Here's a quick tutorial on calculating the complex band structure (CBS).

There is one fundamental things to keep in mind. What you want to do is compute the CBS of a surface or interface. In practice, the way it's implemented in ATK is that we can compute the CBS for a system which fulfills the requirements of an electrode. In short, these are:

• Surface normal along Z, i.e. the C vector should be perpendicular to A and B
• Periodic in Z (and X and Y, but that's a separate story)
• Long enough (see the full electrode requirements for details)

Let us take a simple example of a Si [100] surface, and go through it step by step. We will here assume that you have reasonable experience in using VNL, such that we don't have to explain how to move structures between tools etc.

1. Start by opening the Database and locate "Silicon (alpha)", the standard diamond phase of silicon. You may use the search filter "silicon standard" to isolate it in the list.
2. Send the structure to the Builder.
3. From the menu "Transform" choose "Cleave", and press OK to cleave the structure along the [100] plane.
4. We now have a cell that fulfills the two first requirements above. It is not, however, long enough in Z. The length in Z needs to be a multiple of 5.43 Å, but depending on which method we choose to use, we will need a different number of repetitions to make sure we include all interactions, since the basis set interaction lengths differ from method to method. More specifically:
   • For DFT, 2 repetitions are enough to include even second-order interactions.
   • For the Extended Hückel method, we should use the Cerda GW diamond parameters for good accuracy. This is a long-range basis set, and we actually need 3 repetitions, but then we also get also include all second-order interactions. With only 2 repetitions we would truncate even some first-order basis set overlaps.
5. Silicon being a semiconductor, it feels more comfortable to use the Hückel method, so that we can a more accurate band gap. Therefore, apply 3 repetitions in the C direction, and send the resulting structure to the Script Generator.
6. Insert a "New Calculator", open it, and select the Extended Hückel method and under "Huckel basis set" choose "Cerda.Silicon [GW diamond]" for Si.
7. You should use a lot of k-points in the C direction, for the same reason this is done for electrodes in devices, viz. to get an accurate Fermi level. So let's apply a k-point sampling of (5,5,100).
8. All other settings can be left at their default values.
9. Also insert an "Analysis>ComplexBandstructure" block in the script. Open it, and you will see that it takes as parameter the in-plane wave-vector for which you want to compute the CBS. For now, stick to the default, i.e. the Γ point (kA=kB=0).
10. Assign a suitable name and location to the output file name, and send the script to the Job Manager and run it!

When the job finishes you can inspect the CBS saved in the NC file.

It is recommended to explore this structure a bit further on your own, to verify e.g. that the k-point sampling in A and B were sufficient, and to look at the CBS at other k-points than Γ.

Why dots

How to figure out that part about the Z length of the system

1.  as can be verified by the following steps, which can be omitted if you so prefer, but are highly instructional for understanding electrodes:
   • Repeat the structure 8 times along C (menu "Transform>Repetition")
   • Click the device icon on the left-hand side