Modelling a gallium arsenide surface

This example shows how to use the atomistic simulation environment, or ASE for short, to set up a particular gallium arsenide surface and run the resulting calculation in DFTK. The particular example we consider the (1, 1, 0) GaAs surface separated by vacuum.

Parameters of the calculation. Since this surface is far from easy to converge, we made the problem simpler by choosing a smaller Ecut and smaller values for n_GaAs and n_vacuum. More interesting settings are Ecut = 15 and n_GaAs = n_vacuum = 20.

miller = (1, 1, 0)   # Surface Miller indices
n_GaAs = 2           # Number of GaAs layers
n_vacuum = 4         # Number of vacuum layers
Ecut = 5             # Hartree
kgrid = (4, 4, 1);   # Monkhorst-Pack mesh

Use ASE to build the structure:

using PyCall

ase_build = pyimport("ase.build")
a = 5.6537  # GaAs lattice parameter in Ångström (because ASE uses Å as length unit)
gaas = ase_build.bulk("GaAs", "zincblende", a=a)
surface = ase_build.surface(gaas, miller, n_GaAs, 0, periodic=true);

Get the amount of vacuum in Ångström we need to add

d_vacuum = maximum(maximum, surface.cell) / n_GaAs * n_vacuum
surface = ase_build.surface(gaas, miller, n_GaAs, d_vacuum, periodic=true);

Write an image of the surface and embed it as a nice illustration:

pyimport("ase.io").write("surface.png", surface * (3, 3, 1),
                         rotation="-90x, 30y, -75z")

Use the load_atoms, load_positions and load_lattice functions to convert to DFTK data structures. These two functions not only support importing ASE atoms into DFTK, but a few more third-party data structures as well. Typically the imported atoms use a bare Coulomb potential, such that appropriate pseudopotentials need to be attached in a post-step:

using DFTK

positions = load_positions(surface)
lattice   = load_lattice(surface)
atoms = map(load_atoms(surface)) do el
    if el.symbol == :Ga
        ElementPsp(:Ga, psp=load_psp("hgh/pbe/ga-q3.hgh"))
    elseif el.symbol == :As
        ElementPsp(:As, psp=load_psp("hgh/pbe/as-q5.hgh"))
    else
        error("Unsupported element: $el")
    end
end;

We model this surface with (quite large a) temperature of 0.01 Hartree to ease convergence. Try lowering the SCF convergence tolerance (tol) or the temperature or try mixing=KerkerMixing() to see the full challenge of this system.

model = model_DFT(lattice, atoms, positions, [:gga_x_pbe, :gga_c_pbe],
                  temperature=0.001, smearing=DFTK.Smearing.Gaussian())
basis = PlaneWaveBasis(model; Ecut, kgrid)

scfres = self_consistent_field(basis, tol=1e-4, mixing=LdosMixing());
n     Energy            log10(ΔE)   log10(Δρ)   Diag
---   ---------------   ---------   ---------   ----
  1   -16.58756549260                   -0.58    4.9
  2   -16.72523163768       -0.86       -1.01    1.0
  3   -16.73074016423       -2.26       -1.58    2.7
  4   -16.73127828884       -3.27       -2.16    2.0
  5   -16.73133280018       -4.26       -2.59    2.0
scfres.energies
Energy breakdown (in Ha):
    Kinetic             5.8603371 
    AtomicLocal         -105.6252612
    AtomicNonlocal      2.3498185 
    Ewald               35.5044300
    PspCorrection       0.2016043 
    Hartree             49.5758750
    Xc                  -4.5981324
    Entropy             -0.0000041

    total               -16.731332800181