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/Tutorials/_images/preview19.png

Fig. 46 Plane-averaged electrostatic (Coulomb) potential vs z coordinate. The orange horizontal line is the Fermi energy. The red and green vertical lines indicate how the work function is calculated on either side of the slab. The work function (WF) for the Al(100)/vacuum interface (green) is 4.33 eV. The WF for the Al(100)/LiF(100) interface (red) is 3.63 eV.

In the above figure the work function Φ is calculated as

Φ = local maximum in Coulomb potential - Fermi energy

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] and Kondo and Matsushista [2]

Al(100) Φ [eV]

Al(100)/LiF(100) ΔΦ [eV]

functional

code

Prada et al.

4.37

-0.7

PW91

VASP

Kondo and Matsushista

4.28

-0.59

PBE

Quantum ESPRESSO

This tutorial

4.33

-0.70

PW91

BAND

Note

The above works differ not only in code and functional, but also basis set, k-point sampling, number of layers in the Al or LiF slabs, whether the system is relaxed or not, …

See also

Work function example with Quantum ESPRESSO

Build the initial system

Start AMSinput
Switch to BAND: ADFPanel → BANDPanel

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.

Download the LiF-on-Al.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.

First, build the Al(100) slab:

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/Tutorials/_images/vacuum.png

Similarly, open a new AMSinput window and create the LiF(100) slab:

SCM → New Input
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/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/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/Tutorials/_images/move_to.png

This has created the desired interface geometry.

/scm-uploads/doc/Tutorials/_images/interface.png

Set up the DFT calculation

Then, set the BAND settings:

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

File → Save As with a new name
Run the job

Get work function with Python script

Download WorkFunctionVacuumAndInterface.py
Modify the results_dir variable to give the correct path to the .results folder from the previous calculation. It should contain two files: ams.rkf and band.rkf.
Open a terminal and run the script as $AMSBIN/amspython WorkFunctionVacuumAndInterface.py

This produces a plot like the below:

/scm-uploads/doc/Tutorials/_images/preview19.png

Fig. 47 Plane-averaged electrostatic (Coulomb) potential vs z coordinate. The orange horizontal line is the Fermi energy. The red and green vertical lines indicate how the work function is calculated on either side of the slab. The work function (WF) for the Al(100)/vacuum interface (green) is 4.33 eV. The WF for the Al(100)/LiF(100) interface (red) is 3.63 eV.

Get work function with the graphical user interface

Select the job in AMSjobs and select SCM → View
Fields → Grid → Full Unit Cell
Fields → Grid → Details…
In the popup window, set Grid extends beyond molecule in z direction to: 100 Å
Click Use
/scm-uploads/doc/Tutorials/_images/grid.png

Then, switch to the line graph generator:

Add → Graph Along Line
Extend line by (Å): 0
Number of points along line: 1000
In the Use full cell: dropdown menu, select Line Along z-axis
In the Planes S are to be dropdown menu, select Averaged
In the Field drop-down menu at the top, select Potential → Coulomb Potential

This produces the following plot:

/scm-uploads/doc/Tutorials/_images/elpot_small.png

To extend the plotted potential further out into the vacuum:

Extend line by (Å): 80
Click the Do it button next to Extend line by (Å)

Note that the extension which here is set to 80, which needs to be smaller than the “Grid extends beyond molecule” previously set to 100.

This should produce a figure like the following:

/scm-uploads/doc/Tutorials/_images/elpot_large.png

If you hover over the first and second local maxima at the left hand-side, you can read off the y coordinates as

  • left-hand side (bottom side of slab, Al/vacuum): 0.0176 hartree

  • right-hand side (top side of slab, Al/LiF): -0.0081 hartree

These plane-averaged potentials should be compared to the Fermi energy to get the work function.

SCM → Output
In AMSoutput, do Properties → Band gap information

This gives:

Band gap information

 No band gap

 Fermi Energy:    -0.1413 a.u.
 Fermi Energy:    -3.8443 eV

Consequently, we get

  • bottom side Φ = 0.02555 - (-0.1413) = 0.16685 hartree = 4.33 eV

  • top side Φ = -0.0081 - (-0.1413) = 0.1332 hartree = 3.62 eV