Difference between revisions of "Silicon"
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| + | * [[Silicon Slab Figures|Slab figures]] | ||
* [[Silicon Slab Calculations|Slab calculations]] | * [[Silicon Slab Calculations|Slab calculations]] | ||
* [[Silicon Bulk Slab Comparison|Bulk-slab comparison]] | * [[Silicon Bulk Slab Comparison|Bulk-slab comparison]] | ||
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==Crystal Structures== | ==Crystal Structures== | ||
| − | * [ | + | * [https://www.atomic-scale-physics.de/lattice/struk/a4.html Diamond] |
| − | * [ | + | * [https://www.atomic-scale-physics.de/lattice/struk/a5.html Beta-Tin] |
| − | + | ||
==Elastic Properties== | ==Elastic Properties== | ||
Latest revision as of 10:22, 25 July 2024
Contents
Crystal Structures
Elastic Properties
- Energies calculated with pseudopotentials (PP) using Quantum ESPRESSO and FP-LAPW with Elk
- Energies fit to a Murnaghan equation of state
Our Calculations
| Method | Core Electron Representation | Diamond | Beta-tin | Transition | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| V0 (Å3/atom) | K0 (GPa) | K0′ | VT (Å3/atom) | V0 (Å3/atom) | c/a | K0 (GPa) | K0′ | VT (Å3/atom) | PT (GPa) | ||
| DFT-LDA | Von Barth-Car PP | 19.70 | 94.2 | 4.16 | 15.31 | 0.564 | 90.3 | 15.0 | |||
| Bachelet-Hamman-Schlüter PP | 19.32 | 98.2 | 4.30 | 14.42 | 0.549 | 120.6 | 4.31 | ||||
| PSLibrary 0.1 Ultrasoft PP | 19.68 | 96.4 | 4.19 | 14.80 | 0.517 | 118.4 | 4.01 | ||||
| FP-LAPW [Elk] | 19.67 | 96.2 | 6.04 | ||||||||
| DFT-PBE | Ultrasoft | 20.46 | 88.6 | 4.31 | 15.39 | 0.561 | 107.5 | 4.57 | |||
| KJPAW | 20.52 | 87.6 | 4.2 | 18.89 | 15.35 | 0.557 | 105.1 | 4.59 | 14.31 | 8.68 | |
| PBEsol | KJPAW | 20.08 | 92.9 | 4.15 | 19.02 | 15.01 | 0.553 | 113.9 | 4.43 | 14.36 | 5.63 |
| DFT-TPSS | Ultrasoft | 19.73 | 74.1 | 1.00 | |||||||
| DFT-PZ | VBC | 19.74 | 91.7 | 4.07 | 18.39 | 15.01 | 0.557 | 111.1 | 4.4 | 14.15 | 7.49 |
| RRKJUS | 19.72 | 94.8 | 4.13 | 18.55 | 14.81 | 0.554 | 114.7 | 4.44 | 14.07 | 6.63 | |
| SCAN | VAN | 19.53 | 95.1 | 7.92 | 17.52 | 15.29 | 0.569 | 119.5 | 0.79 | 13.43 | 16.39 |
| VAN.2 | 19.78 | 87.6 | 8.5 | 19.02 | 15.23 | 0.571 | 112.6 | 2.07 | 14.7 | 4.07 | |
| VAN.3 | 19.61 | 94.6 | 7.3 | 17.56 | 15.33 | 0.57 | 110.1 | 1.96 | 13.47 | 16.12 | |
| VAN.4 | 19.59 | 95.4 | 7.53 | 17.57 | 15.33 | 0.57 | 110.1 | 1.96 | 13.47 | 16.14 | |
| TPSS | VAN | 19.59 | 87.2 | 8.8 | 18.2 | 15.04 | 0.561 | 116.8 | 1.69 | 13.98 | 9.04 |
Reference Calculations
Hennig et al. 2010 PRB
| Method | Core Electron Representation | Diamond | Beta-tin | Transition | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| V0 (Å3/atom) | K0 (GPa) | K0′ | VT (Å3/atom) | V0 (Å3/atom) | c/a | K0 (GPa) | K0′ | VT (Å3/atom) | PT (GPa) | ||
| LDA | 19.72 | 96.4 | 4.13 | 17.86 | 14.82 | 0.548 | 116.0 | 4.59 | 13.63 | 5.8 | |
| PBE | 20.48 | 89.0 | 4.12 | 18.42 | 15.36 | 0.550 | 103.6 | 4.52 | 14.04 | 8.4 | |
| PW91 | 20.45 | 89.1 | 4.14 | 18.40 | 15.47 | 0.551 | 103.6 | 4.52 | 14.11 | 10.0 | |
| WC | 20.05 | 94.2 | 4.10 | 18.12 | 15.11 | 0.549 | 112.4 | 4.41 | 13.86 | 6.0 | |
| AM05 | 20.07 | 93.1 | 4.08 | 18.13 | 14.82 | 0.546 | 120.5 | 4.54 | 13.67 | 3.5 | |
| PBEsol | 20.06 | 93.9 | 4.09 | 18.13 | 15.02 | 0.548 | 115.0 | 4.52 | 13.80 | 4.8 | |
| HSE06 | 20.07 | 99.1 | 4.00 | 18.21 | 15.10 | 0.565 | 117.0 | 4.35 | 13.89 | 13.4 | |
| DMC | 19.98 | 98 | 4.6 | 18.14(5) | 15.2 | 0.550 | 107 | 4.6 | 13.9(1) | 14.0±1.0 | |
| EXP | 20 | 99.2 | 4.11 | 18.15 | 13.96 | 11.3-12.6 | |||||
Poisson Ratio
- ν = 0.28 (Hopcroft, 2010)
- ν = -slope of y=log(a), x=log(c) (Chou, 1983)
Phonons
Frequencies by Q-Point
| Method | Pseudopotential | Phonon Frequencies (THz) | |||||||
|---|---|---|---|---|---|---|---|---|---|
| ΓLO/TO | |||||||||
| Experiment | |||||||||
| DFPT-LDA | Ultrasoft | ||||||||
| Norm-conserving | |||||||||
| DFPT-PBE | Ultrasoft | ||||||||
| DFPT-PBEsol | Ultrasoft | ||||||||
Frequency Bands
| Method | Pseudopotential | Phonons |
|---|---|---|
| DFPT-LDA | Ultrasoft | File:Si.fd-3m.LDA USPP.freq vdos.png |
| Norm-conserving | File:Giannozzi1991 Si.LDA vBCNCPP.freq vdos.png<ref name="Giannozzi1991" /> | |
| DFPT-PBE | Ultrasoft | File:Si.Fd-3m.PBE.freq vdos.png |
| DFPT-PBEsol | Ultrasoft | File:Si.Fd-3m.PBEsol.freq vdos.png |
Cutoff Energy Calculations
| Method | Pseudopotential | Diamond | Beta-Tin | Difference |
|---|---|---|---|---|
| PBE | RRKJ | File:DiamondCutoff RRKJ.png | File:BetaSn cutoff.png | File:Cutoffdifference RRKJ.png |
Kpoint Energy Calculations
| Method | Pseudopotential | Diamond | Beta-Tin | Difference |
|---|---|---|---|---|
| PBE | RRKJ | File:DiamondKpoint RRKJ.png | File:BetaSnKpoint RRKJ.png | File:Kpointdifference RRKJ.png |
Equation of State Graphs
| Method | Pseudopotential | Diamond | Beta-Tin | MultiPlot |
|---|---|---|---|---|
| PBE | RRKJ | File:DiamondEOS RRKJ.png | File:BetaSneos RRKJ.png | File:Eos RRKJ.png |
References
- Giannozzi, P., de Gironcoli, S., Pavone, P. and S. Baroni, Ab initio calculation of phonon dispersions in semiconductors, Phys. Rev. B, 43, 7231 (1991).
- Hopcroft, M. A., Nix, W. D., and Kenny, T. W., "What is the Young's Modulus of Silicon?", J. Microelectromech. S. 19, 1057-7157 (2010).
- Chou, M. Y., Lam, P. K., and Cohen, M. L., "Ab initio study of structural and electronic properties of beryllium", Phys. Rev. B, 28, 4179 (1983).
- Hennig, R. G., Wadehra, A., Driver, K. P., Parker, W. D., Umrigar, C. J., and Wilkins, J. W., "Phase transformation in Si from semiconducting diamond to metallic β-Sn phase in QMC and DFT under hydrostatic and anisotropic stress", Phys. Rev. B, 82, 014101 (2010).
