All in all the whole procedure went well and good. The people I talked to were all nice and open. I applied using the ASML system, which I think, still works a bit dodgy. After a call to the HR departement an appointment was swiftly made for the first interview.
First interview (and most important) was technical and lasted roughly two hours. First hour was with two members of the group. They shortly explained what was going to happen. It was a Matlab assessment of 30 min (with a bonus question) including doing a short presentation. Afterwards there was a short review of how it went. Depending on your experience this can be either hard or do-able. I have a feeling little experience can show off quickly. Since I used Matlab since forever it went well for me, so I am not sure how strict they are with the selection on this part. Because of the short time, this part can be harder to prepare if you have little to no Matlab experience.
Second hour was with an architect and head of the group. Questions were asked about your background what experience you have and why ASML. Also the job was explained in more detail and what it entails. They also ask you exactly what (part) ASML is doing in the semiconductor industry and how their machines work. This requires some preparation but should be easy.
Afterwards invited for a second interview. You were required to make an online-test beforehand. The test consisted of a logic part, a personal assessment and a specific ASML test. The latter was based on the actions you take depending on situations arising in the company. The interview itself was non-techical and a HR person attended as well along the group leader. The results of the test were discussed and asked if you agree on it or not and why. The interview felt a bit more like formality, probably because the decision was already made. The interview ended with them saying they will hire me. The send the contract afterwards. Negotiating was not possible.