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Metalic Silicides Interfaces

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Flurite-like strutures

Roadmap

  1. [done] Define structures
  2. [done] Ecut convergence tests
  3. [done] k-sampling convergence tests
  4. [done] Ionic relaxation
  5. [done] calculate Mo chemical potential
  6. [done] Formation energy
  7. [done] Convergence study with number of Si bilayers
  8. [done] Band structure + DOS (see subsection for detailed tasks)
  9. [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:

  1. [done] Read VASP manual in order to understand band structure calculations
  2. [done] Find out Brillouin path to real-space hexagonal cell.
  3. [done] Make dispersion diagram to Si(111) unreconstructed surface (just for testing).
  4. [done] Make dispersion diagram to bulk Si (just for testing).
  5. [done] Make dispersion diagram to 5A structure.
  6. [done] Make dispersion diagram to 5B structure.
  7. [done] Make dispersion diagram to 7A structure.
  8. [done] Make dispersion diagram to 7B structure.
  9. [done] Make dispersion diagram to 8A structure.
  10. [to do] Make dispersion diagram to 8B structure.(*)
  11. [done] Make DOS for bulk.
  12. [done] Make DOS for 5A structure.
  13. [blafis] Make DOS for 5B structure.
  14. [done] Make DOS for 7A structure.
  15. [done] Make DOS for 7B structure.
  16. [done] Make DOS for 8A structure.
  17. [to do] Make DOS for 8B structure.(*)
  18. [done] Calculate Local Potential (HT) for bulk.
  19. [done] Calculate Local Potential (HT) for 5A structure. (\(V=-0.35\) eV)
  20. [done] Calculate Local Potential (HT) for 5B structure. (\(V=-0.35\) eV)
  21. [done] Calculate Local Potential (HT) for 7A structure. (\(V=-0.85\) eV)
  22. [done] Calculate Local Potential (HT) for 7B structure. (\(V=-0.87\) eV)
  23. [done] Calculate Local Potential (HT) for 8A structure. (\(V=-1.07\) eV)
  24. [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

  1. [done] Pick-up structure and scale to match a0 from previous calculations.
  2. [done] Add layers of Si.
  3. [done] K-point convergence.
  4. [done] Formation energy convergence with increasing number of layers.
  5. [done] Make dispersion diagram to C11b-100a structure.
  6. [done] Make dispersion diagram to C11b-100b structure.
  7. [done] Make dispersion diagram to C11b-100c structure.
  8. [done] Make dispersion diagram to C11b-110a structure.
  9. [done] Make dispersion diagram to C11b-110b structure.
  10. [done] Make DOS for bulk.
  11. [done] Make DOS for C11b-100a structure.
  12. [2nd try – more bands] Make DOS for C11b-100b structure.
  13. [done] Make DOS for C11b-100c structure.
  14. [done] Make DOS for C11b-110a structure.
  15. [done] Make DOS for C11b-110b structure.
  16. [done] Calculate Local Potential (HT) for bulk.
  17. [done] Calculate Local Potential (HT) for C11b-100a structure. ($V=-1.44$ eV)
  18. [done] Calculate Local Potential (HT) for C11b-100b structure. ($V=-0.80$ eV)
  19. [done] Calculate Local Potential (HT) for C11b-100c structure. ($V=-0.82$ eV)
  20. [done] Calculate Local Potential (HT) for C11b-110a structure. ($V=-1.12$ eV)
  21. [done] Calculate Local Potential (HT) for C11b-110b structure. ($V=-0.56$ eV)
  22. [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-100a structure.
  23. [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-100b structure.
  24. [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-100c structure.
  25. [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-110a structure.
  26. [SIGTERM ERROR – cause: unknown] Check convergence of IE with increasing size for C11b-110b structure.
  27. [need help] Check convergence of Ef with increasing thinkness for C11b-100b structure.
  28. [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]