How to do the teams breakdown?

You haven't mentioned a Product Owner, or who wants this system and why. You say you are acting as the Scrum Master. Why acting? Are you really the Product Owner?

In Scrum, value is delivered at the end of every Sprint. It is delivered in the form of an increment which the Product Owner can then release in order to achieve a return on investment. If you can account for product ownership then the answers to your questions may become clearer.

In other words, if you can figure out who wants this value, and who would benefit from the iterative and incremental release of it, then you will be in a position to organize teams accordingly. For example if the games engine can be released with limited image and audio assets (just enough to test certain assumptions) then you might organize teams to reflect that decoupling.

Teams can share a Scrum Master as long as his or her commitment to any given team is not compromised. Each team would have its own Scrum meeting, and would self-organize on a daily basis in order to deliver its Sprint Backlog. The Scrum Master would need to make sure that this happens and that the Scrum rules are followed.

I've worked in similar situations and yes it might make sense to have multiple Scrum teams but one single Product backlog which all the teams will use.

Our scrum teams had a maximum of 8 members each and each team had its own Scrum Master. Every team was organized so that it collectively had the expertise to complete a feature or requirement.
You are doing the right thing in assigning the feature to the whole group. Scrum requires the whole Scrum team to take responsibility for the Sprint goal.
So a Scrum team should be cross-functional and this means they should have all the expertise be it in developing code or testing it.

Now it is quite possible that the teams you form may be assigned something they are not fully aware of and they may require the help of a Subject Matter Expert in the other Scrum team. Depending on the capacity of the person involved he or she can collaborate with the Scrum team on an as-needed basis. It is upto the respective Scrum masters to facilitate this and ensure that everything goes off smoothly.

The main thing you have to remember is continuous integration and this is essential because all your Scrum teams are going to be working on the same Product backlog and are working towards one single product release every Sprint.
So ensure that a single repository of code exists and the various modules are checked in daily and integrated properly so as to form a cohesive working increment.

And no there cannot be a sub-team lead. First of all there is no lead in Scrum. Even the Scrum Master is just a facilitator and is usually a servant leader.
Your scrum team has to be self organizing and not even the Scrum master should tell members how to do their work. Scrum masters are agents of the Scrum process, they are not technical leaders. The Scrum Master should help a team self organize but never dictate terms

Awesome! thank you Ian and Prabhu for sharing your experiences and knowledge,

I understand that our situation is unconventional for a regular professional Scrum scenario, but we would love to make it work.

We actually have no Product Owner, I know it is a big lack but it is difficult to have one in our situation. I believe that the Product Owner role needs too much experience and is way too powerful to be taken by any of the students, besides, the professor seems like the right one but he doesn't really have time to get that involved in the project. For now this role is being fulfilled collectively. Any suggestion on this?

I act as the Scrum master. To act (to do something, to take action, to behave in a particular way) not necesarilly means to pretend :).

As for each sprint's value and the iterative incremental releases, it is hard to tell who gets benefit from this, since it is a research project besides the Proffessor, we have no customer or someone expecting results each month. I think we should define each sprint backlog working with him.

Given that, like in many school projects, there are poeople that are very responsible and commited and there are people that are not, that is a challenge.
Regarding the fact that Prabhu highlighted "Scrum master cannot say how things must be done", the self organization for this kind of teams seems difficult. I am a bit afraid that as a Scrum master, for any team not very committed, to make sure that everything runs accordingly to Scrum framework and especially the scrum meeting would take a lot of time.
Let's see how it goes.

Thanks again

Diego Sahagún

From what you say it appears that your Professor might be a good candidate for the Prod Owner role. Remember this does not make him the first among equals since all roles are equal in a truly evolved Scrum team with well defined responsibilities.

Teams self organize over a period of time so it may take a bit of creative Scrum Mastering on your part to get the team to do things the proper way without really explicitly telling them how to do things. Don't despair, it may take 3 sprints or the whole project for your team to learn but leading by example is a good technique in the initial days.
One of the things that you can check as Scrum Master is whether tasks for the Sprint are well defined in the Sprint backlog. This is a clear cut way to check responsibilities without really being intrusive.
At the end of the day do not end up becoming the fall guy if something goes awry. In Scrum the whole team works towards a goal and also takes collective responsibility for failure.