# How is ECR (Electron Counting Rule) done in a structure?

I've been told how to apply the ECR to GaAs{001}(2×4) in my lectures but it makes no sense to me and I don't seem to be able to find any other sources that explain this. (This is a further question on another one posted here .)

Could anyone please tell me how this is done? Or give me some sources on how to apply the ECR?

"This question has been previously asked on the Physics Stack Exchange where it is bountied, but I was told that I should try and post it here as I might be more successful in getting an answer."

This is the explanation I have been given for the following structure:

Count the number of electrons, going down to two of As atoms level with the bottom of the trench and count per unit mesh. There are 8+4 As atoms = 60 valence electrons. There are 6 Ga atoms = 18 electrons. Hence a total of 78 electrons.

Count the bonds that need to be filled :

1. 3 As dimer bonds = 6 e

2. 6 As dangling bonds (2 per dimer) = 12 e

3. Ga dangling bonds (sideways into trench) are empty = 0 e

4. 8 backbonds from top As dimers = 16 e

5. 12 backbonds from Ga to 3rd row As = 24 e

6. 16 backbonds (bulk-like) from 3rd row As to underlying Ga: each takes 5/4 e from As giving 5×16/4 = 20 e

78 electrons for both totals so structure is neutral and should be stable.

I am trying to learn how to do this as I am trying to prove that this is not applicable to the GaAS{001}(2x1) structure, which I believe to be represented like the image below from the help I was given at a previous related question, here.

• You do know that cross-posting is frowned upon? BTW that bounty on Physics is probably serious waste of rep. Jan 18, 2021 at 16:00
• I was informed to do so, I didn't know that it was frowned upon, my apologies. I shall take the question. And it does not seem a waste of rep for me as I do not know how to do this and would love to learn. Jan 18, 2021 at 16:30
• Mithoron, if you could help me that would be very appreciated. Thank you for telling me about the rules. Jan 18, 2021 at 16:31
• Umm, GaAs is simply tetragonal and I don't see a reason for some electron counting. Jan 18, 2021 at 19:34