Development Day For Software Engineers

Well, It seems to be a good practise to reserve some hours between sprints, to let the team shows and discourse about new technologies, patterns and so on. But it can't  make the team slower to get the realese date. I have done this between sprint review and sprint retrospective, in the same day. But remember, there is no Software Engineers in scrum, only development team.

One way can be to can consider 5.5 hours per day if a person is working 8 hours/day. Rest 2.5 can be utilized for Scrum events.

One thing I will point out is that the Scrum states that the next sprint starts immediately after the end of the previous. So the suggestion to add Development Days between the sprints will interrupt that cadence.  

My question is what problem are you trying to solve by doing these?  What kind of value do they provide? Your idea to add them to sprints seems a bit counter to the purpose of sprinting and scrum.  If a developer has an idea that could provide value, they should talk to the PO and get Product Backlog Items added to accomplish the work.  Part of agile/empiricism is the ability to experiment with things to see if the perceived value can be realized.  These seem like good candidates for that if I am understanding the basis of your suggestion.

If a developer has an idea that could provide value, they should talk to the PO and get Product Backlog Items added to accomplish the work.

Additionally, Scrum provides many oportunities throughout the sprint where these ideas may be surfaced and become transparent. Also, one of the scrum master's activities is to facilitating creativity not by merely implementing the framework but encouraging the development team to consider new potential points of view about the product and its value.

Do you have any evidence that development days would provide extra benefits to your scrum team? If so, which are those?