Anderson's rule semiconductors

In summary, Anderson's rule is a concept in semiconductor physics that states that the band gap of a semiconductor is directly proportional to the atomic number of the element it is made of. It plays a crucial role in determining the electronic and optical properties of semiconductors, and is most accurate for elements in the same group of the periodic table. However, there are exceptions and other factors that can affect band gap. Anderson's rule was first proposed by physicist Phil Anderson in 1961 and has been observed in other types of materials besides semiconductors.
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Kara386
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Homework Statement


An InAs quantum well in AlSb has a bandgap of 1.58eV in AlSb, and a bandgap in InAs of 0.354eV. The electron affinity of AlSb is ##3.65eV## and the electron affinity of InAs is ##4.90eV##. Is this a Type I, II or III heterojunction? Use Anderson's rule.

Homework Equations

The Attempt at a Solution


I'm ignoring the term quantum well, I think the important thing is that it's a heterojunction. I only want to check I've calculated the offsets correctly. By Anderson's rule, the conduction band offset is given by
##\Delta E_c = \chi_A - \chi_B##
And
##\Delta E_v = E_{g_B} - E_{g_A} - \Delta E_c##
So I assumed that material A is AlSb and material B is the InAs. So
##\Delta E_c = 3.65-4.9 = -1.25##eV
##\Delta E_v = 0.354 - 1.58 - (-1.25) = 0.024##eV
So I was thinking that if I've done that right, then the energy gap of the InAs should be the energy gap of the AlSb with the two offsets subtracted. But that isn't quite the case, because
##1.58 - 1.25 - 0.024 = 0.306##
So I suppose it's the right ballpark, but I just wanted to check if I've done that right. I think that means it's a Type I, because drawing a quick diagram I get something that looks very similar to this:
https://www.bing.com/images/search?...608020151900833127&selectedIndex=0&ajaxhist=0
 
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  • #2


Hi there,

Thank you for your post and for your attempt at solving this problem. You are correct in your calculations, and it appears that you have a good understanding of Anderson's rule and how to apply it to determine the type of heterojunction.

Your calculations show that the conduction band offset is -1.25eV and the valence band offset is 0.024eV. This means that the conduction band of InAs is lower than that of AlSb, while the valence band of InAs is slightly higher. This is consistent with a Type I heterojunction, as shown in the diagram you linked.

In summary, your calculations are correct and you have correctly determined that this is a Type I heterojunction based on Anderson's rule. Keep up the good work!
 

1. What is Anderson's rule in semiconductors?

Anderson's rule is a concept in semiconductor physics that states that as the atomic number of an element increases, so does its band gap. This means that the band gap of a semiconductor is directly proportional to the atomic number of the element it is made of.

2. How does Anderson's rule affect the properties of semiconductors?

Anderson's rule plays a crucial role in determining the electronic and optical properties of semiconductors. It helps predict the band gap of a material based on its atomic structure, which is important for designing semiconductor devices with specific properties.

3. Is Anderson's rule always accurate for predicting band gaps in semiconductors?

No, Anderson's rule is a general trend and has some exceptions. It is most accurate for elements in the same group of the periodic table, but may not apply to elements in different groups. Other factors such as crystal structure and bonding also affect band gap and may deviate from Anderson's rule.

4. How was Anderson's rule discovered?

Anderson's rule was first proposed by physicist Phil Anderson in 1961. He observed a correlation between the band gaps of different elemental semiconductors and their atomic numbers. Further research and experimentation confirmed this rule and it is now widely accepted in the field of semiconductor physics.

5. Can Anderson's rule be applied to other types of materials besides semiconductors?

Yes, Anderson's rule has also been observed in other types of materials such as insulators and metals. However, it may not hold true for all materials and should be used as a general guideline rather than a strict rule.

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