Work functions at interfaces

This tutorial will show how to use BAND to calculate the work function Φ of the

  • Al(100)/vacuum interface
  • Al(100)/LiF(100) interface
/scm-uploads/doc.2022/Tutorials/_images/preview18.png

The adsorption of LiF(100) will decrease the work function, as compared to vacuum. The results will be compared to plane-wave-DFT results by Prada S., et al. [1]

  Prada et al. (eV) This tutorial (eV)
Al(100) Φ 4.37 4.44
Al(100)/LiF(100) ΔΦ -0.47 -0.42

Al(100)/vacuum

Start AMSinput
Switch to BAND: ADFPanel → BANDPanel

Now generate the Al(100) slab:

Import geometry from xyz file
Build the structure yourself

Download the Al100.xyz file

Select File → Import Coordinates and select the downloaded file

See also

If you are not yet familiar with the editing tools in AMSinput, take a look at our Introduction to Building structures.

Edit → Crystal → Cubic → fcc
Choose Al from the drop-down, note the lattice constant a = 4.05 Å.
Edit → Crystal → Generate Slab
Click the Convert to Conventional Cell button
Leave Number of layers at 2
Click Generate Slab to generate a 4-layer Al(001) (equivalent to Al(100)) slab
/scm-uploads/doc.2022/Tutorials/_images/vacuum.png

Then, set the BAND settings:

XC functional: GGA → PW91
Details → Numerical Quality
Integration: Becke Good
Spline Zlm fit: Good
/scm-uploads/doc.2022/Tutorials/_images/numqual.png
Click the MoreBtn next to K-space
Number of points: 7 7
/scm-uploads/doc.2022/Tutorials/_images/k_space.png
Details → SCF
Electronic temperature: 0.002 hartree
/scm-uploads/doc.2022/Tutorials/_images/eltemp.png

This sets up a 7x7 k-space grid. The integration, spline zlm fit, and electronic temperature options help with the SCF convergence.

Save and run the job.

When the job has finished, the Fermi energy is printed at the bottom of the logfile (SCM → Logfile):

<Jul11-2022> <11:41:08>  FERMI ENERGY:          -0.1632 A.U.
<Jul11-2022> <11:41:08>                         -4.4412 E.V

Thus, the work function Φ = 4.44 eV. This compares well to the value of 4.37 eV reported by Prada et al.

Note

The Fermi energy only matches the work function for 0D, 1D, and 2D-periodic metal systems (not 3D-periodic bulk systems).

If you use Quantum ESPRESSO (which only supports slab calculations under 3D-periodic boundary conditions, i.e., with a vacuum gap), you need to also calculate the vacuum level by plane-averaging the electrostatic potential. The work function is then the difference between the Fermi energy and the vacuum level. See quantum-espresso.org for more details.

Tip

Get the Fermi energy using the following script that you can run with $AMSBIN/amspython:

from scm.plams import *
results_dir = '/path/to/jobname.results'
job = AMSJob.load_external(results_dir)
fermienergy = job.results.readrkf('DOS', 'Fermi Energy', file='engine')
fermienergy *= Units.convert(1.0, 'hartree', 'eV')
print(f"Job: {results_dir}")
print(f"Fermi energy: {fermienergy:.2f} eV")

Al(100)/LiF(100)

When setting up a solid-solid interface, the lattice constants must match. Both Al and LiF are cubic, so if their lattice constants match, also the (100) surface lattice constants will match. At least one of the materials needs to be a bit strained. Here, we will strain the LiF slab to match the Al slab. We will place the LiF slab at a distance of 3.27 Å from the Al slab.

Note

For other interfaces, you may need to apply surface rotations and use surface supercells if the lattice constants of the two materials are very different, in order to not apply too much strain to one of the materials.

SCM → New input
Import xyz
Build the Al(100)/LiF(100) interface

Download the LiF-on-Al.xyz file

Select File → Import Coordinates and select the downloaded file

Edit → Crystal → Cubic → NaCl
Choose LiF from the drop-down
Set the lattice constant to 4.05 Å (the same value as for the Al slab)
Click OK
Edit → Crystal → Generate Slab
Click the Convert to conventional cell button
Set the number of layers to 1
Click Generate slab. This gives a 2-layer LiF(100) slab.
/scm-uploads/doc.2022/Tutorials/_images/LiF.png

We now want to position this LiF slab on top of the Al slab such that the F atom is 3.27 Å directly above the top Al atom

Select all atoms in the LiF slab
Hold the right mouse button and drag them up a bit so that the bottom atoms are above the ab plane (this way they will not overlap the Al slab when you combine the two systems)
Edit → Copy
Switch to the Al(100) AMSinput window
Edit → Paste
Unselect all atoms
Edit → Tune Geometry
Select the bottom F atom. Hold shift and click on the other three LiF atoms (selecting them)
Click the ⬭ next to Atoms to move
/scm-uploads/doc.2022/Tutorials/_images/to_move.png
Click the top Al atom (selecting only this atom)
Click the ⬭ next to Above atoms
Distance to plane: 3.27 Å to first atom (the first atom is the first selected F atom)
Click the Move button
Click Close
/scm-uploads/doc.2022/Tutorials/_images/move_to.png

This has created the desired interface geometry.

/scm-uploads/doc.2022/Tutorials/_images/interface.png
File → Save As with a new name
Run the job

Important

Use the same calculation settings as for the clean Al slab, especially the same number of k-points and functional.

The bottom of the logfile reads:

<Jul11-2022> <11:57:03>  FERMI ENERGY:          -0.1476 A.U.
<Jul11-2022> <11:57:03>                         -4.0163 E.V

So the work function Φ = 4.02 eV, giving ΔΦ = (4.02-4.44) = -0.42 eV, which compares well to the value given by Prada et al.: ΔΦ = -0.47 eV (for a 3-layer LiF(100) slab on Al(100)).

[1]
  1. Prada, U Martinez, G. Pacchioni. Work function changes induced by deposition of ultrathin dielectric films on metals: A theoretical analysis. Phys. Rev. B. 78, 235423. DOI: 10.1103/PhysRevB.78.235423