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Chapter 12: Problem 73

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?

Short Answer

Expert verified
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 by step solution

01

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).
02

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: - \(N: 75 \, pm\) - \(P: 110 \, pm\) - \(As: 120 \, pm\) - \(Sb: 140 \, pm\) - \(Bi: 170 \, pm\)
03

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.
04

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.

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