# Work Function Problem

2D materials (such as graphene) are mostly exfoliated from their 3D bulk counterpart. I am wondering how we can calculate work function for a 2D material? Normally electrostatic potential in the out-of-plane direction is required to obtain E$$_{\rm{vac}}$$, which is later used in the definition of work function (WF=E$$_{\rm{vac}}$$-E$$_{\rm{Fermi}}$$).

Do we need electrostatic potential for both bulk and 2D system to compute work function or is it only the 2D material for which it should be computed?

## 1 Answer

You are right in that the Work function (the term is more pertinent to metals in my opinion) or Ionization energy (a generic term) can be calculated as: Evac - EHOMO. You can calculate the vacuum level in most DFT packages by doing a calculation for the average electrostatic potential in vacuum. This obviously makes sense only for a 2-D material (in bulk, the potential would just be asymptotic with out-of-plane distance).

For a vacuum calculation, you don't need to consider the bulk material at all. You can easily reconcile this because the work-function in the simplest texts is defined as removing an electron from the surface. You can just calculate the electrostatic potential for a range of out-of-plane distances and make sure it saturates ( if the vacuum is thick enough, this should not be a problem). In my experience, I've seen many papers on materials where the potential starts saturating for a distance of 0.1 nm (which is the minimum recommended vacuum in DFT calculations typically).

Edits: There is a slight distinction between EFermi and EHOMO. For semiconductors, at 0 K, the Fermi level is ill-defined. Can lie anywhere in the gap. But in literature, people plot bandstructures with Valence band maximum aligned to zero.

• +1. Great effort for sure, and I like how you used HTML for the subscripts, which requires more effort than MathJax but looks neater in this case :) Jul 28, 2020 at 2:35
• Weird you say that Nike, because I keep telling myself I need to start learning to use MathJax someday. But here, it wasn't required, so I was spared! Jul 28, 2020 at 2:37
• I figured you might have used HTML due to not knowing enough MathJax, because MathJax use it at every opportunity! But in this case if you compare your subscripts to the ones in the question, I think yours look nicer. Jul 28, 2020 at 2:39