[toc][mathjax]
Flurite-like strutures
Roadmap
- [done] Define structures
- [done] Ecut convergence tests
- [done] k-sampling convergence tests
- [done] Ionic relaxation
- [done] calculate Mo chemical potential
- [done] Formation energy
- [done] Convergence study with number of Si bilayers
- [done] Band structure + DOS (see subsection for detailed tasks)
- [current] MoSi2 (C11b structure) (see subsection for detailed tasks)
Structures
Mo-5A
Structural data:
Mo-5B
Structural data:
Mo-7A
Structural data:
Mo-7B
Structural data:
Mo-8A
Structural data:
Mo-8B
Structural data:
Formation Energies
Plane-wave energy cut-off:
$$E_\text{cut}=350~\text{eV}$$
Bulk Si (hex)
Cell properties:
$$a=3.814~\text{\AA{}}~~~c=9.342~\text{\AA{}}~~~\frac{c}{a}=2.449$$
[table id=1 /]
$$\mu_\text{Si}=-5.414~\text{eV}$$
MoSi2
$$\text{Mo}_2\text{Si}_4$$
Cell properties:
$$a=3.213~\text{\AA{}}~~~c=7.867~\text{\AA{}}~~~\frac{c}{a}=2.448$$
MP -Et(0)/eV -u(Mo)/eV 6x6x2 46.529658 12.437 10x10x4 46.494821 12.419 16x16x6 46.504849 12.424 = 20x20x8 46.506589 12.425 = 24x24x10 46.506441 12.425
$$\mu_\text{Mo}=\frac{E_T-4\mu_\text{Si}}{2}$$
$$\mu_\text{Mo}=-12.425~\text{eV}$$
Mo Silicides
MP convergence
Mo-5A =================================================================== MP -Et(0)/eV dE/eV MP -Et(0)/eV dE/eV 6x6x2 48.748943 20x20x1 48.606791 10x10x4 48.720858 -.028085 20x20x2 48.761956 .155165 16x16x6 48.716454 -.004404 20x20x4 48.721787 -.040169 = 20x20x8 48.717030 .000576 => 20x20x6 48.717064 -.004723 24x24x10 48.717159 .000129 = 20x20x8 48.717030 -.000034 = =========================================================================
Mo-5A =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 4 (Si:6;Mo:2) 26x26x78 48.717030 8.62 [CHECKED] 10 (Si12;Mo:2) 26x26x140 81.074181 8.74 [CHECKED] 16 (Si:18;Mo:2) 26x26x202 113.54983 8.75 [CHECKED] 22 (Si:24;Mo:2) 26x26x266 146.03283 8.75 [CHECKED] Formation Energy = 4.38 eV/atom Mo-5B =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 4 (Si:6;Mo:2) 26x26x78 48.638230 8.70 [CHECKED] 10 (Si12;Mo:2) 26x26x140 81.059242 8.76 [CHECKED] 16 (Si:18;Mo:2) 26x26x202 113.54468 8.76 [CHECKED] 22 (Si:24;Mo:2) 26x26x266 146.02796 8.76 [CHECKED] Formation Energy = 4.38 eV/atom Mo-7A =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 6 (Si:10;Mo:2) 26x26x110 70.313708 8.68 [CHECKED] 12 (Si:16;Mo:2) 26x26x172 102.79635 8.68 [CHECKED] 18 (Si:22;Mo:2) 26x26x234 135.27954 8.68 [CHECKED] 24 (Si:28;Mo:2) 26x26x296 177.08821 8.67 [CHECKED] Formation Energy = 4.34 eV/atom Mo-7B =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 6 (Si:10;Mo:2) 26x26x110 70.106821 8.88 [CHECKED] 12 (Si:16;Mo:2) 26x26x172 102.57882 8.90 [CHECKED] 18 (Si:22;Mo:2) 26x26x234 135.06192 8.90 [CHECKED] 24 (Si:28;Mo:2) 26x26x296 [Electronic SC not achived] Formation Energy = 4.45 eV/atom Mo-8A =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 2 (Si:8;Mo:2) 26x26x78 58.659778 9.50 [CHECKED] 8 (Si:14;Mo:2) 26x26x140 91.043848 9.60 [CHECKED] 14 (Si:20;Mo:2) 26x26x202 123.52626 9.60 [CHECKED] 20 (Si:26;Mo:2) 26x26x266 156.86188 8.75 [?] Formation Energy = 4.80 eV/atom Mo-8B ================================================ atomic layers FFT grid -Et(0) / eV Ef / eV 6 (Si:10;Mo:2) 24x24x140 69.976855 9.01 8 (Si:12;Mo:2) 24x24x1?? 80.793244 9.02 14 (Si:18;Mo:2) 24x24x168 113.27340 9.03 20 (Si:24:Mo:2) 24x24x??? --------- ---- Formation Energy = 4.51 eV/atom
Band Structure + DOS
Steps to take:
- [done] Read VASP manual in order to understand band structure calculations
- [done] Find out Brillouin path to real-space hexagonal cell.
- [done] Make dispersion diagram to Si(111) unreconstructed surface (just for testing).
- [done] Make dispersion diagram to bulk Si (just for testing).
- [done] Make dispersion diagram to 5A structure.
- [done] Make dispersion diagram to 5B structure.
- [done] Make dispersion diagram to 7A structure.
- [done] Make dispersion diagram to 7B structure.
- [done] Make dispersion diagram to 8A structure.
- [to do] Make dispersion diagram to 8B structure.(*)
- [done] Make DOS for bulk.
- [done] Make DOS for 5A structure.
- [blafis] Make DOS for 5B structure.
- [done] Make DOS for 7A structure.
- [done] Make DOS for 7B structure.
- [done] Make DOS for 8A structure.
- [to do] Make DOS for 8B structure.(*)
- [done] Calculate Local Potential (HT) for bulk.
- [done] Calculate Local Potential (HT) for 5A structure. (\(V=-0.35\) eV)
- [done] Calculate Local Potential (HT) for 5B structure. (\(V=-0.35\) eV)
- [done] Calculate Local Potential (HT) for 7A structure. (\(V=-0.85\) eV)
- [done] Calculate Local Potential (HT) for 7B structure. (\(V=-0.87\) eV)
- [done] Calculate Local Potential (HT) for 8A structure. (\(V=-1.07\) eV)
- [to do] Calculate Local Potential (HT) for 8B structure.(*)
(*) – These structures needs to be revised.
Paths

hexagonal lattice (BZ above) : \(\Gamma\)-\(M\)-\(K\)-\(\Gamma\)-\(A\)-\(L\)-\(H\)-\(A\)|\(L\)-\(M\)|\(K\)-\(H\)

Rhombohedral lattice (BZ above) : $\Gamma$-$L$-$B_1$∣$B$-$Z$-$\Gamma$-$X$∣$Q$-$F$-$P_1$-$Z$∣$L$-$P$
Si(111) Unreconstructed Surface
For testing porpuses only, I made a K-E dispersion diagram for a 12-layer Si(111) unreconstructed surface, as follows. Results were in agreement with PRB 12 4200 (1975).
For comparing, 12-layer bulk Si bandstructure:
Mo-5A
Mo-5B
Mo-7A
Mo-7B
Mo-8A
Mo-8B
MoSi2 (C11b phase)
Roadmap
- [done] Pick-up structure and scale to match a0 from previous calculations.
- [done] Add layers of Si.
- [done] K-point convergence.
- [done] Formation energy convergence with increasing number of layers.
- [done] Make dispersion diagram to C11b-100a structure.
- [done] Make dispersion diagram to C11b-100b structure.
- [done] Make dispersion diagram to C11b-100c structure.
- [done] Make dispersion diagram to C11b-110a structure.
- [done] Make dispersion diagram to C11b-110b structure.
- [done] Make DOS for bulk.
- [done] Make DOS for C11b-100a structure.
- [2nd try – more bands] Make DOS for C11b-100b structure.
- [done] Make DOS for C11b-100c structure.
- [done] Make DOS for C11b-110a structure.
- [done] Make DOS for C11b-110b structure.
- [done] Calculate Local Potential (HT) for bulk.
- [done] Calculate Local Potential (HT) for C11b-100a structure. ($V=-1.44$ eV)
- [done] Calculate Local Potential (HT) for C11b-100b structure. ($V=-0.80$ eV)
- [done] Calculate Local Potential (HT) for C11b-100c structure. ($V=-0.82$ eV)
- [done] Calculate Local Potential (HT) for C11b-110a structure. ($V=-1.12$ eV)
- [done] Calculate Local Potential (HT) for C11b-110b structure. ($V=-0.56$ eV)
- [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-100a structure.
- [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-100b structure.
- [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-100c structure.
- [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-110a structure.
- [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-110b structure.
- [need help] Check convergence of Ef with increasing thinkness for C11b-100b structure.
- [need help] Check convergence of Ef with increasing thinkness for C11b-110a structure.
k-sampling convergency
Plane-wave energy cut-off: $E_\text{cut}=350~\text{eV}$
Structure: 100a
MP scheme ($\Gamma$-shifted):
MP E0 (ev) 6x18x6 -637.49939 6x18x4 -637.49935 6x18x2 -637.49996 6x18x1 -637.49225 7x21x1 -637.49136 8x24x1 -637.49151 9x27x1 -637.49127 10x30x1 -637.49123 11x33x1 -637.49090 = 12x36x1 -637.49096 = 14x42x1 -637.49086 16x48x1 -637.49091 18x54x1 -637.49089 20x60x1 -637.49098
Structures
100a
100b
100c
110a
110b
Formation Energy convergence
100a =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 9 (Si:24;Mo:12;bulk:54) 100x36x100 506.92667 64.47 * 13 (Si:24;Mo:12;bulk:78) 100x36x140 636.83674 64.49 * 17 (Si:24;Mo:12;bulk:102) 100x36x168 766.78736 64.48 * 21 (Si:24;Mo:12;bulk:126) 100x36x200 896.73144 64.47 * 25 (Si:24;Mo:12;bulk:150) 100x36x240 1026.8101 64.33 -SCF- * Formation Energy = 5.37 eV/atom 100b =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 9 (Si:16;Mo:12;bulk:54) 100x36x100 481.79778 46.28 13 (Si:16;Mo:12;bulk:78) 100x36x140 611.82322 46.19 * 17 (Si:16;Mo:12;bulk:102) 100x36x168 741.75441 46.20 * 21 (Si:16;Mo:12;bulk:126) 100x36x200 871.71271 46.18 * 25 (Si:16;Mo:12;bulk:150) 100x36x240 --------- ----- -SCF- * Formation Energy = 3.85 eV/atom 100c =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 9 (Si:20;Mo:8;bulk:54) 100x36x100 461.45354 38.58 13 (Si:20;Mo:8;bulk:78) 100x36x140 591.39720 38.57 * 17 (Si:20;Mo:8;bulk:102) 100x36x168 721.34542 38.56 * 21 (Si:20;Mo:8;bulk:126) 100x36x200 851.28476 38.56 * 25 (Si:20;Mo:8;bulk:150) 100x36x240 981.22581 38.55 * * Formation Energy = 4.82 eV/atom 110a =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 8 (Si:8;Mo:4;bulk:16) 48x24x100 167.99376 11.64 12 (Si:8;Mo:4;bulk:24) 48x24x140 211.27495 11.67 * 16 (Si:8;Mo:4;bulk:32) 48x24x168 254.59571 11.66 * 20 (Si:8;Mo:4;bulk:40) 48x24x200 297.91156 11.66 * 24 (Si:8;Mo:4;bulk:48) 48x24x240 341.22742 11.66 * * Formation Energy = 2.92 eV/atom 110b =============================================== atomic layers FFT grid -Et(0) / eV Ef / eV 10 (Si:4;Mo:2;bulk:20) 48x24x100 145.17205 9.61 14 (Si:4;Mo:2;bulk:28) 48x24x140 188.53576 9.56 * 18 (Si:4;Mo:2;bulk:36) 48x24x168 231.85614 9.55 * 22 (Si:4;Mo:2;bulk:44) 48x24x200 275.16788 9.55 * 26 (Si:4;Mo:2;bulk:52) 48x24x240 318.48048 9.55 * * Formation Energy = 4.78 eV/atom
Band Structure + DOS
c11b-100a
c11b-100b
c11b-100c
c11b-110a
c11b-110b
Thickness
100b =============================================== layers FFT grid -Et(0) [eV] Ef [eV] Ef/(Mo atom) [eV] 1 (Si:71;Mo:6) 54x36x200 435.84542 23.10 3.85 eV/atom 2 (Si:75;Mo:14) 54x36x200 519.70345 60.30 4.31 eV/atom 110a =============================================== layers FFT grid -Et(0) [eV] Ef [eV] Ef/(Mo atom) [eV] 1 (Si:48;Mo:4) 48x24x200 297.91156 11.66 2.92 eV/atom 2
Additional Notes
Burgers vector
![]() |
[latex]
\begin{equation*}
n_b \vec{a}_{[111]} = n_s ( \vec{a}_{[111]} + \vec{b}) \Leftrightarrow
\end{equation*}
\begin{equation*}
\vec{b} = \frac{n_b-n_s}{n_s} \vec{a}_{[111]} \Rightarrow \vec{b} = \frac{5-4}{4} \vec{a}_{[111]} \Rightarrow
\end{equation*}
\begin{equation*}
\vec{b} = \frac{1}{4} \vec{a}_{[111]}
\end{equation*}
[/latex]