Skip to content

5.4 Silicon vacancy: finite-size and charge-state bookkeeping

These are unexecuted teaching inputs and starting models. Original diagrams are schematics, not calculated results. Validate version-specific syntax, licensed or authorized data, numerical convergence and the scientific model before using this workflow.

5.4.1 Model, units and provenance

PW cutoffs and energies use Ry, common force output uses Ry/bohr, and pressure uses kbar. Geometry cards state their coordinate units. Different executables have distinct grammars and time-unit conventions.

Shared inputs, conventions and evidence

Original schematic: Silicon vacancy: finite-size and charge-state bookkeeping. No numerical results are claimed.
Original schematic: Silicon vacancy: finite-size and charge-state bookkeeping. No numerical results are claimed.

5.4.2 Unexecuted inputs and explicit deltas

Use the accompanying instructions to identify the parent calculation and placement of every delta; a snippet is not automatically a standalone input. Preserve all blank-line and file-provenance requirements.

5.4.2.1 Input block 1

Build a 2 x 2 x 2 conventional diamond-Si supercell: 64 atoms.
Reference: pristine 64-atom cell, fixed converged bulk lattice.
Defect: remove one chosen Si -> nat=63, ntyp=1.
Use a new prefix/outdir; relax internal coordinates at fixed cell.
Start k-mesh test at 2 x 2 x 2; compare denser sampling.
E_form(neutral) = E_63_vac - E_64_bulk + mu_Si
mu_Si = energy per atom of a consistently converged bulk reference.

5.4.3 Worked investigation

5.4.3.1 Intuition and prerequisites

A defect supercell is a periodic array of defects. Its formation energy combines a structural energy difference with an atomic reservoir and, for charged states, an electron reservoir plus electrostatic corrections. Begin with a neutral vacancy, where the bookkeeping is simpler, and treat charged defects as an explicitly advanced extension rather than a one-keyword result.

5.4.3.2 Original neutral-defect workflow

See input block 1 above.

5.4.3.3 Charged extension and checks

Positive tot_charge removes electrons. A periodic compensating background does not by itself yield a converged isolated charged-defect formation energy. With nᵢ defined positive for atoms added, use E_f(q)=E_def(q)−E_bulk−Σnᵢμᵢ+q(E_F+E_VBM+ΔV)+E_corr, while choosing an alignment/correction convention that avoids double counting. Obtain dielectric data and a validated correction workflow before numerical claims; charge transition levels need several independently converged q states.

Exercise: separate chemical-potential, supercell, k-point, structural and spin uncertainties in a neutral-vacancy report. Explain why total energies of q=0 and q=+1 cannot be compared without the electron-reservoir term. Do not interpret a defect band dispersing across the supercell Brillouin zone as automatically an isolated localized level.

5.4.3.4 Lattice response

5.4.5 Sources and further reading