Hi,
Can someone help me derive the primitive unit cell of this layered structure of graphene?
Thanks!
Also, I have another question about semiconductors.
If we have a semiconductor with dopant concentration ND, and that KBT >> Dopant Ionization Energy, such that it can be assumed that all the dopant atoms are ionized (nD = 0)
This then leads to
ne = ND (1)
i.e., the concentration of electrons in the conduction band is equal to the concentration of electrons in the dopant, which seems logical. nh is found through ni^2/ne.
However, if I use the charge balance equation, namely:
nA = 0, NA = 0 (no acceptors) and nD = 0 (dopant atoms ionized).
I get:
ne - nh = ND (2)
which is not equal to equation 1 above. What am I missing here?
Regarding your last question: is it mentioned anywhere if the semiconductor is n-doped or p-doped? In the lecture notes they mention that if the semiconductor is n-doped, then n_e \gg n_h. In that case you can neglect n_h in the charge balance equation.
Thank you, that answers my second question!
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To answer the first question we first need to identify whether the different layers of this graphite stacking are identical from the crystallographic point of view. For that we can for example look at the atoms connected by the hoppings in the vertical direction, and realize that these atoms aren’t the same—they have neighbors in different directions:
Therefore the lattice vector in z-direction has a length of 2 distances between the layers, and the in-plane vectors are exactly the same as for a single graphene sheet.