Electronic structure analysis of solids

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"Electronic structure analysis of solids"에 대한 내용입니다.

목차

1. Give the optimized FCC lattice constants for three elements Si, Al, Ag, and check an error relative to the experimental value. [15 pts = (5 pts/case) x (3 cases)]
2. For above three elements, plot the DOS with showing the convergence with respect to the number of k-points, and identify whether it is a metal or semiconductor. [15 pts = (5 pts/case) x (3 cases)]
3. For above three elements, calculate and plot the band structures, and identify the size and type of the energy gap. [15 pts = (5 pts/case) x (3 cases)]
4. In case of Si, how much is the calculated energy gap different from the experimental value and discuss the origin ? [10 pts]
5. For the metallic cases, which one resembles most the free-electron behavior, N(E)~E1/2 ? In case of FCC-Ag band structure, indicate which bands are caused by d or s electrons ? [10 pts] N(E)~E1/2
6. Find the equilibrium interlayer distance of graphite by PBE and PBE+vdW (for ‘PBE+vdW’.. you should add IVDW=11 in INCAR) [10 pts]. Find the relative energy difference (eV per C atom) between diamond and graphite [10 pts]. Plot the band structure of graphite [15 pts].

본문내용

1. Give the optimized FCC lattice constants for three elements Si, Al, Ag, and check an error relative to the experimental value. [15 pts = (5 pts/case) x (3 cases)]
In diamond structure, the radius of Si is 111pm. Therefore, its length of unit cell is 5.431 Å.
In case of FCC, the radius of Al is 143pm and Ag is 144pm. So, their length of unit cell is 4.05Å and 4.078Å.
We can obtain each optimized lattice constant by checking CONTCAR data.
- optimized lattice constant = (length of unit cell * adjusted coordinates) / initial coordinates　
Therefore, the value of Si is 5.46 Å and FCC-Al is 4.04 Å, FCC-Ag is 4.08 Å.　
1) Si
(optimized lattice constant) = 5.40*0.506/0.500= 5.46 Å (exp. 5.43 Å)
Difference of is 0.03Å ( error percentage is 0.55%)

2) Al
(optimized lattice constant) = 4.00*0.505/0.500= 4.04 Å (exp. 4.05 Å)　　　　　　
Difference of is 0.01Å ( error percentage is 0.24%)　

3) Ag
(optimized lattice constant) = 4.079*0.503/0.500= 4.103 Å (exp. 4.079 Å)　　
Difference of is 0.024Å ( error percentage is 0.58%)　

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