Solid State Electronic Devices - Valence Electrons Question

[hatfarm]

Homework Statement

2. Determine the concentration of valence electrons in doped
(a) Si (a = 0.543 nm)
(b) GaAs (a = 0.565 nm)

Homework Equations

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The Attempt at a Solution

This is the problem, I don't really know what they're looking for. I know what valence electrons are, but doesn't it matter what it's doped with? Why are they giving me the crystal lattice constant? I can't find anything that quite relates these things in the chapters we have gone through, nor in the lecture notes. I'm really stumped, I just have no idea where to start. The TA sent out an email, but here is what it said,

"Many of you have some problems with the problem 2 of HW2, here are some hints:

1) The dopants (too small concentration) don't influence the number of valence electrons.
2) Refer to Figure 3-3 for "valence electrons" definition."


The definition I know, but how does 1 help me at all?

The only thing I can think of is that when the relative spacing of atoms reaches a certain small point (when the band begins to emerge) there are 4N (N being the number of atoms) electrons in the valence band. However, wouldn't this change when they are doped? Wouldn't that change depending on what it was doped with?

Any help would be greatly appreciated. Thank you.

 

[KataKoniK]

Dear forum post,

I understand your confusion about the problem and appreciate your effort in trying to find a solution. Let me try to clarify things for you.

Firstly, the dopants in this problem do not have a significant effect on the number of valence electrons. Therefore, you can assume that the number of valence electrons in doped Si and GaAs is the same as the number of valence electrons in pure Si and GaAs.

Secondly, the crystal lattice constant is given to help you calculate the concentration of valence electrons. The lattice constant is a measure of the distance between atoms in a crystal. By knowing the lattice constant, you can calculate the volume of the unit cell (the basic repeating unit of a crystal). This volume can then be used to determine the number of atoms in the unit cell. And since you know the number of valence electrons per atom, you can calculate the total number of valence electrons in the unit cell.

I suggest referring to Figure 3-3, as suggested by your TA, for a better understanding of the definition of valence electrons. Once you have a clear understanding of the concept, you can use the given information to calculate the concentration of valence electrons in doped Si and GaAs.

I hope this helps. Good luck with your solution.