - Phosphorus has an atomic radius of 110 pm, which closely matches that of Gallium, making it a suitable dopant for GaAs. - It effectively donates electrons to increase the number of charge carriers. Antimony (Sb): - With an atomic radius of 140 pm, Antimony fits well into the crystal lattice of Gallium Arsenide without distorting the structure. - It too serves as an efficient electron donor, aiding in enhanced conductivity. The extra valence electron from group 15 not only increases the carrier concentration but also helps maintain the structural integrity of the doped semiconductor.