Difference between revisions of "Silicon Slab Calculations"

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===Volume===
 
===Volume===
 
PBE diamond bulk 1102.9319 bohr^3 = 20.4971 &Aring;<sup>3</sup>
 
PBE diamond bulk 1102.9319 bohr^3 = 20.4971 &Aring;<sup>3</sup>
 +
 +
==Annotated Bibilography==
 +
 +
* (reference) <br />page 12: <br />Figure 4:

Revision as of 11:12, 26 June 2024

Energy Under Strain

PBEsol

File:Si.PBEsol.Diamond-1 ML.Strain vs Cohesive Energy.png

Phonons

Method Pseudopotential Phonons Brillouin Zone Reference
DFPT-PZ
a = 5.424 Å 		Norm-conserving (TM) File:Si.001.PZ.freq.Fritsch1995.png File:Fd-3m.001.BZ.png Fritsch (1995)
DFPT-PBEsol
(incorrect celldm(1)) 		Ultrasoft File:Old.Si.1 ML.PBEsol.freq vdos.png
DFPT-PBEsol Ultrasoft File:Si.1 ML.PBEsol.freq vdos.png

Tests

Vacuum

  • Si.pbe-n-rrkjus_psl.1.0.0.UPF, Ecut wfc/rho = 50/500, startingwfc='atomic', celldm(1)=10.335466, kpoint: 2-2-1-1-1-0, Gamma q-point
→ Minimum vacuum = 6.7180529 bohr
Celldm(3) 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
Energy (Ry) -91.05486611 -91.02905414 -90.96623064 -90.97347954 -90.97924947 -90.98131755 -90.98193937 -90.98209842 -90.98212589 -90.98212146 -90.98211064
Frequency (THz) 21.399668 14.956531 14.683791 14.821677 14.864115 14.871671 14.875238 14.875516 14.874547 14.876260 14.877172
Celldm(3) 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0
Energy (Ry) -90.98211064 -90.98210091 -90.98209100 -90.98208215 -90.98207546 -90.98207052 -90.98206569 -90.98206092 -90.98205683 -90.98205416 -90.98205135
Frequency (THz) 14.877172 14.875561 14.875605 14.884300 14.876991 14.876809 14.882501 14.878010 14.878940 14.879234 14.870053

K-point Mesh

Mesh Density

  • Quantum ESPRESSO using PS Library 1.0 PZ RRKJ US pseudopotential with Ecut,wfc/rho = 30/300 Ry
  • Unrelaxed atomic coordinates using PP-relaxed lattice parameter a = 10.708 Bohr and 1.6a of vacuum in a3 direction
  • NC denotes a run that ran but did not complete successfully
Structure Pseudopotential nq1 nq2 nq3 Frequency (THz) Time
Infinite Crystal Si.pz-n-rrkjus_psl.1.0.0.UPF 4 4 4 14.686825 5010 min
1 Monolayer * * * * * *
  • PZ/PBE mesh testing was done with celldm(1)= 10.208773524, celldm(3)=2.0, Ecut,wfc/rho = 30/300
Total Energy
X/Y Mesh 1 1 1 2 2 1 4 4 1 6 6 1 8 8 1 10 10 1 12 12 1 14 14 1 16 16 1 18 18 1 20 20 1
PBE NC -91.15925071 -90.98188148 -90.98096535 -90.98091576 -90.98081652 -90.98085760 -90.98086999 -90.98086058 -90.98086731 -90.98086589
LDA/PZ -90.82372513 -90.65027160 -90.64955939 -90.64955378 -90.64952796 -90.64956158 -90.64958106 -90.64957675 -90.64956582 -90.64957273 -90.64957249
Total Energy (Ry)
x y z * * 1 * * 2 * * 4 * * 6 * * 8
1 1 * NC NC NC NC NC
2 2 * -90.48534325 -90.48716920 NC -90.48717819 -90.48717698
4 4 * -90.50777500 -90.50932817 -90.50934385 -90.50934449 -90.50934394
6 6 * -90.50934449 NC NC -90.50718812 not run
8 8 * NC not run not run not run NC

Mesh Center

  • Quantum ESPRESSO using PS Library 1.0 PZ RRKJ US pseudopotential with Ecut,wfc/rho = 50/500 Ry
  • Relaxed atomic coordinates using PP-relaxed lattice parameter a = 10.708 Bohr and 1.6a of vacuum in a3 direction
  • Smallest converged grid parameter was 2 2 2
Mesh Center Point Total Energy (Ry) SCF Cycles
0 0 0 -90.48716920 93
1 0 0 -90.52916013 61
0 0 1 -90.48718293 54
1 1 0 -90.48939869 38
1 1 1 -90.48939583 63
  • Add 10 10 1 at different k-point grid offsets
  • At best k-point grid offset with 2 2 1 and 2 2 2 k-point grids, check total energy change for celldm(3) = 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, etc. until less than 0.0001 Ry
  • Then, run all x x 1 at the most stable k-point grid offset until total energy changes less than 0.0001 Ry

Structure

  • DFT-PBE

1-ML

Modification Total Energy (Ry / 8 atoms) Total Force (Ry / a0 / 8 atoms) ω [Γ (1-3)] (THz)
Bottom of Cell -90.9808882393 0.001189 -1.707084 -0.235194 -0.132992
Centered in Cell -91.05494884 0.000220 -0.317949 -0.195414 0.172351
Built-In Phonon -91.05494922 0.000241 -0.329813 -0.229082 0.016019
2x2 Supercell -91.05616393 0.000913
Build In Displacement Vector

Γ-point, lowest frequency mode

Displacement Factor Total Energy (Ry / 8 atoms) Total Force (Ry / a0 / 8 atoms) ω [Γ (1-3)] (THz)
0.0 -91.05490108 0.001967
0.1 -91.054481 0.016412 -0.322887 -0.189111 0.340710
0.2 -91.053070 0.032972 -0.364120 -0.221765 0.371472
0.3 -91.050710 0.049779 -0.308852 -0.191316 0.326616
0.4 -91.047394 0.066933 -0.348059 -0.270962 0.367059
0.5 -91.043114 0.084544 -0.284463 -0.151811 0.320345
0.6 -91.037859 0.102744 -0.345105 -0.153570 0.498687
0.7 -91.031620 0.121659 -1.000608 -0.236214 -0.135593
0.8 -91.024383 0.141412 -1.583491 -0.278128 -0.180348
0.9 -91.016139 0.162127 -2.078362 -0.369162 -0.281689
1.0 -91.006881 0.183921 -2.543886 -0.341077 -0.267751

2-ML

Modification Total Energy (Ry / 8 atoms) Total Force (Ry / a0 / 8 atoms) ω [Γ (1-3)] (THz)
Bottom of Cell -91.118108725 0.000038 -7.411048 -3.947619 -1.719877
Centered in Cell -91.11810858 0.0000405 -0.317949 -0.195414 0.172351

Volume

PBE diamond bulk 1102.9319 bohr^3 = 20.4971 Å3

Annotated Bibilography

  • (reference)
    page 12:
    Figure 4:
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